Structural Analyses of Emission Permit Auctions Under Cap-And-Trade Programs in the United States

STRUCTURAL ANALYSES OF EMISSION PERMIT AUCTIONS UNDER CAP-AND-TRADE PROGRAMS IN THE UNITED STATES

A DISSERTATION SUBMITTED TO THE DEPARTMENT OF ECONOMICS AND THE COMMITTEE ON GRADUATE STUDIES OF STANFORD UNIVERSITY IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY

Xiaoling Charlene Zhou June 2012

This dissertation is online at: http://purl.stanford.edu/qr983yn4760

ii I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy.

Lawrence Goulder, Primary Adviser

I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy.

Michael Boskin

I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy.

Han Hong

Approved for the Stanford University Committee on Graduate Studies. Patricia J. Gumport, Vice Provost Graduate Education

This signature page was generated electronically upon submission of this dissertation in electronic format. An original signed hard copy of the signature page is on file in University Archives.

iii Abstract

This dissertation conducts empirical studies on emission permit auctions under cap- and-trade programs in the United States. My dissertation for the ﬁrst time conducts structural analyses using the actual auction data from the Acid Rain Program for SO2 and the

Regional Greenhouse Gas Initiative (RGGI) program for CO2.

With detailed bidder-level bidding data of the 17 discriminatory auctions of SO2 allowances held by the EPA from 1993 to 2009, I estimate bidders’ marginal valuation functions using the resampling method proposed by Hortacsu (2002b) and Kastl (2011). I follow their econometric approaches to calculate the efficiency loss caused by the discriminatory format, and test its effectiveness in raising revenue compared to a truthful-bidding uniform price auction. Compared to a best-case scenario of truthful-bidding uniform price auction, the counterfactual results show that the discriminatory format may not necessarily raise more revenue to compensate the efficiency loss in the SO2 allowance auctions. To analyze the RGGI program, I modify a uniform price auction model built by Vives (2011) to characterize emission permit auctions with the presence of secondary trading. Based on the symmetric linear Bayesian demand function equilibrium (LBDFE), I analyze the interaction between the primary auction market and the secondary trading market of emission permits. I then propose a statistical procedure to calibrate model parameters using aggregate level data for the RGGI CO2 allowance auctions during August 2008 to June 2010. With a counterfactual simulation, I discuss the underpricing issue of the uniform price auction relative to the allowance prices in the trading market, and conclude that it is beneficial to open the auctions to general public to increase competition. Based on the empirical results for emission allowance auctions in these two programs, I propose several policy suggestions in designing future emission auctions.

iv Acknowledgment

My journey to completing this dissertation and to obtaining my Ph.D. degree has been long yet rewarding, and I would like to acknowledge all the people who have helped me along the way. I am deeply thankful to my dissertation committee for their guidance and support. My principal adviser Lawrence Goulder has always been extremely patient and encouraging to me and has given me valuable advice ever since my second year at Stanford. Jakub Kastl inspired me to pursue this research topic. No words are enough to express my gratitude towards Jakub when he traveled across country to attend my defense during his sabbatical. Michael Boskin not only mentors me in research, but also provides me ﬁnancial support. I am indebted to him for often granting me time off from our project to work on my own dissertation. Han Hong has contributed the most to my dissertation by guiding me towards major breakthroughs. I really appreciate him generously spending time on all our meetings. I also thank Mar Reguant for being the chair of my defense. I am grateful to Paul Milgrom, Monika Piazzesi, Dallas Burtraw, Suzi Kerr for their helpful comments and suggestions. I have greatly beneﬁted from the feedbacks of seminar participants at the Stanford Environmental and Energy Policy Analysis Center (SEEPAC) seminar and the Applied Lunch at Economics Department. I have been fortunate to work with extraordinary fellow students at Stanford, especially my peers at the Economics Department. My friendship with Alessandra Voena, Elan Dage- nais, Xiaochen Fan, Nan Li, Zhuo Huang, Pasha Stetsenko, Christopher Paik, Xu Tan and many others is the most precious treasure that I have found during these years. My appre- ciation also goes to Dr. Alejandro Martinez and my friends from the Stanford Dissertation Support Group.

v I need to thank my professors from Wuhan University and Peking University who trained me to enjoy economics, as well as all my classmates and colleagues back in China. One special person whom I am immensely grateful to is my husband, Jack Chen. Thank you my dearest love, for standing by me with incredible understanding and encouragement the entire time. Your perpetual support has motivated me to keep moving forward to accomplish my dreams. There are so many more people I want to thank, but the list of names is too long to write them all down. Nonetheless, I am constantly thinking about all of you and the wonders you have brought to my life. Finally, this dissertation is dedicated to my parents, Ji Zhou and Xiaohong Li, who have always believed in me and been proud of me.

vi Contents

Abstract iv

Acknowledgment v

1 Introduction 1 1.1 Emission Cap-and-Trade Policy Background ...... 1 1.2 Overview of the Dissertation ...... 5 1.3 Practices of Emission Cap-and-Trade System ...... 10 1.3.1 Emission Trading Programs in the Past ...... 10 1.3.2 Future Programs Planned ...... 28

2 Emission Permit Auctions under Cap-and-Trade 31 2.1 Multi-unit Auction of Emission Permits ...... 31 2.2 Emission Permit Auctions in the United States ...... 36

2.2.1 SO2 Auctions under the EPA’s Acid Rain Program ...... 36

2.2.2 CO2 Auctions under the Regional Greenhouse Gas Initiative . . . . 38 2.2.3 Virgina NOx Allowances Auction ...... 40 2.3 Emission Permit Auctions in Europe ...... 42

2.3.1 UK CO2 Abatement Auction ...... 42 2.3.2 Auctions by Member Countries of EU ETS ...... 43 2.4 Desirable Properties and Potential Problems of Emission Permit Auctions . 59

3 Efﬁciency Loss and Revenue Extraction of Discriminatory Auctions 64 3.0 Introduction ...... 64

vii 3.1 Issues with Discriminatory Auctions of Emission Permits ...... 68 3.1.1 Inefﬁciency of Discriminatory Auctions ...... 68 3.1.2 Revenue Ranking Ambiguity of Auction Formats ...... 69 3.2 Structural Econometric Models for Discriminatory Auctions ...... 73 3.2.1 Theoretical Foundation: Wilson’s Model ...... 73 3.2.2 Identiﬁcation Condition: Hortacsu’s Model ...... 76 3.2.3 K-Step Bids: Kastl’s Model ...... 79 3.2.4 Resampling Procedure ...... 82

3.3 Empirical Analysis of SO2 Auctions ...... 83 3.3.1 Auction Characteristics and Data ...... 83 3.3.2 Bootstrap Resampling Estimation ...... 91 3.3.3 Counterfactual Results ...... 96 3.4 Summary ...... 106

4 Underpricing of Uniform Price Auctions 108 4.0 Introduction ...... 108 4.1 Literature on the Underpricing of Uniform Price Auctions ...... 112

4.2 RGGI CO2 Allowance Markets around Auction Dates ...... 115 4.2.1 Secondary Markets for Trading RGGI CO2 Allowances ...... 116 4.2.2 RGGI Futures Trading Pattern and Underpricing in RGGI Auctions 127 4.3 Model of Uniform Price Auctions for Emission Permits ...... 132 4.3.1 Model Setup ...... 135 4.3.2 Linear Equilibrium Characterization ...... 137 4.3.3 Comparative Statics and Analytical Results ...... 143

4.4 Empirical Analysis of RGGI CO2 Auctions ...... 149 4.4.1 Auction Characteristics and Data ...... 149 4.4.2 Empirical Procedures ...... 154 4.4.3 Calibration Results ...... 160 4.4.4 Counterfactual Analysis ...... 162 4.5 Summary ...... 166

viii 5 Policy Implications and Emission Auction Designs 171 5.1 Pricing Scheme – Enhance Allocative Efﬁciency ...... 171 5.2 Reserve Price – Combat Underpricing ...... 173 5.3 Minimize Friction of Entry and Bidding Costs ...... 175 5.4 Prevent Collusion and Market Manipulation ...... 178

6 Conclusions 179

A Appendix 182 A.1 Appendix to Chapter 1 ...... 182 A.2 Appendix to Chapter 2 ...... 183 A.3 Appendix to Chapter 3 ...... 190 A.4 Appendix to Chapter 4 ...... 192

A.4.1 Derivation of Conditional Expectation of ti by Ollikka (2011) . . . 192 A.4.2 Vives (2011) Solution of the Uniform Price Auction Equilibrium . . 193 A.4.3 Comparative Statics ...... 196 A.4.4 RGGI Auctions Summary Table ...... 202

Bibliography 203

ix List of Tables

2.1 Categories of Multi-unit Auction Formats ...... 32 2.2 Allowances Reserved for EPA Auctions ...... 37 2.3 Allowances for Auctions in Phase I, EU ETS ...... 44 2.4 EU ETS Phase I Auction Clearing Prices ...... 49

3.1 Numbers of SO2 Auctions Participated by Unique Business Bidders . . 88

3.2 Summary Statistics for SO2 Spot Auctions ...... 91 3.3 Counterfactual Clearing Prices in Truthful Bidding Auctions ...... 99 3.4 Efﬁciency Loss from EPA Discriminatory Auctions ...... 102 3.5 Difference in Revenue between Discriminatory and Truthful Bidding Uniform Price Auctions ...... 105

4.1 Monthly RGGI COATS Transactions with Price Recorded ...... 118 4.2 Monthly RGGI Futures Trading at CCFE ...... 122

4.3 Monthly RGGI Allowances OTC Trading at CantorCO2e ...... 125

4.4 Average CCFE CO2 Futures Prices Compared to Auction Prices . . . . 130

4.5 Available Data from RGGI CO2 Auctions ...... 153 4.6 Mean Slope and Intercept of Calibrated Bid Functions B = 1000 . . . . 161 4.7 Mean of Calibrated Parameters M and λ B = 1000 ...... 163 4.8 Counterfactual Clearing Prices of the No Trading Case B = 1000 . . . . 165

A.1 Summary of Cap-and-Trade Programs in Chapter 1 ...... 182

A.2 List of Business Type Bidders in SO2 Spot Auctions ...... 183

A.3 List of Potential Bidders in RGGI CO2 Auctions ...... 186

x A.4 EU ETS Allowance Auctions in Phase II ...... 188

A.5 Details of Bidders - SO2 Spot Auctions ...... 190

A.6 CO2 Spot Auctions Details ...... 191

A.7 CO2 Spot Auctions Details ...... 202

xi List of Figures

1.1 History of ARP, CAIR, CSAPR and Former NBP Programs ...... 12 1.2 Covered States in ARP, NBP and CAIR Programs ...... 18

2.1 Bidder i’s Payments under Different Sealed-Bid Auction Formats . . . 34

3.1 Bidder’s Demand and Auction Revenues under Different Pricing Rules 71 3.2 Bid Curve and Residual Supply Curve of Bidder #14 in 2008 Auction . 93 3.3 Clearing Price Distribution for Bidder #14 in 2008 Auction ...... 94 3.4 Estimation of Marginal Valuations for Bidder #14 ...... 95 3.5 Upper/Lower Envelopes of Estimated Marginal Valuations for Bidder #14 ...... 98 3.6 Counterfactual Revenue Comparison for 2008 ...... 104

4.1 Prices of COATS Transactions by Date ...... 119

4.2 RGGI CO2 Allowances Spot Market Price Index from CantorCO2e . . 124 4.3 RGGI Futures Daily Trading Volume and Price ...... 128 4.4 Different Price Trend of Emission Permits around Auction Days . . . . 131

4.5 CO2 Allowance Prices around Auction Dates ...... 133 4.6 Downward Bias of Discrete Bid Price Statistics ...... 168 4.7 Calibrated Mean Bid Schedules ...... 169 4.8 Conﬁdence Interval of Mean Bid Schedules ...... 170

xii Chapter 1

Introduction

1.1 Emission Cap-and-Trade Policy Background

To control air pollution, it has become common for governments to implement “cap- and-trade” programs, which are a type of environmental policy using tradable permits, called allowances,1 to limit annual emissions of certain chemical gases. The practices of using cap-and-trade system to control emission pollution, such as chloroﬂuorocarbons

(CFCs), sulfur dioxide (SO2), nitrogen oxides (NOx) and carbon dioxide (CO2), have been implemented for nearly two decades. It dated back to late 1980s when a cap-and-trade system was ﬁrst developed to combat ozone depletion through eliminating CFCs. Since the 1997 Kyoto Protocol2 which came into force in 2005 was signed and ratiﬁed by 191 countries, designing environmental policies to reduce emissions to certain aggregate levels has become a global trend, and cap-and-trade has become the most prevalent policy framework for that purpose. “Among economists at least, the use of tradable emission allowances under an aggregate emission cap is generally considered a mature policy technology. It has become the default policy option in controlling a variety of large scale air emissions.”

1In this dissertation, the terms “permit” and “allowance” are used interchangeably referring to the tradable assets under an emission cap-and-trade program. 2The Kyoto Protocol is an international treaty for reducing greenhouse gas to fight global warming. The Protocol was initially adopted on December 11, 1997 in Kyoto, Japan, and it entered into force on February 16, 2005. As of September 2011, 191 states have signed and ratified the protocol. The only remaining signatory that has not ratified the protocol is the United States.

1 CHAPTER 1. INTRODUCTION 2

(Porter et al. (2009)) In a cap-and-trade program, a central regulatory authority sets an upper limit (the cap) on the total amount of a pollutant that may be emitted by a particular class of emitters (usually referred as compliance entities) during a compliance period. According to the schedule of the emission cap for each compliance period of the program, the regulator issues an amount of allowances equal to the cap and distribute them to compliance facilities with emission sources. Each of these allowances represents the right to discharge one unit of the regulated air pollutant. For example, in the United States the Acid Rain Program assigns each allowance equivalent to one (short) ton of SO2, and the Regional Greenhouse

Gas Initiative permits one allowance to cover one (short) ton of CO2; while the carbon trading program in the European Union assigns one allowance equivalent to one metric 3 tonne of CO2. The total number of allowances cannot exceed the cap, thus limiting total emissions to the level of the allowance budget. Every allowance is attached with a vintage year, namely the year in which the allowance is issued. An allowance can be used to cover emissions discharged during its vintage year4, but may not be used for compliance prior to its vintage year. In some programs, banking of permits are allowed so that they may be used to cover emissions discharged after their vintage years. Speciﬁcally, if emission permits are bankable, an allowance of vintage year y may be saved for use in year y + 1 or later,5 but not vice versa. To distribute the emission permits to compliance entities, a regulator can give them away for free or sell them at fees. If the allowances are distributed for free, the allocation rule can be “grandfathering” or “output-update”. Grandfathering means that the allocation is done by a pre-determined schedule based on compliance entities’ historical emissions

3 The CO2 allowances in the carbon trading programs in fact cover all “greenhouse gas equivalents”, denoted as CO2e. These are the gases listed in Annex A of the Kyoto Protocol, including carbon dioxide (CO2), methane (CH4), nitrous oxide (N2O), sulfur hexafluoride (SF6), hydrofluorocarbons (HFCs), perfluorocarbons (PFCs), and nitrogen trifluoride (NF3). 4If banking is allowed, an allowance can be used to cover emissions discharged after its vintage year as well. 5Some programs define a conversion ratio on the face value of banked allowances to avoid over-banking, such as the U.S. EPA’s NOx Budget Trading Program. It means that one banked allowance of previous vintage year is equivalent to less than one unit of emissions. The actual face value of banked allowances is discounted according to the conversion ratio specified in the program implementation rules, so banked allowances are not as valuable as the current vintage allowances. CHAPTER 1. INTRODUCTION 3

level, while output-update is a contingent schedule based on their heat output year by year. If the regulatory authority decides to distribute allowances for fees, it can either hold auctions to sell to multiple buyers at once, or contract brokerages to make individual sales. In fact, in a cap-and-trade program, initial allocation of emission allowances can be done by the combination of one or more of above mechanisms. In reality, the past programs have chosen either completely grandfathering or completely auctioning or combining grandfathering with a small portion of auctions6. Trade in “cap-and-trade” means that emission permits are tradable. Participants in the program can buy and sell permits among one another. Compliance entities are required to hold a number of permits sufficient to cover their emissions. At the end of each compliance period, the regulator validates their total emissions during the period, and they must surrender an matching amount of allowances usable in that period. Therefore, after the initial allocation, program participants can decide on their actions according to their holding of allowances. Compliance facilities can compare their abatement costs to the trading price of allowances, and choose to: (i) bank some allowances for future; (ii) sell some allowances to other participants; and (iii) buy more allowances from others. The tradability of permits motivates those emitters with lower abatement costs to reduce more emissions so that they can sell their surplus of permits to other firms for a profit. Sources with higher abatement costs would save money by purchasing allowances compared to what they would otherwise have to spend on abating more emissions by themselves. Trading of allowances also provides incentives for energy conservation and technology innovation that can both lower the cost of compliance and yield pollution prevention benefits. As a market-based mechanism, the cap-and-trade system can maintain a mandatory cap on emissions while providing flexibility in how regulated sources comply. Consequently, it ensures that all compliance entities together reach the emission reduction target at the lowest total cost. Therefore, cap-and-trade is more cost-effective than other command-and-control policy alternatives. Emission permits are fully marketable commodities. The structure of emission markets can be explained more clearly as follows. There is a primary market composed of auctions, through which government sells allowances to program participants for the initial issuance.

6Very few exceptions occurred in the past when the regulators chose to entrust brokerages to sell allowances. One example is Denmark during Phase I of the EU ETS CHAPTER 1. INTRODUCTION 4

Compliance entities and maybe other interested parties enter auctions as bidders in order to obtain holdings of some newly issued allowances. Besides creating a channel for people to buy allowances, auctions make participants reveal their opinions regarding the value of allowances through bidding, providing price signals for private trading. Meanwhile, there is a secondary market of allowance trading among market participants themselves. The secondary market for emission allowances comprises the trading of physical allowances as well as the trading of the financial derivatives of allowances, such as futures and option contracts. A physical allowance trade occurs when the parties involved in the transaction register the transfer of ownership in the allowance tracking system. Futures, options, and other financial derivatives are called “exchange-traded” when they are traded on a public exchange, and are called “over-the-counter” (OTC) when they are traded privately. Many financial derivatives eventually result in the transfer of physical allowances, but they can be cash settled as well. Note that the secondary market does not have to happen after the primary market, as the trading of futures and forward contracts can predate the issuance of allowances in auctions. Also, note that depending on the percentage of auctioned allowance, the size of primary auction market could be significantly smaller than the size of secondary trading market, which is the size of entire emission cap. The secondary market is important for several reasons. First, it gives firms the ability to obtain allowances at any time during the period without auctions. Second, it provides firms a way to protect themselves against the potential volatility of future auction prices. Third, it provides price signals that assist firms in making investment decisions in markets affected by the cost of compliance. Among various segments of the secondary trading market, public exchanges are particularly attractive to firms that need a simple way to trade standard products. Moreover, public exchanges effectively eliminate the risk of default by counter- parties, since the exchange constantly monitors the account holdings of each participant to ensure that they have posted sufficient financial security to meet their obligations. On the contrary, the OTC market is attractive to firms that prefer contracts with non-standard provisions. Firms with on-going business relationships may have other ways to manage the CHAPTER 1. INTRODUCTION 5

risk of default by the other party.7 Compliance entities may prefer to buy allowances bun- dled with other goods and services from their fuel suppliers or operations service providers. The OTC market allows parties to create contracts speciﬁcally tailored to their needs. As a result, if the secondary market of allowance trading is active, liquid, and of sufﬁcient depth, it will help accomplish the cost-effectiveness for the entire cap-and-trade program.

1.2 Overview of the Dissertation

Objective of the Studies

This dissertation is an empirical study on emission permit auctions conducted in several existing cap-and-trade programs. The initial allocations of emission permits have always been a heatedly discussed issue. Auction, as a theoretically favorable approach of distributing allowances, has attracted much attention, but there have been very few empirical studies looking into the actual auction data from the existing cap-and-trade programs to endorse the merit of this allocative mechanism. I try to ﬁll this gap in the literature so as to provide empirical evidence for adopting certain auction format and implementation rules. By studying the actual auctions with observed data, I aim to accomplish four goals: First, evaluate the performance of these emission permit auctions. Second, compare several auction formats that are commonly adopted in cap-and-trade systems. Third, discuss the complications related to particular auction rules in reality and their potential impact on the implementation of cap-and-trade systems. Last but not the least, provide policy suggestions for designing emission permit auctions of future cap-and-trade programs.

Motivation and Signiﬁcance

The appeal of a cap-and-trade program lies in the prospect that using such market-based mechanism we can achieve overall emission reduction target most efﬁciently and at the lowest social cost. This argument is grounded on the famous “Coase Theorem”, which states

7For instance, firms may enter into forward contracts rather than futures contracts. The primary difference between a futures contract and a forward contract is that a futures contract typically requires parties with an open interest to post financial assurance which the exchange draws upon or adds to until the contract reaches expiration, while a forward contract requires that all financial settlement occur at expiration. CHAPTER 1. INTRODUCTION 6

that regardless of the initial assignment of property rights8 bilateral negotiation between regulated entities will lead to the same efficient outcome (Coase (1960)). It means that in a cap-and-trade system, no matter how the emission permits are distributed initially, the final allocation of permits will be independent of the initial allocation mechanism, and the market equilibrium will be cost-effective. We call this the independence property, which is the key reason that cap-and-trade systems have been employed and have evolved as the preferred policy instrument for emission control. However, the validity of the independence property relies on certain theoretical conditions, such as the absence of transaction costs, income effects and third-party impacts. In reality, those conditions are not always all satisfied. As a result, the initial allocation mechanism is often crucial to the performance of cap-and-trade programs. If the initial allocation is too inefficient, the market equilibrium might never be able to approach the cost-effective outcome, and we will be burdened with a huge deadweight loss. A possible solution to the failure of the independence property is to begin with a mechanism whose allocative outcome is already very close to the most efficient outcome. In the context of cap-and-trade, it is well-accepted that an auction in theory tends to be much more allocatively efficient than “grandfathered” free allotment. Since there is no easy way for the regulatory authority to figure out which sources can reduce the same amount of emissions at cheaper costs than others, “grandfathering” compliance entities with free allowances based on their historical emissions is generally far from the eventual market equilibrium. On the contrary, in emission permit auctions, participating entities reveal their valuations of the allowances, which are directly associated with their abatement costs. In addition, even in the ideal scenario when the independence property holds true and efficiency is not a concern, there is still an issue of distributional equity, because with different initial allocation mechanisms, surplus is transferred among participating parties dif- ferently. The ones who were given more emission rights than needed will profit as market reaches equilibrium. End consumers of products whose manufacturing generates emissions may subsidize polluters much more in one allocation rule than another. A frequent criticism is that free allocation of emission permits in the form of grandfathering will grant regulated

8The emission allowances in cap-and-trade systems represent tradable rights of emitting regulated chemical gases. CHAPTER 1. INTRODUCTION 7

firms “windfall profit”. On the contrary, selling emission permits to regulated entities in auctions raises revenue for the cap-and-trade program. Such auction revenue can be used for investment in renewable energy technology or energy efficiency technology to further accelerate emission reduction. It might also be used to correct for distortionary taxes such as payroll tax, creating a “double dividend”. In other words, emission permit auctions not only enhance the probability of a more efficient initial allocation, but also generate revenue that increases overall social benefit. Therefore, it is more sensible to primarily rely on auctions to distribute emission permits initially. In the past, most cap-and-trade programs have freely allocated almost all emission permits through “grandfathering”. The main argument for free allocation is to prevent regulated industries from suffering revenue loss due to increased costs of buying emission permits so as to maintain business operation. However, Goulder et al. (2010) use a computational general equilibrium model to simulate U.S. economy and conclude that it is only necessary to freely allocate less than 15% of total allowances in order to prevent regulated industries’ profit loss, while a majority of the allowances should be auctioned in the initial allocation. Responding to the overwhelming criticism of “grandfathering” as well as the preference for auctions from academia, policy makers have switched from dominantly using “grandfathered” free allocation to emphasizing auctions. The United States took the lead in conducting large scale emission permit auctions in the Regional Greenhouse Gas Initiative to sell over 95% of the allowance budget quarterly. Very soon, the world’s largest cap-and-trade program, the European Union Emission Trading Scheme, will commit to auction over 60% of allowances during its third compliance phase starting in 2013. All proposed cap-and-trade programs plan to auction allowances in large scales. Particularly, the next-in-line carbon trading program to be launched in California is preparing to have 50% of its total 2.5 billion allowances auctioned between 2012 and 2020. With the prospect of more and more periodic large emission permit auctions in the near future, finding appropriate auction designs becomes a pressing task. Holt et al. (2007) said that “A carefully designed allowance auction can help maximize the benefits of the cap and trade program.” CHAPTER 1. INTRODUCTION 8

Unfortunately, auction theory has yet to provide a deﬁnitive answer as to which commonly adopted emission permit auction format is superior in terms of the revenue and efﬁ- ciency as well as some other criteria of evaluating auction performance.9 Given the lack of theoretical guidance, empirical work is crucial when evaluating the relative effectiveness of these mechanisms. My dissertation is thus a theory-driven empirical study, seeking ex-post evidence to examine ex-ante predictions about the advantages and weaknesses of various auction designs. Not only it is important that my work address the demand of ex-post analyses on the performance of existing emission permit auctions, but also the empirical results in the following chapters have substantial policy implications. They will be useful for modifying auction rules of current cap-and-trade programs, as well as learning lessons from the past to prevent similar complications in future programs.

Methodology

My analyses in this dissertation use a structural econometric approach, which use observed bidding data from auctions to estimate the model primitives and bidder valuations based on a theoretical model of the auction, and simulate counterfactual auction outcomes from estimated structural parameters.10 As opposed to structural analyses, a lot of empirical research on auctions has relied on reduced-form analyses, in which researchers compare different auction mechanisms by looking at changes resulting from “policy experiments”. For example, some auction markets have used different auction formats or rules in different time periods or in auctioning similar commodities to the same potential bidders. The structural approach has great advantages over the reduced-form method and is particularly suitable for studying emission permit auctions because of three reasons. First, to conduct reduced-form analysis, there must be a large number of auctions to form a decent sized dataset with enough observations. Otherwise, the regressions are bound to suffer from a small sample size, causing serious doubts about the validity of the results. As to emission markets, due to the fact that cap-and-trade systems start being used as an environmental policy instrument only recently, there has not been any single program having conducted auctions frequently enough within its short history to sufﬁce for a reduced-form

9The theoretical properties of different emission permit auction formats will be discussed in Chapter 2. 10Hortacsu (2011) provides a thorough survey of the structural empirical works. CHAPTER 1. INTRODUCTION 9

study. Instead, with a structural analysis, I can draw meaningful conclusions with only a handful of auctions in my dataset. Second, the “natural experiment” perspective taken by the reduced-form methodology imposes a strong assumption that researchers can control for factors that may have changed over time or across different auctions, such as information structures and formation of bidder population. Any observed differences that cannot be explained by observable control variables are attributed solely to the auction format. On the contrary, the advantage of the structural methodology used here is that I can hold the ex-ante information sets of the bidders constant when constructing counterfactual simulations from the estimation of model primitives (Hortacsu (2002b), Kastl (2011)). Furthermore, the policy experiment studies in general only use aggregated price data from auctions, rather than utilizing bidder level data. It therefore can not analyze the distributional impacts through a change of mechanism. Namely, researchers will not be able to compare the allocative efﬁciency of different auction formats in reduced-form studies. However, structural estimation recovers all bidders’ valuations in an auction, from which calculation of efﬁciency change is then straightforward.

Organization of the Chapters

This dissertation is organized as follows: The remainder of Chapter 1 brieﬂy describes all the existing emission cap-and-trade programs in the world, and previews a few future programs currently still in the planning stage. Chapter 2 gives an overview of all past emission permit auctions and the various auction formats that have been adopted in practice, followed by a brief discussion of the major issues of emission permit auction designs.

As described in Chapter 2, there have been emission permit auctions held for both SO2 and NOx in the U.S., and CO2 allowances auctions have occurred in both America and Eu- rope. However, for the purpose of conducting structural analyses, I focus on cap-and-trade programs with periodic auctions rather than the ones with only one time trial. In addition, I only study auctions with available data that is plausible for structural analysis, meaning either detailed bidder level data or aggregate level summary data with at least some type of CHAPTER 1. INTRODUCTION 10

distributional information. As a result, my empirical studies are narrowed down to two cap- and-trade programs, which are reported in Chapter 3 and Chapter 4 respectively. Chapter 3 examines the efﬁciency loss and revenue extraction effectiveness of the discriminatory auction format adopted by the U.S. EPA to sell SO2 allowances under the Acid Rain Pro- gram. Chapter 4 analyzes the underpricing of the uniform price auction format used by the

Regional Greenhouse Gas Initiative to sell CO2 allowances in ten northeastern states of the U.S. Chapter 5 uses the empirical results from Chapter 3 and 4 to offer policy suggestions for modifying auction designs in current cap-and-trade programs as well as proposing desirable auction features to be included in future programs. Chapter 6 summarizes previous chapters and concludes the dissertation by discussing the contribution of this study.

1.3 Practices of Emission Cap-and-Trade System

1.3.1 Emission Trading Programs in the Past

During the past two decades, there have been a number of emission cap-and-trade systems existing in several developed countries, including: CFCs trading under Montreal Pro- tocol, SO2 and NOx trading under Clean Air Act Amendments, SOx and NOx trading under the Regional Clean Air Incentive Market in Southern California, CO2 trading in the

European Union Emission Trading Scheme, CO2 trading under the Regional Greenhouse Gas Initiative, as well as some other recent programs and ones currently in planning phase.

1.3.1.1 CFC Trading under Montreal Protocol

The U.S. CFC trading program under the Montreal Protocol is the earliest emission cap-and-trade program in history. The 1987 Montreal Protocol on Substances that De- plete the Ozone Layer required reductions of ozone-depleting emissions from the use of chloroﬂuorocarbons (CFCs) and halons. This agreement was ratiﬁed by the United States and 22 other countries in September, 1987. The Protocol called for a 50% reduction in the production of particular CFCs from 1986 levels by 1998, and froze halon production and consumption at 1986 levels beginning in 1992. Each country that signed the agreement was allowed to choose its own mechanism for limiting emissions. The United States CHAPTER 1. INTRODUCTION 11

implemented a cap-and-trade system in 1988 to help it comply with the Protocol.11 The Montreal Protocol defined consumption as production plus imports, minus exports. Consequently, in implementing the agreement, The U.S. Environmental Protection Agency (EPA) distributed allowances to companies that produced or imported CFCs and halons to place limitations on both the production and use of CFCs by issuing allowances. Based on 1986 market shares, USEPA distributed allowances to 5 CFC producers12, 3 halon producers, 14 CFC importers, and 6 halon importers. Because different types of CFCs have different effects on ozone depletion, each CFC was assigned a different weight on the basis of its depletion potential. If a firm wishes to produce a given amount of CFC, it must have enough amount of allowances calculated on this basis. Title VI of the Clean Air Act Amendments of 1990 modified the trading system to allow producers and importers to trade allowances within groups of regulated chemicals segregated by their ozone depleting potential. EPA requires that each time a production allowance is traded, one percent of the allocation is “retired” to assure further improvement in the environment. Nearly 600 million kilograms of CFCs were apportioned among producers by this rule. Through mid-1991, there were 34 participants in the market and 80 trades. The market price of most of the CFCs was well in excess of $1 per pound. The timetable for the phase-out of CFCs was subsequently accelerated, and a tax on CFCs was introduced in addition to the trading system. By the year 2000, CFC phase-out was completed in the United States, and the CFC cap and trade program was considered a success.

1.3.1.2 U.S. EPA Programs of SO2 and NOx under Clean Air Act Amendments

In 1990, United States Congress passed Title IV of the 1990 Clean Air Act Amendments

(CAAA) with a focus of reducing SO2 and NOx emissions, the primary components of acid rain. The EPA subsequently launched several cap-and-trade programs under CAAA,

11Canada, Mexico and Singapore also implemented trading programs in CFCs, seeking to ease the phaseout of CFCs through tradable production quotas. In Singapore, CFC use permits were allocated quarterly, half on the basis of historical use and half through sealed bids. In registering to participate in the bidding, users and importers speciﬁed the quantity of CFCs they wanted and their offer price. The lowest winning bid price served as the price for all allocations, including those based on historical use. 12The production of CFCs was highly concentrated, with two producers Du Pont and Allied Signal accounting for 75% of domestic production, and Du Pont alone holding a 49% market share. And it is worth noting that the Protocol did not allow for allowance trading across countries. CHAPTER 1. INTRODUCTION 12

including the nationwide Acid Rain Program (ARP) and the regional NOx Budget Trading Program (NBP) in the Northeast. These programs are targeting the electric generating units (EGU) in fossil fuel ﬁred power plants. Regulated power plants are required to surrender

SO2 or NOx allowances for compliance at the end of every year. In March 2005, EPA issued the Clean Air Interstate Rule (CAIR) to build on the success of these programs and achieve signiﬁcant additional emission reductions.13 As a result, NBP program was replaced by CAIR NOx program after 2008. However, the CAIR were later challenged in supreme court and EPA was consequently required to modify the rule. In July 2011, EPA ﬁnalized the Cross-State Air Pollution Rule (CSAPR) to replace the CAIR in 2012. Currently, CSAPR is still under a pending judicial review, which delays the implementation of the CSAPR, so the CAIR is temporarily left in place to maintain the tightened emission reduction requirements through the year of 2012. Figure (1.1) shows the timeline of history regarding EPA’s SO2 and NOx programs.

Figure 1.1: History of ARP, CAIR, CSAPR and Former NBP Programs

13Sources and more program details, please refer to http://www.epa.gov/captrade/programs.html CHAPTER 1. INTRODUCTION 13

Acid Rain Program (ARP) The ARP is the ﬁrst program that EPA established under the Clean Air Act. Its primary goal is to achieve an annual emissions reduction of 10 million tons of SO2 and 2 million tons of nitrogen oxides (NOx) below 1980 levels. The centerpiece of the ARP is a nationwide cap-and-trade system for SO2 emissions launched since 1995. Although the ARP also includes the component of NOx reduction compliance, the NOx regulation instead used a more traditional regulatory approach of setting an emission rate limit for certain types of coal-ﬁred boilers. Sources affected by ARP’s NOx provisions need to demonstrate compliance by achieving an annual average emission rate at or below mandated levels. Since coverage of emission sources in ARP’s NOx portion overlaps the

EPA’s later NBP program, I only discuss the SO2 component of the ARP.

To achieve the goal of reducing 10 million tons of SO2, the ARP imposed a two-phase tightening schedule on fossil fuel-ﬁred power plants:

• Phase I (began in 1995 through 1999): Affected 263 units at 110 mostly coal-burning electric utility plants located in 21 eastern and midwestern states (accounting for about 22% of heat input at U.S. fossil-fueled generating units and about 17% of

capacity in 1990). They were required to reduce their SO2 emissions in aggregation to about 5.7 million tons per year. An additional 182 units joined Phase I of the program as substitution or compensating units, bringing the total of Phase I affected units to 445.

• Phase II (began in 2000): Tightened the annual emissions limits imposed on large, higher emitting plants and also set restrictions on smaller, cleaner plants ﬁred by coal, oil, and gas, encompassing over 2,000 units in all. The program affects existing utility units serving generators with an output capacity of greater than 25 megawatts and all new utility units. Virtually all existing and new fossil-fueled electric generating units in the continental United States become subject to a tighter cap on aggregate annual

emissions. And the total SO2 emissions have been restricted at about 8.95 million ton per year.

As in a standard cap-and-trade system, the ARP SO2 allowances are fully tradable and bankable. There is no discount against banked allowances. The initial distribution of allowances in the ARP are implemented primarily by “grandfathering” free allocation to CHAPTER 1. INTRODUCTION 14

power plants, with 2.8% of annual budget reserved for auction. The EPA conducts the auction once a year in late March to sell the reserved allowances. The EPA SO2 auctions, as well as trading of ARP SO2 allowances, are open to any individual, corporation, or gov- erning body, including brokers, municipalities, environmental groups, and private citizens. Some individuals and groups purchase allowances as an environmental statement, because withholding allowances from the market prevents those allowances from being used by regulated sources to cover emissions. In another word, environmental buyers help “retire” allowances. Each allowance is assigned a serial number, and there is a Allowance Tracking System (ATS) in place to track the holding of allowances and the compliance of regulated facilities.14 For the purpose of allowance trading, transactions are settled by the electronic transfer of ownership between two accounts in the EPA ATS. Two exchanges, New York Mercantile Exchange (NYMEX) and Chicago Climate Futures Exchange (CCFE) that established in late 2004 and 2005 respectively, provide standardized SO2 future contracts as well as clearing services for off-exchange transactions. In addition, there are several brokers and trader companies bringing together parties that have SO2 allowances to trade on OTC market. The private trades are facilitated by several electronic trading platforms provided by big brokerages, such as Intercontinental Exchange Inc. (ICE) and TradeSpark (CantorCO2e). The most common trading structure involves spot sales with immediate settlement accounting and delivery into ATS with payment by wire transfer in three business days. The secondary market of the ARP SO2 allowances were very active over the years. For instance, futures trading on the CCFE was nearly 1.9 million allowances in the ﬁrst half of 2007; and daily spot trading volumes for immediate settlement are estimated in the 10,000 to 25,000 ton range in early 2007. As indicated by transfers recorded at the EPA ATS, trading has grown to over 10 million tons per year by then. The four largest brokers – Cantor Fitzgerald, Evo- lution, ICAP Energy, and TFS Energy – form the basis of the Platts emission price index for SO2 allowances.

In 2010, the SO2 allowance trading program that existed since 1995 was replaced by

14For general public, tracking can be done by accessing the EPA’s Emission and Allowance Database at http://camddataandmaps.epa.gov/gdm/index.cfm?fuseaction=allowances.wizard CHAPTER 1. INTRODUCTION 15

four separate trading programs established under the CAIR. SO2 allowance trading essentially ended in 2010 when EPA issued the CSAPR due to the severe segregation of SO2 allowance market.

NOx Budget Trading Program (NBP) The EPA designed the Ozone Transport Com- mission (OTC) NOx Budget Program in 9 northeast U.S. states15 during 1999-2002 to reduce summertime NOx emissions, which cause ozone formation in ozone season when ground-level ozone concentrations are highest. The program originally caps summertime NOx emissions at 219,000 tons in 1999 and 143,000 tons in 2003, less than half of the 1990 baseline emission level of 490,000 tons. Since 2003, it has been superseded and replaced by the NBP under the NOx State Im- plementation Plan (also known as the “NOx SIP Call”). The program coverage expanded considerably to 19 states (including 8 original OTC states),16 with the number of sources increased from 300 under the previous regime to 1500 under SIP Call rules. Under this program, all wholesale electric generators with EGUs of 25MW or larger, large industrial facilities such as steel, chemical, pulp and paper, and reﬁning that have non-EGUs (e.g. boilers) with heat inputs of 250 MMBtu per hour and larger, and in some states, cement kilns are affected under the trading program. In addition, the number of allowances expanded from 135,000 to approximately 500,000 per year. Allowances are freely tradable throughout the 19-state region. The NBP is implemented in two phases:

• Phase I: On May 1, 2003, all facilities regulated under the OTC were required to reduce emissions by 35-40% . The emissions reduction obligations are differentiated by industry sector, with EGUs making roughly 80-85% reductions from prevailing levels in the late 1990s, while non-EGUs are obligated to reduce NOx emissions by

15OTC coverage comprises the states of Maine, New Hampshire, Vermont, Massachusetts, Connecticut, Rhode Island, New York, New Jersey, Pennsylvania, Maryland, Delaware, the northern counties of Virginia, and the District of Columbia. New Hampshire dropped out of OTC in 2003 since it was excluded from the EPA regulations. 16The states that are currently affected under the ﬁnal program are: AL, CT, DE, IL, IN, KY, MA, MD, MI, NC, NJ, NY, OH, PA, SC, TN, VA, WV, and DC. Parts of Georgia and Missouri are expected to participate in future years as well. CHAPTER 1. INTRODUCTION 16

roughly 65% from the same baseline period and cement kilns are required to make 35% reductions.

• Phase II: On May 31, 2004 (and May 1 each year thereafter), sources in an additional 11 states will be required to control NOx to the same levels as sources in the original 8 state region.

Each state has a NOx emissions budget, and has considerable flexibility in allocating its budgeted emission allowances to sources. Affected sources are allocated allowances by their respective state governments. So far, all states have chosen to freely allocate NOx allowances, with one exception that Virginia conducted a one-time auction in 2004 to sell some amount of 2004 and 2005 vintage allowances. Porter et al. (2009) documented the Virginia NOx auction as: “On June 30 2004, the Commonwealth of Virginia’s Department of Environmental Quality (DEQ) sold 3710 allowances for emission of nitrogen oxides (NOx) in fiscal years 2004 and 2005 using a sequential English clock auction. The auction raised over $10.5 million, 19 percent above its target revenue of $8.8 million.” Allowances and transactions are recorded in the EPA NOx Allowance Tracking System (NATS). Compliance is conducted every year on the last business day of November. Dur- ing the compliance process, all regulated units’ NATS accounts are frozen by the states, and will only be unfrozen after the states review the actual emissions and deduct the corresponding number of allowances (usually within 90 days). NOx allowances are bankable. However, the states have imposed a restriction on banking in the form of “progressive flow control” (PFC). It requires that there be discounted compliance value to banked NOx allowances if the region-wide surplus of banked allowances exceeds 10% of that year’s total allocation. The PFC ratio varies each year conditional on the size of total banked allowances and the corresponding discount factor on their face value is computed by a rather complex formula.17 The official PFC ratio and the

17The discount factor is not linear and is cumulative. By law, if the number of allowances carried over region-wide from year y exceeds 10% of the total regional budget for year y + 1 (referred as the “banking threshold”), then only a fraction of banked allowances may be used to cover the year y + 1 NOx emissions at one-ton face value; the remaining banked allowances may only be used for 50% of face value, or half of a ton. The PFC proportion of the banked allowances that may be used at face value is determined by the ratio of 10 percent of the regional budget divided by the regional total of banked allowances. For example, if the region-wide NOx budget for 2005 is 500,000 tons and there are banked 2003 and 2004 vintage allowances CHAPTER 1. INTRODUCTION 17

corresponding discount factor for use of banked allowances are usually not known until March of a given vintage year. This is typically when the EPA releases region-wide emissions data for the previous year and the size of the bank is revealed. If the PFC threshold has been reached, banked allowances will trade at a discounted price to current vintage.18 As to the secondary market of the NBP NOx allowances, trading is taken place very similarly as the ARP SO2 allowance trading, with active futures trading on CCFE and NYMEX as well as OTC trading facilitated by major brokers.

Clean Air Interstate Rule (CAIR) and Cross-State Air Pollution Rule (CSAPR) On March 10, 2005, EPA issued the CAIR, which builds on the ARP and the NBP and aims to function as a tightened continuation of these two programs. It includes three separate cap-and-trade programs to achieve the required reductions: the CAIR NOx ozone season trading program, the CAIR NOx annual trading program, and the CAIR SO2 annual trading program. The CAIR NOx ozone season and annual programs began in 2009, while the

CAIR SO2 annual program began in 2010. All these programs are operating with the same allowance tracking system as the ARP and the NBP. CAIR covers 27 eastern states and the District of Columbia (D.C.) and requires reductions in annual emissions of SO2 and NOx from 24 states and D.C. (to achieve improvements in ﬁne particle pollution in downwind areas) and emission reductions of NOx during the ozone season from 25 states and D.C. (to achieve improvements in ozone pollution in downwind areas). Figure (1.2) shows the difference coverage of regions in CAIR compared to the ARP and the NBP.

In 2010, there were 3,349 affected EGUs at 955 facilities in the CAIR SO2 and NOx annual programs and 3,309 EGUs and industrial facility units at 953 facilities in the CAIR together of 75,000 tons, then PFC for 2005 is calculated as follows:

(0.1 × budget2005) 0.1 × 50000 PFC005 = = = 0.67 (banked2003+2004) 75000 If you hold 100 vintage 2003 or 2004 allowances at the end of 2005, you can use the ﬁrst 67 tons at a 1:1 rate for 2005 compliance. The remaining 33 tons can only be used at a 2:1 rate for 2005 compliance. So the effective discount factor of 2003 and 2004 vintage allowances for use in 2005 is 0.67+(1−0.67)/2 = 0.835. 18For example, if vintage 2005 allowances are trading for $400/ton and PFC is 0.67, then vintage 2003 or 2004 allowances will trade around ($400 × 0.835 = $334/ton. CHAPTER 1. INTRODUCTION 18

NOx ozone season program. The variation in the number of units covered under the programs is due to the difference in states that are included in each program. The CAIR programs cover a range of unit types, including units that operate year round to provide baseload power to the electric grid as well as units that provide power on peak demand days only and may not operate at all during some years. Over the first decade of the ARP, allowance prices were stable and significantly lower than projected. When CAIR was proposed in late 2003, allowance prices were influenced by the more stringent CAIR SO2 budget and the new compliance deadlines. With the start of the CAIR SO2 program in 2010, the Acid Rain SO2 market essentially has become the

CAIR SO2 market. Soon after the CAIR was set in place, it was challenged at the United States Supreme Court. A December 2008 court decision kept the requirements of CAIR in place temporarily but directed EPA to issue a new rule to implement Clean Air Act requirements concerning the transport of air pollution across state boundaries. On July 6, 2011, the EPA submitted the replacement rule, the CSAPR, to Supreme Court for review. The CSAPR will require 27 states in the eastern half of the U.S. to improve signiﬁcantly air quality by reducing power plant emissions of SO2 and NOx that cross

Figure 1.2: Covered States in ARP, NBP and CAIR Programs CHAPTER 1. INTRODUCTION 19

state lines and contribute to smog (ground-level ozone) and soot (ﬁne particle pollution) in other states. The ﬁrst phase of compliance begins January 1, 2012 for SO2 and annual NOx reductions and May 1, 2012 for ozone season NOx reductions. Additional SO2 reductions are required by sixteen Group 1 states in 2014 to eliminate their contribution to downwind air quality problems. Under the CSAPR, the national trading program is in fact split into four separate trading groups for SO2 and NOx. On December 30, 2011, The United States Court of Appeals for the D.C. Circuit issued its ruling to stay the CSAPR pending judicial review. While this decision will delay implementation of the CSAPR, it will also leave the CAIR in place while the CSAPR is under review. All the requirements in CAIR, the CAIR Federal Implementation Plans (FIPs) and EPA-approved CAIR State Implementation Plans (SIPs) are federally enforceable and all sources that are covered by the three CAIR trading programs must continue to comply with the requirements of those programs throughout 2011.

1.3.1.3 Local Programs of Ozone Emissions at State Level

Regional Clean Air Incentives Market (RECLAIM) Regional Clean Air Incentives Market (RECLAIM) is a federally-approved regional emissions trading program operating in the state of California since 1994. Geographically, RECLAIM covers all of Los Angeles and Orange counties along with half of Riverside County, which is region is the smoggiest in the nation. The South Coast Air Quality Management District (SCAQMD) started the RECLAIM on January 1, 1994, making it the oldest of the local emission trading markets. The program established a cap-and-trade system to reduce emissions of nitrogen oxides (NOx) by 75% and sulfur oxides (SOx) by approximately 60% from by 2003. The emission permits in the RECLAIM are designed into the form of trading credits. Each credit can be used to cover one pound of NOx (or SOx) emission. The NOx and SOx RECLAIM Trading Credits (RTC) markets are separate, so there is no interpollutant trading in RECLAIM. And the RTCs were issued at a zero-cost basis (free allocation) to all sources. As of 2004, the RECLAIM’s NOx trading program includes 311 participating facilities whose yearly emissions are greater than 4 tons (8000 pounds) per year at the start of the program, and among them 33 facilities also participate in the SOx trading program. RECLAIM facilities are divided into two zones and two cycles. The two zones are CHAPTER 1. INTRODUCTION 20

based on geographical location. Zone 1 is the coastal, and Zone 2 is the inland. Coastal zone reductions are more valuable due to upwind impacts from coastal to inland areas.19 As a result, coastal zone facilities can only use coastal zone RTCs (except in limited cir- cumstances20), while inland zone facilities can use RTCs from both zones. The program is further divided into overlapping two cycles. Cycle 1 credits are valid January 1st and expire December 31st of the same year. Cycle 2 Credits are valid from July 1st until June 30th of the following year. A facility is assigned to one of these cycles and allocated RTCs accordingly. RECLAIM does not explicitly include banking as each RTC expires at the end of its 12 month term. However, credits can be exchanged between the cycles, so two vintages of credits are available for time periods within each compliance year. Facilities may use cross-cycling or a combination of cycles as a means of meeting quarterly compliance. The two compliance cycles are intended to provide flexibility, promote a liquid market and guard against price swings that might occur if all RTCs expired at the same time. This creates some opportunity for limited banking. Every RTC is identified by vintage, compliance cycle and zone, but does not have a unique serial number. There is a filing fee associated with all transfers of RTCs to help fund administration of the RECLAIM program. The fees are the same for either internal or external transfer, regardless of the size of the transaction. Since RECLAIM was adopted, there have been a number of changes to the way the program functions. One major change is on the coverage of regulated sources. Prior to the year 2000, credits traded on average below $1.00 per pound. In 2000, the California energy crisis caused a sharp increase in demand for NOx RTCs. Consequently, the RECLAIM remove the power sector from the market by exempting them from further compliance. Another major change is regarding to the scheduled emission cap. The system was designed

19Los Angeles is located in a basin with a mountain range directly east of it. The industrial area is typically located close to the coast. LA’s traditional status of dirtiest air in the nation is a direct result of this geography. In the morning, the wind blows in from the Pacific Ocean and picks up the air pollutants. By mid-day, the airflow has stagnated because the mountain range that forms the eastern boundary of the LA basin has blocked the air. In the evening, the airflow reverses directions and heads back out to sea, taking the air pollutants along. The next day, the whole cycle starts again. 20Existing coastal facilities can use inland RTCs if the quantity that they are buying, plus the quantity that they were originally allocated for that year, is less then the quantity of tradable and non-tradable RTCs that they were originally allocated for their first year in the program (typically 1994). New coastal facilities may only use coastal RTCs. CHAPTER 1. INTRODUCTION 21

to reduce emissions of NOx by 70% from 1994 to 2003. However, due to the setting of too generous caps, emissions were reduced at only a fraction of the rate expected at the time of the program’s adoption. As a result, RECLAIM reduced its NOx trading credits budget in July 2005.

Texas Ozone Emission Cap-and-Trade Programs Texas Natural Resources Conser- vation Commission (TNRCC) has implemented and administered two cap-and-trade programs of emission allowances for ozone emissions in the Houston-Galveston-Brazoria ozone nonattainment area (eight-county HGB area)21: Mass Emissions Cap and Trade (MECT) Program and Highly-Reactive Volatile Organic Compound Emissions Cap and Trade (HECT) Program. The MECT is a mandatory program that caps nitrogen oxides (NOx) emissions from applicable stationary facilities in the HGB area starting 2002. Required reductions from a 1997-1999 baseline are expected to be significant and potentially as great as 90%. The TNRCC established the region’s final cap in 2007. The MECT program has a 12-month control period beginning January 1 and ending December of each year. The initial control period began on January 1, 2002. Adopted in December 2004, the HECT program establishes a mandatory annual cap for emissions of HRVOCs on all stationary sources at sites in the HGB area with the capacity of more than 10 tons of HRVOC per year. Same as the MECT program, the HECT allowances are allocated on an annual basis and cover emissions from January 1 through December 31 of each year. The HECT program began on January 1, 2007. So far, it is currently only active in Harris County. For both programs, the TNRCC will subtract allowances from each account based on the unit’s actual emissions for compliance, which occurs in the first quarter of the year following the compliance period. Allowances are freely traded and can be banked. Banked allowances can only be used for the year following the allocation year and will expire if they go unused after this period. In addition, facilities must use current vintage allowances prior to submitting banked allowances for compliance. This nuance limits the potential size

21The eight county region of HGB ozone nonattainment area is comprised of Harris, Galveston, Brazoria, Liberty, Montgomery, Fort Bend, Waller, and Chambers counties. CHAPTER 1. INTRODUCTION 22

of banked allowances, thus ensuring that actual emissions stay relatively close to the cap for each year.22 In the past, the TNRCC has awarded facilities that undertake emission reduction activities with Discreet Emission Reduction Credits (DERCs) or Mobile Discreet Emission Reduction Credits (MDERCs). DERCs generated in the HGB area can be used as allowances under the MECT and HECT programs with certain limitations, while MDERCs can be used without limitation.

Illinois Emissions Reductions Market System Faced with a challenge in achieving the reduction in volatile organic material (VOM) emissions required by the federal Clean Air Act, Illinois implemented Emissions Reductions Market System (ERMS) in 2000. The ERMS is a cap-and-trade program for VOM emissions in the Chicago ozone nonattainment area located in six counties and three other townships in northeastern Illinois.23 The ERMS is only directed at major stationary sources located in the area that have baseline VOM emissions of 10 tons per season. Such sources, referred to as “participating sources”, must hold “trading units” for their actual VOM emissions. Under ERMS, participating sources are required to obtain a Clean Air Act Permit Program (CAAPP) permit, which establishes their allotment schedules of freely granted “trading units” based on historical VOM emissions or “baseline emissions”. Each year, starting with the 2000 ozone season, each participating source is issued trading units based on the initial allotment set during the issuance of its CAAPP permit. At the end of each ozone season (May 1 through September 30), sources must hold sufﬁcient trading units to cover their actual VOM emissions during the season. Surplus allotment trading units (ATUs) may be sold to other sources or banked for use in the following season. With the full ﬂexibility and substitutability of ATUs of various vintage years, the ERMS overall has accomplished reducing the amount of VOM emissions in the Chicago area as required by the Clean Air Act to make incremental progress toward

22Source: http://www.tceq.texas.gov/airquality/banking 23The Chicago ozone non-attainment area covered in the ERMS program include Cook, DuPage, Kane, Lake, McHenry, and Will Counties, Aux Sable Township and Goose Lake Township in Grundy County, and Oswego Township in Kendall County. CHAPTER 1. INTRODUCTION 23

complying with the ozone air quality standard.24

1.3.1.4 Carbon Trading Schemes in the World

The carbon trading schemes currently in practice or in plan are all stemmed from the 1997 Kyoto Protocol. In this international treaty, most developed nations agreed to legally binding targets for their emissions of the class of six major greenhouse gases, including carbon dioxide (CO2), methane (CH4), nitrous oxide (N2O), sulfur hexafluoride (SF6), hydrofluorocarbons (HFCs), perfluorocarbons (PFCs), and nitrogen trifluoride (NF3). Emis- sion quotas (known as “Assigned amounts”) were agreed by each participating ’Annex 1’ country, with the intention of reducing the overall emissions by 5.2% from their 1990 levels by the end of 2012. All European Union (EU) member countries signed and and ratified the treaty. Following the general layout of Kyoto Protocol, United Kingdom volunteered to imple- 25 ment the first ever economy-wide CO2 cap-and-trade program in world history by 2002. As the Kyoto Protocol was coming into force on February 16, 2005, EU officially launched the EU Emission Trading Scheme on January 1, 2005. Although the United States has not ratified the treaty and is therefore not bound by it, there have been tremendous effort at both federal and state level to implement CO2 cap-and-trade programs in America. In 2008, the Regional Greenhouse Gas Initiative finally took place and became the first carbon trading program outside Europe. The latest international effort of carbon trading system in practice is the New Zealand emission trading scheme, although it is not a cap-and-trade program because there is no fixed cap for CO2 emissions in New Zealand.

United Kingdom Emission Trading Scheme (UK ETS) The UK Greenhouse Gas Emissions Trading Scheme was introduced by the UK Government in 2002 as part of the UK Climate Change Programme. At the time, emissions trading was already being developed internationally - as part of the Kyoto Protocol - and the European Commission had proposed that EU-wide trading would start in 2005. The UK ETS was created as a pilot

24Source: http://www.epa.state.il.us/air/erms/overview.html 25Denmark ran a pilot greenhouse gas trading scheme between 2001 and 2003, but it only involved eight electricity companies. CHAPTER 1. INTRODUCTION 24

prior to the mandatory European Union Emissions Trading Scheme (EU ETS). Being the first multi-industry carbon trading system in the world, it was designed to be a voluntary system. No industries and no firms were mandated to participate. The scheme recruited 38 participants from UK industries and organizations who promised to make reductions in their carbon emissions. They agreed to hold sufficient allowances to cover their actual emissions every year, and participate in a cap-and-trade system with an annually-reducing cap. In return they received a share of a £215 million “incentive fund” from the Department for Environment, Food and Rural Affairs (DEFRA). The allocation of “incentive fund” was determined through an auction conducted by DEFRA in March 2002. In the auction, each of the 34 participants bids a schedule of their willingness of abatement for 2006 at various unit prices. The product of the unit price and the willing quantity of abatement at the price, which the participant has promised in his bid, will be the award payment he receives from the “incentive fund”. In this manner, the auction clears at a price level where the sum of all participants’ award payments equal to £215 million. In the end, 34 of the 38 participants won in the auction, and hence became “direct participants” of the EU ETS program. The auction outcome consequently determines the total amount of emission reduction for 2006 from all winning participants based on their baseline emission levels. To make phased progress towards the 2006 target during the intermediate years of 2002-2005, the 2002 target was then set as 20% of the 2006 target, rising to 40%, 60% and 80% in each of the subsequent years. As a result, a direct participant making a commitment to abate by 1 tonne in 2006 would be committed to a total abatement of 3 tonnes over the period

2002-2006 as a whole. After the auction, DEFRA issues an amount of CO2 allowances each year equal to total baseline emissions substract the total promised abatement from all direct participants of that year, and allocate them to direct participants pro rata to their winning quantities in the auction. The UK ETS then ofﬁcially started operating as a cap-and-trade program with an allowance cap since April 2002. Participation has since expanded to 54 sectors of the UK economy. In the program, allowances are perfectly tradable and bankable. After the EU ETS activated in 2005, the UK ETS has now run in parallel with it. Management of the scheme transferred to the Department of Energy and Climate Change in 2008, and it has CHAPTER 1. INTRODUCTION 25

closed to include new entrants since 2009.

European Union Emission Trading Scheme (EU ETS) The European Union Emis- sion Trading Scheme (or EU ETS) is the largest multi-national, greenhouse gas emissions trading scheme in the world. It is one of the EU’s central policy instruments to meet their cap set in the Kyoto Protocol. The program caps the amount of carbon dioxide that can be emitted from large installations with a net heat supply in excess of 20 MW, such as power plants and carbon intensive factories in the energy and industrial sectors. The EU ETS currently covers more than 10,000 installations which are collectively responsible for close to half (46%) of the EU’s emissions of CO2 and 40% of its total greenhouse gas emissions.

In order to neutralize annual irregularities in CO2 emission levels that may occur due to extreme weather events (such as harsh winters or very hot summers), emission allowances for any plant operator subject to the ETS are given out for a sequence of several years at once. Each such sequence of years is called a Trading Period. The scheme has planned out three trading periods:

1. Phase I (2005-2007): created to operate apart from international climate change treaties such as the pre-existing United Nations Framework Convention on Climate Change (UNFCCC, 1992) or the Kyoto Protocol.

2. Phase II (2008-2012): expanded the scope of the scheme significantly. The EU’s ”Linking Directive” introduced the Clean Development Mechanism (CDM) and Joint Implementation projects (JI) credits as specified in the flexible mechanism of the Kyoto Protocol26.

3. Phase III (2013-2020): will have a number of rules changed, including: [1] the setting of an overall EU cap, with allowances then allocated to EU members; [2] tighter limits on the use of offsets; [3] limiting banking of allowances between Phases II and

26Joint Implementation projects (JI) defined by Article 6 of the Kyoto Protocol, which produce Emission Reduction Units (ERUs). One ERU represents the successful emissions reduction equivalent to one tonne of carbon dioxide equivalent. Clean Development Mechanism (CDM) defined by Article 12, which produces Certified Emission Reductions (CERs). One CER represents the successful emissions reduction equivalent to one tonne of carbon dioxide equivalent. CHAPTER 1. INTRODUCTION 26

III; and [4] a move to auctioning a greater share (>60%) of allowances rather than free allocation .

The allowance of a certain vintage year is only valid during its own trading period. After voluntary trials in the UK and Denmark, Phase I commenced operation in January 2005 with all 15 (now 25 of the 27) member states of the European Union participating. During Phases I and II, allowances for emissions have typically been given free to ﬁrms. But several member states conducted small scale auctions occasionally either during Phase I or during Phase II. For Phase III, the European Commission has planned to conduct large scale auctions to prevent wind fall proﬁts for regulated industries.

Regional Greenhouse Gas Initiative (RGGI) The Regional Greenhouse Gas Initiative (RGGI) is the ﬁrst mandatory carbon trading program within the United States. It is a cooperative effort among ten states in the northeast and mid-Atlantic regions, including Connecticut, Delaware, Maine, Maryland, Massachusetts, New Hampshire, New Jersey, New York, Rhode Island and Vermont.27 In 2003, New York State proposed and attained commitments from other nine states to form a cap-and-trade program for CO2 emissions from power sector. It targets the fossil fuel-ﬁred electricity generating plants with more than 25 megawatts (MW) of capacity. Currently, 209 facilities region-wide are subject to compliance, and approximately 95% of the emissions from the electric power generation sector in the participating states are regulated under the program. The program began full operation on January 1, 2009 with the aim to reduce participating states’ carbon emissions to 10% below their 2009 level by 2018.

Although RGGI is composed of individual CO2 Budget Trading Programs in each of the ten participating states, regulated power plants can use a CO2 allowance issued by any participating states to demonstrate compliance with an individual state program. In this manner, the ten state programs, in aggregate, function as a single regional compliance market for CO2 emissions. For all participating states together, CO2 emissions are initially capped at levels comparable to that at the beginning of the 2000’s decade, and then ramp

27New Jersey formerly participated, but Governor Chris Christie removed the state from RGGI in 2011. As a result, only nine states currently participate in the initiative. Several states and Canadian provinces so far acting as observers are Pennsylvania, Quebec, New Brunswick, and Ontario. CHAPTER 1. INTRODUCTION 27

down gradually. From 2009 to 2014, the RGGI cap is 188 million tons of CO2 per year. Beginning in 2015, the cap will decrease by 2.5% per year, and reach a total reduction of 10% by 2018. RGGI compliance occurs in three-year control periods. At the end of each control period, power plants must submit one allowance for each ton of CO2 emitted over the preceding three years. The first three-year compliance period ran from January 1, 2009 till December 31, 2011. Each RGGI allowance has its vintage year specified, and is bankable without restrictions. Thus, 2009 vintage allowances can be also be used in 2010 and beyond. Normally, in a standard cap-and-trade program, an allowance can not be used to cover emissions discharged earlier than its vintage year. However, in the RGGI program, allowances with vintage years that are in the same compliance period are perfectly substi- tutable. For instance, the 2010 vintage allowances can be used to comply for the emissions happening in 2009 when the first compliance requirement is due after the end of 2012.

RGGI distributes CO2 emissions allowances to the market primarily through auctions, which account for over 95% of all the allowances in circulation, making it distinctive among existing cap-and-trade programs. Auctions are conducted quarterly. The ﬁrst RGGI

CO2 auction took place in September 2008. Auction proceeds are used to promote energy conservation and renewable energy, although as of 2010 three states had used some of the money to balance the overall budget. Overall, 80% of the auction proceeds have been in- vested in consumer beneﬁt programs, including energy efﬁciency, renewable energy, direct energy bill assistance and other greenhouse gas reduction programs.

Besides the quarterly auctions, market participants can also obtain CO2 allowances in various secondary markets, including the Chicago Climate Futures Exchange (CCFE) and the Green Exchange. Allowance purchases are settled by the electronic transfer of ownership between two accounts in the RGGI CO2 Allowance Tracking System (COATS), which is the platform that records all data regarding RGGI states’s CO2 Budget Trading Program, such as conducting auctions, tracking ownership transfers, and processing compliance.28

28 The RGGI CO2 allowance tracking system (RGGI-COATS) allows the public to view 10 different kinds of reports on emissions, market participants, market prices and transactions in order to track the RGGI market. CHAPTER 1. INTRODUCTION 28

New Zealand Emissions Trading Scheme (NZ ETS) The New Zealand Emissions Trading Scheme (NZ ETS) is a national all-sectors all-greenhouse gases uncapped emissions trading scheme ﬁrst legislated in September 2008. Tradable emission units will be issued by free allocation to emitters, with no auctions in the short term. As the emissions is not capped under New Zealand program, it is not considered as a Cap-and-Trade program, but simply an carbon emission trading system. Although the NZ ETS covers all sectors, individual sectors of the economy have different “entry dates” when their obligations to report emissions and surrender emission units have effect. Forestry, a net sink which contributed net removals of 14 Mts of CO2e in 2008 or 19% of New Zealand’s 2008 emissions, entered on 1 January 2008. The stationary energy, industrial processes and liquid fossil fuel sectors (34 Mts, 45% of 2008 emissions) entered the NZ ETS on 1 July 2010. The waste sector (landﬁll operators) will enter on 1 January 2013. Methane and nitrous oxide emissions from agriculture (35 Mts or 47% of 2008 emissions) are scheduled to enter the scheme from 1 January 2015.

1.3.2 Future Programs Planned

California AB-32 and Western Climate Initiative

In September 2006, the California Legislature passed the California Global Warming Solutions Act, AB-32, which was signed into law by Governor Arnold Schwarzenegger. AB-32 requires the California Air Resources Board (CARB) to develop regulations and market mechanisms to reduce California’s greenhouse gas emissions to 1990 levels by 2020, representing a 25% reduction statewide, with mandatory caps beginning in 2012 for signiﬁcant emissions sources. On December 17, 2010 CARB adopted a cap-and-trade program to place an upper limit on statewide greenhouse gas emissions.29 The program will take effect beginning in 201230 , with a limit placed that year that will be reduced by two percent each year through 2015 and three percent each year from 2015 to 2020. The rules apply ﬁrst to utilities and large industrial plants, and in 2015 will begin to be applied to fuel distributors as well, eventually

29This is the ﬁrst program of its kind in the United States. 30The year of 2012 is set to be a trial run with only an emission reduction target set but no compliance requirement imposed, and the compliance will start in 2013. CHAPTER 1. INTRODUCTION 29

totaling 360 businesses at 600 locations throughout the State of California. Currently, AB-

32 is planning to use auctions to distribute about 50% of the total CO2 allowances. The auction format has been chosen as the sealed-bid uniform price auction with a reserve price. The ﬁrst auction is scheduled to be held in November 2012. Since 2007, seven U.S. states and four Canadian provinces have joined together to create the Western Climate Initiative (WCI), a regional greenhouse gas emissions trading system. The WCI built on existing greenhouse gas reduction efforts in the individual states as well as two existing regional efforts. In 2003, California, Oregon and Washington created the West Coast Global Warming Initiative, and in 2006, Arizona and New Mexico launched the Southwest Climate Change Initiative. In February 2007, the Governors of ﬁve western states, Arizona, California, New Mex- ico, Oregon, and Washington, signed an agreement directing their respective states to develop a regional target for reducing greenhouse gas emissions, participate in a multi-state registry to track and manage greenhouse gas emissions in the region, and develop a market- based program to reach the target. Until late 2011, the initiative included two types of participants: partners and observers. For several years, the partners were the U.S. states of California, Montana, New Mex- ico, Oregon, Utah, and Washington, and the Canadian provinces of British Columbia, Man- itoba, Ontario, and Quebec. All states except California withdrew in 2011. As of Decem- ber 2011, the remaining WCI members are California and the Canadian provinces British Columbia, Manitoba, Ontario, and Quebec. The observers included at various times Alaska, Colorado, Idaho, Kansas, Nevada, Wyoming, the province of Saskatchewan (which objects to WCI plans for a cap and trade system), and the Mexican states of Baja California, Chihuahua, Coahuila, Nuevo Leon, Sonora and Tamaulipas.

United States: American Clean Energy and Security Act, 2009

The American Clean Energy and Security Act (H.R. 2454), a greenhouse gas cap-and- trade bill, was passed on June 26, 2009, in the House of Representatives by a vote of 219-212. The bill originated in the House Energy and Commerce Committee and was introduced by Rep. Henry A. Waxman and Rep. Edward J. Markey. It was never passed in CHAPTER 1. INTRODUCTION 30

the Senate. The American Clean Energy and Security Act of 2009 (ACES) was an energy bill in the 111th United States Congress (H.R. 2454 ) that would have established a variant of an emissions trading plan similar to the European Union Emission Trading Scheme. The bill was approved by the House of Representatives on June 26, 2009 by a vote of 219-212. However, in July 2010 it was reported that the Senate would not consider climate change legislation before the end of the legislative term. As a result, the act as well as any hope of a federal level cap-and-trade program died in the Senate in July 2010.

Australia: Clean Energy Bill, 2011

The Australian government proposed the Clean Energy Bill in February 2011. It is a package of legislation that will establish a proposed Australian emissions trading scheme (ETS) designed to reduce carbon dioxide emissions and limit global warming. This plan means to make the transition from a ﬁxed-price carbon tax to a ﬂoating-price ETS within a few years. Under the scheme, around 500 entities will be required to buy permits for each tonne of CO2 emitted. There has not been any detailed rules of the program that’s decided yet. But to mitigate the potential cost of implementing the ETS on Australian citizens, personal income tax will be reduced as a compensation. Chapter 2

Emission Permit Auctions under Cap-and-Trade

2.1 Multi-unit Auction of Emission Permits

When government agencies hold auctions to sell emission permits, they usually use “multi-unit auction”. Multi-unit auction by its name means that multiple units of identical items are for sale all at once.1 And the more fundamental distinction of multi-unit auction from the conventional single-unit auction is that bidders demand more than one unit of auctioned item. In such auctions, bidders can bid for different quantities at different prices. Multi-unit auctions conventionally can be categorized in two dimensions. The ﬁrst dimension is the number of rounds of bidding, one or more than one, before the ﬁnal determination of the clearing price is achieved. Single-round auctions are also known as sealed-bid auctions, meaning that after the bidder submits a bid there is no further interaction and the bidder simply awaits an announced outcome. In contrast, a multiple-round auction (also known as open auction) involves interaction because the bidder has a chance to change the bid in response to information that is learned after each round. The second dimension is how the payment (price for winning units) is set for the buyers. They could be charged for the same unit price for all items they win, or they may be required to pay different prices for different units. 1For a very clear introduction to multi-unit auctions, see Krishna (2009), part II.

31 CHAPTER 2. EMISSION PERMIT AUCTIONS UNDER CAP-AND-TRADE 32

Table 2.1: Categories of Multi-unit Auction Formats

pricing rule uniform pricing non-uniform pricing single-round discriminatory auction, uniform price auction no. of (sealed-bid) Vickrey auction rounds multi-round clock auction open discriminatory auction (open)

Based on these two dimensions of characteristics, we have four basic categories of auction formats as listed in Table (2.1). In the practice of auctioning emission permits, only three types of auctions in Table (2.1), discriminatory auction, uniform price auction and clock auction, have ever been adopted in past cap-and-trade programs. I will focus on discussing these auction formats, as well as Vickrey auction.

2.1.0.1 Sealed-Bid Auctions

Sealed-bid multi-unit auctions are the most widely used formats in practice. In such auctions, every bidder submits multiple bidpoints at once. Each bidpoint speciﬁes a pair of price and quantity, stating how many units he demands at that bid price. The auctioneer receives the entire bid schedule composed of multiple price-quantity pairs from the bidder. Apparently, after ranking the bid prices from high to low, such bid schedule can trace out his cumulative demand at each bidpoint. Essentially, each bidder submits a non-increasing demand curve. After receiving bids from all participating bidders, auctioneer can aggregate their bid schedules to come up with the aggregate demand curve. When total demand at one bidpoint equals or just exceeds the supply of allowances, that bidpoint determines the clearing price. The auctioneer aggregates individual bid functions and ﬁnd where the aggregate bid function meets supply, i.e., aggregate demand equals supply, determining the the auction clearing price. For example, there are N bidders in a sealed-bid multi-unit auction selling Q units CHAPTER 2. EMISSION PERMIT AUCTIONS UNDER CAP-AND-TRADE 33

of emission permits.2 Bidder i submit his bid schedule of price-quantity pairs from his demand function qi = Di(p). We can deﬁne the residual supply function as RSi(p) = N ∗ ∗ ∗ Q − ∑ j6=i D j(p). The auction clears at the price level p where Di(p ) = RSi(p ). When the auction clears, how much bidders pay for the awarded allowances from each of their winning bidpoints is decided by different pricing rules of different auction formats.

• Uniform Price Auction: It is also known as single-price auction. Participants bid a price-quantity schedule and bids are used to determining the uniform market- clearing price. A uniform-price auction identiﬁes a single price for all winning bidders. In the uniform price auction, the market clearing price is charged to all inframarginal units.

• Discriminatory Auction: It is also known as “pay-as-bid” auction. A discriminatory auction yields ﬁnal prices that differ among buyers and depends on the amount of each buyer’s bid. In the discriminatory auction, bidders pay their infra-marginal bids.

• Vickrey Auction: It is named after Nobel Laureate William Vickrey, who was the ﬁrst economist to use the tools of game theory to understand auctions. Each bidder is charged at their opportunity cost of winning the quantity of auctioned allowances.

Figure (2.1) can help explain the payment rule of these three auction formats more −1 clearly. From bidder i’s perspective, he submits his demand curve Di (q). After all bidders −1 submit their bid schedules, bidder i is faced with a residual supply curve RSi (q). Under uniform price auction format, his payment is the rectangular area in Figure (2.1b). Under discriminatory auction format, his payment is the trapezoid area underneath his demand curve in Figure (3.1a). And Vickrey’s payment is the trapezoid area underneath the residual supply curve in Figure (3.1b). Vickrey (1961) argued, if the auctioneer charges the bidder only the area under the residual supply curve, then the bidder’s optimal response will be to bid his marginal valuation.

2All remaining sections and chapters in this dissertation will use this setting to model auctions: Q unit of a perfectly divisible good is auctioned to N (N ≥ 2) symmetric risk neutral bidders who maximize their own expected utility. CHAPTER 2. EMISSION PERMIT AUCTIONS UNDER CAP-AND-TRADE 34

Figure 2.1: Bidder i’s Payments under Different Sealed-Bid Auction Formats

(a) Discriminatory

(b) Uniform Price

Due to its complexity, Vickrey auction is rarely used in practice. However, the payment structure defined by Vickrey auction guarantees truthful bidding to be the dominant strategies for all bidders, that is all bidders will bid their true marginal valuation, this format can ensure maximum efficiency. As a result, Vickrey auction provides an ideal benchmark to evaluate the performance of other auction formats and to understand any deviation from the potential most efficient outcome.

2.1.0.2 Clock Auction

People normally refer to multi-round uniform price auction as clock auction. In a clock auction, seller announces a sequence of prices and bidders name quantities until a market- clearing price is found and auction ends. So bidders no longer submit their entire demand schedules all at once. But for each round, they only submit of bid of quantity. Clock auctions can be conducted in two ways. One is English clock (ascending bid) auction, and the other is Dutch clock (descending bid) auction. It is worth mentioning that the clock auction is strategically equivalent to a sealed-bid uniform price auction if bidders in the clock auction observe only the prices and prices decline in a ﬁxed sequence, i.e. no new information each round other than the current price. Although an ascending clock auction is generally considered to be more transparent, its implementation is more expensive and complex. Nonetheless the UK Emissions Trading Scheme Auction in 2002 used a dynamic auction for GHG emission reduction incentives.

The formats that have been used previously in the ﬁeld to auction emission allowances include the sealed-bid discriminatory auction (used for SO2 allowances under Acid Rain Program), the sealed-bid uniform price auction (used for RGGI allowance auctions and for CO2 allowance auctions in several EU ETS member countries), English clock auction (used for Virginia NOx auction of allowances to comply with the NOx SIP Call), and Dutch clock auction (used in UK to auction out the UK ETS CO2 abatement subsidy). How these auction types rank in economic efﬁciency and in raising revenue varies depending on numerous factors, including competitiveness, risk aversion of bidders, reserve prices, the presence of resale markets, and disclosure of bid information. CHAPTER 2. EMISSION PERMIT AUCTIONS UNDER CAP-AND-TRADE 36

2.2 Emission Permit Auctions in the United States

2.2.1 SO2 Auctions under the EPA’s Acid Rain Program

U.S. EPA has been conducting discriminatory price auction annually to sell out SO2 emission allowances under the Acid Rain Program (ARP). The auction was first held in 1993, which predated the official launch of the ARP on January 1, 1995, and has been held annually since, usually on the last Monday of March. The purpose of the early auctions was to jump start the market and to provide price signals for future trading after the program began. For the first 13 years, the auctions were administrated by the Chicago Board of Trade (CBOT). CBOT was not compensated by EPA for its services nor allowed to charge fees. Beginning with the fourteenth auction in 2006, CBOT chose to stop administering the auctions for EPA. Consequently, EPA started to handle all aspects of the auctions since 2006. A small fraction (about 3%) of the total number of allowances were reserved from the annual allowance budget for the auctions. Auctions are divided into two segments: (1) a spot auction for allowances of current vintage year, and (2) an advance auction for allowances that are usable for compliance in 7 years from auction, although they can be traded earlier. The two segments are conducted separately. The total number of allowances provided for selling in each auction was pre-announced and know by all participants. Table 2.2 lists the total quantity offered for each vintage in each auction. Bidding is open to the general public whoever register at the EPA’s tracking system and deposit enough fund in the auction platform to cover its bids. The majority of bids come from power plants, utilities or brokerages. However, there are environmental groups or individuals participating the auctions buying small number of allowances simply to “retire” them. In an auction, each bidder is asked to specify a price and a quantity demanded at that price as one bidpoint. Bid prices is quoted as the amount a bidder is willing to pay for the emission allowance for one tonne of SO2, and can be specified up to 2 significant digits. Bid quantities are specified in terms of integer numbers with the minimum quantity requested to be 1 unit (authorizing 1 tonne of SO2 emission). There is no limit to the number of price- quantity pairs submitted by a bidder. EPA may not set a minimum price for allowances CHAPTER 2. EMISSION PERMIT AUCTIONS UNDER CAP-AND-TRADE 37

Table 2.2: Allowances Reserved for EPA Auctions

Year of Auction Spot Auction Advance Auction Advance Auction 7-year 6-year 1993 50,000 100,000 / 1994 50,000 100,000 25,000 1995 50,000 100,000 25,000 1996 150,000 100,000 25,000 1997 150,000 125,000 25,000 1998 150,000 125,000 / 1999 150,000 125,000 / 2000 and after 125,000 125,000 /

from the Auction Reserve. Allowances are sold on the basis of bid price, starting with the highest priced bid and continuing until all allowances have been sold or the number of bids is exhausted. Bids could be submitted by mail or by fax anytime after the Bid Form was posted on the CAMD website (or otherwise made available) in mid January until the bid deadline, which is 3 business days before the date of the auction. Complete Bid Forms must be received by EPA by the close of business (4:00 p.m. Eastern Daylight Time) on the deadline date. Each bid must also include a certiﬁed check, an EPA Letter of Credit Form, or a statement of intent to use to a wire transfer to cover the total cost of the bids.3 EPA will post the results on the Acid Rain Program Auctions Web site at 12:00 noon on the auction day, and winning bids were settled within 2 weeks after the auctions.4 The payment by each bidder whose order was accepted was determined according to discriminatory price auction rule. EPA returns proceeds and unsold allowances from the auctioning of reserve allowances on a pro rata basis to those units from which EPA originally withheld allowances to create the Auction Reserve.

The Acid Rain Program allows regulated facilities to offer their freely granted SO2

3EPA will only accept an EPA Letter of Credit Form that is signed by a bank that is a member of the Federal Reserve and is a participant in the FEDWIRE funds transfer system. 4The days that it took to settle winning bids and transfer awarded allowances varied year by year, from 2 days to 13 days. CHAPTER 2. EMISSION PERMIT AUCTIONS UNDER CAP-AND-TRADE 38

allowances for sale in the same auction with EPA’s reserved allowances. These entities that wish to sell their own allowances via auction are required to submit a supply schedule in the form of pairs of asking price and quantity. These privately offered allowances are then added to the reserved supply, which makes the auction seemingly a double auction. However, allowances from the Auction Reserve have higher priority in the clearing process and are sold before allowances offered by private holders. After the entire reserved supply is sold out, then it starts to sell privately offered allowances in ascending order, starting with allowances with the lowest asking price in the aggregate supply schedule. If by the time the aggregate demand exhausts all the allowances from the Auction Reserve the price is already lower than the lowest asking price among private offers, none of the privately offered allowance can be sold.

2.2.2 CO2 Auctions under the Regional Greenhouse Gas Initiative

The RGGI program represents a substantial break from the past cap-and-trade programs by distributing emission permits to the system primarily through auctions.5 Rather than give the allowances away mostly for free as other programs did, RGGI periodically conducts auctions to sell majority portion of the annual budgets for each participating states. When the 10 states signed on the RGGI agreement, they agreed to auction at least 25% of the emission allowances to benefit consumers and to support strategic energy investments with auction revenues. Later, several RGGI states have decided to auction 100% of their annual CO2 allowance budgets. Indeed, approximately 94% of the total CO2 allowances in circulation initially entered the market through auctions. The auctions are held quarterly in March, June, September and December each year, usually on a Wednesday. The first two auctions took place on September 25, 2008 and December 17, 2008 respectively, even before the official launch of the RGGI program on the 2009 New Year. By June 2010, there have been eight successful auctions conducted, selling a total of 257.74 million allowances and generating over $622.8 million in auction

5Other existing emissions cap-and-trade programs have chosen “grandfathering” the regulated entities with free allocation in the initial distribution of emission allowances. while the US EPA Acid Rain Program conducts SO2 auctions once a year to allocate around 2.8% of the total allowances, the EU ETS has only a couple of member countries occasionally holding localized auctions selling 0.3% - 8.8% of their allowance budgets. CHAPTER 2. EMISSION PERMIT AUCTIONS UNDER CAP-AND-TRADE 39

proceeds. The first two auctions only sell allowances of 2009 vintage. Starting auction 3, each auction of the first eight auctions was divided into two separate parts: a spot auction selling the allowances of current vintage year and a future auction selling the allowances of 3-year- in-advance vintage. The RGGI auctions have been conducted using a single-round, sealed-bid, uniform- price format, in which each bidder may submit multiple confidential bids for a specific quantity of CO2 allowances at a specific price. Each bidder receives the quantity of CO2 allowances specified in their winning bids at a uniform clearing price. Any party that meets qualification requirements can participate in the RGGI auctions. The participating bidders are classified into compliance entities or non-compliance entities, depending on whether they own CO2 emitting source units or not. The participating states of RGGI agreed that releasing individual level information may increase the ability of market participants to manipulate the market and could reduce the level of competition or adversely affect participation in the auction. In recognition of this, but also to allow the maximum level of public disclosure in accordance with the applicable laws, the participating states release aggregate auction results in a way that maintains enough level of transparency regarding the development of the RGGI CO2 Budget Trad- ing programs while ensuring individual privacy as well as the robustness and fairness of auction participation for all bidders. A small portion of allowances is still awarded to regulated entities through either fixed- 6 price sales or free allocations in the forms of credits and awards. Regardless of how CO2 allowances initially enter the market, they can be traded in the secondary market.

6 Additional CO2 allowances can also be awarded for approved CO2 emissions offset projects (project- based greenhouse gas emissions reductions or carbon sequestration that occurs outside the capped electricity generation sector). In 2009, there was a one time award by certain participating states of early reduction allowances (ERAs). ERAs were awarded for qualifying CO2 emissions reductions achieved at CO2 budget sources during 2006 through 2008, prior to the launch of the program. Approximately 20 million CO2 allowances have been allocated by individual states, through either ﬁxed-price sales or free allocations. CHAPTER 2. EMISSION PERMIT AUCTIONS UNDER CAP-AND-TRADE 40

2.2.3 Virgina NOx Allowances Auction

Under EPA’s NBP, each state has a NOx emissions budget, and has considerable flexibility in allocating its budgeted emission allowances to sources. Virginia held a one time auction to sell NOx allowances for vintage year 2004 and 2005. This is one of the first known cases where allowances were auctioned with the explicit intention of maximizing government revenues. On June 30, 2004, the Commonwealth of Virginia’s Department of Environmental Quality (DEQ) sold 3710 allowances for emission of nitrogen oxides (NOx) in fiscal years 2004 and 2005, using a sequential English clock auction. The auction sold 1855, approximately 8%, of its NOx allowances for each vintage, and raised over $10.5 million, 19 percent above its target revenue of $8.8 million. When designing the auction, the DEQ’s main goal for the auction was to maximize revenue generated fro the state. However, the law that enabled the auction of the allowances required that all allowances be sold by June 30, 2004, only 3 months away from when the DEQ contracted with the Interdisciplinary Center for Economic Science (ICES) at George Mason University to assist in designing the auction In March of 2004. The limited time frame required a mechanism that could be easily and quickly implemented in a short period of time, thus limited the choices of potential formats. In addition, as a political considera- tion it was essential that the DEQ avoid negative political consequences from the auction, either the bidding agents for regulated firms being accused of paying too much in case of discriminatory pricing, or the Virginia DEQ being second-guessed for not extracting “maximal” revenue from the buyers. Given these considerations, the DEQ sent a request for proposals (RFP) for brokerage services to implement an auction on May 17 for a 10-day period as mandated by state procurement rules. In the RFP, it did not specify an auction form. Most proposals from brokerages plan on using a sealed bid design. Astonishingly, the proposal from Amerex Energy of Houston recommended an English clock auction with assurances of accomplishing the auction execution within the short remaining time period. Since the auction format experiment conducted by ICES suggested that English clock auction will generate more revenue than sealed-bid uniform price auction, Amerex’s proposal was selected for its potential to achieve higher revenues, and the contract for services was CHAPTER 2. EMISSION PERMIT AUCTIONS UNDER CAP-AND-TRADE 41

signed on June 8, only 22 days before the final deadline to hold the auction. The extremely tight deadline for holding the auction drove a number of choices about the final auction design. A web- based auction design was chosen to maximize participation and to minimize the time needed for software development. To prevent bidders from using strategies based on default, all bidders had to demonstrate credit-worthiness with a credit instrument or an escrow account with their maximum possible bid.7 On June 24, the auction was held in two sessions. Vintage 2004 allowances were sold in the morning and 2005 allowances in the afternoon. Bidders included energy companies from across the 19-state region and a number of brokerage houses. In each case, the first two rounds were executed in 15 min each with all subsequent rounds executed in only 10 min each. Starting prices, at $1900 and $2900 for 2004 and 2005 respectively, were set, based on morning spot prices. In any round in which there was excess demand, the clock price ticked up by a predetermined increment in the next round: $50 for the first 2 rounds and $25 for any round after that. Starting with 18 bidders, the 2004 auction went 15 rounds in 160 min. There were 10 winning bidders at the clearing price of $2325, which was 3.3 percent higher than a morning transaction on the spot market. Sixteen bidders entered the 2005 auction, which went 19 rounds in 200 min. There were five winning bidders at the clearing price of $3425, a 7 percent premium over the morning spot market trades. All of the winning bidders were energy firms. The $10.5 million in net revenues were deposited to the state’s general fund. The Cantor Fitzgerald market index for 2004 NOx allowances rose 4.36 percent on the day, and 6.14 percent for 2005 allowances.8 English clock auction eliminates the right of participants to specify bids. Instead, it uses a clock to quote successive prices, and each bidder is required only to indicate his quantity demanded at the standing price. In each round, a price is posted on an electric “clock”. In response to the clock price, each bidder indicates the quantity he is willing to purchase for that round. The clock price increases by a predetermined increment into every next round, and bidders submit a new set of demanded quantities at the updated price subject to the

7Some potential bidders refused to participate due to this requirement. 8There is an active private market for the trading of NOx allowances. In the month of May 2004, 3000 allowances (0.6 percent of the total allowances available) were traded in the over-the-counter market. Brokers post a current bid/ask spread for 50 tons. According to www.natsource.com on June 23, the day prior to the auction, the spread for 2004 allowances was $2200/$2350 and for 2005 allowances $3150/$3200. CHAPTER 2. EMISSION PERMIT AUCTIONS UNDER CAP-AND-TRADE 42

constraint that the quantity demanded in current round has to be smaller than last round. When the total demand in a round equals to or just falls short to the total supply, the auction terminates. The auction clearing price is determined by the clock price at the last round. In case that the total demand is smaller than total supply, certain rationing rule may apply to allocate the remaining quantity.

2.3 Emission Permit Auctions in Europe

2.3.1 UK CO2 Abatement Auction

Since the UK Emissions Trading Scheme was a voluntary emissions trading system created as a pilot prior to the mandatory European Union Emissions Trading Scheme, the UK Department for Environment, Food and Rural Affairs (DEFRA) recruited 34 “direct participants” 9 from UK industries and organizations by running an auction to allocate emission allowances in 2002. In return these “direct participants” who won in the auction received a share of a £215 million “incentive fund” (subsidy payments), which is the budget at which UK government aimed to spend to make firms reduce CO2 emission. The UK Government made available £215 million over 5 years as an incentive for direct participants to enter into the scheme and to reduce their greenhouse gas emissions. The incentive payments were allocated by a descending clock auction. The organizations that were interested in obtaining incentive payments for making emission reductions participated in the auction during which they offered a quantity of emission reduction in exchange for a given price per tonne of barbon dioxide equivalent (tCO2e). The UK ETS Auction was operated on the PowerAuctionTM software system in March 2002. This auction allowed any organization to offer abatement of its UK emissions over the period 2002-2006, as against baseline emissions in 1998-2000, in exchange for a subsidy per tonne. Firms entering the auction were required to commit to a specified level of abatement in 2006. The auction aimed to “buy” as much abatement as possible, within a fixed budget of

9Participants in UK ETS due to winning the UK emission Allowance auction are referred as “Direct participants”, as oppose to “agreement participants”, the other group of the two principal groups of potential participants in emissions trading. CHAPTER 2. EMISSION PERMIT AUCTIONS UNDER CAP-AND-TRADE 43

£215 million. The auction was conducted using a descending clock format, with a starting price per tonne of abatement in 2006 of £100. Auctioneer called out price which started high and decreased each round. In each round, the 38 participating bidders stated the number of tonnes of CO2 they would abate (virtually their business as usual emission level subtracting the number of emission allowances they needed), and the tonnes abated could only decrease as prices decreased. Auctioneer multiplied tonnes of abatement times price to calculate the total amount subsidy. If the total cost exceeded budget, auctioneer lowered the price. When total cost ﬁrst fell short of budget, auction ended and the allocation was implemented. After nine auction rounds, a market clearing price was established at £53.37 per tonne of CO2-equivalent. 34 bidders out of the 38 participants won. In exchange for a subsidy payment at this level, the direct participants were assigned abatement commitments totaling 3.96 million tonnes of CO2e (1.1 million tonnes C) in 2006, and the corresponding phased abatement obligations for the intermediate years. Once the intermediate-year commitments implied by the 2006 target are taken into account, the auction closing price of £53.37 per tonne of CO2e abatement in 2006 is equivalent to a subsidy payment of £17.79 per tonne of CO2e abatement in a single year.

The UK CO2 abatement auction was unconventional multi-unit auction format because the total number of auctioned objects were uncertain, and bidders were essentially bidding on their supply instead of their demand. But the essence of this auction is just like a Dutch clock auction.

2.3.2 Auctions by Member Countries of EU ETS

In line with the European Directive 2003/87/EC establishing the EU Greenhouse Gas Emissions Trading Scheme, countries are allowed to auction a maximum of 5% of their total allocation in the ﬁrst trading period (2005-2007, referred as Phase I), so called trial phase, and 10% in the second trading period (2008-2012, refered as Phase II), the Kyoto commitment period. Three countries, Ireland, Hungary, Lithuania, conducted a limited times of auctions in Phase I. Since 2008, member countries have started to auction EUAs periodically. The UK is the ﬁrst Member State in the EU to auction allowances in Phase CHAPTER 2. EMISSION PERMIT AUCTIONS UNDER CAP-AND-TRADE 44

Table 2.3: Allowances for Auctions in Phase I, EU ETS

Ireland Hungary Lithuania Denmark EU25 Total Planned 502,201 791,523 552,000 5,025,000 7,499,201 % in Budget 0.75% 2.5% 1.5% 5% 2005 0 0 0 0 0 250,000 2006 + 963,000 1,197,000 0 sale 2,410,000 2007 or 2008 345,000 1,177,500 552,000 sale 2,074,500 Actual 1,558,000 2,374,500 552,000 0 4,484,500 Actual % 2.33% 7.5% 1.5% 0%

II of the EU ETS. Germany has been selling allowances via an exchange since January 2008. Lithuania, the Netherlands and Austria have also auctioned allowances.10 In the third trading period (2013-2020, referred as Phase III), EU ETS is planning the switch to a centralized distribution of emission permits, and will require member countries to auction at least 60% of EUAs.

2.3.2.1 Phase I (2005-2007)

Among the twenty-ﬁve EU ETS member states at the time, four countries, Ireland, Hungary, Lithuania and Denmark, announced in their National Allocation Plans (NAP) for the ﬁrst trading period (Phase I) that they will apply auction of part of the allowances. In the end, Denmark decided not to have an auction, but organized direct sales through an agent, while the other three countries carried out their auctions. The auction format used by all the other three countries was the sealed-bid uniform- price auction. Table (2.3) lists the quantities of allowances planned and actually sold in the Phase I auctions in these three countries.11 10Further information on these auctions is available at: http://ec.europa.eu/environment/ climat/emission/auctioning en.htm 11Fazekas (2008) provided a thorough survey for the auction design, implementation and results of the Phase I EU ETS auctions. CHAPTER 2. EMISSION PERMIT AUCTIONS UNDER CAP-AND-TRADE 45

Ireland

Ireland was the first EU ETS Member State to auction CO2 allowances. Ireland’s Na- tional Allocation Plan contained a provision to auction up to 1% of total allowances during Phase I in order to fund the administration of the scheme. At the beginning, the Irish EPA set aside 502,201 allowances, approximately 0.75% of the total national allocation, to be auctioned in two separate auctions. The rationale behind the decision of running two auctions is to make sure that not all allowances would happen to be auctioned during a “low” period in market prices. The first auction took place in January 2006 with 250,000 allowances provided for sale, and the second one was held in December 2006 to sell 963,000 allowances. The total of over one million allowances sold in these two auctions accounted for 1.81% of Ireland’s national allowance budget for Phase I. Right around the time when Phase I program was about to conclude, the Irish EPA decided to launch the third and final auction of 345,000 allowances for the EU ETS Phase I on March 6, 2008. The bidding in auction 3 was open for almost a week and closed on March 12, 2008. Auction 3 brought the total amount of Ireland’s auctioned Phase I allowances to 2,558,000, about 2.33% of the total allocation. Besides the allowances originally set aside by the Irish EPA under its NAP provision, the auctioned allowances for these three auctions came from two sources: any remaining allowances from the new entrants reserve (NER), and the undistributed allowances due to the closing of existing installations12. In designing the auction, regulators emphasized simplicity. As a result, the sealed-bid uniform price auction format was selected. The bidding in the auctions was subjected to a minimum incremental bidding quantity, called lot size. The bid price for the last lot(s) becomes the clearing price for settlement of all successful bids. For the first auction, the lot size was set at 500 allowances in order to accommodate smaller bidders. In the second and third auction, the lot size increased to 1,000 allowances. In addition, a undisclosed reserve price was set to limit the lowest bid price allowed in the first two auctions; while there was no reserve price for auction 3. The Irish auction was different from those in the other two countries in that it required a

12If an generating facility closed operation, the share of freely allocated allowances for this installation then became undistributed, and thus was included in Phase I auctions CHAPTER 2. EMISSION PERMIT AUCTIONS UNDER CAP-AND-TRADE 46

pre-qualification process. To ensure sufficient participation and demand, the Irish auctions were open to the broader market. All bidders with a valid account in the EU ETS registry system can enter the bidding. Regulators was concerned that such opening of the market might expose the auction to the risk of speculative bidding and create difficulties in bid val- idation. Therefore, potential bidders were required to pass pre-qualification and put down a fixed amount of deposit. The deposit was deducted from the amount owed by auction winners and refunded to auction losers. Any winners not honoring their bids would forfeit their deposits. For the first auctions, e3,000 deposit was collected in the pre-qualification stage. The deposit increased to e15,000 in auction 2, but then dropped to e2,000 in auction 3. After auction 1 was closed, the EPA will dispatch a notification email to winners regarding the results. All amounts of payment from successful bidders must be recorded as paid within five working days of the dispatch of the email notification or the associated bid will be considered void and the deposit forfeited. Starting from the second auction, the settlement period for completing electronic funds transfer was shortened to two days. Once the correct payment has been received, the EPA would transfer the appropriate number of allowances to the Registry accounts for all successful bidders. Refunds to unsuccessful bidders were much slower for bidders from outside the eurozone than for those in the eurozone. Any remaining allowances unsold after the auction are retired on 30 June 2008 in accordance with the procedure established for all pilot phase allowances.

Hungary

In the Hungarian National Allocation Plan, the Hungarian government set aside 791,523 allowances for auctioning, which is about 2.5% out of the 31.6 million tonnes CO2 emission cap. After combining the additional allowances from unclaimed allowances of the new entrants reserve (NER) and those undistributed due to the closures of existing facilities, Hungary sold a total of 2.4 million emission allowances at two auctions in December 2006 and in March 2007 respectively, which was about 7.5% of the national allocation budget. The ﬁrst auction took place on December 11, 2006 to sell a total of 1,197,000 EUAs. Bids for a total demand of 3.42 million allowances were received. The auction clearing price was settled at e7.42 per tonne. On March 26, 2007, a total of 1,177,500 emission CHAPTER 2. EMISSION PERMIT AUCTIONS UNDER CAP-AND-TRADE 47

allowances were offered in the second auction. Buyers submitted bids to demand a total of 2.4 million allowances, and the clearing price ended up at e0.88 per tonne. All entities or individuals holding an account at an emissions trading registry of any of the EU member states were able to participate in the auction through one of the Climex Alliance partners. Participants submitted bids for any quantity of emissions allowances up to the limit of the total number of allowances offered for sale. The lot size for minimum incremental bid quantity was 500 allowances, and the price tick of the minimum incremental bid price is 1 eurocent. The auction format was a sealed-bid uniform price auction where the single clearing price was set by the lowest bid accepted by the auctioneer. A reserve price was set for each of the auction. Although the reserve prices were undisclosed before each auction, they were released when auctioneer determined the auction clearing price. The reserve price for the first auction was set at the Point Carbon 2007 EUA closing price index of the day before the auction minus 90 cents. Taking time value into account, that was around 60 cents less than the spot market price. In the second auction the reserve price was 85% of the closing December 2007 forward price for the day before the auction rounded off to 2 decimals. With all bids ranked by descending bid price, the clearing price was the bid price for the last lot, but it could not be lower than the reserve price determined by the auctioneer. Since setting the reserve price may result in unsold allowances, each auction would have comprised a maximum of two sessions: if the whole amount of allowances were not sold during the first session, a second session would be held to repeat the bidding process. But at both Hungarian auctions, one session was sufficient to sell all offered EUAs. The electronic auction was implemented on the euets.com CO2 trading platform. Bid- ders had to place their bids in the given time period and could not withdraw them after the termination of the bidding phase. The bids were not visible to other bidders, which is known as a blind auction. Although there was no pre-qualification process required, bidders needed to deposit a 100% collateral to cover all potential payments associated with their bids. The collaterals were due two working days before the date of the auction, and were required to be deposited at the clearing house of euets.com, APX B.V. or that of the Climex Alliance. The clearing and settlement of the auction was completed in two business days following the auction. Successful bidders could request the transfer of the purchased CHAPTER 2. EMISSION PERMIT AUCTIONS UNDER CAP-AND-TRADE 48

allowances by the clearing house to their holding accounts one business day after clearing. Bidders could request the refund of any unused collateral one business day after clearing.

Lithuania

The Lithuanian Environmental Investment Fund offered 552,000 EU allowances for sale, which was 1.5% of the total allocation budget. On September 10, 2007, Vertis Envi- ronmental Finance and New Values announce the successful execution of the Lithuanian auction of EU Allowances. By then, the market price of Phase I EU ETS allowances was unfortunately at history low. The auction was arranged by Vertis and was executed on the Climex trading platform. The bidding period lasted for one hour. During this time bidders were free to modify or withdraw their bids. The submitted bids, however, could not be withdrawn or changed after the end of the bidding phase. The auction was blind, which means that bidders could not observe bids from other opponents. The lot size of minimum incremental bid quantity was 1,000 allowances, and the price tick for the minimum incremental bid price was 1 eurocent. Similarly to the procedure used in Ireland and Hungary, the Lithuania adopted the sealed-bid uniform price auction where all successful bidders pay the same clearing price. All bids were ranked in descending order by price. There was a undisclosed reserve price set for the auction. The clearing price was determined by the bid price for the last lot at which the cumulative demand exhausted all offered allowances or the reserve price, whichever one is higher. The reserve price was then released during the determination of clearing price: it was 85% of the market price of allowances. There was no pre-qualiﬁcation process, but bidders needed to deposit a 100% collateral to cover all potential payments associated with their bids. The clearing and settlement of the auction was completed in one business day following the auction. In the end, the auction clearing price was settled at e0.06 per tonne, the total amount offered was sold for a total of e33,120 which barely covered its administrative costs. CHAPTER 2. EMISSION PERMIT AUCTIONS UNDER CAP-AND-TRADE 49

Table 2.4: EU ETS Phase I Auction Clearing Prices

e per tonne 1/27/2006 12/2006 3/27/2007 9/10/2007l Ireland 6.87 Ireland Hungary Lithuania Auction clearing price 26.32 7.42 Hungary 0.88 0.06 Daily trading price 26.10 7.10 0.98 0.06

2.3.2.2 Phase II (2008-2012)

In line with the rules laid down in the National Allocation Plans, some member states conducted auctions in the second trading period. The Directive 2003/87/EC allows the auctioning or sale of up to 10% of the allowances allocated by the member state in Phase II. Half of the EU countries had been planning to hold auctions starting since 2008, to sell all together around 3% of the total allowances issued during 2008-2012. A minimum of 389 million tonnes will be auctioned. These auctions are not covered by the Auctioning Regulation. Originally, eleven countries planned to auction fractions of their EUAs: Austria, Bel- gium, Germany, Hungary, Ireland, Italy, Lithuania, Luxembourg, Netherlands, Poland and UK. However, no information on EUA auctions could be found for Italy, Luxembourg and Poland. The other eight countries have set aside EUAs for Phase 2 auctions as follows.

1. Austria: 500,000 allowances per year (2 million total) will be auctioned, that is a share of 1.22%.

2. Belgium: Flanders will auction 922,000 ton of emission allowances during the second trading period in one or several sessions. This corresponds to 0.29% of the total Belgian allocation for the period 2008-2012. Revenues will be used to purchase ERUs, CERs, AAUs.

3. Germany: 40 million, 8.8% of total allocation will be auctioned.

4. Hungary: 4.3% of total allocation will be auctioned. CHAPTER 2. EMISSION PERMIT AUCTIONS UNDER CAP-AND-TRADE 50

5. Ireland: Up to 0.5% of the total allowances. Revenue from sales of allowances will be used by the EPA to defray the administrative costs of the scheme.

6. Lithuania: 2.7% of total allocation will be auctioned.

7. Netherlands: 3.2 million, 4% of total allocation will be auctioned.

8. United Kingdom: 17 million, 7% of total allocation plus any surplus from the NER will be auctioned.

So far, Belgium and Hungary has not performed any auctions yet. Ireland planed to auction off 557,065 EUAs (0.5% of total budget) in Phase II, but eventually decided to directly sell 185,000 allowances through brokerage in January 2009, and the same number again in February 2010. The remaining 187,065 allowances were sold in March 2011. As a result, only five countries had indeed conducted Phase II auctions to sell EUAs by March 2012. United Kingdom is the first member state in the EU to auction allowances in Phase II of the EU ETS. Germany has been auctioning allowances weekly via European Energy Exchange (EEX) since January 2008, while Lithuania used the same platform to conduct three auctions in late 2011 and early 2012. Austria has held bi-annual auctions on Climex platform. Netherlands have experimented different platforms by contracting Dutch State Treasury Agency for the first auction, Climex for the second and third auction, and EEX for the remaining six auctions.13

United Kingdom

On November 19, 2008, UK held its first auction of carbon trading allowances (EUA) under EU ETS, making the UK the first country in Europe to hold an auction in Phase II of the EU ETS. The Treasury has appointed Department for Environment, Food and Rural Affairs (DEFRA) to conduct the auctions, and DEFRA has appointed the UK Debt Management Office (DMO) to act as its agent in running the auctions in Phase II.

13Further information on these auctions is available at: http://ec.europa.eu/clima/policies/ets/auctioning/ second/index en.htm CHAPTER 2. EMISSION PERMIT AUCTIONS UNDER CAP-AND-TRADE 51

The UK National Allocation Plan for the second trading phase in the EU ETS set aside 7% of the allowance cap for auctioning, amounting to approximately 86 million allowances over the phase. Before the first auction was conduction, future auctions had been scheduled to take place periodically with specific dates and volumes pre-announced up to April 2010 on the UK Debt Management Office’s website. Dates for future auctions would be announced in due course. For the first auction in 2008, the Community Emission Trad- ing Scheme (Allocation of Allowances for Payment) scheme 2008 was issued, but it was replaced by changed rules in the Community Emission Trading Scheme (Auctioning of Al- lowances) scheme 2009. As of January 2010, a non-competitive bidding facility had also been put in place. The non-competitive session was included to facilitate broader access to the auctions. As a result, each auction will be conducted in two sessions: the first is the non-competitive auction where bidders only submit one bid quantity and accept whatever clearing price is determined in the following competitive session; the second is the competitive auction. The non-competitive bidding window is open for five working days, and then the competitive bidding window is open for two hours afterwards. The noncompetitive bidding session allowed businesses that participate in the EU ETS to bid for up to 10,000 EUAs at the clearing price determined at auction. One special feature of the UK EUA auctions is the Primary Participants. Participants at the UK auctions must place bids through a Primary Participant, who acted as a bidding agent, into a competitive bidding session using a bespoke Bloomberg auction platform. The Government has approved four Primary Participants to facilitate the competitive stage of the auctions: Barclays Capital, JP Morgan, BNP Paribas and Morgan Stanley. Organiza- tions can apply to DECC to become Primary Participants and will be assessed against the eligibility criteria set out in the Scheme. After the close of the competitive bidding window, each Primary Participants will be notified by the auctioneer regarding the quantities they win and the total amount due for payment. Payment by a Primary Participant for allowances allocated must be received into the nominated bank account on the second working day after the day on which the Primary Participant receives the notice. An independent observer was appointed by HM Treasury for each auction through an open competition in order to provide Monitoring Reports. CHAPTER 2. EMISSION PERMIT AUCTIONS UNDER CAP-AND-TRADE 52

Germany

Kreditanstalt fYr Wiederaufbau (KFW) is an bank group that helped the German government in 2008 and 2009 to directly sell EUAs through the trading market such as the European Emission Trading Exchanges in London (ECX) and Leipzig (EEX). Starting in January 2010, these sales were replaced by an auctioning procedure in accordance with the legal stipulations of the Allocation Act 2012. For the selection of an appropriate exchange to be the auction platform, the Federal Environment Ministry invited an open competition. Among the several bids received, the Energy Exchange (EEX) in Leipzig was able to win the contract. The concept for auctioning on the exchanges builds upon the positive experiences of KFW sales in previous years and is based as much as possible on the existing (exchange) infrastructure of the market. After the German Federal Environmental Agency commissioned KFW to conduct the selling and management of the auctions, the auctions have been held weekly in Leipzig since January 2009. So far, the Federal Republic of Germany has been offering an annual amount of 40 million emission allowances (EUAs) for auctioning. The overall volume of emissions auctioned amounts to about 9% of the national emissions trading budget. The proceeds go to the Federal Republic. Further allowances from the National Reserve are also auctioned to cover the costs arising from tasks taken over by the German state in the context of emissions trading. 300,000 allowances for immediate delivery (spot contract) are auctioned every Tuesday and 570,000 allowances to be delivered by December of the current year (futures contract) are auctioned every Wednesday between January and Octo- ber. From November every year, 870,000 allowances per week of the remaining allowances are auctioned on the spot market. In auctions on the spot market, the minimum bid amount is 500 allowances, on the derivatives market 1,000 allowances. A sealed-bid uniform price format is used in the auctions. If two bids are equal they are ranked according to the time of receipt. The price at which the total amount of bids reaches or exceeds the available quantity of allowances determines the auction clearing price. As auctions are conducted with a closed order book, each bidder can only see his own bids. The auction results are published within the trading system following the auction and on the EEX website the following day. CHAPTER 2. EMISSION PERMIT AUCTIONS UNDER CAP-AND-TRADE 53

Lithuania

The Lithuanian ministry of the environment originally contracted the European En- ergy Exchange (EEX) to auction off a total volume of 1.7 million EU emission allowances (EUA) on its behalf through two uniform price auctions on December 12, 2011 and Jan- uary 26, 2012, selling 850,000 EUAs respectively. Right after the second Lithuanian auction on EEX, the ministry extended its contract with EEX to organize another auction for an additional 850,000 EUAs on March 15, 2012. These allowances are volumes from the Lithuanian new entrant reserve (NER) for the second phase of EU emissions trading (2008 to 2012) which are not needed. The Lithuanian auctions used the same rules as the German auctions, of which the format is sealed-bid uniform price auctions. In the auction on January 12, 2012, Lithuania sold 850,000 spot carbon permits via EEX at 7.46 euros ($9.68) a tonne each, raising 6.34 million euros ($8.2 million) for government coffers. Six companies took part in the auction, and the bidding volume amounted to more than 6 million EUAs. In the auction on March 15, 2012, Lithuania sold 850,000 EU Allowances for spot delivery on German bourse EEX at a price of 7.80 euros per unit, raising 6.63 million euros for government coffers. The total bidding amount was 4,021,000 EUA. Thus, participants bid more than 4-fold the determined volume. 5 companies took part in the auction in which the price was determined at EUR 7.80 per EUA.

Netherlands

The Dutch Government sold a total of 16 million EUAs during Phase II, which is 4% of the total allocation in the Netherlands. One of the objectives of the auctions in this period is to gain experience with the auction method in preparation for the enlarged allowance auctions in Phase III EU ETS. In the ﬁrst auction held in 2010, the so-called “spot contracts” were sold (in contrast with “future contracts”). The Ministry of Finance was assigned to organize the auction because it has extensive experience with auctions in the capital market. More importantly, the Ministry of Finance organized a sale of emission rights from the ’New Entrants Reserve’ in 2007. The New Entrants Reserve is meant to allocate emission permits to newcomers who are yet unknown, to known newcomers and to honor any successful appeals to the administrative courts. CHAPTER 2. EMISSION PERMIT AUCTIONS UNDER CAP-AND-TRADE 54

The Dutch auctions have adopted the same format as the German and Lithuanian auctions: sealed-bid uniform price auctions. They have been conducted according to the prin- ciples of the Dutch Direct Auction (DDA), an auction method with which the DSTA has gained experience over the past few years. Four banks acquired the role of carbon dealer (intermediary) for this auction: Barclays, Credit Suisse, JP Morgan and Orbeo (SociZte GZnZrale). The tasks of these carbon dealers include bringing in compliance buyers, providing advice on the process and clearing and settling transactions with the buyers. Netherlands have experimented different auction platforms. The ﬁrst 4 million allowances were auctioned by the Dutch State Treasury Agency at the ﬁrst auction in April 201014. Climex conducted the second and third Dutch EUA auction, selling 2 million allowances each in October and November 2010, both starting at 10.00 AM CET on the auction day15. Participation in the Climex auctions was free of charge for Climex Members. Successful buyers also didn’t have to pay a transaction fee. It was therefore an excellent opportunity to become acquainted with such auctions at no further costs. . The sales of the remaining 8 million allowances were divided into six auctions throughout 2011 and 2012: two auctions sell 2 million EUAs each, and following four auctions sell 1 million EUAs each. These 6 auctions are carried out by EEX16.

14On April 15, 2010, the DSTA auctioned 4 million EUAs for the State of the Netherlands in the first Dutch carbon auction. The clearing price was e14.10 per allowance. The total revenue of the auction is e56.4 million. Bid-to-cover ratio was 4.18. Allocation to compliance buyers at clearing price was 100%. Allocation to non-compliance buyers at clearing price was 52.29%. Total allocation compliance buyers was 60.48%. Total allocation non-compliance buyers was 39.52%. 15After the DSTA experience, Dutch Government decided to auction a total of 4 million EUAs in 2010 via two consecutive auctions on Climex, and the auction dates were originally scheduled on October 14 and November 18 respectively. However, the first Dutch auction was cancelled on October 14 due to a technical difficulty at Climex. After the unfortunate cancellation, the auction has been rescheduled for Wednesday October 27, 2010. On October 27, 2010, Climex executed the auction in which 72 bids were placed with a total volume of 3,331,000 EUAs. Bidders ranged from compliance buyers and utilities to banks and brokers. The total volume of 2 million EUAs offered was sold at a clearing price of e14,90 per tonne in 33 transactions. On November 18, 2010, the second Climex auction for 50 bids were placed with a total volume of 4,100,000 EUAs. Bidders ranged from compliance buyers and utilities to banks and brokers. The total volume of 2 million EUAs offered was sold at a price of e14.83 per tonne in 29 transactions. 16The fourth Dutch auction, which was its first EEX auction, sold off 1 million EUAs as planned. The total amount of bid quantity was 3,278,000 EUAs. Participants demanded more than 3 times the auction volume. 7 companies took part in the auction and the clearing price was determined at e6.95 per EUA. At the time of the Dutch EEX auction, the reference price in secondary trading on the EEX Spot Market was e7.00 per EUA. CHAPTER 2. EMISSION PERMIT AUCTIONS UNDER CAP-AND-TRADE 55

Austria

Austria has offered 500,000 Phase II EUAs for sale by auction annually starting 2009. The auctioning regulation, in which the modalities for the auction are defined, was published on January 16, 2009. According to the Austrian allocation plan and the respective ordinance, during Phase II EU ETS, 500,000 EUAs would be auctioned on an annual basis totals to 2 million EUAs, accounting for 1.3% of the total amount throughout the period. The Austrian Federal Ministry of Agriculture, Forestry, Environment and Water Man- agement (BMLFUW) is responsible for the EUA auctions, and has assigned the auctions to take place on the Climex trading platform. Climex has conducted two Austrian auctions per year from 2009 to 2012, using a sealed-bid uniform price format. Participation in the auctions will be free of charge for all Climex Members. The Climex Spot Platform was closed during the morning and reopened after the auction in order to give members the opportunity to trade their newly acquired EUAs in auctions. Auction participants must be Climex members and need to fully collateralize their bids. Delivery by clearing house APX-ENDEX can only take place to registry accounts of national registries which have been allowed to re-open after the closure of all registries on Mid January 2011. Each Austrian auction consists of two different sessions: the first is the non-competitive auction; the second is the competitive auction, which takes place directly after the non- competitive auction. The clearing price will be settled in the competitive auction. The auction will be conducted with a closed order book, so bidders can only see their own bids. While the platform is open, a bid can be placed. Offer may be changed or deleted at any time. With the closure of the platform, bids are binding and must be confirmed by e-mail. During the first, non-competitive session, 100,000 EUAs will be auctioned. The minimum lot size is 50 EUAs, and the maximum amount demanded per buyer is 2,500 EUAs. Even non Climex members can participate in the non-competitive session. By placing the bid during the non-competitive process, the bidder accepts the whatever clearing price determined in the competitive session. During the second part of the auction, 200,000 EUAs will be auctioned to competitive bidders. Climex membership is required for this session. The minimum price (reserve price) for the competitive auction is e7.16/t, calculated by multiplying the average spot CHAPTER 2. EMISSION PERMIT AUCTIONS UNDER CAP-AND-TRADE 56

end-of-day prices for EUA of January and February 2009 with the factor of 0.9. The reference price17 for the competitive auction is e9.55/t, calculated by multiplying the average Spot end of day prices for EUA from January and February 2009 with the factor of 1.2. The clearing price is applied to all successful offers including all non-competitive bids plus the competitive bids above the clearing price.18 The two auctions in every year will alternate between “100,000 non-competitive + 200,000 competitive” and “200,000 competitive only”. Auction 1, 3, 5, 7 are the combination of non-competitive and competitive parts, while auction 2, 4, 6, 8 are competitive part only. After completion of the competitive auction, the successful participants on the part of a bill BMLFUW. After payment of the cost of the certiﬁcates are transferred to the register account of the participant.

17The reference price is created as follows. the reference price is 1.2 times the lowest daily closing price (closing price) for EUA 08-12 (spot price) of the two months preceding the auction. If not specified for the entire amount of available certificates valid tenders, the remaining allowances will be auctioned at a later date. If the quantity offered, the quantity of allowances, the existing certificates are distributed proportionally to the respective bids. 18On March 16, 2009, the first auction of Austrian EUAs took place. The full available volume of 200,000 EUAs was sold in Competitive Auction, at a price of e11.65, more than 8 times overbid. In the Non- Competitive Auction 5,050 of the available 100,000 EUAs were transacted. On October 13, 2009, the second auction will be competitive only, with 200,000 EUAs offered for sale, closed at a price of e14.23.. On March 23, 2010, 3rd Austrian Auction closed at e12.78, no interest in non-competitive auction. On November 8, 2010, the 4th Austrian Auction sold at a price of 14.30 per tonne in 21 transactions. In the auction 52 bids were placed with a total volume of 1,312,500 EUAs. Bidders ranged from compliance buyers and utilities to banks and brokers. On April 11, 2011, in auction 5, the full volume of the Competitive Auction - 200,000 EUAs - was sold at a selling price of e16.41. There was no apparent interest in the 100,000 EUAs offered at the Non-Competitive Auction which closed prior to the Competitive Auction. The auction was well attended and 5 times oversubscribed. A total of 33 bids were placed in the competitive auction. Bidders included compliance buyers, brokers and traders. On November 28, 2011, in auction 6, Austria failed to sell 200,000 EU Allowances on Monday as prices fell below the minimum level it would accept for the permits. The 7h auction has been scheduled to take place on April 16, 2012. The Austrian Government will auction 400,000 EUAs through Climex. The non-competitive auction for 300,000 EUAs runs from 9:00 clock on April 12, 2012 until 9:45 clock on April 16, 2012. During this period it is possible to place offers. Tenders will be binding on April 16 at 9:45 clock - at the end of the non-competitive auction. The competitive auction will be held on April 16, 2012 from 10:00 - 11:00 clock instead. CHAPTER 2. EMISSION PERMIT AUCTIONS UNDER CAP-AND-TRADE 57

2.3.2.3 Phase III (2013-2020) Proposal

From 2013, all allowances not allocated free of charge must be auctioned, which accounts for over 60% of total EUAs. Since electricity generators will not receive any allowances free of charge (with the potential exception of those in 10 new Member States which may continue to allocate limited volumes of allowances for free on a transitional basis), it is expected that roughly half of the allowances will be auctioned, i.e. some one billion allowances per year. In the current second trading period (2008-2012), no more than 4% of the allowances are auctioned. In addition, in the aviation sector 15% of the EU Aviation Allowances (EUAAs), i.e. some 30 million per year, will be auctioned from 2012, see the Commission’s decision of 30 June 2011. The Auctioning Regulation provides for allowances to be auctioned in the form of spot products, which means delivery within a maximum of ﬁve working days after the auction. Spot products have been chosen for their simplicity and because, unlike futures, they do not lock-in the trading of the auctioned allowances to the auction platform(s), which could have a potential negative impact on competition between trading places in the secondary market. The auction format will be a single-round, sealed bid, uniform price auction. During a single bidding window of the auction, bidders can place any number of bids, each specifying the number of allowances they would like to buy at a given price. The bidding window must be open for at least two hours. Directly following the closure of the bidding window, the auction platform will determine and publish the clearing price at which demand for allowances equals the number of allowances offered for sale in the auction concerned. During a single bidding window of the auction, bidders can place any number of bids, each specifying the number of allowances they would like to buy at a given price. The bidding window must be open for at least two hours. Directly following the closure of the bidding window, the auction platform will determine and publish the clearing price at which demand for allowances equals the number of allowances offered for sale in the auction concerned. In order to limit the impact of auctions on the secondary market, the auctions will be relatively frequent. The Auctioning Regulation provides that the common auction platform CHAPTER 2. EMISSION PERMIT AUCTIONS UNDER CAP-AND-TRADE 58

will hold auctions at least weekly for EU allowances (EUAs). The volume auctioned on all auction platforms will be spread evenly throughout the calendar year, with reduced frequency over holiday periods in the summer and no auctions during the Christmas and New Year period. The first auction for EU ETS Phase III allowances is expected to start after Summer 2012. This early auctioning of 120 million phase 3 allowances in 2012 is to ensure a smooth transition from the second to the third trading period of the EU ETS that underpins the proper functioning of the secondary market. The volume of early auctions in 2012 will be deducted, in equal parts, from the volumes to be auctioned in 2013 and 2014. 24 Member States will do so by means of a procurement procedure jointly with the Commission, which is currently calling for a transitional common auction platform. Ger- many, Poland and the United Kingdom informed the Commission of their decision to opt out of the common auction platform(s) and appoint their own auction platforms. EEX in Leipzig will conduct auctions of allowances in the transition to the third trading period for Germany. Poland and the United Kingdom have yet to decide their auction platforms of choice. Any ETS operator or aviation operator is eligible to apply for admission to bid in the auctions, and so are their parent, subsidiary or affiliate undertakings. Operators can also form business groupings to bid as an agent on their behalf. To ensure the effective competition and openness of the EUA markets, investment firms and credit institutions, authorized and regulated under EU law, may apply for admission to bid. Bidders will be able to access the auctions through the Internet. The auction platform shall also offer dedicated connections. The costs of the auction process, including the costs of setting up the auction platform(s) and carrying out due diligence checks on customers, will in general be paid for by the bidders through the fees they pay to an auction platform to participate in the auctions. The costs of the single auction monitor will be deducted from the auction proceeds and will be borne by the Member States. CHAPTER 2. EMISSION PERMIT AUCTIONS UNDER CAP-AND-TRADE 59

2.4 Desirable Properties and Potential Problems of Emis- sion Permit Auctions

The literature on auction design typically lays out the following desirable properties for auction selection:

1. Allocative efﬁciency: allowances should be allocated to the buyers that value them the most;

2. Effectiveness of revenue extraction : revenue obtained by the government through auctions may be less distortionary than other sources, such as taxes;

3. Price discovery for trading: auction prices provide informative signals about market prices and underlying values;

4. Robustness to collusion and market manipulation: auction rules should promote competition;

5. Fairness and transparency: auction rules should promote conﬁdence in the political and regulatory process;

6. Minimization of transaction cost: bid submission costs should be minimized.

Given these objectives, we usually care about several issues or ramiﬁcations of certain auction formats.

Inefﬁciency

Achieving an efﬁcient assignment of goods is an important challenge of auction design.19 If there is only partial participation of bidders, either due to high friction of entry or because of smaller bidders’ lack of resources in strategizing and forecasting given complex auction rules, the bidders who need permits most may not have an opportunity to bid for them. 19Such efﬁciency includes allowing non-emitting parties who value reductions in emissions to buy permits (and not use them). See Israel (2007) on environmentalist participation in U.S. SO2 emission permit markets. CHAPTER 2. EMISSION PERMIT AUCTIONS UNDER CAP-AND-TRADE 60

Even if all bidders participate, however, there is no guarantee that those willing to pay the most to avoid further abatement will acquire the right number of permits to ensure efficiency. For example, coordinated bidding (“collusion”), market manipulation, and/or the exercise of unilateral market power all have the potential to distort auction outcomes. Collusion in particular can distort market outcomes, undermining the efficiency and price discovery benefits of an auction.

Ambiguity of Revenue Ranking

Revenue generated by auction can be a substitute for distortionary taxes. This is the so- called “double dividend” effect (see e.g., Goulder et al. (1999), and Parry, Williams, and Goulder (1999)). Also, it can be less costly politically to raise money through an auction rather than via direct or indirect taxation. However, the revenue ranking for commonly adopted multi-unit auction formats is not certain. Any one format can be better than another under some circumstances (Ausubel and Cramton (2002)), so the revenue ranking can only be answered empirically case by case., Goulder et al. (1999), and Parry, Williams, and Goulder (1999)). Also, it can be less costly politically to raise money through an auction rather than via direct or indirect taxation. However, the revenue ranking for commonly adopted multi-unit auction formats is not certain. Any one format can be better than another under some circumstances (Ausubel and Cramton (2002)), so the revenue ranking can only be answered empirically case by case.

Failure in Price Discovery (Underpricing)

Possible reasons that auction clearing price might deviate from the true market value include: asymmetry among bidders (one or a few have the market power), inelastic demand (steep marginal valuation curve), over-adjustment for “winner’s curse”, and resolution of bids too low (bid points too sparse). CHAPTER 2. EMISSION PERMIT AUCTIONS UNDER CAP-AND-TRADE 61

Collusion or Market Manipulation

Collusion may happen under several circumstances include: explicit communication among bidders, pre-auction transparency (transparent registration), real-time transparency (revealing the identities of bidders), and so on (Marshall and Marx (2009)). Most of the times, collusion presents in a more implicit form than direct communication among bidders. To a degree, even strategic collusion is one of the serious but difficult issue that auction designers usually concern, because firms with an interest in colluding can respond to market rules in creative and sometimes unexpected ways. As a result, the early design of the Federal Communications Commission (FCC) spectrum license auctions stressed the importance of high transparency and flexibility for bidders.20 Pre-auction transparency in the form of transparent registration, and real-time transparency in the form of revealing the identities of bidders, can also have significant pro- collusive effects (Marshall and Marx (2009)). Transparency in bidding is a common objective of federal auctions and procurements, which demands certain level of information revelation. Unfortunately, the information revealed during the auctions facilitated retalia- tory bidding, signaling, market division, and gaming of the auction’s activity rules, which were detrimental both to revenue and allocative efficiency (Lopomo et. al. (2011)). Recent FCC auctions have moved to an anonymous format that masks bidder identities and thereby reduces bidders opportunities and incentives for anti-competitive behavior . Novel features of carbon allowance auctions, such as a “price collar” to bound the price of permits, could also create an environment quite sensitive to collusion.

High Transaction Cost and Friction of Entry

It has happened before that bidders refuse to participate auctions due to the requirement of pre-qualification with an escrow account, or some other specific inconvenient requirements. It is common that bidders may be reluctant to participate due to liquidity restriction, such as putting down financial securities way ahead of time, or unable to withdraw funds much later than auction. Bidding itself could be a source of high transaction cost. It may be more costly to

20The FCC has held auctions for spectrum licenses since 1994 using primarily a clock auction. CHAPTER 2. EMISSION PERMIT AUCTIONS UNDER CAP-AND-TRADE 62

submit bids or change bids if the auction platform is not electronic or if using the electron auction platform requires a lot of training in advance. The time needed to strategizing in face of complex auction rules also deters potential bidders. The appropriate auction design should minimize transaction costs associated with participating the auction (e.g., time spent submitting bids). The auction should impose minimal burdens on bidders, but also deter exploitative behaviors, such as costly ex-post defaults by liquidity-constrained bidders, that disrupt the auction process.

Scope of the Study

Unfortunately, due to the complex characteristics of multi-unit auctions (even for those basic formats that commonly used in practice) and the non-existence of pure dominant bidding strategy in general, auction theory could not give us definitive conclusions when comparing different auction designs in terms of one or more properties of efficiency, revenue extraction, price discovery, and collusion prevention. Given the lack of guidance from multi-unit auction theory, we need to evaluating the performance and relative effectiveness of different auction mechanisms for emission permit auction empirically. Also, since it is difficult to directly compare any pair of these formats, it is often useful to indirectly compare each of them with the Vickrey auction. Since the payment rule of Vickrey auction results in truthful bidding, it provides an ideal benchmark to evaluate the performance of other auction formats and to understand any deviation from the potential most efficient scenario. Considering the data availability, it provides more convincing conclusions to look at cap-and-trade programs with periodic auctions rather than just occasional or even just one time auction. Also, a structural methodology requires the observed auction data to have bidder level bidding details or at least aggregate level data with thorough summary statistics revealing distributional information across bidders. Therefore, my empirical analyses of this dissertation will only study emission permit auctions from two programs: the discriminatory SO2 auctions under the Acid Rain Program by U.S. EPA and the uniform price

CO2 auctions under the Regional Greenhouse Gas Initiative in the northeastern U.S.

For the SO2 market, I have collected annual auction results during 1993-2009 from CHAPTER 2. EMISSION PERMIT AUCTIONS UNDER CAP-AND-TRADE 63

EPA’s clean air markets website21, which contain the detailed bidding data, bidder information, auction size and clearing prices for 17 spot auctions of current-year vintage, 18 advance auctions of 7-year-in-advance vintage, and 4 advance auctions of 6-year-in-advance vintage (1994-1997). The secondary market trading data for SO2 have two parts: the over- 22 the-counter physical allowances trade price series are from two brokerages, CantorCO2e and Evolution Markets23; the SFI future price series are from Chicago Climate Futures 24 Exchange (CCFE)’s Historical Data Services . I will only use the data of 19 SO2 spot auctions, with which I will discuss the allocative efﬁciency and revenue extraction effectiveness of discriminatory emission permit auctions in Chapter 3.

For the CO2 market, I have collected the summarized auction results during September 2008 to June 2010 from RGGI’s ofﬁcial website25, which contain clearing prices, descriptive statistics on bids and bidders, and quantity information without bidding details for 8 quarterly spot auctions of current-year vintage and 6 quarterly future auctions of 3-year- in-advance vintage. The secondary market trading data for CO2 also have two parts: the over-the-counter physical allowances trade price series are from RGGI’s CO2 Allowance Tracking System (COATS)26; the RGGI future price series are from Chicago Climate Fu- tures Exchange (CCFE)’s Historical Data Services. I will use both the data of 8 RGGI

CO2 spot auctions and the CCFE daily RGGI futures price, with which I will investigate the failure in price discovery (underpricing) of uniform price emission permit auctions in Chapter 4. In Chapter 5, I will also discuss policy suggestions for emission permit auction designs regarding collusion and bidding/entry costs.

21http://www.epa.gov/airmarkets/trading/auction.html. The webpage providing all data for EPA’s annual SO2 allowances auction results. 22 http://www.cantorCO2e.com/ 23http://new.evomarkets.com/ 24http://www.ccfe.com/ccfeContent.jsf?id=4571401. The webpage providing time series of settlement prices for all future contracts traded on CCFE. 25 http://www.rggi.org/CO2-auctions/results and http://www.rggi.org/CO2-auctions/market monitor. The market monitor reports on auction and secondary market are prepared by Potomac Economics, RGGI, Inc.’s independent market monitor. 26http://rggi.org/tracking/data/allowance transactions. The price data rely on the self report of the transaction parties, so there are many missing prices and unreported transactions if the physical deliveries have not occurred yet. Chapter 3

Efﬁciency Loss and Revenue Extraction of Discriminatory Auctions

3.0 Introduction

The most frequently used criteria to evaluate auction performance are efficiency and revenue. If the auctioned goods have a private value component to bidders, mechanism designers are often concerned whether the auction format allocates goods to the buyers with the highest valuations, namely, whether the auction outcome is allocatively efficient. In a multi-unit auction, rational bidders submit their bids strategically in response to the auction rules in order to maximize their surplus. Therefore, they normally don’t bid truthfully at their marginal valuations but shade their bids, and a bidder with a higher marginal value for an additional unit of goods may lose that unit to a bidder with a lower marginal value. As discussed in section 1.2, the “Coase Theorem” points out that such allocative inefficiency will be resolved if bidders can trade among each other after the auction; that is, the higher value bidder is willing to buy his losing unit from the winning lower value bidder outside the auction. In this way, the final distribution of auctioned goods is still efficient, although some portion of the surplus is retained and transferred among bidders rather than being extracted by the auctioneer. For cap-and-trade systems, the trading market is an inherent component. Emission permits are designed to be tradable. To an extent, the efficiency of the initial allocation is

64 CHAPTER 3. EFFICIENCY LOSS AND REVENUE EXTRACTION 65

not the biggest concern for policy makers, because we expect the secondary trading market of emission permits to eventually correct any allocative inefﬁciency. However, we also discussed in section 1.2 that such Independence Property of the “Coase Theorem” often fails if there are transaction costs or friction associated with trading. In other words, if the secondary trading market of emission permits is not liquid, it is not able to effectively real- locate allowances among bidders to correct for the inefﬁciency resulting from the auctions. The Acid Rain Program (ARP) has been a successful example of existing cap-and-trade programs. It not only reaches the SO2 and NOx emission reduction targets with cost sav- ings of about 33% ∼ 67% compared to a “command-and-control” system (Ellerman et al. (2000)), but also establishes a mature secondary trading market and an exemplary auction market. Joskow, Schmalensee and Bailey (1998) observe the growth of the market of the

ARP SO2 allowances and conclude that the program had developed a reasonably efficient and liquid trading market by mid-1994. However, after the ARP had run for a decade, the EPA started to put more focus on the issue of nonattainment1 in downwind states, and consequently issued the Clean Air Interstate Rule (CAIR) with regional caps and a reduced aggregate cap which superseded the ARP requirements. Since 2010, the Acid Rain SO2 market has essentially become the CAIR SO2 market, while the trading volume and frequency of SO2 allowances have dropped significantly by May 2010. Looking forward, the EPA has announced the final Cross-State Air Pollution Rule (CSAPR) to split all the states into four separate trading groups with spacific caps on the aggregate emissions from each state. Given the circumstance, the trading market of SO2 allowances may be much more segmented and thinner than before. If this is the case, the efficiency of the initial allocation then becomes a crucial issue. The EPA holds discriminatory auctions every year to distribute a portion of the ARP SO2 allowance budget. If the allocative efficiency of the SO2 allowance auctions was not a real concern before, it should be one in the near future. Unfortunately, a discriminatory auction almost always leads to inefficient equilibrium, no matter what kind of information structures bidders are facing, even in relatively competitive bidding environment. It is necessary to look back at the EPA’s SO2 allowance auctions in the past and test how much efficiency loss there was associated with the discriminatory

1In United States environmental law, a nonattainment area is an area considered to have air quality worse than the National Ambient Air Quality Standards as deﬁned in the Clean Air Act Amendments of 1970 (P.L. 91-604, Sec. 109). CHAPTER 3. EFFICIENCY LOSS AND REVENUE EXTRACTION 66

auction format, so that we can have a clear idea about the magnitude of inefﬁciency we may face moving forward with the CSAPR and whether a modiﬁcation to the current auction design is needed. On the other hand, the discriminatory format might have a redeeming advantage in terms of revenue. Since in a discriminatory auction, bidders pay for every unit they have won at the bid price they submitted for that unit, rather than the lower bid price for the last clearing unit, the auctioneer might expect to extract more revenue from the discriminatory format. Hausker (1992) examines the politics of auction design and how equity goals strongly shaped the design ultimately adopted by Congress. He explained that the reason for choosing the discriminatory price format for the SO2 auction was “House staff expected that a discriminatory auction would raise more revenue than a Vickrey auction.” However, auction theory does not predict which auction format will perform better in terms of raising revenue. The revenue ranking among various multi-unit auction formats may change from case to case and can only be answered with empirical tests.

In this chapter, I examine whether the EPA’s SO2 allowance auctions have indeed resulted in efﬁciency loss, and whether discriminatory auction format has at least compensated efﬁciency loss with higher auction revenue in selling SO2 emission permits to market participants. To carry out this investigation, I conduct a structural analysis on individual bidders’ bidding data from 17 EPA annual spot auctions from 1993 to 2009. Recent structural analyses have developed empirical methodologies that use bid data to estimate bidder valuations and conduct counterfactual experiments. Different from reduced-form studies which treat changes in auction format in a particular market as a “natural experiment”,2 the structural empirical research on multi-unit auctions can compare different auction formats counterfactually, even if only one auction format is used in practice. Building on the seminal work of Wilson (1979), several researchers have proposed econometric models to estimate bidders’ marginal valuations in an auction using observed bidding data (Hortacsu (2011)).3 This chapter follows the direction of structural

2Researchers measure the difference between the true value and bid price as the differential between the when-issued (or resale) price and the auction price. Controlling for observables, this approach tests if the differential is larger for one of the pricing rules using data before and after a change in format. it relies on the assumption that bidders’ true valuations are currently reﬂected in resale markets, and that one can control for any changes in information from the close of the auction until after market trading. 3Hortacsu (2011) gives a thorough review of structural research on sealed-bid multi-unit auctions. In CHAPTER 3. EFFICIENCY LOSS AND REVENUE EXTRACTION 67

literature to analyze actual bidding data from the EPA’s annual SO2 emission allowance auctions by applying the econometric models proposed by Hortacsu (2002b) and improved by Kastl (2011). The basic idea of this methodology is to assume equilibrium behavior, namely, buyers bid strategically complying with game theory. Based on the equilibrium characterization drawn from the game theory auction model of Wilson (1979), the empirical analyst can recover the auction primitives (distribution and shape of valuations) using observed bidding data from auctions, in order to estimate the structural parameters of the auction model and use them to simulate counterfactual auction outcomes. I assume the independent private value information structure and a non-parametric framework. After recovering the marginal valuation of each bidder in each SO2 auction using detailed bidding data released by the EPA, I find through my counterfactual results that the discriminatory SO2 auctions have created an average of 7.14% efficiency loss, and have extracted less revenue compared to an upper bound of a truthful-bidding uniform price auction. Therefore, the EPA’s discriminatory price auction of SO2 emission allowances in fact is cursed by inefficiency, while its revenue extraction is not overwhelmingly effective either. As a result, it is difficult to defend the discriminatory auction format in the context of cap-and-trade policy design when “there is broad consensus among economists specializing in auction design that a discriminatory auction is not best-suited for emission permits [due to] several disadvantages of this auction format...”(Lopomo et al. (2011)). This chapter is organized as follows: Section 3.1 reviews the past literature on the efficiency property of the discriminatory auction and its revenue extraction effectiveness compared to other auction formats. Section 3.2 introduces the structural econometric models of multi-unit auctions. Section 3.3 describes the market and data of the annual EPA SO2 auctions, explains the procedures of structural estimation, and reports the empirical results. Section 3.4 summarizes the results and major insights of this chapter. this line of work, studies are done within the information structure of either independent private value (IPV) or pure common value (CV). Hortacsu (2002b), Kastl (2011) and Kang and Puller (2008) use econometric models assuming IPV, while Fevrier, Preget, and Visser (2000) and Armantier and Sbai (2006) carry out the estimation with CV paradigm. CHAPTER 3. EFFICIENCY LOSS AND REVENUE EXTRACTION 68

3.1 Issues with Discriminatory Auctions of Emission Per- mits

3.1.1 Inefﬁciency of Discriminatory Auctions

The most severe weakness of discriminatory is its allocative inefficiency. Discrimina- tory auction almost always leads to inefficient equilibria, no matter what kind of information structures bidders are facing.4 Even in an idealized “perfect competition” setting in which all bidders lack market power, the discriminatory auction will not lead to an efficient, or even asymptotically efficient, distribution outcome (Jackson and Kremer (2007)). Krishna (2009) concluded in his textbook of auction theory by Proposition 13.7 that “Every equilibrium of the discriminatory auction is inefficient”. In a discriminatory auction, bidders will shade bids below their marginal valuation. The equilibrium bidding incentives for discriminatory auction format have been analyzed in a variety of theoretical papers including Ausubel and Cramton (2002), Engelbrecht- Wiggans and Kahn (1998a, 1998b), Swinkels (1999), Wang and Zander (2002), Back and Zander (1993) and Wilson (1979). Truthfully bidding the marginal valuation would yield no gain for bidders because the payoff is zero in the event of winning. Therefore, bidders have strong incentives to shade bids on all units and significantly mark down bids for their earlier units that have higher marginal values. The amount by which a bidder shades his bid relative to his marginal valuation, however, depends on where he believes the market clearing price, or equivalently, the residual supply function will lie. If competing bidders have private information about their marginal valuations, the residual supply functions for each bidder will be random. Hence, what is relevant for a strategic bidder trying to make an optimal decision under uncertainty is the distribution of residual supply functions that he is going to face. Intuitively, bid shading that varies across units demanded or bidders implies that the order of bid prices does not correspond to the order of valuations. As a result, some lower-price bid that fails to win any unit of goods will have a corresponding

4Uniform price auction may also lead to some inefficiency. When bidders have some market power, uniform pricing rule motives bidders to shade bids. However, the convergence to efficiency is rapid as the number of bidders grows, so it is likely that uniform price auction reaches allocatively efficient outcomes if the auction is relatively competitive. CHAPTER 3. EFFICIENCY LOSS AND REVENUE EXTRACTION 69

valuation higher than a winning bid. This inevitably leads to inefficiency. The theoretical argument against the inefficiency of discriminatory auction is a consensus, and many empirical studies have documented statistically significant inefficiency from the past practices of auctioning spectrum and financial securities. Still, some papers that structurally test the data from the discriminatory treasury bills auctions in several countries find that the inefficiency in those countries’ auctions are not very serious. Hortacsu (2002b) reported that, for the Turkish Treasury auctions of 13-week Treasury bills between October 1991 and October 1993, the ex post inefficiency of the discriminatory auction is 0.000089% of total surplus; Similarly, Kang and Puller (2008) analyze 30 Korean Treasury auctions of the 3-year bond conducted btween September 1999 and April 2002, which have used both discriminatory format in 10 auctions and uniform price auction format in 20 auctions. They are able to compare the efficiency properties of the two formats and concludes that discriminatory auction better allocates treasury bonds to the highest value financial institutions. These examples suggest that whether inefficiency is a problem for a specific discriminatory auction is again an empirical question. I aim to measure the magnitude of potential efficiency loss in the EPA SO2 auctions in the similar way as above empirical papers in section 3.3.3.2.

3.1.2 Revenue Ranking Ambiguity of Auction Formats

The revenue ranking debate dated back to Friedman (1960). Engelbrecht-Wiggans and Khan (1998a, 1998b) and Ausubel and Cramton (2002) show that Revenue Equivalence Theorem does not hold in multi-unit auction environment. In particular, different mechanisms are not allocatively equivalent in general. The comparison of discriminatory auction and uniform price auction formats in terms of revenue is an empirical question, even given independent private values. Either format can be better than the other under different circumstances. Despite the widespread use of both formats, the revenue property of each format in multi-unit settings is theoretically ambiguous. In multi-unit auctions, using either the uniform-price or discriminatory pricing rule, bidder have incentives to shade their bids below the valuation and the incentive may differ CHAPTER 3. EFFICIENCY LOSS AND REVENUE EXTRACTION 70

for each unit demanded. But the strategic considerations are quite different in the two auction formats. Suppose a bidder submits a demand schedule with a different price for each of x units of a good. I have explained in above section 3.1.1 that in a discriminatory auction, a rational bidder would not bid his full marginal valuation for any unit that he might win because he wants to retain some surplus, so he tends to significantly shade his bids for the earlier units that have much higher marginal values than their belief about the auction clearing price. The incentive to bid shading is different with the uniform pricing rule. In uniform price auctions, a bidder should shade his bid below his marginal valuation at quantities that might be pivotal and might therefore determine the market clearing price. That is, he would bid below valuation for the xth unit of goods if that bid has some probability of lowering the market-clearing price that is paid for all other x − 1 units. This result is very similar to a monopsony buyer who reduces demand in order to drive down the market price. Due to the difference in bid-shading pattern, it will be ambiguous to compare the revenues from a discriminatory auction with a uniform price auction. Similar as the revenue illustration in section 2.1, I display in figure (3.1) the bid curves and revenues from a discriminatory auction and a best case Vickrey auction (truthful bidding uniform price auction). In a discriminatory auction, bidder i pays his inframarginal bids, so his payment is the trapezoid area on the left side of figure (3.1a), i.e. the area under his “shaded” bid curve up to the quantity he wins. In this case, the auctioneer’s revenue is the trapezoid area on the right side of figure (3.1a), i.e. the area under the aggregate bid function up to the total supply quantity. In a uniform price auction, bidder i pays his marginal bids (pays the market clearing price for all the quantity he wins), so his payment is the rectangular area on the left side of figure (3.1b), i.e. the rectangle under the auction clearing price up to the quantity he wins. In this case, the auctioneer’s revenue is the rectangular area on the right side of figure (3.1b), i.e. the rectangle under the auction clearing price up to the total supply quantity. The incentive for bid-shading is not as strong in uniform price auction, because even if bidder i bid very close to the red line of his true marginal valuations, he only pays for the rectangle underneath. So the “best case” uniform price auction is truthful bidding, which CHAPTER 3. EFFICIENCY LOSS AND REVENUE EXTRACTION 71

Figure 3.1: Bidder’s Demand and Auction Revenues under Different Pricing Rules

(a) Discriminatory Auction

(b) Best Case Vickrey Auction

will be the maximal revenue that can be extracted in a uniform price auction. Since bidders do not shade their bids as much, the market clearing price in a uniform price or Vickrey auction will be higher than in a discriminatory auction. Hence, the auctioneer extracts higher revenues from marginal units. However, in the discriminatory price auction, the auctioneer extracts more revenue from inframarginal units. Therefore, the revenue trade- off between a discriminatory versus a uniform price or Vickrey mechanism depends on the amount of bid-shading each bidder decides to undertake in the discriminatory auction. The revenue ranking for multi-unit auction formats is not only ambiguous theoretically, the extensive empirical studies on treasury auctions also have mixed ﬁndings. Both CHAPTER 3. EFFICIENCY LOSS AND REVENUE EXTRACTION 72

reduced-form analyses and structural analyses in the past have provided examples of one format raising higher revenue than another and vice versa. Among the literature of reduced- form studies, Umlauf (1993) finds the uniform price auction yields higher revenue using data from Mexican 30-day Treasury Bill auctions. Simon (1994) finds that uniform-price auctions yield less revenue while the latter two do not find statistically significant differences. Along the line of structural empirics, Fevrier, Preget and Visser (2002) and Ar- mantier and Sbai (2006) assume symmetric common value paradigm in their econometric models. Armantier and Sbai (2006) parametrically estimate the constrained strategic equilibrium using data from 118 French government discriminatory bond auctions held between May 1998 and December 2000. Their counterfactual result reports that a shift from the discriminatory to the uniform price format would increase revenue for the government. Fevrier, Preget and Visser (2002) adopted a semi-parametric approach on data from 45 French government discriminatory bond auctions held during January 2005 and December 2005. They find that French government would had received 5% less under the uniform price format. Under independent private value setting, Hortacsu (2002b) studied 27 discriminatory treasury auctions held by the Turkish government. He finds that the discriminatory format generated a higher revenue than this hypothetical best case for the uniform price auction. Kang and Puller (2008) find in Korean treasury auctions that the discriminatory auction yields statistically higher revenue. But Kastl (2011) examines a dataset of 28 uniform price auctions selling 3-month treasury bills issued by Czech government and concludes uniform price auction performs well in terms of revenue maximization as the employed mechanism only failed to extract at most 0.03% worth of expected most efficient surplus. I use the similar approach as Hortacsu and Kastl to measure how much revenue could counterfactually be extracted from the best case Vickrey auction (truthful bidding uniform price auction) to compare with the actual discriminatory auction revenue from annual SO2 auctions in section 3.3.3.3. Burtraw et al. (2009) experiments under the circumstances of tacit or explicit collusion, but they could not draw a general conclusion in comparing revenues between discriminatory and uniform price auction. Similarly, Shobe et al. (2010)’s experiments specifically for emission permit auctions show that under a loose cap, aggressive bidding behavior in initial discriminatory auctions yields higher revenues than in the other auction formats, but CHAPTER 3. EFFICIENCY LOSS AND REVENUE EXTRACTION 73

after repeating the experiments discriminatory auction’s advantage in revenue disappeared.

3.2 Structural Econometric Models for Discriminatory Auc- tions

All empirical structural estimation papers in the IPVP setting are based on Wilson (1979)’s theoretical work. The starting point for estimation of share auctions within the IPVP is Hortacsu (2002b). Kastl (2011) extend Hortacsu’s non-parametric methodology.

3.2.1 Theoretical Foundation: Wilson’s Model

Wilson (1979) models bidding in sealed-bid multi-unit auctions as a static game in which bidders maximize expected proﬁts. Assume that bidders are risk-neutral, ex-ante symmetric and have independent private values for the auctioned objects. At the time when bids are submitted, the participants are assumed to know the total supply of goods for sale, the total number of bidders, and their own valuation. Bidders do not know their rivals’ valuations but have a common prior on the distribution of the valuation function. The assumption that bidders are ex-ante symmetric implies that each bidder has the same distribution of latent demand, but we will loosen this assumption later during the econometric estimation in order to address possible asymmetries. We will assume that bidders are symmetric within group and allow for two different groups of bidders with different distributions of the private signal. The details of the multi-group “resampling” procedures will be further explained in section 3.2.4. There are N bidders in the auction, who are bidding for Q amount of perfectly divisible goods. Each bidder i receives a private signal, si, which represents his private information regarding his utility from winning a given quantity. Bidder i’s marginal utility from winning q units of the goods is given by the marginal valuation function v(q,si,s−i). In the symmetric independent private value (S-IPV) setting, their marginal valuations are ex-ante symmetric: v(q,si,s−i) = v(q,si). The private signals si are distributed identically and independently across bidders, namely, s1,··· ,sN are drawn i.i.d. from a known distribution CHAPTER 3. EFFICIENCY LOSS AND REVENUE EXTRACTION 74

Fs(·). Bidders’ strategies are bid functions which map bidders’ private signals into demand curves. Speciﬁcally, each bidder i submits his bid as a function of the price and his private signal, qi = yi(p|si), which speciﬁes the quantity demanded by bidder i at each price p. These demand functions are strictly decreasing and differentiable. After the auctioneer has collected all submitted bids, the market clearing price pc is determined as the price level at which the aggregated demand of all bidders exhaust the total supply Q,

c Q = ∑yi(p ,si) i

c c R yi(p |si) Thus, bidder i receives quantity yi(p |si) obtaining surplus 0 v(q,si)dq. If the auction c c is uniform price format, he pays p yi(p |si); If the auction is discriminatory format, he c c R yi(p |si) −1 c c R yi(p |si) −1 c pays 0 yi (q|si)dq = p yi(p |si) + 0 yi (q|si) − p dq. We can denote the surplus of bidder i at any realization of the market clearing price p with one combined formula: Z yi(p|si) Z ∞ v(q,si)dq − pyi(p|si) − τ yi(p|si)dp 0 p where τ is an indicator that takes value of either 0 or 1. When τ = 0, the objective is bidder i’s expected surplus under uniform price format; when τ = 1, the objective is his expected surplus under discriminatory format. From bidder i’s perspective, he is faced with a residual supply curve composed of all competitors’ bid functions, which are deﬁned by the realization of their signals:

RSi(p) = Q − ∑ y j(p|s j) j6=i

At the market clearing price pc, bidder i’s bid function intersects with his residual supply curve c c c yi(p |si) = RSi(p ) = Q − ∑ y j(p |s j) j6=i CHAPTER 3. EFFICIENCY LOSS AND REVENUE EXTRACTION 75

Denote the probability distribution of the market clearing price conditional on submitting the demand function yi(p|si) as H(p,yi(p|si)).

h i h i c c H(p,yi(p|si)) = Pr yi(p|si) ≤ Q − ∑ yi(p|s j) = Pr p ≤ p yi(p |si)) j6=i

Observe that for every p and yi(p|si), H(·) is a probability distribution generated by the random variables {y j(p|s j)} and potentially Q and N. Bidder i’s expected proﬁt maximization problem is:

Assuming strictly decreasing (downward sloping), differentiable demand functions, the Euler-Lagrange necessary condition for the above optimization problem is:

For the uniform price auction (τ = 0), this reduces to

Hyi p,yi(p|si) v(yi(p|si),si) = p − yi(p|si) (3.1) Hp p,yi(p|si) and for the discriminatory price auction (τ = 1), this equals to

H p,yi(p|si) v(yi(p|si),si) = p + (3.2) Hp p,yi(p|si)

Note that “bid-shading factor” exists for auction of either pricing rule. For the discriminatory auction the shading factor is H(·) . The denominator can be interpreted as the Hp(·) “density” of the market clearing price when bidder i bids yi(p|si), or the probability of winning at least yi(p|si) units; the numerator can be interpreted as the probability of winning exactly yi(p|si) units. In the uniform price auction, bidders shade their bid by an amount Hyi (·) − yi(p|si) . The numerator is the shift in the probability distribution of the market Hp(·) clearing price due to a change in bidder i’s bid. It is always negative since increasing a bid CHAPTER 3. EFFICIENCY LOSS AND REVENUE EXTRACTION 76

increases the market clearing price and therefore decreases the probability that the market clearing price is lower than a given p. The optimality conditions for the two auction formats state that in equilibrium bidders will never bid a price that is higher than their valuation, v(yi(p|si),si) ≥ p.

3.2.2 Identiﬁcation Condition: Hortacsu’s Model

Hortacsu (2002b) pioneered the method of structural estimation of multi-unit auctions within the S-IPV paradigm. He directly followed the optimality condition from the Wilson model and applied the identiﬁcation methodology proposed in Guerre et. al. (2000) into the discriminatory auctions. The main idea of Hortacsu’s method lies in the assumption that the bid functions we observe in the auction data are indeed generated by a symmetric Bayesian-Nash equilibrium satisfying the optimality condition of discriminatory auction. Such condition allows us to nonparametrically identify the marginal valuations of the bidders using observed bids. In order to do this, we deﬁne

h i

Gi(p,q) = Pr q ≤ Q − ∑ y j(p|s j) si (3.3) j6=i which is the probability that, at price p, a demand of quantity q will be less than the (stochastic) residual supply faced by bidder i. Since we can observe the bid schedules for all bidders in my sample, the joint distribution of {y j(p|s j), j 6= i} can be estimated from the data, and function Gi(·) can subsequently be calculated for all (p,q) pairs using equation (3.3). Then, since

In this way, given q = yi(p|si), we have identiﬁed the marginal valuation function v(·,si) at each price p. It should be noted that this procedure actually did not assume anything about the symmetry of the bidders.5 Similarly, it also does not require the independence of bidder’s signal distribution, as optimality condition (3.2) would hold true if bidders’ signals are correlated. Wilson’s theoretical model is set up under the assumptions of continuity: perfectly divisible good, continuous strategy space, continuous marginal valuation functions, and continuous bid schedules. However, in real life practices, almost all multi-unit auction markets set auction rules requiring a minimum price increment (tick) and a minimum bid quantity (lot size). We also always observe bidders submitting ﬁnite number of bidpoints in their bids. This occurs both because bidders are in reality limited in the number of bidpoints they are allowed to submit and because they choose to submit even fewer bids than the allowed number. For example, in Kastl’s data set of Czech treasury bills auctions, the bidders are restricted to submit at most 10 bidpoints, yet the average number of submitted bidpoints is less than 3 and the maximum number of submitted bidpoints is 9. Similarly, the bidding data from EPA’s SO2 auctions showed that the maximum number of bidpoints submitted by a bidder averages at 15.72 even though there is no restriction on bidpoints submissions at all. The discrete number of price-quantity pairs make up “step-function” bids, rather than continuous, strictly decreasing bid functions discussed above. As illustrated in Figure (?), from bidder i’s bid schedule, his demand curve is constructed by drawing, at the height corresponding to each bid price, a horizontal line with length corresponding to the associated bid quantity. These lines are then joined end-to-end with a hollow point at the left end and a solid point at the right end, starting with the highest bid price and working down to the lowest. Similarly, the aggregate demand of all bidders can be drawn in the same manner

5The necessary condition for optimality derived from Wilson’s model, equation (3.2), implicitly deﬁnes a type-dependent bid function. The ex ante symmetry of the signal si implies that the functional form of the bid function is stable conditional on si. So in a symmetric Bayesian-Nash equilibrium, bidders’ strategies are symmetric, yi(p|·) = y j(p|·) = y(p|·). CHAPTER 3. EFFICIENCY LOSS AND REVENUE EXTRACTION 78

into a right-continuous step-function. The auction supply is then represented by a vertical line at quantity Q on the horizontal axis. The estimation equation (3.4) has to be modified to take into account of the discreteness in order to use observed auction data. Hortacsu maintains the divisibility of the quantities, but restrict the prices to lie on a discrete grid. His adjustment works as follows: Define a set of possible prices on the grid as a vector ~b with elements b1 > ··· > bK. Even if a bidder only submits a limited number of price-quantity pairs, the step function formed by those bidpoints implicitly defines bid quantities for all points on the price grid. Each bidder submits a series of quantities associated with each of these prices, so his cumulative demand quantities become the vector ~qi = {qi,1 ≤ ··· ≤ qi,K+1}. Here, we also assume bK+1 = qi,0 = 0. A Bayesian Nash equilibrium strategy in this setting would be a vector valued mapping of the form ~qi(si), where the quantity requested at each point of the price grid is a function of a bidder’s private information. c In this manner, the market clearing price will be determined as p = bk∗ , the price at which total demand just falls short of the total supply:

N ∗ k = max{k : ∑ qi,k ≤ Q} i=1

Correspondingly, the probability distribution function of the market clearing price conditional on bidder i submitting the bid vector ~qi is:

h i h i

Gi(bk,~qi) = Pr qi,k ≤ Q − ∑ q j,k = Pr bk∗ ≤ bk ~qi j6=i

Thus the discretized version of optimality equation (3.4) would be:

Gi(bk,~qi) v(qi,k,si) = bk + bk − bk+1 (3.5) Gi(bk,~qi) − Gi(bk+1,~qi)

This is a direct analogue from the continuous condition as a conjecture based on the intuition behind the equations. Hortacsu examined the derivation more carefully in the Ap- pendix 8.1 of his paper, and concluded that Equation (3.5) is a very close approximation of Equation (3.4), though not completely correct. To eventually obtain Equation (3.5), CHAPTER 3. EFFICIENCY LOSS AND REVENUE EXTRACTION 79

subtle modiﬁcations are needed to account for the cases in which the monotonicity constraint on the bid function is binding, which might have observable consequences on both the observed bids and the marginal valuation function that rationalizes these bids. Hortacsu (2002b) further developed an econometric procedure to estimate condition (3.5) for Turkish treasury bills auctions.

3.2.3 K-Step Bids: Kastl’s Model

Kastl (2008, 2011) extends Hortacsu’s procedure by explicitly taking into account that bidders submit a step demand function. His analysis focuses on strategic decisions of the bidders on where to locate each step. The decision implicitly depends on the location of other steps. To rationalize the fact that bidders use fewer steps that what they are allowed to and that the number of steps differs across auctions and bidders, Kastl assumes that for each bidpoint bidders face a cost of submission that might differ across bidders and/or time. Suppose there is an upper limit on the allowed number of bidpoints K. Here, K can be as large an integer as necessary if the auction rule does not impose any restriction on bidpoints. Bidder i chooses to submit Ki ∈ {0,··· ,K} bidpoints. Under the assumption that bidder i’s valuation is strictly increasing in si and weakly decreasing and continuous in q, Kastl develops a model that incorporates bidding costs and characterizes a set of conditions for the uniform price auction that any Bayesian Nash equilibrium has to satisfy for every step k in the Ki–step demand function. In the text below, for the simplicity of notation, I ignore the subscript to use K instead 6 of Ki and use qk instead of qi,k when the elaboration involves only bidder i. His bid vector is~b = {b1 ≥ ··· ≥ bK} with corresponding cumulative demand quantities {q1 ≤ ··· ≤ qK}.

Here, q0 = bK+1 = 0. Also, denote ~s = {s1,··· ,sN} and ~y(·|s) = {y1(·|s1),··· ,yN(·|sN)}.

The expected proﬁt of bidder i who is employing strategy yi(·|si) in a discriminatory auction

6 It is important to note that K, in its full notation Ki, representing the number of price-quantity pairs submitted by bidder i, differs by bidders in an auction. CHAPTER 3. EFFICIENCY LOSS AND REVENUE EXTRACTION 80

given that other bidders are using {y j(·|s j)} j6=i can be written as:

c K hZ qi EU (s ) = E v(q,s )dq − {qc > q }b (q − q ) i i Q,s−i|si i ∑ I i k k k k−1 0 k=1 K c c i − ∑ I{qk ≥ qi > qk−1}bk(qi − qk−1) k=1

c c where qi = qi (Q,~s,~y(·,s)) is the auction clearing quantity bidder i obtains conditional on the realization of (Q,~s) and the submitted strategy vectors~y(·|s). I{·} is an indicator function equal to 1 if the argument is true and 0 if otherwise. A Bayesian Nash equilibrium in this setting is thus a collection of functions such that almost every type si of bidder i is choosing his bid function so as to maximize his expected proﬁt:

yi(·|si) ∈ arg maxEUi(si) .

At auction clearing price pc, we can rewrite the expected proﬁt as:

K Z q h c k i EUi(si) = ∑ Pr(bk > p > bk+1 si) v(q,si)dq k=1 0 K c hZ qi i + Pr(b = pc s )E v(q,s )dq − b qc b = pc ∑ k i Q,s−i|si i k i k k=1 0

Note that maximization of this expected proﬁt with respect to quantity demanded at kth step, qk, results in expression involving realizations of the auction clearing price only in the interval [bk+1,bk]. Strategies in any equilibrium must be locally optimal, namely, no local deviation can be proﬁtable. Using a local perturbation argument, Kastl showed that the necessary condition for a K-step equilibrium for discriminatory auction is:7

c c c c Pr bk > p > bk+1 ∪ (p = bk ∧ q = qk) si v(qk,si)−bk = Pr bk+1 ≥ p si (bk −bk+1)

7In Kastl’s proof, he stated that this condition must be satisﬁed for every step k < K. But at the last K v(q,s ) = b q = qc step it has to satisfy i K where supQ,s−i i due to the pro rata rationing rule in case of a tie. However, in my dataset, there were very few cases of tying. In addition, EPA’s auction rule chooses tying bids at random to assign remaining quantity, not pro rata. CHAPTER 3. EFFICIENCY LOSS AND REVENUE EXTRACTION 81

Here, with some arbitrarily small non-degenerate supply uncertainty, which is commonly made assumption in practice8, there would be no positive measure of residual supplies that would vertically overlap with bidder i’s bid at point (qk,bk) and thus above equation would simplify to:

c c Pr bk > p > bk+1 si v(qk,si) − bk = Pr bk+1 ≥ p si (bk − bk+1)

Rearrange this equation, we obtain the formula to identify and estimate the marginal valuation: c Pr(bk+1 ≥ p si) v(q ,s ) = b + b − b (3.6) i,k i k c k k+1 Pr(bk > p > bk+1 si) c Recall that Gi(bk,~qi) = Pr(bk∗ ≤ bk|~qi(si)) = Pr(bk ≥ p |si), so equation (3.5) has almost the same expression as equation (3.6). Besides the theoretical distinction in how vector~b is deﬁned,9 these two optimality conditions have a more important difference appearing in the denominator of the “bid shading factor”. In Hortacsu’s formula, the denominator is c c Gi(bk,~qi)−Gi(bk+1,~qi) = Pr(bk ≥ p > bk+1 si). Since with step function Pr(p = bk|si), the probability that auction clears at bk, can be strictly positive, Hortacsu’s formula would therefore cause a downward bias in the estimated shading factor and thus might bias in favor of the discriminatory auction when calculating auction revenue. Kastl (2008) also obtained a K-step optimality condition for uniform price auction, and Kastl (2011) developed an econometric procedure to estimate the condition for Czech treasury bills auction. His econometric procedure can be easily adjusted to apply to discriminatory auction data and to estimate condition (3.6). Despite the difference in their c treatments of Pr(p = bk|si), due to the extreme similarity of the formula construction, the econometric procedures to estimate marginal valuation functions for discriminatory auction based on Kastl (2008) and Hortacsu (2002b) are exactly the same.

8For example, in treasury bills auctions, supply uncertainty is due to non-competitive bids that promise to buy certain quantity at whatever clearing price turns out to be; in electricity auctions, it comes from the uncertain residual demand. 9In Hortacsu’s model, the indexes k and k+1 refer to adjacent prices on the discretized price grid; whereas in Kastl’s model, they refer to bids at subsequent steps of the submitted bid curve. Also, in Hortacsu’s setup, the prices are ﬁxed to lie on a K dimensional grid (potentially a very ﬁne one) which are likely a higher number than observed bidpoints; whereas in Kastl’s setup, the prices are determined by another set of necessary conditions. CHAPTER 3. EFFICIENCY LOSS AND REVENUE EXTRACTION 82

3.2.4 Resampling Procedure

Assume we have T auctions in our data sample where bidders have private values and can be split into G groups. In Section 3.3, my empirical analysis uses G = 3, namely, I allow for asymmetry among bidders and divide them into three different groups (see Section

3.3.1.2). Fix a single bidder i and a single auction t, to empirically recover vit(x) from optimality condition, we can use “bootstrap” resampling method to estimate Pr(bk+1 ≥ c c p q~it) and Pr(bk > p > bk+1 q~it). The procedure goes as follows:

1. Fix bidder i from group g ∈ G among Ntg bidders belonging to group g (total Nt

bidders) in auction t, and specify bidder i’s “step-function” demand vector q~it(p);

2. From the sample of Ntg bid vectors in the data set, draw with replacement a random

sample of Ntg − 1 bid vectors; from each of the groups other than g (denoted as h),

draw with replacement a random sample of Nth bid vectors; giving equal probability of 1 (or 1 respectively) to each bid vector in the original sample; Ntg Nth

3. Construct the residual supply function by subtracting the sum of these Nt − 1 (i.e., G Ntg − 1 + ∑h6=g Nth) “resampled” bid vectors from the total supply Qt;

4. Intersect with bidder i’s bid to ﬁnd the market clearing price for this resample condi-

tional on q~it;

5. Repeat steps 1-4 (a large number) B times for each bidder and for all bidders in the data set. This generates B auction clearing prices for each bidder i;

6. Count the frequency with which above B clearing prices (a) remain below a given c bk and (b) fall between two consecutive bk and bk+1 to estimate Pr(bk+1 ≥ p q~it) c and Pr(bk > p > bk+1 q~it) respectively. Counting frequency is done using kernel c estimation on the B clearing prices to form simulated distributions of Pr(p q~it).

In summary, this resampling procedure generates B auction clearing prices for auction t conditional on bidder i’s step bids. One can obtain the empirical distribution of the auction c clearing price by kernel estimation on those B observations. Probabilities Pr(bk+1 ≥ p c q~it) and Pr(bk > p > bk+1 q~it) can then be computed with the cumulative density function generated from the kernel estimation. CHAPTER 3. EFFICIENCY LOSS AND REVENUE EXTRACTION 83

3.3 Empirical Analysis of SO2 Auctions

3.3.1 Auction Characteristics and Data

My data set consists of 17 SO2 allowance auctions conducted once a year from 1993 to 2009. I do not extend my sample to auctions held after 2009 because starting from 2010 the auction platform was changed from bidding in paper to online bidding. During the transition of auction platform, there might be signiﬁcant change in auction characteristics and institutional environment.

3.3.1.1 Auction Characteristics

The SO2 allowance auction was conducted by US EPA. It began in 1993 and has been held annually, usually on the last Monday of March. For the ﬁrst 13 years, the auctions were administrated by the Chicago Board of Trade (CBOT). CBOT was not compensated by EPA for its services nor allowed to charge fees. Beginning with the fourteenth auction in 2006, CBOT chose to stop administering the auctions for EPA. Consequently, EPA started to handle all aspects of the auctions since 2006. Auctions are divided into two segments: (1) a spot auction for allowances of current vintage year, and (2) an advance auction for allowances that are usable for compliance in 7 years from auction, although they can be traded earlier. The two segments are conducted separately, so they can be considered as two independent auctions. Since the advanced auctions attracted much fewer bidders, which would affect the robustness of the empirical results, I will consider only the spot auctions. As listed in Chapter 2, Table (2.2), the schedule of total quantity supplied for each auction was pre-announced and known by all participants. The ﬁrst 3 auctions held in 1993 - 1995 each supplied 50,000 allowances for sale; Auction 4 - 7 during 1995-1999 each supplied 150,000 allowances; and all auctions since year 2000 supplied 125,000 allowances. The auctions used the sealed-bid discriminatory auction format. Each bidder is asked to specify a schedule of prices and quantities demanded at each price. The minimum price tick is $0.01, and the minimum quantity increment is 1 allowance. Prices are quoted by each CHAPTER 3. EFFICIENCY LOSS AND REVENUE EXTRACTION 84

allowance. The bid quantities were not subject to maximum quantity constraints.10 Bidders can submit as many bidpoints as they wanted, namely, there is no limit to the maximal number of price-quantity pairs submitted by a bidder. EPA may not set a minimum price for allowances from the Auction Reserve. Allowances are sold on the basis of bid price, starting with the highest priced bid and continuing until all allowances have been sold or the number of bids is exhausted. Bids could be submitted by mail or by fax anytime after the Bid Form was posted on the CAMD website (or otherwise made available) in mid January until the bid deadline, which is 3 business days before the date of the auction. Complete Bid Forms must be received by EPA by the close of business (4:00 p.m. Eastern Daylight Time) on the deadline date. Each bid must also include a certiﬁed check, an EPA Letter of Credit Form, or a statement of intent to use to a wire transfer to cover the total cost of the bids.11 EPA will post the results on the Acid Rain Program Auctions Web site at 12:00 noon on the auction day, and winning bids were settled within 2 weeks after the auctions.12

The Acid Rain Program allows regulated facilities to offer their freely granted SO2 allowances for sale in the same auction with EPA’s reserved allowances. These entities that wish to sell their own allowances via auction are required to submit a supply schedule in the form of pairs of asking price and quantity. These privately offered allowances are then added to the reserved supply, which makes the auction seemingly a double auction. How- ever, allowances from the Auction Reserve have higher priority in the clearing process and are sold before allowances offered by private holders. After the entire reserved supply is sold out, then it starts to sell privately offered allowances in ascending order, starting with allowances with the lowest asking price in the aggregate supply schedule. If by the time the aggregate demand exhausts all the allowances from the Auction Reserve the price is already lower than the lowest asking price among private offers, none of the privately offered

10It is not usual that bid quantities have no maximum constraints. Most treasury bills auctions impose upper limit on the total demand from each bidder. This rule is normally applied in emission permit auctions too. For example, in the RGGI CO2 auctions, any one bidder is constrained to demand in total at most 25% of the auction supply. 11EPA will only accept an EPA Letter of Credit Form that is signed by a bank that is a member of the Federal Reserve and is a participant in the FEDWIRE funds transfer system. 12The days that it took to settle winning bids and transfer awarded allowances varied year by year, from 2 days to 13 days. CHAPTER 3. EFFICIENCY LOSS AND REVENUE EXTRACTION 85

allowance can be sold. In this situation, the auction is effectively single-sided, rather than a double auction. Cason (1993) theoretically elaborated the lack of seller’s incentive resulted from such design, which was in fact consistent with the reality. Only 10 out of 17 auctions had some amount of privately offered allowances. Also, the order of selling reserved allowances ﬁrst usually led to the failure in selling those offered ones. Only 7 auctions ended with any offered allowances being sold, and only in 3 auctions their quantities exceeded 1% of the scheduled supply (1.9%, 2.2%, and 2.7% respectively). Schmalensee (1998) inter- viewed some participating sellers and found out that many owners who offered allowances for sale in auctions tend to set much higher asking prices relative to their guesses of the possible auction clearing price. The main motivation for them to participate as sellers are not to actually sell those allowances, but to show company stakeholders that they made an effort to get the best price when trying to sell allowances. Since they couldn’t sell them in the auctions, it justiﬁed their normal routines of paying brokerages commissions to sell on the secondary market. So it is safe to consider EPA auctions as standard multi-unit auction. Still, the possibility of having privately offered auction added to pre-scheduled supply, no matter how slim, provides small non-degenerate supply uncertainty. In the context of my empirical analysis, it ensures that Kastl’s estimation equation (3.6) be valid for the institutional environment of EPA’s auctions.

3.3.1.2 The Bidders

SO2 allowance auction is open to the general public. Anyone can participate by opening an account in the Allowance Tracking System (ATS). Regulated sources, including utility companies, power plants and generating facilities, are automatically given facility accounts in the ATS. They participate the auctions as compliance entities. These entities varies by size and generating capacities, so some ﬁrms may have more market power than others on the market of SO2 allowances. For discriminatory auctions, a bidder’s incentive is not about depressing the auction clearing price because he pays for different unit of emission permits at different prices that he bids, his market share or market power would not affect his bidding strategy as much. Therefore, compliance bidders strategize similarly when faced with the discriminatory pricing rule in the SO2 allowance auction. And it is reasonable that we treat them as ex-ante symmetric bidders. It is worth noting here that even though CHAPTER 3. EFFICIENCY LOSS AND REVENUE EXTRACTION 86

some compliance firms have certain market power, they still have enough competitors in auctions and in secondary trading so that they can not unilaterally manipulate the market of SO2 allowances. Besides compliance entities, all other individuals and organizations, who have pre- registered by EPA, are assigned with a General Account. Those who wish to bid can submit a Bid Form including payment. These non-compliance bidders are generally from two categories: some of them are environmental bidders, and the rest are brokerages and financial institutes. The environmental bidders consist of college classes, schools, law school environmental organizations, and bigger environmental groups (such as Clean Air Conservancy Trust, Acid Rain Retirement Fund, Adirondack Council, and Environmental Resources Trust). They are bidding to retire some allowances, rather than gaining profit. They have all the incentive to truthfully bid at their willingness-to-pay in order to ensure they can win the desired amount. They usually only submit one bidpoint for a small number of allowances (less than 10 normally). If an environmental bidder submit more than one bidpoint, it is usually an environmental organization that are trusted by several different parties to bid on their behalf, and each bidpoint could be from one of those trustees’ specified at their willingness-to-pay. (Israel (2007)) Therefore, I assume that environmental bidders do not shade their bids even faced with discriminatory pricing rule. This assumption is not crucial to the results of my empirical analysis because environmental bidders are negligible in their effects on the auction outcome. They together demand very small amount of allowances, which can be seen in Table (A.7) of Appendix A.3. In each auction, the total demand from all environmental bidders is less than 0.2% of supply.13 For brokerage firms and financial institutes, it is harder to distinguish compliance bidders’ bidding motivation from theirs. Most of the times, they submit bids on behalf of a client that is a compliance entity; but they may still participate bidding as their own investment from time to time. Nonetheless, I consider these firms as a separate group from

13The ﬁrst auction in 1993 was an exception. The total demand from environmental bidders in 1993 is 17.1% of supply. But with the total demand from all bidders being 6.43 times of supply, environmental bidders take up only 2.6% of total demand. In addition, several environmental bids with large quantities over 100 allowances were submitted at the lowest prices, under $3, while the clearing price was $131. Even though envrironmental bidders together demand 8576 allowances, the actually number won by them was only 11 units. CHAPTER 3. EFFICIENCY LOSS AND REVENUE EXTRACTION 87

compliance bidders, assuming they are similar with one anther inside the group. In my dataset, bidders can be identified by name. Therefore, for each auction I divide all bidders into three groups. Group 1 is the environmental type bidders; Group 2 is the compliance type bidders; and Group 3 is the financial type bidders. As discussed above, no bidder from any of these 3 groups are expected to have dominant market power over all other bidders, and they don’t seem to be able to unilaterally manipulate the auction outcome. As a result, it is reasonable to assume that within each group, bidders are ex- ante symmetric. And I allow for inter-group asymmetry so that bidders can have different characteristics across groups. Also, it is reasonable to use the model in Section 3.2 and rely on the optimality condition which implying intra-group symmetric bidding strategies. In the following, I refer to the compliance bidders and financial bidders together as business bidders who bid strategically, in contrast with the environmental bidders who bid truthfully. I report the results of dividing bidders into three groups (environmental bidders, compliance bidders and financial bidders) assuming intra-group ex-ante symmetry and inter-group asymmetry. For robustness check, I also repeat my analysis with two groups (environmental bidders versus business bidders) by pooling compliance bidders and financial bidders together, and the results are basically the same as using three groups. It is interesting to see whether the business type participated auctions repeatedly over the years. I focus on business bidders’ participation for two reasons. First, only business bidders respond to auction format by bidding strategically. Second, business bidders demanded and obtained over 99% of all allowances. To any extent, the participation of environmental bidder, which may or may not have any pattern over the years, doesn’t make any difference to the auction outcomes. Therefore, I only discuss statistics regarding business bidders. Participation varied widely among the total of 149 unique business bidders observed in the sample. Based on the number of auctions participated for each of these 149 bidders listed by Table (A.2) in Appendix A, I calculate the distribution of bidders’ participation frequency in Table (3.1). The average number of auctions that business bidders ever participated is only 1.9 (standard deviation is 1.59). Specifically, 84 entities participated only one auction. 38 entities entered twice. 12 entities participated 3 times. Only 15 bidders, about 10% of all business bidders, subitted bids in more than 3 auctions. CHAPTER 3. EFFICIENCY LOSS AND REVENUE EXTRACTION 88

Table 3.1: Numbers of SO2 Auctions Participated by Unique Business Bidders

Times of Participation Number of Bidders 1 84 2 38 3 12 4 5 5 3 6 3 7 2 8 1 12 1 Grand Total 149 Bidders

3.3.1.3 Information Structure

Let us now brieﬂy discuss the assumption of private values which is necessary for the identiﬁcation of bidders marginal values outlined in the econometric model. (1) The size of EPA auctions are too small compared to the total cap and the trading volume on secondary market, so participants who are very alert about the market price or are very active on the secondary trading market usually don’t think it is worthwhile to compete in the auctions.

(2) The main motive for bidders to purchase SO2 emission allowances from the EPA auctions is to use them for compliance or to hold them for future use, rather than for resale. So common value is not a proper assumption even though there is a very liquid secondary trading market. (3) Also, it is important to note that there is an active futures market ac- companying the active resale market, hence any private information about the resale value should be already reﬂected in the prices on the futures market. Therefore, the variation in the bids should rather be ascribed to other private information than related to the resale value. programs are targeting the electric generating units (EGU) in fossil fuel ﬁred power plants. An electric generating unit is a combustion device (boiler or turbine) used to power one or more electric generators. A typical power plant houses several generating units, which may be of different vintages, scales, or types. CHAPTER 3. EFFICIENCY LOSS AND REVENUE EXTRACTION 89

For environmental type bidders, they don’t care about resale at all. They only care about the social benefit of reducing SO2 pollution and their own valuation of improved air quality. It is apparent that for environmental type bidders, the private value assumptions are appropriate. A justification for the private value model: although big and liquid secondary market, major purpose of buying at auctions are using for compliance. Track certain allowance transferring history. See how much speculators bid and win in each auction. If not many speculators participate, meaning resale value not much, then private value more suitable. The most important assumption is the underlying value structure. Typically, researchers assume either a private value setting (in which the bidder knows her own value but not the rivals’ values, denoted below as IPVP setting), a common value setting (in which the good has a unique common value but bidders have different signals of the common value, denoted below as CVP setting) or a more general affiliated value setting. The value structure could be modeled as common value if each bidder’s motivation for purchasing emission allowances is to trade them in secondary markets where there is one common future price but traders have different forecasts of that price. However, the value structure is better char- acterized as private values if winning bidders hold allowances to fulfill their compliance requirements. EPA maintains an Allowance Tracking System (ATS). As each allowance is assigned a serial number, and the information regarding ownership transfers is required to be report to EPA’s tracking system. It is publicly accessible to check whether the winners in the EPA auctions resell the allowances they have won. According to my calculation based on the tracking system, less than 7% of all allowances from the auctions were involved in ownership transfer transactions within 6 months after the auctions, among which only 3% allowances were transfered between economically distinct organizations. It means that the purpose of bidders entering the auctions were not for resale, but for obtaining allowances for covering their emission or for holding in the long run. This would imply that the case for a common resale value of the auctioned securities is not very strong. “buy-and-hold” behavior was very pronounced based on the tracking information. There exist three possible sources of private information in the emission allowances CHAPTER 3. EFFICIENCY LOSS AND REVENUE EXTRACTION 90

market. First, each bidder may have different compliance requirement based on their emission history or a different capacity of abating their emissions which is not known to their rivals. Second, financial intermediaries may serve to purchase securities for regulated firms or simply purchase themselves as investment, or each primary dealer may have a different level of commitment to place orders for customers. The terms of purchase arrangements can make winning units in the auction more valuable to some brokers than to others. Fi- nally, each bidder may have different forecasts of long-run cost of emission abatement which generate different values to holding allowances. Because of these sources of bidder- specific values, a private value model is more sensible for my analysis. All these facts together leads me to believe that the private values model might be appropriate for the

EPA’s SO2 allowance auctions.

3.3.1.4 Description of the Data

The data contain the price-quantity pairs for each bidder (identiﬁed by the entity’s name), the quantity of SO2 emission allowances provided, and the market clearing prices for the auctions. For each auction, I observe all individual bids, the pre-announced supply quantity and the market clearing price. I also observe the ﬁnal allocation. Table 3.2 displays various summary statistics for the auctions in the data set. Cover ratio is the ratio of the number of allowances to be sold in the auction to the total number of allowances demanded by bidders. To get an indication as to the amount of dispersion of valuation among bidders, I calculate the quantity-weighted variance of the price bids. Bidders submitted bids for as little as 6.7 × 10−4 percent and for as much as 100% of total quantity supplied. Even though there is no restriction on the number of bidpoints that bidders could submit (there is no limit to the number of price-quantity pairs submitted by a bidder), yet the average number of bidpoints submitted by a bidder in my sample is 3.46, with the highest of 5.05 for 2008 auction and the lowest 2.12 for 2002 auction. And the maximal number of bidpoints submitted from one bidder in an auction averages at 16, with the highest record of one bidder submitting 31 bids in the 1998 auction. Within the business type, the average number of price-quantity pairs submitted for this type is 4.52 for spot auctions. The environmental type bidders who enter the auctions to retire small numbers of allowances usually only submit one price-quantity pair. Both types CHAPTER 3. EFFICIENCY LOSS AND REVENUE EXTRACTION 91

Table 3.2: Summary Statistics for SO2 Spot Auctions

Mean Std Dev Max Min Number of Bidders 27.3 7.84 44 14 Total Number of Bids 91.5 27.18 159 53 Average Number of Bids 3.46 0.85 5.05 2.12 Bidpoints Max 15.72 6.28 31 8 Bid Prices ($) 220.4 216.8 845.19 33.44 Bid Quantitiesa (%) 0.05 0.015 1 6.7 × 10−6 Cover Ratiob 4.52 1.74 8.16 2.31 Auction Clearing Price ($) 236.36 222.65 860.07 36.2

aAs a share of total quantity offered for sale, across all steps bRatio of total demand to supply together, the average number of bids submitted in my sample is 3.02. There is no detectable trend in the number of bidpoints used.

3.3.2 Bootstrap Resampling Estimation

The characteristics of the EPA SO2 allowance auction suggest that the market being analyzed is not far from satisfying the theoretical assumptions needed to take the empirical methods in Section 3.2 to the data. I will use Kastl’s formula to calculate estimated marginal values.

3.3.2.1 An Example of the Resampling Procedure

I will demonstrate my analysis and resampling procedure by showing the results for the 16th auction held in 2008. In this auction, there are 19 bidders participating, among which 6 bidders are the environmental type. The remaining 13 business bidders are split into 9 compliance type bidders and 4 ﬁnancial type bidders. To compete for 125,000 allowances of 2008 vintage in the spot auction, each bidder submits his bid of demand schedule. From all the received bids, there are 96 bidpoints in total. Environmental bidders submit 6 bidpoints, and business bidders are accounted for the remaining 90 bidpoints. The average number of bidpoints in a submission is 5.05. The average number bidpoints is 1 for environmental bidders, and is 6.92 for business bidders. Company named “Constellation CHAPTER 3. EFFICIENCY LOSS AND REVENUE EXTRACTION 92

Energy Inc.” submits the most bidpoints, 15 price-quantity pairs, followed by “TransAlta Energy Marketing (U.S.)” who submits 14 bidpoints. Aggregate demand over all bid quantities is 599,370, meaning that the cover ratio of demand over supply is 4.79. All the 6 environmental bidders bid to buy fewer than 10 allowances, and their demand together is 32 allowances. However, demand from business bidders is much more disperse. The maximal bid quantity from a single bidpoint is 125,000 (100% of supply), and the minimal bid quantity is 500 (0.4% of supply). The average bid quantity is 5.33% of supply with a standard deviation of 14.35%. 6 environmental bidders and 11 business bidders win positive amount of allowances. Out of the 96 bidpoints, 52 of them (about 54.2%) are successful. The auction clearing price is $380.01. The highest bid price is $651.00, and the lowest bid price is $0.27. The median bid price is $380.06. The arithmatic average of all bid prices is $358.46 with a standard deviation of 96.13, while the quantity weighted average bid price is $190.58. EPA received $48.7 million from the auction, and the quantity weighted winning bid price is $389.91. I will focus on bidder #14, “TransAlta Energy Marketing (U.S.)”, who belongs to group 2, the compliance type. It submitted 14 bidpoints, totaling a demand of 8% of the scheduled supply. In Figure (3.2), his bid schedule is displayed in the blue downward staircases with red stars highlighting his bidpoints. As discussed in section 3.2.4, I use B = 5000 iterations to randomly draw 6 bid schedules from the 6 group-1 environmental bidders; draw 8 bid schedules from the remaining 8 group-2 compliance bidders excluding TransAlta; and draw 4 bid schedules from the 4 ﬁnancial bidders. In this way, I construct a bootstrap sample of N − 1 = 18 bid schedules from the 3 bidder groups, and add them up to form the residual supply faced by bidder #14. The ﬁgure shows 20 different realizations of the resampled residual supply curves in black upward staircases. In this manner, I obtain 5000 auction clearing prices, each of which is at where bidder #14’s demand curve intersects with one resampled supply curve. They generate an empirical distribution of clearing prices which can be smoothed with kernel estimation. I choose normal kernel for this step. The his- togram and probability density function of the auction clearing prices are shown in Figure (3.3). We see that all bidpoints lie within the support of resampled market clearing price distribution. CHAPTER 3. EFFICIENCY LOSS AND REVENUE EXTRACTION 93

Figure 3.2: Bid Curve and Residual Supply Curve of Bidder #14 in 2008 Auction

3.3.2.2 Standard Error

Our marginal valuation estimator is a non-linear function of the distribution of the market clearing price, which is estimated, so to compute the asymptotic variance of the marginal valuations, I employ the “jackknife-after-bootstrap” method as discussed in Efron (1992). I repeat the estimation procedure J = 1000 times, each time generating a new

B = 5000 bootstrap sample of bid functions in my application. Speciﬁcally, letv ˆB(qi,k) be the estimate for the marginal valuation of bidder i for his bidpoint k that demands qi,k units of SO2 allowances, calculated using B bootstrap simulations of the auction clearing price. I repeat the bootstrap estimation exercise for J times and obtain J estimates of

{vˆB( j)(qi,k), j = 1,··· ,J} at each qi,k. Then the “jackknife-after-bootstrap” estimator of the CHAPTER 3. EFFICIENCY LOSS AND REVENUE EXTRACTION 94

Figure 3.3: Clearing Price Distribution for Bidder #14 in 2008 Auction

variance of the estimated marginal valuation is deﬁned to be:

J J 1 1 2 VAR jack vˆB(qi,k) = ∑ vˆB( j)(qi,k) − ∑ vˆB( j)(qi,k) (3.7) J − 1 j=1 J j=1 wherev ˆB( j)(qi,k) is the bootstrap estimate of v(qi,k,si) calculated over a set of resamples of bid schedules that do not contain the bid vector ~qi.

3.3.2.3 Estimation of Marginal Valuations

With the distribution of the auction clearing price, we can recover the marginal valuations for the bidder by using the optimality condition equation (3.6). Figure (3.4) shows CHAPTER 3. EFFICIENCY LOSS AND REVENUE EXTRACTION 95

the point estimates of marginal valuation of bidder #14 at quantities for which he submitted a bid. The horizontal axis is the percent of total supply he requested, with the prices on the vertical axis. Once again, bid vector and marginal valuation vector are represented as staircases. The points marked with a “v” correspond to the point estimates of the marginal valuation for each bid quantity. I also plot the 5-95% conﬁdence band around my point estimates. We can see that the ﬁrst (leftmost) bid is much farther apart from its marginal valuation, which is consistent with the theoretical prediction in most auction literature that bidders tend to choose much more bid-shading for the earlier quantities than later quantities.

Figure 3.4: Estimation of Marginal Valuations for Bidder #14 CHAPTER 3. EFFICIENCY LOSS AND REVENUE EXTRACTION 96

3.3.3 Counterfactual Results

It is straightforward to see that in a discriminatory auction a bidder never submits a bid with bid prices above his marginal valuations for any q that has a chance of being accepted. All such bids are strictly dominated by bidding the marginal value for that q instead. How- ever, this is not always true for uniform price auction. Kastl (2011) provides an important critique on the conclusion that bidders always have negative “bid shading factor” to uniform pricing rule, which was drawn from the continuous optimality condition (3.1). He showed that in the discrete bid function setting where bidders only submit finite number of price-quantity bidpoints, it may be optimal for them to bid beyond their true marginal valuations in a uniform price auction. Kastl finds that bidding above one’s marginal valuation is quantitatively important in Czech auction context. Although this would not affect my estimation of marginal valuations from a discriminatory auction, it unfortunately imposes a challenge to exercise counterfactual comparison with the outcome in a hypothetical uniform price auction. Because if bidders indeed bid above their marginal values, the calculation based on truthful bidding at each step of the marginal valuation function may underestimate the counterfactual revenue from uniform price auction.14 Therefore, in my counterfactual analysis, I compare the actual bidding outcome of discriminatory auction to the results from a best case Vickrey auction, rather than directly compare to a uniform price auction. In a private values setting, it is well-known that the Vickrey auction achieves truthful revelation of marginal valuations.15 Since we have demonstrated in section 2.1 that a bidder’s payment in a Vickrey auction is the trapezoid area underneath his residual supply curve, the best case Vickrey auction in terms of extracting the highest revenue is when the auction environment is perfectly competitive and all bidders’ residual supply curves are flat. Apparently, the best case Vickrey auction can in fact be interpreted as a uniform price auction in which bidders truthfully bid their marginal valuation schedules without actually receiving any payments. Performing this counterfactual experiment correctly requires the knowledge of the full functional form of marginal valuation function v(q,s). Since I estimate only certain points

14The estimate of the efﬁciency loss of a discriminatory auction as done in Hortacsu (2002b) remains valid as it involves only the estimates of the actual marginal values. 15See Ausubel and Cramton (2002) and Krishna (2009) Chapter 13 for a discussion of the Vickrey auction. CHAPTER 3. EFFICIENCY LOSS AND REVENUE EXTRACTION 97

on the marginal valuation function, I have to account for the marginal valuations in between the points of my estimation. I deal with this issue by constructing its upper and lower envelope with step functions that have steps at the estimated marginal valuations. Note that we can either bound the marginal valuation to the right of the last step from below by zero or from above by the last estimated marginal value. But the latter is not legit because it assumes it is possible that bidders have positive marginal value for infinite amount of allowances, i.e., non-satiated demand, and will always end up one bidder winning all the supply in my analysis. Thus, I assume that the marginal value for quantities larger than the last bidpoint is zero. Similarly, we also have the tricky question how to bound the marginal valuation to the left of the first step. I assume that the estimated first marginal value is also equal to the highest possible marginal value. Kastl (2011) mentioned that “this assumption should not be too influential since for the important (large) bidders whose demands are essential for market clearing, the market usually clears at one of their ‘interior’ steps”, so using these bounds should be appropriate in most cases. For the purpose of robustness check, he also tried using the first step plus a mark-up as the maximum marginal valuation for quantities smaller than the first bidpoint. I followed his lead and did robustness check in the same manner, and obtained qualitatively similar results as before. According to the premise that the marginal valuation function passing through these point estimates is weakly decreasing in quantity, the upper (lower) envelope provides an upper (lower) bound as to what the marginal valuation function should be. For the point estimates in Figure (3.4), the upper and lower envelopes are illustrated in Figure (3.5). There are two caveats that should be noted before using the upper and lower envelopes for counterfactual analysis. First, multi-unit auctions could have multiple equilibria with complex structure. The lower envelope is valid only for symmetric equilibria. Luckily, given the composition of bidders in the EPA SO2 auctions, it is reasonable to expect intra- group symmetric equilibrium of bidding strategies. Second, in theory, even if all bidders are ex-ante symmetric, multi-unit auctions is still possible to end in asymmetric equilibria. But from the experience during the period of my dataset, there has not been obvious unilateral manipulation from one or two very big bidders, so a symmetric equilibrium is a close approximation for the reality, and the validity of the lower envelope should not be a concern. CHAPTER 3. EFFICIENCY LOSS AND REVENUE EXTRACTION 98

Figure 3.5: Upper/Lower Envelopes of Estimated Marginal Valuations for Bidder #14

3.3.3.1 Truthful Bidding Clearing Price

Using the upper and lower envelope constructed above, I obtain the auction clearing prices resulted from truthful bidding. Table (3.3.3.1) reports the results and compares them to the actual clearing prices in the EPA discriminatory auctions. The second column is the actual realized clearing price observed in my dataset, and the third and ﬁfth column are the clearing price under truthfully bidding the lower and upper envelope respectively. The fourth and sixth column are the percentage difference by which actual clearing price in discriminatory auction is lower than the clearing price from truthfully bidding the lower and upper envelope respectively. The table reveals that the actual auction clearing prices are lower than that would be obtained under truthful bidding. On average, the EPA auction’s CHAPTER 3. EFFICIENCY LOSS AND REVENUE EXTRACTION 99

clearing price is 2.01% lower than the one generated from lower envelope, and is 4.91% lower than the one gernerated from upper envelope. This result is not surprising as bidders do have very strong incentive to understate their marginal values in bid prices. They try to “guess” the clearing price before the auction, and submit bid prices closer to their antic- ipated clearing price level for each bid quantity. All bidders together drive the aggregate demand curve non-trivially lower.

Table 3.3: Counterfactual Clearing Prices in Truthful Bidding Auctions

Year Actual pc TruthBid-L % Difference TruthBid-U % Difference 2009 62.00 65.41 5.21% 71.89 13.76% (0.06) (0.20) 2008 380.01 384.19 1.09% 394.51 3.68% (0.06) (1.74) 2007 433.25 446.55 2.98% 463.15 6.46% (1.14) (0.91) 2006 860.07 885.07 2.82% 891.68 3.54% (2.69) (3.00) 2005 690.00 696.59 0.95% 706.89 2.39% (0.23) (1.13) 2004 260.00 268.72 3.25% 269.59 3.56% (0.79) (0.98) 2003 171.80 171.81 0.01% 171.81 0.01% (0.03) (0.01) 2002 160.50 161.15 0.40% 163.41 1.78% (0.10) (0.41) 2001 175.00 175.02 0.01% 175.07 0.04% (0.15) (0.10) 2000 126.21 129.74 2.72% 131.61 4.10% (0.51) (0.49) Continued on next page CHAPTER 3. EFFICIENCY LOSS AND REVENUE EXTRACTION 100

Year Actual pc TruthBid-L % Difference TruthBid-U % Difference 1999 200.55 208.93 4.01% 209.95 4.48% (1.91) (1.48) 1998 115.01 116.59 1.36% 119.69 3.91% (0.13) (0.08) 1997 106.75 111.41 4.18% 113.57 6.01% (0.76) (0.61) 1996 66.05 68.31 3.31% 69.11 4.43% (0.08) (0.36) 1995 130.00 131.57 1.19% 133.30 2.48% (0.27) (0.59) 1994 150.00 150.66 0.44% 160.65 6.63% (0.73) (2.19) 1993 131.00 131.00 0.00% 156.39 16.24% (0.01) (0.30) Note: Bootstrap standard error in parentheses.

3.3.3.2 Efﬁciency Loss

A more important counterfactual experiment than ﬁnding the best case auction clearing price is to test “the most damning disadvantage” (Lopomo et. al. (2011)) of discriminatory auction – allocative inefﬁciency. Since all strategic bidders shade bids in discriminatory auctions, and the bid shading factors vary with different quantities and different signals, it is most likely that when auction clears, some bidder with lower marginal value at certain quantity win the allowances over another bidder who actually has higher marginal value for that quantity. After recovering the marginal valuations at observed bidpoints, it is possible to examine whether there are winning bidpoints of lower marginal valuation than any losing CHAPTER 3. EFFICIENCY LOSS AND REVENUE EXTRACTION 101

bidpoints. For discriminatory auction, the answer is usually yes. Then I can further calculate exactly how much surplus is lost due to the misplacement of allowances to relatively lower value bidpoints. This can be easily done by compute the total surplus (the combined surplus of payments from bidders to auctioneer and bidders’ remaining utility after paying for allowances) for the actual realized auction outcome as well as the hypothetical Vickrey (efficient) outcome. The actual realized surplus is summing the product of bid quantity with point estimate of marginal valuation for each winning bidpoint. Then I sort the point estimates of marginal valuation for all bidpoints in descending order and locate the clearing bidpoint that exhausts supply. The Vickrey surplus is summing the product of bid quantity with point estimate of marginal valuation for all the bidpoints before that hypothetical clearing bidpoint. The magnitude of efficiency loss for the EPA discriminatory auctions is thus defined in terms of percentage difference: subtracting actual surplus from Vickrey surplus, then dividing by Vickrey surplus. Table (3.4) reports the results after calculating the allocative efficiency loss for all EPA auctions in my sample. Compared to truthful bidding at lower envelope of marginal valuations, the average efficiency loss is 1.37%; compared to truthful bidding at upper envelope of marginal valuations, the average efficiency loss is

7.14%. In conclusion, the efﬁciency loss in EPA’s SO2 auctions has been quite signiﬁcant.

3.3.3.3 Effectiveness of Revenue Extraction

Kastl (2011) shows that estimating bidders’ marginal valuations using a model assuming continuously differentiable bid functions may introduce some bias against uniform price auction in terms of revenue extraction. In his model of equilibrium bidding in step functions, a bidder may bid a price higher than his marginal valuation. The intuition is most easily understood for a price-taker where there is no bid shading factor; the bidder equates marginal value with the expectation of the market-clearing price, conditional on her bid. In a uniform-price auction with steps, there may be positive probability that the market clearing price is below the bid price, so bids in equilibrium may be above the marginal value. As a result, the ex post revenue generated by an auction with step functions could be higher than revenue from a multi-unit Vickrey auction in which bidders bid their true marginal valuation. CHAPTER 3. EFFICIENCY LOSS AND REVENUE EXTRACTION 102

Table 3.4: Efﬁciency Loss from EPA Discriminatory Auctions

Year TruthBid-L TruthBid-U Year TruthBid-L TruthBid-U (%) (%) (%) (%) 2009 1.60 18.53 2000 0.65 9.28 (0.07) (0.93) (0.15) (0.84) 2008 1.17 12.20 1999 1.63 5.48 (0.16) (0.33) (0.74) (0.82) 2007 1.21 3.10 1998 1.00 1.76 (0.29) (0.26) (0.02) (0.02) 2006 0.50 2.98 1997 2.19 4.54 (0.31) (0.34) (0.82) (1.08) 2005 0.93 3.50 1996 0.58 3.77 (0.14) (0.23) (0.17) (0.17) 2004 0.67 2.42 1995 0.65 5.22 (0.18) (0.18) (0.16) (0.37) 2003 1.10 1.92 1994 0.61 8.32 (0.13) (0.26) (0.17) (1.20) 2002 6.33 9.45 1993 0.04 25.52 (0.10) (0.16) (0.01) (0.65) 2001 2.42 3.41 (1.02) (1.40) Note: Bootstrap standard error in parentheses. CHAPTER 3. EFFICIENCY LOSS AND REVENUE EXTRACTION 103

Therefore, I here calculate counterfactual revenues of the best case Vickrey auction using the similar steps taken in section 3.3.3.1. After finding the auction clearing price that would have resulted if the bidders had revealed their marginal valuation truthfully, I can calculate the revenue in the best case Vickrey auction (i.e., truthful bidding uniform price auction) using the upper and lower envelope for each bidder’s marginal valuation functions. Similar as section 3.3.3.1, I aggregate the upper and lower envelope of the estimated marginal valuations across all bidders, and find the intersection of this aggregate schedule with the total supply. Figure (3.6) illustrates this exercise for 2008 SO2 allowance auction to compare its counterfactual revenue under a “non-strategic” uniform price auction. In this figure, I overlay the aggregated bid schedule and the aggregated upper envelope of the estimated marginal valuation functions. With supply normalized to 1, the counterfactual revenue is given by the rectangle formed by the intersection of the aggregate marginal valuation curve and total supply. Notice the actual realized revenue from discriminatory auction is the area underneath the line marked with “x”, which is larger than the rectangle on the left side but smaller on the right side. Visually, we are able to tell that the rectangle area is bigger. Specifically, in 2008 auction the actual auction revenue is 1.17% lower than the counterfactual revenue from the best case scenario. I calculate the percentage difference between actual revenue and truthful bidding revenue for both upper and lower envelope of the estimated marginal valuation and list the results in Table (3.5). The results show that 13 auctions out of the total 17 in my sample have actual realized revenue lower than the uniform price auction revenue from truthful bidding at the upper envelope of marginal valuations. In addition, 6 auctions even have actual realized revenue lower than the counterfactual revenues from both upper envelope and lower envelope. It should be emphasized that above counterfactual comparison is to compare observed discriminatory auction outcome against the best case scenario of uniform price auction. It is not a direct comparison between a realistic uniform price auction versus discriminatory auction. Since bidders will strategically shade their bids in a uniform price auction, auctioneer would not be able to extract as much revenue as I calculate for the “non-strategic” scenario, let alone that bidders’ real marginal valuation functions could be lower than the upper envelop at many unobserved bid quantities. In reality, a uniform price auction could CHAPTER 3. EFFICIENCY LOSS AND REVENUE EXTRACTION 104

Figure 3.6: Counterfactual Revenue Comparison for 2008

have generated far less revenue. As a result, it is unclear about the direct revenue ranking between the EPA’s discriminatory auction and an alternative of uniform price format. Nonetheless, the counterfactual results at least show that discriminatory auction can not warrant a much higher revenue at all time. Given the significant efficiency loss that we detected in section 3.3.3.2, the EPA’s discriminatory auctions did not overwhelmingly outperform alternative auction formats in terms of revenue. The bottom line is, when regulators are faced with the trade-off between efficiency and revenue in designing allowance auctions, discriminatory format should at least provides a prospect of dominating other formats with regard to revenue in order to compensate for the allocative inefficiency that almost always exists. CHAPTER 3. EFFICIENCY LOSS AND REVENUE EXTRACTION 105

Table 3.5: Difference in Revenue between Discriminatory and Truthful Bidding Uni- form Price Auctions

Year TruthBid-L TruthBid-U Year TruthBid-L TruthBid-U (%) (%) (%) (%) 2009 6.63 -2.99 2000 0.83 -0.60 (0.10) (0.27) (0.40) (0.37) 2008 1.49 -1.17 1999 -0.90 -1.39 (0.02) (0.43) (0.90) (0.70) 2007 -0.48 -4.05 1998 0.32 -2.29 (0.25) (0.19) (0.11) (0.06) 2006 -0.22 -0.96 1997 -0.94 -2.82 (0.30) (0.33) (0.67) (0.52) 2005 0.85 -0.62 1996 -0.24 -1.40 (0.03) (0.16) (0.12) (0.51) 2004 1.53 1.20 1995 0.30 -1.00 (0.30) (0.37) (0.20) (0.44) 2003 0.01 0.01 1994 5.47 -1.08 (0.01) (0.01) (0.51) (1.36) 2002 -2.66 -4.10 1993 19.55 0.14 (0.01) (0.24) (0.01) (0.19) 2001 0.02 0.01 (0.01) (0.01) Note: Bootstrap standard error in parentheses. R −R * Revenue differences are calculated as actual truth f ul × 100%. Rtruth f ul CHAPTER 3. EFFICIENCY LOSS AND REVENUE EXTRACTION 106

3.4 Summary

In this chapter, I apply the econometric models for sealed-bid discriminatory auction by

Hortacsu (2002b) and Kastl (2011) to detailed bidding data from 17 spot auctions of SO2 emission allowances under the Acid Rain Program. Since the revenue ranking among various auction formats is an empirical question, the choice of a certain auction format for designing an emission permit auction needs to be supported by empirical evidence. It is informative to policy makers to measure at best how much more social benefit could possibly be gained by switching auction format in terms of both allocative efficiency and revenue. Compared to a best case scenario of the uniform price auction outcome from truthful bidding, my empirical results show that the efficiency loss in the SO2 allowance auctions on average is about 7%, while the revenue ranking between the two is inconclusive. Com- pared to the findings of 0.000089% inefficiency in Turkish Treasury auctions by Hortacsu

(2002b), the efficiency loss in the EPA’s SO2 allowance auctions seems quite significant. Currently, the EPA only auctions 2.8% of the annual budget, so the auction market is com- paratively very small, and the majority of compliance entities can not rely solely on auctions as the source of obtaining allowances. In other words, the strategic and analytical sophistication of the bidders in the EPA SO2 allowance auctions tend to be low. Some bidders may not have spent enough resources in strategizing. As a result, many bidders don’t understate their valuations that much in their bids. If the size of the SO2 allowance auction expands to a scale where the amount of auctioned allowances is comparable to the amount of freely allocated allowances, I suspect that the efficiency loss and the revenue difference from the best-case outcome of the uniform price auction could be even bigger. Given the significant efficiency loss in the past SO2 allowance auctions, it is not reassuring to see that the discriminatory format may not necessarily raise more revenue to compensate its inefficiency than the best-case outcomes of alternative auction formats. One important point that we should pay attention to is that the revenue extraction effectiveness of the discriminatory auction relative to uniform price auction is greatly affected by the shape of bidders’ marginal valuation functions. If the downward slopping marginal valuation functions for auction participants are very steep, the discriminatory format usually CHAPTER 3. EFFICIENCY LOSS AND REVENUE EXTRACTION 107

raises much higher revenue than its alternatives. On the contrary, if the marginal valuation functions are relatively ﬂat, the discriminatory auction can hardly outperform a uniform price auction with respect to revenue. In a cap-and-trade program, auction bidders’ marginal valuations directly represent their marginal abatement cost of reducing emissions.

For SO2 emissions, there are quite a few options of different abatement technologies that compliance ﬁrms can choose from, such as using low-sulfur coal, or fuel switching to natural gas, or installing scrubbers, etc. The marginal abatement cost of SO2 reduction changes drastically by the abatement quantity. Consequently, the marginal valuation functions of bidders in the SO2 allowance auctions tend to be steep. Even so, the discriminatory auction can not guarantee to extract revenue beyond the level of truthful bidding uniform price auction at the upper envelope of estimated marginal valuations. In the context of CO2 emissions reduction, which has narrower choices of abatement technologies than SO2, the marginal valuation functions are generally much ﬂatter for auction bidders. Therefore, it is reasonable to believe that the discriminatory auction would do worse in raising revenue than a uniform price auction in its best-case scenario in auctioning CO2 emission permits. If it is more sensible to choose auction formats with uniform pricing rule (either uniform price auction or clock auction) for future emission permit auctions, especially the ones in

CO2 cap-and-trade programs. Chapter 4

Underpricing of Uniform Price Auctions

4.0 Introduction

As introduced in Chapter 1, a cap-and-trade program inherently establishes a secondary trading market of emission permits besides the primary auction market. In theory, the trading market provides a continuous summary of current opinions among market participants concerning the market valuation of permits and information about the marginal cost of abating emissions. If the secondary market is liquid, the spot trading price should be equal to the marginal abatement cost at equilibrium, which will be approximately the same for all firms. As a result, the spot trading price in a liquid secondary market reflects the intrinsic value of emission permits, which theoretically results in the most cost-effective distribution of emission permits across firms. One of the most important functions of emission permit auctions is to provide correct price signals for secondary trading. If an auction is well designed and the secondary market is mature, the auction price would closely mirror the spot trading price. Even if the secondary market is not mature and perhaps not well informed about the intrinsic value of the allowances, the auction is expected to contribute to the discovery and realization of the intrinsic value. The clearing price of a well designed auction is thus expected to be very close to the spot price in the secondary market. In order words, precise price discovery in an auction can help identify a market price close to the equilibrium marginal abatement cost, so it is important that emission permit auctions provide reasonably accurate price signals.

108 CHAPTER 4. UNDERPRICING OF UNIFORM PRICE AUCTIONS 109

For CO2 cap-and-trade programs, a particularly prevalent auction format to sell emission permits is the single-round, sealed-bid, uniform price auction, which is adopted in the Regional Greenhouse Gas Initiative (RGGI) program. Uniform pricing rule strongly appeals to policy makers because it is considered fair for all program participants to pay the same price, and hence is more politically acceptable than other alternatives. However, the uniform price auction is known to suffer from “underpricing” relative to the secondary market, i.e. the clearing price in the uniform price auction tends to be lower than the trading price in the secondary market. Such underpricing has been widely documented in many empirical studies on treasury bill auctions (Spindt and Stolz (1992), Keloharju et al. (2005) and Pacini (2006), Goldreich (2007)). Multi-unit auction theory suggests that as long as some common value component exists among bidders, uniform pricing rule gives bidders an incentive to strategically shade their bids and effectively reduce their demand at every price level. The intuition for bid shading and demand reduction in the uniform price auction is as follows: when a bidder desires multiple units of the goods being auctioned, there is a positive probability that his bid price on later units will be pivotal and thus determine the clearing price. Since the clearing price is what the bidder pays for all other units that he wins, he has an incentive to bid less than his true marginal value on later units in order to reduce the price he will pay on the earlier units. Although by shading his bid the bidder may not get as many units as he actually wants at the clearing price, he will save on the total cost by paying less for all the units that he does win in the auction. Therefore, the auctioned commodity will be underpriced relative to a liquid secondary market representing the equilibrium of all bidders’ truthful valuations. The underpricing of uniform price auction makes it inferior compared to the discriminatory price format with respect to their price discovery functionality (Ausubel and Cramton (1998), List and Lucking-Reiley (2000)). Although there is also bid shading in discriminatory auctions, the shading occurs more for the earlier units than later units, thus having less downward pressure on the clearing price. In other words, since lowering the bid on one unit does not affect the price paid on other units in discriminatory auctions, bidders’ motivation to depress the clearing price is not as strong as it is in uniform price auctions. In fact, the evidence from the SO2 allowance market indicates that the EPA’s discriminatory auction contributed importantly to price discovery and the auction price and spot-market CHAPTER 4. UNDERPRICING OF UNIFORM PRICE AUCTIONS 110

price tracked together closely (Ellerman et al. (2000)). The SO2 auction experience clearly demonstrates that an auction need not disrupt the spot market price signal.1 The quarterly Regional Greenhouse Gas Initiative (RGGI) auctions launched in 2008 have involved more than 95% of the annual CO2 allowance allocations. Regulated entities under the RGGI program take these auctions very seriously and bid strategically. Thus, the underpricing problem, as predicted by auction theory and frequently observed in treasury bill auctions, would likely happen in the uniform price auctions of the RGGI CO2 allowances. In section 4.2, I collect trading data from several segments of the secondary market of RGGI allowances during September 2009 to June 2010, and show first that the RGGI secondary market is quite liquid during that period. Among the trading prices from various secondary market segments, I select an appropriate proxy representing the secondary trading price to compare with the RGGI auction prices. It is no surprise that I observe significant and persistent underpricing in the RGGI uniform price auctions, as well as a strong interaction between auctions and the seconary market of RGGI CO2 allowances. Previous literature on the underpricing of uniform price auction has all used the pure common value framework. In order to better understand such underpricing of the RGGI allowance auctions, I use a theoretical framework more suitable for the characteristics of emission permit auctions, which has an affine information structure with both private value and common value components. In this way, I can capture the feature that emission permits have both private use value and common trading value for regulated firms. In section 4.3, I modify the uniform price auction model constructed by Vives (2010). This model is introduced to study emission permit auctions by Ollikka (2011), which is the closest work to this chapter. It characterizes the symmetric linear Bayesian demand function equilibrium (LBDFE) and points out the importance of the interaction between the auction and the concurrent secondary trading market. The analytical results of the model show that the underpricing in emission permit auctions exists not only because bidders exercise their monopsonistic power over the residual supply, hoping for a lower clearing price, but also

1 It is worth noting that even though the SO2 auction is for a small portion of all allowances, it is relatively large compared with allowance trading activity in the spot market because most allowances are allocated directly to compliance entities. So an auction needs not disrupt the spot market price signal even if the number of allowances sold at the auction is much greater than the quantities traded in the spot market on a daily or weekly basis. CHAPTER 4. UNDERPRICING OF UNIFORM PRICE AUCTIONS 111

because with a liquid secondary market high value bidders reduce demand much more on account of their inclination to fill their remaining demand with purchases from secondary trading. In particular, the underpricing is positively affected by the liquidity of the trading market, the volatility of the trading price, and the accuracy of bidders’ signals of the trading value; and it is negatively affected by the heterogeneity of regulated firms’ abatement technologies and the intensity of competition in the auction. As emission permit auctions will play an even bigger role in the near future given all existing and future CO2 cap-and-trade programs have planned to increase the percentage of auctioned allowances, it is very important to understand whether the presence of a liquid trading market will alleviate or exacerbate the underpricing of uniform price auctions. The underpricing directly reduces auction revenue, which undermines the possible “double dividend” and other social benefit from the usage of the auction revenue as discussed in Chapter 1 (section 1.2). Without a better understanding of how entities strategically behave in response to the trading market, simply designing auction as an isolated mechanism may result in distortions to the market of emission permits. This chapter addresses this issue by answering two main questions: Firstly, what bidding strategy do bidders use in the uniform price auction of emission permits when there is a competitive trading market? Secondly, how does resale opportunity impact the underpricing of uniform price auction and how should it be addressed in policy design? Based on the model in section 4.3, I conduct an empirical analysis on the first eight RGGI auctions in section 4.4 using structural method. To my knowledge, this is the first structural analysis on actual auction data from the RGGI program. I propose a statistical procedure to estimate bidders’ marginal valuations on average with only aggregate level auction data. More often than not, detailed bidder level data are not complete or simply not available.2 Without bidder level data, research in the past almost exclusively relied on a reduced-form method to analyze the summary statistics released by auctioneers. Instead I adopt a random sampling method to construct sample moments which are the counterparts of the announced auction statistics, so as to calibrate auction primitives and obtain counterfactual auction outcomes, and compare the magnitude of underpricing under different

2This could happen for many reasons, such as conﬁdentiality restriction imposed to prevent collusion, hoarding or other anti-competitive behaviors, because releasing individualized bidding details may reveal bidders’ private information to each other, even when explicit information sharing is prohibited. CHAPTER 4. UNDERPRICING OF UNIFORM PRICE AUCTIONS 112

conditions. My ﬁndings show that even though the presence of resale opportunity worsens “bid shading” in a uniform price emission permit auction, the concurrent trading market does not necessarily exacerbate the underpricing because the participation of non-compliance bidders enhances the competition in auctions. This chapter is organized as follows: Section 4.1 reviews the past literature on underpricing of uniform price auctions. Section 4.2 introduces the institutional background of the RGGI program, and describes how the CO2 allowance market has experienced a cyclical price movement. The description helps identify the existence of underpricing in the

RGGI uniform price auction of CO2 allowances. Section 4.3 builds a model of sealed-bid uniform price auction with the presence of resale opportunity on a liquid trading market, which comprises the theoretical foundation for the rest of the paper. Section 4.4 describes the approach of structural analysis using summary data of the eight RGGI auctions and reports the empirical results. Section 4.5 summarizes the results and major insights of this chapter.

4.1 Literature on the Underpricing of Uniform Price Auc- tions

Previous literature has identiﬁed underpricing as a major weakness of uniform price auction. Multi-unit auction theory points out that when bidders demand more than one unit of auctioned items but pay for all units at the same price, bidding his marginal valuation truthfully is not a dominant strategy for any later units except for the ﬁrst one (Krishna (2009), Chapter 7). Bidders tend to shade their bids by understating their marginal values for those units. Such “bid shading” presents in the form of “demand reduction”: When bidders submit downward sloping demand schedules, each bidder faces an upward-sloping residual supply curve over which he is a monopsonist. He therefore faces a quantity-price trade-off: if he reduces his demand at every price level, he can lower the auction clearing price, so that he pays less for every unit goods he wins even at the cost of winning fewer units than he actually desires at that price. Bidders tend to mutually give each other the CHAPTER 4. UNDERPRICING OF UNIFORM PRICE AUCTIONS 113

monopsonistic market power and exercise it by pivoting their bid curves downward from their marginal value curves, hence the auctioned objects will be underpriced relative to the secondary market. Ausubel and Cramton (2002) explained the incentive for “bid shading” in multi-unit auctions in very general setting. They concluded that, in uniform price auctions, bidders always strategically bid lower than their marginal value, no matter whether they have independent private values or interdependent values with common value component, also no matter whether their marginal value function is flat (constant) or downward sloping (decreasing). Many empirical studies have documented observed underpricing in treasury bill auctions that use sealed-bid uniform price formats by comparing auction prices with trading prices from either “when-issued” market3 or post-auction secondary market. Spindt and Stolz (1992) investigate the US Treasury bill market for each week of 1982 through 1988 and find that it is cheaper to buy a bill in the primary market than to buy the same bill in the secondary market. They explain this “underpricing” as a predictable consequence of auction-theoretic and microstructural differences in the primary and secondary market mechanisms. Pacini (2006) studies the Italian primary market of treasury bonds by considering the uniform-price auctions for CCTs and BTPs held during the three-year period of 1998-2000. His examination of the stop-out prices in Italian treasury bonds auctions showed a significant presence of underpricing with respect to current prices on the secondary market. Keloharju, Nyborg and Rydqvist (2005)’s work on Finnish Treasury bond auctions during 1991-2000 quantifies that the uniform price format used in Finland causes an average underpricing of 0.041. Goldreich (2007) examines the extent to which the auction mechanisms are responsible for underpricing in the U.S. Treasury auctions between June 1991 and December 2000. Based on common value framework, he empirically finds that the average price received by the Treasury from uniform price auctions is less than the price of the same securities in the concurrent secondary market. Although there were a few studies on discriminatory treasury bill auctions suggesting the presence of underpricing, Ellerman et al. (2000) review the SO2 allowance auctions under the EPA’s Acid Rain Program, which use discriminatory format, and show that the

3The when-issued market is a forward market for the Treasury securities that are being auctioned, with delivery to take place on the issue date. CHAPTER 4. UNDERPRICING OF UNIFORM PRICE AUCTIONS 114

auction prices closely track the prices in the secondary market from very early on. By August 1994, the prices reported by the three brokerage firms for allowances traded in the spot market were almost identical to the level established by the 1994 auction. In retrospect, it appears that the EPA’s annual auction contributed importantly to price discovery at a time when expectations about compliance costs were varied greatly across participants within the industry. In the market of SO2 allowances, the discriminatory auction price actually played a leading role in identifying the equilibrium value of emission allowances and set the context for an active secondary market so that the spot trading price moved to that value as the market matured. Nonetheless, uniform price auction may outperform discriminatory auctions in many other aspects, such as political acceptability and allocative efficiency. Holt et al. (2007) as well as Burtraw et al. (2010) conduct experiments to detect the underpricing of uniform price auction specifically for the setting of a cap-and-trade program. They test how different multi-unit auction formats perform with respect to price discovery in case of an unanticipated demand shift – an increase in permit values – due to production cost reductions for some bidders but not for others. Their results also show that there was again a downward bias in prices of the single-round, uniform-price auction relative to the Walrasian predictions, as experiment subjects tended to bid low on some units in an effort to reduce the clearing price, although auction prices tracked the demand shift. Almost all the past research on the underpricing in uniform price auctions was built on the assumption of pure common value (Wilson (1979), Back and Zander (1993), Wang and Zander (2002), Kremer and Nyborg (2004a), Kremer and Nyborg (2004b)). These papers assume that the auctioned objects have a constant intrinsic value v, which may be uncertain at the time of auction, but it will be realized on the secondary market and it is the same ex-post for all bidders. The pure common value models are not suitable for emission permit auctions because allowances have “use values” that vary across bidders. Compliance entities will use the allowances that they win in an auction to cover their emissions, so the use value of the allowances reflects the saving of abatement cost. Since the marginal abatement costs differ widely across entities that have different generating technology and equipments, the use value is an independent private value. Meanwhile, in emission permit auctions bidders do have common value component CHAPTER 4. UNDERPRICING OF UNIFORM PRICE AUCTIONS 115

from the existence of secondary trading market of allowances. In a cap-and-trade program, auction is only a part of the large system of emission markets. The compliance entities ac- tively trade emission permits on the secondary market, while many non-compliance entities participate auctions simply for the purpose of resale. A lot of evidence in the existing cap- and-trade programs suggests that the secondary market of emission permits always grow rapidly and become very liquid shortly after a program launches. Joskow, Schmalensee and Bailey (1998) concluded that the Acid Rain Program created under the Clear Air Act

Amendments of 1990 had developed a reasonably efficient private trading market of SO2 emission allowances by mid-1994, which was only a short year after the first SO2 auction and even half a year before the program officially started. Shobe (2010) mentioned that the trading volume in the secondary market for the RGGI CO2 allowances rose dramatically during mid-2009, which was an indicator of increased liquidity. He wrote, “... the volatility of RGGI allowance futures prices has fallen dramatically since the early months of trading and has had periods of considerable trading volume provides support for the proposition that the market has become relatively effective...” Hence an appropriate model should allow for both common value and private value.4 In this paper, I construct a uniform price auction model with an affine information structure similar as Vives (2010) to capture both the private use value and the common resale value of emission permits.

4.2 RGGI CO2 Allowance Markets around Auction Dates

As discussed in Chapter 1, the market structure of emission permits consists the primary market of auctions (from regulatory authority to program participants) and the secondary market of trading (among all the market participants). Unlike other cap-and-trade

4Independent private value (IPV) models suffer from the lack of sensibility to compare auction prices to secondary market prices, so many papers modeling multi-unit auctions using the IPV paradigm would have to argue that any price discrepancy between auctions and resales is because the resale markets for those objects are very thin or very small. For example, Hortacsu (2002b) argued that the liquidity in the resale market of Turkish treasury bills is not very large compared to the primary auction market, and on average only 4% of the total volume of auctioned treasury bills are traded on the secondary market, especially before 1993. As a result, he ignored the potential common value components coming from the resale price and modeled the Turkish treasury bill auctions in independent private value paradigm. CHAPTER 4. UNDERPRICING OF UNIFORM PRICE AUCTIONS 116

programs, the primary market of RGGI allowances is signiﬁcant with comparable size to its secondary trading market, because RGGI auction nearly the entire budgets of emission allowances. In fact, over 95% of the CO2 allowances in circulation initially entered the market through auctions. Supposedly, with almost all allowances being auctioned in initial allocation, if the auctions are efﬁcient, i.e. the facilities that value the allowances more than others win more allowances in auctions than others, they won’t have much desire to trade between each other outside of auctions, thus we don’t expect much volume on the secondary market and the trading activities would be very limited. In other words, the secondary trading market should be relatively illiquid. However, I will analyze the trading data from several segments of the secondary market of RGGI allowances in section 4.2.1 and show that RGGI’s secondary market grew into mature and liquid soon after trading started in August 2008. Theories and experimental results predict that there will be underpricing in uniform price auction. As RGGI uses uniform price auction to sell the majority portion of allowances, will we observe underpricing in the RGGI auctions? I will discuss in section 4.2.2 the RGGI allowance market movement around auction dates and show that significant and persistent underpricing is observed in RGGI auctions compared to secondary market.

4.2.1 Secondary Markets for Trading RGGI CO2 Allowances

In between the quarterly auctions, interested parties can buy and sell RGGI CO2 allowances on various segments of the secondary market. The secondary market for the RGGI allowances comprises the trading of physical allowances and ﬁnancial derivatives, such as futures and options contracts. A physical allowance trade occurs when the parties of the transaction register the transfer of ownership in COATS. Futures or other ﬁnan- cial derivatives of the RGGI CO2 allowances are called “exchange-traded” when they are traded on a public exchange, and are called “over-the-counter” (OTC) when they are not traded on one of the public exchanges. The information regarding trading price of RGGI

CO2 allowances comes from the following sources: (1) transaction prices associated with CHAPTER 4. UNDERPRICING OF UNIFORM PRICE AUCTIONS 117

allowance ownership transfers reported to RGGI COATS database; (2) prices reported publicly through futures trading at trading exchanges (CCFE or NYMEX); (3) prices reported in the over-the-counter (OTC) trading.

4.2.1.1 COATS Transfers

To facilitate the market-based regulation, RGGI has created the infrastructure, called

CO2 Allowance Tracking System (COATS), to track allowance market activity. COATS is an electronic platform operating as the registry for the RGGI CO2 allowances and for tracking recorded ownership of allowances. Each allowance has a unique serial number, so COATS can record the ownership transfer of each allowance, conduct quarterly auctions, and monitor compliances when regulated entities surrender allowances to cover their emissions. When parties record a change of ownership on the COATS database, they are required to record a price, if a price were speciﬁed in the transaction resulting the ownership transfer. As of 7/31/2010, out of the 570 non-auction allowance transfer transactions recorded on COATS, 214 have no price information and the remaining 356 have a positive price recorded (including 333 transactions for compliance period 1 allowances and 23 transactions for compliance period 2 allowances). As seen in Table 4.1, a total of 161,091,127 allowances had been transferred between accounts with 55,987,063 allowances of compliance period 1 (approximately 34.8%) having a recorded price (as well as another 558,000 allowances for compliance period 2). Most of the allowance transfers without a recorded price took place between two accounts of the same owner. Although the COATS record of transactions represents actual transfers of ownership, it unfortunately has some problems in correctly representing the market price. First, the transaction contracts resulting in the COATS transfers are usually not standardized. For example, parties may agree on delayed delivery, or may carry out a sequence of trades, or may bundle allowance exchange with other exchanges. It means that the price of the transactions may reﬂect particular aspects of the transactions causing in a price above or below the current market value of allowances. Secondly, the date of the reported transfer may not be the same as the date that the price of the transaction is established by the parties. Thirdly, since those private transactions don’t usually take place at public exchanges which ensure CHAPTER 4. UNDERPRICING OF UNIFORM PRICE AUCTIONS 118

Table 4.1: Monthly RGGI COATS Transactions with Price Recorded

Month Num. of Volume Weighted Minimum Maximum Transactions Avg. Price Price Price Sep-08 1 5,000 3.45 3.45 3.45 Oct-08 4 22,051 3.65 3.45 6.00 Nov-08 2 3,000 3.75 3.50 4.25 Dec-08 11 1,117,000 3.68 3.38 3.73 Jan-09 13 506,200 3.56 3.38 5.50 Feb-09 13 702,755 3.71 3.07 5.50 Mar-09 14 2,190,000 3.55 3.50 3.78 Apr-09 7 1,049,000 3.69 3.61 3.70 May-09 13 3,756,000 3.47 3.30 3.66 Jun-09 34 5,491,765 3.35 2.94 3.55 Jul-09 45 2,452,000 3.30 3.05 3.54 Aug-09 14 1,426,000 2.94 2.93 2.97 Sep-09 18 1,111,012 2.82 2.19 3.50 Oct-09 10 1,260,000 2.46 2.45 2.54 Nov-09 4 885,000 2.49 2.29 2.50 Dec-09 15 2,802,198 2.10 2.05 2.72 Jan-10 26 9,251,296 2.27 2.17 3.82 Feb-10 9 613,000 2.12 2.12 2.12 Mar-10 19 12,254,734 2.08 2.07 2.10 Apr-10 22 1,918,500 2.13 2.10 2.19 May-10 8 238,000 2.18 2.07 2.21 Jun-10 18 5,307,000 1.98 1.88 2.15 Jul-10 10 1,625,552 1.90 1.86 2.00 CHAPTER 4. UNDERPRICING OF UNIFORM PRICE AUCTIONS 119

delivery and clearance, the parties involved in such contracts are facing higher risk of default, which may well be reflected as risk premium in their prices. As a result, we can see in Figure 4.1 how dispersed the un-weighted prices in COATS records are in a short period of time, even in a single day. Such dispersion, in the presence of an active secondary market, is consistent with the concern that the reported prices reflect idiosyncratic circumstances, many of which would not likely be reflected in the bidding strategies in an auction.

Figure 4.1: Prices of COATS Transactions by Date

Also, COATS transactions have been intermittent. There are intermittent surges in activity accompanied by many periods in which little trading activity occurs. For example, there was no transaction recorded between April 3 and May 4 in 2009. The ﬁrst transfer of vintage 2012 allowances recorded on COATS with a price reported occurred on December 4, 2009 at a price of $1.86. The next vintage 2012 transaction recorded on COATS was on January 5, 2010 at a price of $3.40. The infrequency of COATS transfers greatly reduces the value of these transfer prices. In fact, since RGGI auctions almost all of the allowances CHAPTER 4. UNDERPRICING OF UNIFORM PRICE AUCTIONS 120

in the annual budget, for vintages being auctioned for the ﬁrst time, no COATS prices could exist before the auctions. Throughout the period covered in this study, the difference between the prices reported to the COATS system and the prices of futures trading have remained substantial. For example, the volume-weighted average percentage difference between COATS transaction prices and futures prices has varied widely over time. While in most months, the volume weighted average percentage difference between COATS transaction prices and futures prices is on the order of 2% to 5%, it has reached as high as 18% in September of 2009 and 10% in November of 2009.

4.2.1.2 Futures Trading

Trade of RGGI allowance futures takes place on regulated commodities exchanges, such as the Chicago Climate Futures Exchange (CCFE) and the Green Exchange initiated at the New York Mercantile Exchange (NYMEX). On the public exchanges, traders exchange standardized contracts for promises of future delivery of allowances. The value of these “derivative” contracts5 are standardized, the risk of default is minimized, 6 and the costs of transaction are low. Thus, prices of such derivatives depend less on unobservable transaction risks and costs but more on the value of the underlying asset. Futures contracts are traded on a daily basis, and trading is regulated and reported con- sistently,7 which is quite different from trading on unregulated over-the-counter markets, where prices have to be inferred from surveys of dealers and some prices are difﬁcult to

5 In the secondary market, CO2 emission allowances are traded as commodities. Thus CO2 futures contract is traded as a derivative whose underlying asset is CO2 emission allowances. 6The risk of default is very low for traders because all contracts are with the exchange rather than with other traders, and any trader who submits an open interest has to have enough fund in his account at the exchange to back up his position. 7A futures contract requires parties with an open interest to post financial assurance in an account with the exchange until the contract reaches expiration. The exchange continually withdraws and deposits funds according to changes in the prices of the contracts in which the party has interest. For example, if a firm buys a contract for 1,000 allowances at $3.50/allowance, the purchasing firm (firm with a long position) must put $3,500 in an account (or whatever share of the entire liability the exchange requires). If the futures price declines to $3/allowance, the exchange transfers $500 from the account of a firm with a long position to the account of a firm with a short position(firm that sold a contract), and the firm with a long position is only required to keep $3,000 in the account. At the end of the delivery month, allowances are exchanged for funds according to the closing price on the last day of the month. CHAPTER 4. UNDERPRICING OF UNIFORM PRICE AUCTIONS 121

interpret since trades may involves bundles or swaps. RGGI allowance purchases are settled by the electronic transfer of ownership between two COATS accounts and do not involve the complications of physical delivery. Conse- quently, a signiﬁcant number of purchases of RGGI allowances take place just after the expiration date of a futures contract. Even the transactions that do not result in actual changes of ownership provide traders with strong ﬁnancial incentives to correctly anticipate the future price of allowances. Because considerable economic value is at stake, exchanges are thought to provide an excellent platform for revealing information about the market value of goods.

RGGI CO2 allowance futures trading began on the CCFE in August of 2008 and on NYMEX in December of 2008. Most trading activity has been on the CCFE. Compared with CCFE, the trading size in NYMEX is negligible. Therefore, we focus primarily on CCFE’s information on futures trading. Table (4.2) shows the monthly trading volume in the CCFE futures market. The futures market grew very fast, and the volume was large compared to the total issuance of any vintage year. We can consider the futures market as a fairly liquid secondary market for CO2 allowances.

4.2.1.3 Options Trading

Standard options contracts for RGGI CO2 allowances are also traded on the Chicago Climate Futures Exchange (CCFE). Two categories of options are traded:

Call Options - Call options give the purchaser the option to buy a fixed number of CO2 allowances of a certain vintage year at a particular strike price at any time prior to the expiration date. For example, suppose a firm holds a call option with a 2009 vintage year, $5 strike price, and June 2009 expiration date. If the price of the corresponding futures contract rose to $5.75, the firm could exercise the option to buy CO2 allowances at $5 and immediately sell them at $5.75. Alternatively, if the price of the futures contract stayed below $5, the firm would let the option expire without exercising it. One standard options contract can be exercised for 1,000 RGGI CO2 allowances. Put Options - Put options are similar to call options but they give the purchaser the option to sell a certain number of CO2 allowances of a particular vintage year at a specified strike price any time prior to the expiration date. CHAPTER 4. UNDERPRICING OF UNIFORM PRICE AUCTIONS 122

Table 4.2: Monthly RGGI Futures Trading at CCFE

Month Volume Weighted Minimum Maximum (×103 ton) Avg. Price Price Price Aug-08 690 5.37 5.31 5.63 Sep-08 3,282 4.28 3.38 5.10 Oct-08 4,830 3.77 3.18 4.50 Nov-08 1,874 3.89 3.52 4.25 Dec-08 6,367 3.59 3.24 4.30 Jan-09 6,608 3.94 3.70 4.13 Feb-09 5,195 3.59 3.42 3.81 Mar-09 21,648 3.70 3.57 3.85 Apr-09 42,451 3.53 3.47 3.60 May-09 40,055 3.41 3.32 3.52 Jun-09 131,638 3.38 2.97 3.57 Jul-09 82,098 3.16 2.93 3.33 Aug-09 104,644 2.91 2.88 2.94 Sep-09 132,835 2.53 2.28 2.90 Oct-09 63,056 2.40 2.28 2.48 Nov-09 20,684 2.25 2.07 2.33 Dec-09 42,951 2.16 2.03 2.26 Jan-10 4,256 2.15 2.04 2.24 Feb-10 10,897 2.06 2.01 2.11 Mar-10 6,477 2.10 2.07 2.18 Apr-10 2,581 2.13 2.07 2.18 May-10 4,577 2.08 1.99 2.19 Jun-10 4,321 1.95 1.86 2.07 Total 744,015,000 ton allowances CHAPTER 4. UNDERPRICING OF UNIFORM PRICE AUCTIONS 123

Although it is possible to infer the underlying spot price of a option contract, the price in options trading is not directly comparable to the auction price.

4.2.1.4 Over-the-Counter Trading

Contracts for immediate delivery (spot contracts) or future delivery (forward contracts) of allowances are routinely traded outside of exchanges in what is referred to as over-the- counter (OTC) trading. Unlike exchange transactions, these trades, usually mediated by brokers, lack the standard terms and conditions of delivery and are thus subject to higher trading costs and unknown (at least to the outside observer) default risk.8 These factors can lead to signiﬁcant differences between the reported transaction price and the price reported in standardized exchanges. Further, the price of the trade is not required to be made public, although, as noted, the transfers of ownership recorded on the COATS system do require the recording of a price when one is available. As time passes, forward contracts for RGGI allowances will turn into delivered allowances and, hence, into recorded transactions in COATS. At any point in time, there will be an unknown amount of overlap between OTC transactions and COATS transactions. CantorCO2e is one of the biggest brokerage on the

RGGI CO2 allowance market. It publishes daily Market Price Index for its clients. Figure

(4.2) shows the Market Price Index (MPI) of the spot trading of RGGI CO2 allowances provided by CantorCO2e. We can see that OTC prices actually track CCFE futures market prices very closely, in spite of all sources of uncertainty related to OTC trading.

However, the OTC trading for RGGI CO2 allowances is not as frequent as in the futures market. Table (4.3) lists the monthly volume and related prices for CantorCO2e’s trading. Notably, there was no transaction before March 2009 and after October 2009. We can see in Table (4.3) that the OTC trading volume in the highest month is less than 10% of the size of one auction, and the total trading volume in 2009 is 13,949,000, only 8.5% of the total 163,473,313 auctioned 2009 vintage allowances in the ﬁrst 6 RGGI spot auctions. Even though these transactions are only from CantorCO2e, one of the many brokerages, it still

8Firms with on-going business relationships may have other ways to manage the risk of default by the other party. For instance, firms may enter into forward contracts rather than futures contracts. The primary difference between a futures contract and a forward contract is that a futures contract typically requires parties with an open interest to post financial assurance which the exchange draws upon or adds to until the contract reaches expiration, while a forward contract requires that all financial settlement occur at expiration. CHAPTER 4. UNDERPRICING OF UNIFORM PRICE AUCTIONS 124

Figure 4.2: RGGI CO2 Allowances Spot Market Price Index from CantorCO2e CHAPTER 4. UNDERPRICING OF UNIFORM PRICE AUCTIONS 125

Table 4.3: Monthly RGGI Allowances OTC Trading at CantorCO2e

Month Num. Volume Weighted Minimum Maximum Of Trade Avg. Price Price Price < Feb-09 0 0 – – – Mar-09 51 2,899,000 3.84 3.55 3.95 Apr-09 48 2,815,000 3.62 3.45 3.75 May-09 22 2,335,000 3.42 3.25 3.55 Jun-09 34 1,750,000 3.15 2.75 3.55 Jul-09 26 1,175,000 3.19 2.95 3.34 Aug-09 7 550,000 2.93 2.88 2.95 Sep-09 16 2,425,000 2.34 2.29 2.51 > Oct-09 0 0 – – – Total 204 13,949,000

convinces us that the trading on the OTC market is relatively sparse, and the prices from these transactions may contain much more noise than the futures price in reﬂecting market opinions regarding the value of CO2 allowances. As OTC prices actually closely track the CCFE futures prices, there is little to be gained from using OTC prices as a separate source of the secondary market price of CO2 allowances.

4.2.1.5 Secondary Market Price Proxy and Possible Explanations for Liquid Trad- ing

By transacting a standard CCFE RGGI futures contract, two parties agree to exchange 1000 allowances of a certain vintage at a particular price at a speciﬁc month in the future (called the “delivery month”). At the end of the delivery month, the contracted number of allowances must be physically transferred to the buyer’s account in the COATS registry and funds must be transferred to the seller, unless the seller buys back the futures contract.

All RGGI CO2 futures contracts expire at the end of the delivery month. Therefore, on any given day in a year, if a futures contract for allowances of that vintage year has delivery month in the same month of that day, the futures contract is called the “front-month” futures. In other words, the “front-month” futures expire at the end of the current month. CHAPTER 4. UNDERPRICING OF UNIFORM PRICE AUCTIONS 126

More generally, the “front-month” futures contract is the next contract to expire. So if there is no contract to expire at the end of current month, then the term refers to the contract with the expiration date after but most adjacent to the end of current month). As time gets closer to the expiration date, the price of futures contract approaches to the value of underlying asset – the CO2 allowances. In theory, the price of futures contract on the expiration date should be equal to the price of RGGI CO2 allowances on the spot market. Since the “front-month” futures are the closest to their expiration dates, their price is the closest to the spot price of RGGI allowances at any given day. We can treat “front-month” futures price as the best proxy for the spot price of emission permits on the secondary market. Therefore, among the various RGGI markets of secondary trading, CCFE futures market is the most liquid one. Thus, I use the daily price of the “front-month” futures of current vintage allowances as the secondary market price of RGGI emission permits. As shown above that the secondary market of RGGI allowances are indeed quite liquid. Since the primary focus of designing the RGGI auction has been put on the allocative efﬁciency (Holt et al. (2007)), a liquid secondary market would not be predicted to follow an auction market that sells almost all the RGGI allowances. The possible explanations for this counter-intuitive market structure may include the following arguments. First, bidders reduce demand strategically to depress the auction clearing price, but it leaves them with unﬁlled demand of allowances that they need to obtain from secondary trading in order to satisfy their compliance requirement. Second, the RGGI auctions are open to non-compliance entities, who could be the major force driving the secondary trading. Third, the participation in RGGI auctions is only partial in that many small facilities may choose not enter auctions, implying likely high friction of entry or high transaction costs. CHAPTER 4. UNDERPRICING OF UNIFORM PRICE AUCTIONS 127

4.2.2 RGGI Futures Trading Pattern and Underpricing in RGGI Auc- tions

4.2.2.1 Cyclical Valley Pattern of Futures Trading

RGGI CO2 auctions are taking place at 9:00 AM to 12:00 PM ET on the auction day, usually a Wednesday, and the auction results will be announced normally on the following Fridays at 10:00 AM ET.9

An interesting phenomenon has emerged on the markets of RGGI CO2 allowances since the beginning of RGGI program. Figure (4.3) shows the price trend of the CCFE RGGI “front-month” futures on the daily basis, together with the daily trading volume. We can see in Figure (4.3) a distinctive valley pattern of RGGI futures trading: as the futures price climbs up or dips down, the timing of auctions always coincide with the trough. There are three interesting characteristics of this valley pattern:

1. Down-then-up cyclical pattern of CO2 futures price around auction dates.

2. Futures trading volume tends to be high right before or right after auction dates, showing a down-then-up co-movement along with the futures price.

3. Auction prices are usually lower than the average futures price around auction dates.

Comparing Figure 4.4b with Figure 4.4a, we can see an obvious difference of the trading price movement patterns around the auction dates between the SO2 and CO2 markets: for SO2 permits, auctions have no apparent relationship with the moving direction of secondary market prices which would go up or down during the days before or after the auction dates; in contrary, for CO2 permits, the timing of the auctions always coincide with the trough, i.e., the turning points of the price-going-down-and-back-up cycles. Why do the auctions under these two cap-and-trade programs have such distinct impact on their secondary trading markets? Considering the two emission trading systems share many

9Auction 1 was held on a Thursday, and its result was sent to bidders no later than 5:00 PM on the following Monday, i.e. 9/29/2008. Auction 2, though held on a Wednesday, announced its result either on the following Friday or on the following Monday, no later than 5:00 PM, while the actually announcement time was unclear to the author. CHAPTER 4. UNDERPRICING OF UNIFORM PRICE AUCTIONS 128

Figure 4.3: RGGI Futures Daily Trading Volume and Price CHAPTER 4. UNDERPRICING OF UNIFORM PRICE AUCTIONS 129

common features, such as the same group of participants, the potential cause of the different market interaction patterns would likely lie in the two major distinctions of program policy design: one is the auction format (SO2 uses discriminatory auction versus CO2 uses uniform price auction), and the other is the relative size of auctioned permits to freely- allocated permits. Dufﬁe (2010) presidential address, inattentive traders, down-then-up trading price even if the supply shock of assets are expected. the true market value lies above the bust (bottom) of the price valley. Based on Dufﬁe, estimate the true market value around each auction date.

4.2.2.2 Observed Underpricing in RGGI Auction Clearing Prices

To put the price disparity between auctions and futures trading into perspective, we can compare each auction clearing price with the average futures price in percentage. Table (4.4) lists the ratio of the underpricing in auctions with respect to average futures price calculated using various measures, including:

1. One-Week-Before Average Futures Price: the CCFE RGGI “front month” futures average price from the Monday 1 week ago till the day before auction day, 7 business day average.

2. Two-Week-Before Average Futures Price: the CCFE RGGI “front month” futures average price from the Monday 2 weeks ago till the day before auction day, 12 business day average.

3. Two-Week-Before-and-One-Week-After Average Futures Price: the CCFE RGGI “front month” futures average price from the Monday 2 weeks ago till the Friday 1 week after auction day, 21 business day average.

4. One-Week-Before-and-After Average Futures Price: the CCFE RGGI “front month” futures average price from the Monday 1 week ago till the Friday 1 week after the auction day, 15 business day average. CHAPTER 4. UNDERPRICING OF UNIFORM PRICE AUCTIONS 130

Table 4.4: Average CCFE CO2 Futures Prices Compared to Auction Prices

Auction Clearing 1-Week 2-Week 2-Week Before 1-Week 2-Week # Bid ($) Before Before +1-Week After Before+After Before+After 1 3.07 -33.72% -35.18% -27.54% -25.17% -25.73% 2 3.38 -1.91% -9.04% -8.41% -3.96% -8.47% 3 3.51 -5.79% -5.67% -5.22% -5.14% -4.27% 4 3.23 -7.26% -7.69% -4.18% -2.73% -3.67% 5 2.19 -20.56% -22.52% -17.85% -14.52% -16.31% 6 2.05 -2.92% -5.22% -4.23% -2.35% -3.81% 7 2.07 -1.63% -1.70% -1.64% -1.58% -1.84% 8 1.88 -8.52% -8.90% -6.51% -5.32% -5.37%

5. Two-Week-Before-and-After Average Futures Price: the CCFE RGGI “front month” futures average price from the Monday 2 weeks ago till the Friday 2 weeks after the auction day, 25 business day average.

As we can see from Table (4.4), the underpricing ratios are relatively on the same scale for different measures. For Auction 1 that closed at $3.07, the clearing price was approximately 30% below the average future prices for all the 5 measures of different periods around the auction date of September 25, 2008. Combining the information in Figure (4.3) and Table (4.4) together, we can see that there was a subsequent 50% increase in futures prices from the bottom just after the auction 1 results were announced on September 29, 2008. After wide swings in price between early October and late November of 2008, the futures price again fell precipitously leading up to Auction 2 (December 17, 2008) which closed almost about 10% below the average future prices of the previous 2 weeks. Such down-the-up pattern maintained in the following auctions all the way through early 2010. Not only is the impact of auctions on the futures market reﬂected by the cyclical valley pattern in the trading prices, but it is also reﬂected through the trading volume. Again in Figure (4.3), we can see that the trading volume stays low near the auction dates. Each auction day represents a pulse in market liquidity, and the valley in trading volume synchronizes with the valley in future prices. CHAPTER 4. UNDERPRICING OF UNIFORM PRICE AUCTIONS 131

Figure 4.4: Different Price Trend of Emission Permits around Auction Days

(a) RGGI CO2 Allowances Price in Auctions and Futures Trading

(b) ARP SO2 Allowances Price in Auctions and Futures Trading CHAPTER 4. UNDERPRICING OF UNIFORM PRICE AUCTIONS 132

The valley pattern is by far unique to the RGGI allowances market. Compare with the

EPA SO2 allowances market, we don’t see a similar pattern in the SO2 futures trading. In

Figure (4.4), there is no persistent co-movement between the CCFE SO2 futures price and

EPA annual auction prices. Since EPA only auctions out less than 2.8% of SO2 allowances, its annual auctions are too tiny to affect the trading market; on the other hand, bidders of

SO2 auctions would not care too much to modify their bidding strategy for the purpose of resale simply because auction market is too small compared to the trading market. This further suggests that the pattern on the RGGI CO2 allowances markets likely has something to do with the interaction between auctions and secondary trading. We can zoom in to see the movement of CCFE futures price around auction dates more closely in Figure (4.5). The interesting phenomenon on the RGGI allowances market inspires the research question of this paper: how emission permit auctions interact with the secondary trading market and how much underpricing in the auctions is caused by such interaction between auctions and trading. I provide an explanation to this phenomenon from the perspective of multi-unit auction theory.

4.3 Model of Uniform Price Auctions for Emission Per- mits

I explore the design features of a uniform price multi-unit auction for emission permits in the context of a cap-and-trade program. I model the auction as a mechanism selling multiple units of homogeneous goods in the environment of incomplete information and with presence of a competitive trading market. Similar as the supply function equilibrium model developed originally by Klemperer and Meyer (1989), the demand function equilibrium models for multi-unit auctions have a continuum of equilibria for bidders’ strategy. How- ever, if we assume bidders to use linear strategies, it is optimal for them to adhere to linear bid functions, given all competitors use linear strategies. Vives (2010) presents a model that allows for both private and common values in the absence of exogenous noise. The auction setup in this section is close to Ollikka (2011) that introduces Vives’ model into the context of emission permit auctions. Similar as Ollikka (2011), I modify the Vives’ model CHAPTER 4. UNDERPRICING OF UNIFORM PRICE AUCTIONS 133

Figure 4.5: CO2 Allowance Prices around Auction Dates CHAPTER 4. UNDERPRICING OF UNIFORM PRICE AUCTIONS 134

to characterize the institutions of the RGGI quarterly auctions and in general the uniform price auctions of emission permits. In the cap-and-trade system, surrendering allowances is the substitute for abating emissions. Compliance entities acquiring emission permits will eventually use them to save on the cost of abatement. So the allowances have “use value” that is primarily determined by the emission abatement cost function of the regulated emitter. Compliance bidders in the RGGI auctions are mainly electricity companies. They own diverse portfolios of different generating units. Some units cost more to reduce the same amount of emissions than others. For example, the units that allow fuel switching can reduce emissions much cheaper than the units that can only rely on scrubbing or sequestrating. Depending on their production portfolio and abatement technology, the compliance entities have very different marginal abatement costs, which are completely idiosyncratic and private information. On the other hand, the secondary market, specially the competitive trading market on public exchange, is both an alternative source to buy emission permits and a place to sell allowances that market participants have acquired. That means, emission permits have “trading value”. When the trading market is liquid enough, it works as a competitive market where all players are price takers when buying or selling allowances. The secondary market price is the realization of the intrinsic value10 of emission permits that is the same for everyone and is fundamentally inﬂuenced by many common factors such as the relative costs of primary fuels, weather conditions, the growth of the economy, relative costs of other climate policy mechanisms, among others. So the “trading value” is common information for all auction bidders, even though it is a random variable at the time of auction. This model hence builds on an afﬁne information structure that captures both the private use value and the common trading value in the emission permit auctions. The solution concept used in the model is based on symmetric linear Bayesian demand function equilibria (LBDFE).

10In theory, the intrinsic value of allowances on the secondary market is determined by the supply and demand forces that equalize the marginal abatement costs of all compliance entities on the emission market. In this paper, I denote the intrinsic value as the expectation of the trading value, µ. In other words, µ is the hypothetical true market value of one unit emission permit at the market equilibrium, where supply equals demand subject to the total cap. CHAPTER 4. UNDERPRICING OF UNIFORM PRICE AUCTIONS 135

4.3.1 Model Setup

Consider a uniform price auction of Q units identical emission permits with uncertain ex-post value. There are N ≥ 3 risk neutral bidders competing to buy permits in the auction.

Bidders value the auctioned allowances with the value function Ui(qi). The marginal value of bidder i for quantity q is dUi = u (q ), which measures his willingness to pay. Assume i dqi i i the marginal value function is linear for bidder i = 1,··· ,N, in the form of,

ui(qi) = vi − λqi . (4.1)

The downward-slopping marginal value of owning allowances is consistent with the decreasing marginal beneﬁt of emissions for the compliance entities. As their marginal abatement cost usually increases with emissions, their marginal saving of substituting abatement with using permits mirrors it and decreases, so does the marginal value of allowances in the auction. The parameter λ > 0 represents how fast the marginal value diminishes, and is assumed to be the same for all bidders, including non-compliance bidders. For the non- compliance bidders, λ can be an adjustment for transaction costs, opportunity costs, or risk aversion.11

Bidders have a payoff type, i.e., the “value parameter” vi of their linear marginal value function, which is a combination of “use value” and “trading value” for each unit of emission permits. Assume that the intrinsic value of each allowance is µ at the time of auction. If bidder i uses one allowance for the purpose of compliance, it gives the bidder a use value of

θi. Each bidder has complete information regarding his own use value. θi is independently 2 and identically distributed and follows normal distribution, θi ∼ N(µ,σθ). This distribution is common knowledge for all bidders. If bidders choose not to use a tradable permit but instead to sell it on the competitive trading market, they obtain trading value V. As the common value component in bidders’ 2 valuation structure, V is a random variable following normal distribution, V ∼ N(µ,σV ).

11Risk aversion implies diminishing marginal valuation in multi-unit demand context. Instead of assuming non-compliance entities to be risk averse bidders, I take into account the risk aversion by assuming diminishing marginal value so as to avoid the computational complexity. Also, this setting helps to ensure the existence of a linear equilibrium, because under the extreme circumstance where non-compliance entities only care about the common value, the linear strategy will collapse if bidder’s marginal value is ﬂat. CHAPTER 4. UNDERPRICING OF UNIFORM PRICE AUCTIONS 136

2 The distribution is also common knowledge for all bidders, of which the variance σV can be interpreted as the volatility of secondary trading price. Although bidder i has incomplete information of trading value V, he receives a signal si at the time of auction, which is an unbiased estimator of the trading value conditional on a certain V, i.e., E(si V) = V.

Deﬁne εi = si −V, the noise of bidder i’s signal. It is obvious that E(εi V) = 0. I assume 2 that the noise εi follows identical normal distribution across bidders, εi ∼ N(0,σε). I also assume that the noise is independent from V, Cov(εi,V) = 0, as well as independent across 2 2 bidders, Cov(εi,ε j) = 0 for j 6= i. Apparently, si = V + εi means that Var(si) = σV + σε, 2 and Cov(si,s j) = σV for j 6= i. Therefore, at the time of auction, the value parameter vi of bidder i is a weighted average of his use value θi and his signal of trading value si, namely,

vi = (1 − ω)θi + ωsi

= (1 − ω)θi + ωV + ωεi .

The weight ω ∈ [0,1] measures how much the trading opportunity matters for bidders, or how liquid the trading market is. If ω = 1, it means that either the trading opportunity does not exist or the trading market is so illiquid that no one expects to trade there, hence agents only care about their use values. If ω = 0, it means that the trading market is extremely liquid, almost like a money market, so that idiosyncratic values don’t matter any more.

Given the valuation structure, being the sum of independent normal variables, vi also follows normal distribution:

E(vi) = E[(1 − ω)θi + ωV + ωεi] = µ ,

2 2 2 2 2 2 Var(vi) = (1 − ω) σθ + ω σV + ω σε , and 2 2 2 2 Cov(vi,v j) = (1 − ω) Cov(θi,θ j) + ω Cov(si,s j) = ω σV .

To simplify the notations, let ti = (1 − ω)θi + ωV, which will be the true value parameter CHAPTER 4. UNDERPRICING OF UNIFORM PRICE AUCTIONS 137

realized for bidder i after the auction. I introduce three parameters δ2, τ2 and ρ, where

2 2 2 2 2 δ = (1 − ω) σθ + ω σV , 2 2 2 τ = ω σε , ω2σ2 ρ = V . 2 2 2 2 (1 − ω) σθ + ω σV

The model is a pure private value model if ρ = 0 (i.e., ω = 0), meaning that there is no correlation between bidders’ value parameters. If the signals of trading value are perfect 2 (i.e., σε = 0), even with the presence of a common value component V, the model reduces 2 to a private value model. If 0 < σε < ∞ and 0 < ρ < 1 (i.e., 0 < ω < 1), bidders have both private and common values. And if ρ = 1 (i.e., ω = 1), the model is a pure common value model.

In a multi-unit auction, each bidder submits a non-increasing bid curve qi = q(vi, p) to maximize his expected proﬁts. His strategy deﬁnes the quantity of allowances qi he demands at each price point p given his value parameter is vi. If we write the strategy function in the form of Di(p) = q(vi, p), the bid Di(p) is a monotonic demand function decreasing in p. The aggregate demand in the auction is D(p) = Di(p) + D−i(p), where N D−i(p) is the demand of all other bidders except bidder i, namely, D−i(p) = ∑ j6=i D j(p) = N ∑ j6=i q(v j, p). The auction clearing price is determined at the bid price that equalizes the N total demand and supply, Q = D(p) = ∑i=1 q(vi, p). Let us assume that there is a unique market clearing pricep ˆ(q(v1, p),··· ,q(vN, p)) for any realization of the value parameters 12 {v1,··· ,vN}. All demand above the clearing price will be accepted. With the uniform price format, bidders pay the same clearing price for all awarded units.

4.3.2 Linear Equilibrium Characterization

It is well known that, in games where strategies are demand (or supply) functions, the (Nash) equilibrium is not deterministic; that is, there exists a continuum of equilibria whose

12If there is no market clearing price, then the auction clearing price falls to be the reserve price; if there is more than one such price, then the largest one is chosen. An alternative way of description would be to set the stop-out price as the highest price at which aggregate excess demand is nonnegative; or if there is no such price, to set p = r (implying that the reserve price is r). See Wang and Zander (2002). CHAPTER 4. UNDERPRICING OF UNIFORM PRICE AUCTIONS 138

clearing prices differ significantly (see, e.g., Klemperer and Meyer (1989)). However, if we assume that bidders submit bid schedules that are linear in prices, there is a unique symmetric linear equilibrium. It is optimal for a bidder to submit linear bids, given that the other bidders play linear strategies, thus leading to a unique linear equilibrium. Note that the strategy space is not restricted to the class of linear bid schedules, but rather, all bidders simultaneously choose linear bids as their best responses to competitors’ linear strategies from all possible forms of bid functions. For the uniform price mechanism, the linear Bayesian Nash equilibrium has been widely used in modeling financial, electricity and other markets that sell multiple units of homogeneous goods through auctions, because the behavior of selecting linear strategies have been commonly observed in practice. A great deal of research has found empirical support for bidders’ straightforward choice of linear strategies in the multi-unit auction setting, as opposed to submitting complex and sophisticated bid functions. Hortacsu (2002a) studies the Turkish treasury bill auctions using a nonparametric approach. He demonstrates that a straight interpolation through bid points can, on average, explain 92% of the observed variation, and argues that a divisible good auction that generates linear equilibrium bidding strategies can provide a good description of the data. Similarly, Hortacsu and Puller (2008) find that linear bids provide an excellent fit in the spot market for electricity in Texas. In the dataset I obtained from EPA’s annual SO2 allowance auctions, I use a straight line to fit through each bidder’s bid of price-quantity pairs,13 and obtain the average R2 across all bidders with more than one bidpoint to be 0.907. Furthermore, Rostek et al. (2010) point out that the linear equilibrium aptly describes electricity and other divisible good markets by quoting industry insiders’s comments regarding the fact that bidders collect information about their residual market by estimating their price impact from price-quantity data.14 Based on this observation, they show that such estimates from bidders are independent of price levels, which imply a linear equilibrium.

13I regress bid price on bid quantity for all bidders with more than one bidpoint and for all auctions in my sample. 14Peter Cramton wrote in his report for the Federal Energy Regulatory Commission (2003):“... in my experience advising dozens of bidders in electricity and other markets, I have found that bidders, either explicitly or implicitly develop their bid curves by taking into account the price-quantity trade-off from incremental increases in bid prices. In some cases, I have observed power companies explicitly compute the residual demand curves in order to determine their optimal price-quantity bids in power markets.” (p. 26) CHAPTER 4. UNDERPRICING OF UNIFORM PRICE AUCTIONS 139

Since the major players on the RGGI CO2 emission allowance markets are similar to the electricity market, e.g., electric utilities and power plants, it is reasonable to expect the bidders in the RGGI CO2 auctions to adopt linear strategies as well.

q(vi, p) = a + bvi − cp (4.2)

As this model setup is a direct modiﬁcation of Vives (2010) model, the derivation of solution to the auction equilibrium is essentially the same as Vives’ steps. I will recap his derivation steps below using the parametric notations applicable to my model setting. Recall that in the equilibrium aggregate demand equals supply, Q = D(p), so every bidder N faces a residual supply curve Si(p) = Q − D−i(p) = Q − ∑ j6=i D j(p), over which he has monopsonist N Si(p) = Q − (N − 1)a − b ∑ v j + (N − 1)cp . j6=i

−1 Vives rewrites the equation in the form of inverse residual supply Si (qi),

N (N − 1)a + b∑ v j − Q q p = S−1(q ) = j6=i + i i i (N − 1)c (N − 1)c q ≡ H + i i (N − 1)c

N (N−1)a+b∑ j6=i v j−Q where Hi ≡ (N−1)c . Therefore, the clearing price p = pˆ(q(v1, p),··· ,q(vN, p)) provides bidder i all the information about the values of others.

Knowing all players use the symmetric linear strategy, bidder i will chooses qi to maximize his expected proﬁt conditional on p. Under the uniform price rule, Vives demonstrates CHAPTER 4. UNDERPRICING OF UNIFORM PRICE AUCTIONS 140

that the maximization problem becomes

" # Z qi −1 max E[πi vi, p] = E ui(x)dx − Si (qi)qi vi, p qi 0 " # Z qi = E (ti − λx)dx − pqi vi, p 0 λ = E (t − p)q − q2 v , p . i i 2 i i

Taking p and qi out of the expectation notation, then replacing p with the inverse residual supply function, Vives gets

λ 2 max E[πi vi, p] = E[ti vi, p] − p qi − qi qi 2 qi λ 2 = E[ti vi, p] − Hi − qi − q . (N − 1)c 2 i

The ﬁrst order condition is15

2 E[ti vi, p] − Hi − qi − λqi = 0 . (N − 1)c

Rearrange the equation, Vives rewrites the ﬁrst order condition as

h 1 i E[ti vi, p] − p = + λ qi . (N − 1)c

He then deﬁnes the aggregate market information as

N 1h i Ii ≡ ∑ v j = Q − (N − 1)a + (N − 1)cp − qi . (4.3) j6=i b

Ii is a random variable consisting of all the information that is uncertain to bidder i when submitting his bids. As E[ti vi, p] is informationally equivalent to E[ti vi,Ii], the ﬁrst order

15The second order condition is fulﬁlled when c > 0. CHAPTER 4. UNDERPRICING OF UNIFORM PRICE AUCTIONS 141

condition can be also expressed as

h 1 i E[ti vi,Ii] = + λ qi + p . (4.4) (N − 1)c

Vives (2009) as well as Ollikka (2011) both show that, with normal random variables, it is possible to derive the conditional expectation of ti by

E[ti vi,Ii] = A˜ E[ti] + B˜(vi − E[vi]) +C˜(Ii − E[Ii]) (4.5) where A˜, B˜ and C˜ are coefﬁcients determined by the variances of ti, vi and Ii. Note that

E[ti] = µ,E[vi] = µ, and E[Ii] = (N − 1)µ.

E[ti vi,Ii] = Aµ˜ + B˜(vi − µ) +C˜(Ii − (N − 1)µ) = A˜ − B˜ − (N − 1)C˜ µ + Bv˜ i +CI˜ i

Redefine the coefficients, and the conditional expectation can be specified as (see the Ap- pendix A.4.1 for derivation):

E[ti vi,Ii] = Aµ + Bvi +CIi , (4.6) where

τ2 A = τ2 + (1 − ρ + Nρ)δ2 δ2[τ2 + (1 − ρ)(1 − ρ + Nρ)δ2] B = [τ2 + (1 − ρ)δ2][τ2 + (1 − ρ + Nρ)δ2] ρτ2δ2 C = [τ2 + (1 − ρ)δ2][τ2 + (1 − ρ + Nρ)δ2]

Plug equation (4.3) and (4.6) into the ﬁrst order condition (4.4), Vives gets

Ch i h 1 i Aµ + Bv + Q − (N − 1)a + (N − 1)cp − q = + λ q + p . (4.7) i b i (N − 1)c i CHAPTER 4. UNDERPRICING OF UNIFORM PRICE AUCTIONS 142

Rearrange the bid strategy function and isolate vi,

1h i v = cp − a + q . (4.8) i b i

Substitute equation(4.8) into (4.7) h 1 i Bh i Ch i + λ q + p = Aµ + cp − a + q + Q − (N − 1)a + (N − 1)cp − q (N − 1)c i b i b i 1h i 1h i ch i = Aµ + CQ − aB − (N − 1)aC + B −C q + B + (N − 1)C p b b i b

Equating the coefﬁcients of qi and p on both sides, Vives solves three simultaneous equations (see the Appendix A.4.2 for details):

 h i Aµ + 1 CQ − aB − (N − )aC =  b 1 0  1 1 b (B −C) = (N−1)c + λ   c b (B + (N − 1)C) = 1

The system of simultaneous equations has a unique set of solutions for {a,b,c} if τ2/δ2 < ∞, a > 0, and c > 0. Therefore, there is a unique symmetric linear Bayesian demand function equilibrium (LBDFE) for the uniform price auction in the form of

q(vi, p) = a + bvi − cp , with

M Q a = · + (c − b)µ (4.9) 1 + M N (1 − ρ)δ2 N − 2 − M b = · (4.10) τ2 + (1 − ρ)δ2 λ(N − 1) N − 2 − M c = (4.11) λ(N − 1)(1 + M) where ρτ2N M = (1 − ρ)[τ2 + (1 − ρ + Nρ)δ2] CHAPTER 4. UNDERPRICING OF UNIFORM PRICE AUCTIONS 143

The solution holds if and only if N − 2 − M > 0.

4.3.3 Comparative Statics and Analytical Results

2 2 2 2 2 Recall that δ , τ and ρ are combinations of parameters ω, σV , σθ and σε. Given the number of bidders, N, the total number of allowances on sale, Q, and the value diminishing 2 2 2 coefﬁcient, λ, the four parameters ω, σV , σθ and σε are the only factors that may affect the equilibrium strategy, thus affect the auction clearing price. The following section discusses the comparative statics of the slope of linear equilibrium bid strategy and the underpricing of auction in terms of: [i] the weight on trading value (ω), [ii] the volatility of trading 2 2 2 price (σV ), [iii] the heterogeneity in use values (σθ), and [iv] the accuracy of signals (σε) respectively.

Slope Impact

In the equilibrium, bidder i submits his bid schedule q(vi, p) = a+bvi −cp, so the slope 1 N−2−M of his demand curve is − c . Note that those four parameters come into c = λ(N−1)(1+M) only through M. It is easy to show that c decreases with M.

∂c −λ(N − 1)(1 + M) − λ(N − 1)(N − 2 − M) 1 = = − < 0 ∂M λ2(N − 1)2(1 + M)2 λ(1 + M)2

According to the chain rule, if a factor x acts on c through M, the impact from the change of x is measured as ∂c ∂c ∂M = ∂x ∂M ∂x 2 2 2 In Appendix A.4.3, I show that the derivatives of M over ω, σV , σθ and σε have following signs. CHAPTER 4. UNDERPRICING OF UNIFORM PRICE AUCTIONS 144

∂M τ2N h ρ(1 − ρ)(N − 1)δ2 i 2ω(1 − ω)σ2σ2 = 1 − · θ V ∂ω (1 − ρ)2D D δ4 2Nρ(1 − ρ)(1 − ρ + Nρ)δ2 ωσ2 + ε (1 − ω)[(2 − ω)σ2 + ωσ2 ] > 0 (1 − ρ)2D2 δ2 θ V 2 ∂M τ N 2 2 2 2 = 2 2 4 [τ + (1 − ω) σθ] > 0 ∂σV (1 − ρ) D δ 2 2 2 2 2 ∂M τ N h ρ(1 − ρ)(N − 1)δ iω (1 − ω) σV 2 = − 2 1 − 4 ∂σθ (1 − ρ) D D δ τ2Nρ(1 − ρ)(1 − ρ + Nρ) − (1 − ω)2 < 0 (1 − ρ)2D2 2 2 ∂M N(1 − ρ + Nρ)ω σV 2 = 2 > 0 ∂σε (1 − ρ)D

2 2 2 Therefore, the signs for the partial derivatives of c over ω, σV , σθ and σε are

∂c < 0 ∂ω ∂c 2 < 0 ∂σV ∂c 2 > 0 ∂σθ ∂c 2 < 0 ∂σε

As c decreases in ω, the more liquid is the secondary trading market or the more important is trading to bidders, the steeper is each bidder’s demand curve, hence the more 2 2 will be the “bid shading”. Similarly, as c decreases in σV and σε, the more volatile is the secondary trading price or the more uncertain are bidders’ signals of the trading value, the steeper is the demand curve, and the more will be the “bid shading”. On the contrary, as c 2 increases in σθ, the more heterogeneous are bidders’s use values, the ﬂatter is the demand curve, thus the less will be the “bid shading”. We can even get a glimpse at some extreme situations. If there is no trading allowed or the trading market is extremely illiquid with huge transaction costs, we have ω = 0, leading CHAPTER 4. UNDERPRICING OF UNIFORM PRICE AUCTIONS 145

2 to M = 0. Or if the signals are perfect, we have σε = 0, also leading to M = 0. In these two cases, the LBDFE coincides with the full-information equilibrium (denoted by superscript f f f f ), where bidders’ strategy becomes q (ti, p) = c (ti − p). It is obvious that c < c , so if 2 ω > 0 or σε > 0, bidders will shade bids more and demand functions will pivot steeper. Private information yields market power that exceeds the full-information level. For large 2 2 2 enough ω, or high enough σε relative to σV and σθ, the linear equilibrium collapses as M increases too much: N − 2 − M → 0 and c → 0. The market tends to collapse when 2 the trading value element is too important (ω really high), signals are too noisy (σε really 2 high), or bidders are too homogeneous with similar use values (σθ very low).

Price Impact

From the market clearing condition, we obtain the auction clearing price as

1 Q p = a + bv˜− (4.12) c N where 1 N v˜ ≡ (∑ vi) . N i=1 Therefore, the price p reveals aggregate informationsv ˜, whose expectation is E[v˜] = µ. We can simplify p by substitute equation (4.9) into equation (4.12),

1h M Q Qi p = · + (c − b)µ + bv˜− . c 1 + M N N

The expected clearing price

1h M Q Qi E[p] = · + (c − b)µ + bE[v˜] − c 1 + M N N 1h 1 Qi = cµ − · c 1 + M N 1 Q = µ − · c(1 + M) N CHAPTER 4. UNDERPRICING OF UNIFORM PRICE AUCTIONS 146

In Appendix A.3, when we solve for c, equation (A.4) gives

1 1 1 c = − , λ 1 + M N − 1 so we can rewrite the expected clearing price as

1 + M −1 Q E[p] = µ − λ1 − · N − 1 N λ(N − 1) Q = µ − · N − 2 − M N

The partial derivatives ofp ¯ = E[p] over any parameter x will be

∂p¯ ∂p¯ ∂M = · . ∂x ∂M ∂x

We know that ∂p¯ λ(N − 1) Q = − · < 0, ∂M (N − 2 − M)2 N it is easy to obtain the signs of following partial derivatives.

∂p¯ ∂p¯ ∂M = · < 0 ∂ω ∂M ∂ω |{z} |{z} (−) (+) ∂p¯ ∂p¯ ∂M 2 = · 2 < 0 ∂σV ∂M ∂σV |{z} |{z} (−) (+) ∂p¯ ∂p¯ ∂M 2 = · 2 > 0 ∂σθ ∂M ∂σθ |{z} |{z} (−) (−) ∂p¯ ∂p¯ ∂M 2 = · 2 < 0 ∂σε ∂M ∂σε |{z} |{z} (−) (+)

Also, note that ∂p¯ λ(N − 1) 1 = − · < 0 ∂Q N − 2 − M N CHAPTER 4. UNDERPRICING OF UNIFORM PRICE AUCTIONS 147

∂p¯ λ(N − 1) Q = · > 0 ∂N N − 2 − M N2 Let the amount of underpricing be the difference between the auction price and the average marginal valuation, µ − λQ/N. It will take the form of

h 1 i ∆ = + λ Q/N . (N − 1)c

We know that ∂∆ 1 Q = − · < 0, ∂c (N − 1)c2 N as before we have

∂∆ ∂∆ ∂c = · > 0 ∂ω ∂c ∂ω |{z} |{z} (−) (−) ∂∆ ∂∆ ∂c 2 = · 2 > 0 ∂σV ∂c ∂σV |{z} |{z} (−) (−) ∂∆ ∂∆ ∂c 2 = · 2 < 0 ∂σθ ∂c ∂σθ |{z} |{z} (−) (+) ∂∆ ∂∆ ∂c 2 = · 2 > 0 ∂σε ∂c ∂σε |{z} |{z} (−) (−) as well as ∂∆ h 1 i 1 = + λ · > 0 ∂Q (N − 1)c2 N ∂∆ h 1 i Q = − + λ · < 0 ∂N (N − 1)c2 N2 1 1 The impact of the change in N is obvious, because (N−1)c is of order of N , underpricing 1 must be of order N2 . 2 2 In summary, the clearing price is decreasing in ω, σV , σε, and Q, and is increasing in 2 2 2 σθ and N. On the contrary, the amount of underpricing is increasing in ω, σV , σε, and CHAPTER 4. UNDERPRICING OF UNIFORM PRICE AUCTIONS 148

2 Q, and is decreasing in σθ and N. Before I discuss its empirical application to the RGGI CO2 auctions, I summarize the analytical results of the uniform price auction for emission permits as a conclusion below.

Conclusion. With τ2/δ2 < ∞ and N − 2 − M > 0, where

ρτ2N M = , (1 − ρ)[τ2 + (1 − ρ + Nρ)δ2] there is a unique symmetric LBDFE, at which bidders submit their bids using the same demand function q(vi, p) = a + bvi − cp. The coefﬁcients in the equilibrium demand is 2 2 2 2 2 determined by ω, σV , σθ and σε through intermediate parameters ρ, δ and τ ,

M Q (1 − ρ)δ2 N − 2 − M N − 2 − M a = · +(c−b)µ, b = · , c = . 1 + M N τ2 + (1 − ρ)δ2 λ(N − 1) λ(N − 1)(1 + M)

1 In equilibrium, we have λ(1+M) > c > 0, a > 0. And the following properties hold. 1 (i) The slope of equilibrium demand has absolute value c , which decreases with M and 2 2 λ. Namely, the slope is steeper (c is smaller) with increases in ω, σV , and σε, and is ﬂatter 2 (c is larger) with increases in σθ. 2 2 (ii) The expected clearing price p¯ is decreasing in ω, σV , σε, and Q, and is increasing 2 in σθ and N. 2 2 (iii) The amount of underpricing is increasing in ω, σV , σε, and Q, and is decreasing 2 in σθ and N.

According to above analytical conclusions, we can predict the hypothetical auction results in a scenario where trading is prohibited.

Hypothesis. In the uniform price auction for emission permits where bidders submit linear bid schedules q(vi, p) = a + bvi − cp, if secondary trading market is prohibited outside of auctions, bidders will not shade bids as much as they would have done in the scenario with trading. However, whether the auction clearing price will go up and whether the underpricing of auction will be alleviated is ambiguous, because the prohibition of trading CHAPTER 4. UNDERPRICING OF UNIFORM PRICE AUCTIONS 149 will drive away the non-compliance bidders and reduce the competition in the auction, thus may result even lower clearing price and larger underpricing.

In the following section of empirical analysis, I will use a random sampling method to calibrate the model with the RGGI auction data, and provide counterfactual results for the hypothesis.

4.4 Empirical Analysis of RGGI CO2 Auctions

The main idea of this section is that based on a proper underlying model we can construct theoretical counterparts of the auction summary statistics announced by RGGI, and we can calibrate the relevant parameters of the model by replacing them with the announced statistics as proxy.

4.4.1 Auction Characteristics and Data

In each spot auction supplies roughly 15%–22% of the annual budget of the allowances of current vintage year. They are conducted using a single-round, sealed-bid, uniform- price format. Each bidder submits multiple confidential bids on the electronic platform in COATS. Each bid contains a specific quantity demanded at a specific price. The bid quantity must be in multiples of 1000 allowances, while the bid price has a minimum tick of $0.01 and is quoted as “price per allowance”.16 A reserve price, which is the minimum allowable bid price, is set at $1.86 per CO2 allowance. Each auction is noticed at least 45 days in advance. Each auction is noticed at least 45 days before the date of the auction on the RGGI auction website. The Auction Notice provides the auction date and time, categories of eligible bidders, requirements for qualification, quantity of CO2 allowances to be auctioned, and information and procedures for participation. Bidders who wish to buy allowances from the auctions need to declare their

16The 1000 lot size requirement won’t affect the model and empirical method in this paper, as it simply scales up the units. CHAPTER 4. UNDERPRICING OF UNIFORM PRICE AUCTIONS 150

participation intent one month ahead of time, and are required to put down enough security deposit to suffice their bids one week before the auctions.17 Any party that meets qualification requirements can participate in the RGGI auctions. The participating bidders are classified into compliance entities or non-compliance entities, depending on whether they own CO2 emitting source units or not. Auction rules limit the number of allowances that associated entities may purchase in a single auction to 25 percent of the CO2 allowances offered for sale in that auction. Any unsold CO2 allowances in an auction may be offered for sale in future auctions according to each RGGI participating state’s regulations.

The RGGI CO2 auction takes place from 9:00 AM to 12:00 PM ET on the auction day, usually a Wednesday. Bidders can submit an unlimited number of bids; however, only one bid may be submitted for any given price. Also, bidders can cancel or change their bids at their discretion until the bidding window closes. Auction platform automatically ranks bidders’ bids by their bid price from high to low, and notes the cumulative demand at each bid. The clearing price is determined by the marginal bid at which the cumulative demand summed over all bidders just exhausts the total supply of allowances. Each bidder wins his cumulative demand above the clearing price, and pays the uniform clearing price for all units of awarded allowances. If the auction clears at the reserve price due to excessive supply, any unsold CO2 allowances may be offered for sale in future auctions. The Friday following each auction at 10:00 AM ET,18 the RGGI participating states publish the auction clearing price and notify each winning bidders of the amount of allowances they have won. Two weeks after each auction, awarded allowances will be transferred into winning bidders’ COATS accounts, and any remaining funds from their security deposit can be withdrawn afterwards. Weeks after each auction, Potomac Economics, RGGI’s independent market monitor, would release the auction result report, which contain clearing prices, descriptive statistics

17In order to participate the auctions, potential bidders have to put down enough deposit to cover all possible payment upon winning the allowances one week in advance. The due date of ﬁnancial security is usually the previous Wednesday before the auction day. This is a good indicator that the secondary market price one week before the auction day or even earlier would likely be taken into account by the bidders. 18Auction 1 was held on a Thursday, and its result was sent to bidders before 5:00 PM on the following Monday. Auction 2 was held on a Wednesday, but its result was announced before 5:00 PM on the next Monday. CHAPTER 4. UNDERPRICING OF UNIFORM PRICE AUCTIONS 151

on bids and bidders, and quantity information but without bidding details. RGGI provides market oversight by publishing independent market monitor reports to release auction results to the public. The participating states of RGGI agreed that releasing individual level information may increase the ability of market participants to manipulate the market and could reduce the level of competition or adversely affect participation in the auction. In recognition of this, but also to allow the maximum level of public disclosure in accordance with the applicable laws, the participating states release post-auction results in a way that maintains enough level of transparency regarding the development of the RGGI CO2 Budget Trading programs while ensuring individual privacy as well as the robustness and fairness of auction participation for all bidders. The details of bidder level bids are extremely confidential, so no individual identifiable bidding behavior can be observed. Upon approval of the auction results, the participating states release the clearing price and the total number of allowances sold 2 days after the auction. After financial settlement has taken place and allowances have been awarded to winning bidders, the participating states will release a Post-settlement Auction Report through the independent market monitor containing aggregate auction information in the following categories:

1. A summary of bidder participation and demand, including data of: number of potential bidders, number of participating bidders (N), number of winning bidders (n), cover ratio of total demand to supply (α), total number of allowances supplied for sale (Q), total number of allowances sold;

2. The dispersion of projected demand for allowances, including statistics of: the relative shares of projected demand for RGGI allowances by compliance entity;

3. The dispersion of bids, including statistics of: Herﬁndahl-Hirschman Index (HHI) of bid quantity concentration, number of bidders subgrouped by the submitted demand levels;

4. A summary of purchased allowances by type of bidder, including the statistics of: the percentage of allowances won by compliance entities and their afﬁliates; CHAPTER 4. UNDERPRICING OF UNIFORM PRICE AUCTIONS 152

5. A list showing amounts of allowances awarded to each winning bidder (bidder identities redacted);

6. A summary of bid prices, including data of: reserve price (r), minimum bid price 19 (bmin), maximum bid price (bmax), median bid price (bmed), mean bid price (bmean), 20 clearing price (bs) .

In addition, the participating states commit to release the names of potential bidders (those who received approval of their Qualification Application and filed a complete Intent to Bid) together with the Post-settlement Auction Report. The cumulative list of Potential Bidders, from Auction 2 onward, will be released along with the Post-settlement Auction Report after each subsequent auction. The Post-settlement Auction Reports have been prepared and provided by Potomac Economics, RGGI Inc.’s independent market monitor. Potomac Economics monitors the RGGI Allowance market in order to protect and foster competition, as well as to increase the confidence of the states, participants, and public in the allowance market. Table (4.5) lists the available data relevant to this empirical study for all the eight RGGI

CO2 auctions held from September 2008 to June 2010. As discussed in Section 4.2.1, “front-month” futures price can be considered as the best proxy for the spot price of emission permits on the secondary market, so I use the daily price data of the “front-month” futures of current vintage RGGI CO2 allowances in the empirical analysis. RGGI allowance purchases are settled by the electronic transfer of ownership between two COATS accounts and do not involve the complication of physical delivery. Conse- quently, a signiﬁcant number of purchases of RGGI allowances take place just after the expiration date of a futures contract. Even the transactions that do not result in actual changes of ownership provide traders with strong ﬁnancial incentives to correctly anticipate the future price of allowances. Because considerable economic value is at stake, exchanges are thought to provide an excellent platform for revealing information about the market value of goods.

19Mean bid price is the volume weighted average bid price. 20 Auction clearing price is also called stop-out price, so I use bs as its notation. CHAPTER 4. UNDERPRICING OF UNIFORM PRICE AUCTIONS 153

Table 4.5: Available Data from RGGI CO2 Auctions

(a) Summary of Bidder Participation and Demand Auction Cover Herﬁndahl Active Winning Total # Ratio -Hirschman Bidder Bidder Supply α Index N n Q 1 4.1 446 59 44 12,565,387 2 3.5 459 69 46 31,505,898 3 2.5 602 50 42 31,513,765 4 2.6 578 54 48 30,887,620 5 2.5 584 46 34 28,408,945 6 2.6 587 62 40 28,591,698 7 2.3 710 51 40 40,612,408 8 1.3 992 43 42 40,685,585

(b) Summary of Bid Prices Auction Maximum Median Mean Minimum Clearing # Bid Price Bid Price Bid Price Bid Price Price bmax bmed bmean bmin bs 1 12.00 2.51 2.77 1.86 3.07 2 7.20 3.00 3.03 1.86 3.38 3 10.00 3.33 3.24 1.86 3.51 4 12.00 2.89 2.83 1.86 3.23 5 12.00 2.10 2.30 1.86 2.19 6 5.00 2.00 2.12 1.86 2.05 7 5.00 2.06 2.07 1.86 2.07 8 4.00 2.00 2.01 1.86 1.88 CHAPTER 4. UNDERPRICING OF UNIFORM PRICE AUCTIONS 154

Trade of RGGI CO2 futures takes place on regulated commodities exchanges, such as the Chicago Climate Futures Exchange (CCFE) and the Green Exchange of New York

Mercantile Exchange (NYMEX). The trading of RGGI CO2 allowance futures began on the CCFE in August of 2008 and began on NYMEX in December of 2008. Most trading activity has been on the CCFE. Compared with CCFE, the trading size in NYMEX is negligible. Therefore, I rely on the data of CCFE’s futures trading. I use the daily “front month” futures price data to estimate parameters µ as the moving 2 21 mean and estimate σv as the moving variance of the time series. I try two ways to estimate the moving mean and moving variance. One is the generic way by calculating the average price of the period from 2 weeks before till 1 week after any given day (21 business days) and the corresponding 21-day variance. The other is to assume the daily price time series as an ARCH process. The estimation results are relatively close for the two methods. For the purpose of showing counterfactual results in an intuitive way and being able to easily compare with Table (4.4) in Section 4.2.2, I report the results based on the 21-day moving 2 2 average σv and 21-day moving variance σv.

4.4.2 Empirical Procedures

Besides all the summary statistics of bid prices, the known parameters from our dataset 2 include N, n, µ, σv, Q. The ﬁrst step of this empirical analysis is to calibrate out the rest unknown parameters. Given the deﬁnitions of the intermediate parameters in the process of derivations, we aim to recover the slope and intercept of the mean demand curve, i.e., c and a + bµ, then to back out M and λ. We will use the following data to calibrate the model:

1. Use bmax, bmin, bs to randomly sample the bid price points of each bidder;

2. Use α, Q for aggregate demand;

3. Use bmed for mid point in aggregate demand;

4. Use HHI, bmean for sample variance of the value parameters vi;

21The moving variance of the daily futures price time series reﬂects the price volatility directly, as the volatility is ratio of the moving variance over the moving mean. CHAPTER 4. UNDERPRICING OF UNIFORM PRICE AUCTIONS 155

5. Use bs, Q in market clearing condition.

In real-world auctions, there is usually a minimum bid quantity restriction because no auction goods can be perfectly divisible. For example, in EPA SO2 auctions, bid quantities have to be integer numbers; and in RGGI CO2 auctions, the bid quantities have to be multiples of lot size 1,000 units. Also, there is naturally a smallest price increment restriction for all real-world auctions. For emission allowances auctions, it is usually set by default at $0.01. In real auctions, a bidder submits several pairs of price-quantity combinations as his bids. Even when there is no restrictions on how many bids are allowed, the average number of bids submitted in many real life multi-unit auctions tended to be under 10, and most number of bids from an individual bidder normally would not go above 20. According to past experiences, if there is a large minimum tick set for the incremental price points allowed, bidders tend to submit even fewer number of bids. In the case of RGGI auctions, the minimum tick is $0.01. A bidder certainly would not submit his incremental demand for every penny, but rather pick out only a subset of bid points on his linear demand curve and lump the incremental demand in between two adjacent price points together in his submission. As a result, what the auctioneer sees from each bidder is a step function underneath his demand curve, instead of a continuous line. When the bids are aggregated over all bidders, the auctioneer only obtains the incremental demands at realized price points submitted by a subset of bidders, leaving the aggregate demand step function lying inward the hypothetical aggregate demand curve. The discreteness of the bids casts some complications onto the empirical analysis using the continuous model, as it causes a downward bias of the bid statistics (such as mean bid) compared to the would-be counterparts from a continuous demand function. Figure (4.6) shows the intuition of how the downward bias of mean bid price occurs due to the discreteness of submitted bid schedules. To account for the reality of discrete bids, I use random sampling of price points for each bidder to correct for the bias. For an auction that has n winning bidders among N participating entities, given the data of bmax, bmin and bs, I draw B random samples in the following way. Assume each bidder submit K bids, which are K points on his equilibrium demand curve qi = a + bvi − cp in descending order of price. Let the price points of bidder i’s bids CHAPTER 4. UNDERPRICING OF UNIFORM PRICE AUCTIONS 156

(1) (k) (K) (1) (k) (K) be {pi ,··· , pi ,··· , pi } and let his demand quantity points be {qi ,··· ,qi ,··· ,qi }, (k) (k+1) (k) (k+1) where pi ≥ pi and qi ≤ qi . As there are n winning bidders and N − n losing bidders, it is apparent that the highest bid price of each winner is above the clearing price, while the highest bid price of each loser is below bs. Also, since one of the n winners (1) submits the maximum bid bmax, one pi is ﬁxed at bmax. For each random sample, I (1) draw (n − 1) number of pi uniformly from the interval of [bs,bmax], and draw (N − n) (1) 22 number of pi uniformly from the interval of [bmin,bs − 0.01]. With the realization of (1) (1) {pi }i∈{1,···,N}, I then randomly draw (K −1) points uniformly from the interval [bmin, pi ] for each i ∈ {1,··· ,N}. All the numbers will be rounded to the nearest 0.01 level. In addition, I will set K to be 5, 10, 20 and carry out calibrations for each K value respectively to test for the robustness of the empirical results. Throughout the rest of this paper, how bidders are indexed does not matter because the calibration is done at the aggregate level. But for simplicity in notations, I index the winners as i ∈ {1,··· ,n} and the losing bidders as i ∈ {n + 1,··· ,N}. I also use the following notations. 1 N 1 n v = ∑ vi, vn = ∑ vi, N i=1 n i=1 N N (k) 1 (k) (k) 1 (k) q = ∑ qi , p = ∑ pi , N i=1 N i=1 (k,l) (l) (k) (k,l) (k) (l) ∆qi = qi − qi , ∆pi = pi − qi .

Aggregate Demand

(K) In each random sample, the lowest bid price from each bidder is {pi }i∈{1,···,N}, and (K) (K) the demand of each bidder is qi = a + bvi − cpi . With Q lots of allowances (1000 22Take Auction 3 as an example, 50 bidders participated in bidding with 42 bidders winning at a clearing price of $3.51. The maximum bid is $10.00 and the minimum bid is $1.86. In every random sample, I randomly pick 41 price points in [3.51,10.00] and 8 price points in [1.86,3.50]. This generates 49 highest bid prices besides one bidder’s highest bid price at $10.00. CHAPTER 4. UNDERPRICING OF UNIFORM PRICE AUCTIONS 157

allowances per lot) on sale and a cover ratio of α, when all bidders submit the same equilibrium bid schedule, the aggregate demand satisﬁes

N N N h (K)i (K) ∑ a + bvi − cpi = Na + b ∑ vi − c ∑ pi = αQ i=1 i=1 i=1 or equivalently, αQ a + bv − cp(K) = (4.13) N

Median Bid

(m+) For a bidder i, denote his bid price right above or right at bmed as pi and his bid (m−) price right below bmed as pi . According to the linear strategy he adopts, his demand at (m+) pi is (m) (m+) (m+) qi = qi = a + bvi − cpi , so his reminder demand after the median bid price is

(m,K) (K) (m) ∆qi = qi − qi (K) (m+) = a + bvi − cpi − [a + bvi − cpi ] (m+) (K) = c[pi − pi ]

(m,K) The deﬁnition of median bid tells us that summing up ∆qi over all bidders will be half of the aggregate demand.

N α (m+) (K) (m+) (K) Q = c ∑ [pi − pi ] = cN[p − p ] (4.14) 2 i=1

Equation (4.14) isolates parameter c so that we obtain

αQ c = (4.15) 2N[p(m+) − p(K)] CHAPTER 4. UNDERPRICING OF UNIFORM PRICE AUCTIONS 158

Mean Bid

The mean bid is deﬁned as the area below the aggregate step demand curve divide by the aggregate demand αQ. The numerator equals the sum of the areas below each individual step bid functions, so the product of bmean and αQ should be the sum of areas under all bidders’ step bids.

N K−1 h (K) (K) (k,K) (k−1,k) (1,K) (1)i ∑ pi qi + ∑ ∆pi ∆qi + ∆pi qi = αQ · bmean (4.16) i=1 k=2

(1) It is reasonable to assume that the variation of the ﬁrst bid quantity qi is not too big over (1) (1) bidders, so I make an approximation to substitute qi with q .

N N (1,K) (1) ∼ (1,K) (1) ∑ ∆pi qi = ∑ ∆pi q i=1 i=1 N h i (1,K) (1) = ∑ ∆pi a + bv − cp i=1

We can rearrange the mean bid equation (4.16) to get

N N K−1 N h i (K) (K) (k,K) (k−1,k) (1,K) (1) ∑ pi qi = αQ·bmean −c ∑ ∑ ∆pi ∆pi − ∑ ∆pi a+bv−cp (4.17) i=1 i=1 k=2 i=1

Sample Mean of Value Parameter vi

Although we can not directly observe the sample of vi, we can use the expectation of v as the sample mean of the value parameters vi. It is easy to show that E(v) = E(vi) = µ. Use this into equation (4.13), we get

αQ a + bµ = + cp(K). (4.18) N CHAPTER 4. UNDERPRICING OF UNIFORM PRICE AUCTIONS 159

Sample Variance of Value Parameter vi

(K) (K) Again from each bidder’s demand qi = a + bvi − cpi , we have

(K) (K) bvi = qi + cpi − a, thus the sample variance of value parameter vi can be expressed as

N N 2 1 2 1 1 h (K) (K) (K) (K)i ∑ (vi − v) = 2 · ∑ qi + cpi − q + cp N i=1 b N i=1 N 2 2 1 n 1 h (K) (K)i h (K) (K)i o = 2 ∑ qi + cpi − q + cp b N i=1

(K) 1 N (K) αQ 2 2 Note here q = N ∑i=1 qi = N . Since we know the variance of vi is Var(vi) = δ + τ , the sample variance should be approximately equal to δ2 + τ2.

N 2 2 2 2 2 1 h (K) (K)i h (K) (K)i b (δ + τ ) = ∑ qi + cpi − q + cp N i=1

Expand the term of summation,

N 2 N 2 N N 2 h (K) (K)i h (K)i (K) (K) 2 h (K)i ∑ qi + cpi = ∑ qi + 2c ∑ pi qi + c ∑ pi . i=1 i=1 i=1 i=1

We have the statistics of Herﬁndahl-Hirschman Index (HHI) of demand concentration, which is deﬁned as (K) N hq i2 HHI = 10000 ∑ i , i=1 αQ so we get N 2 2 h (K)i2 α Q HHI ∑ qi = . i=1 10000 CHAPTER 4. UNDERPRICING OF UNIFORM PRICE AUCTIONS 160

In summary, we can use HHI and bmean to calculate

2 2 N K−1 2 2 2 α Q HHI αQ · bmean 1 (k,K) (k−1,k) b (δ + τ ) = + 2c − ∑ ∑ ∆pi ∆qi 10000N N N i=1 k=2 N h i h i2 h i2 1 (1,K) (1) 2 (K) αQ (K) − ∑ ∆pi a + bv − cp + c p − + cp (4.19) N i=1 N

Auction Clearing

The RGGI announces the awarded quantities of allowances to winning bidders, denoted ∗ as qi . Following the notation customs above, the corresponding bid price of bidder i at his (∗+) awarded quantity is pi , i.e., his bid price right above or right at bs.

n n ∗ h (∗+)i ∑ qi = ∑ a + bvi − cpi i=1 i=1 h (∗+)i = n a + bvn − cp = Q

That means, Q a + bv = + cp(∗+) (4.20) n n

4.4.3 Calibration Results

The empirical analysis is conducted by taking the number of bids from each bidder to be K = 5,10,20 and by random sampling B = 1000 times for each of the K value. The ﬁrst goal of calibration is to recover the expected demand function, or mean bid schedule as called in the following. As the sample average bid schedule takes the form of

q = a + bv − cp, the mean bid schedule is q = a + bµ − cp . (4.21)

Using the empirical conditions discussed above, we obtain from each random sample the values of slope (c) from equation (4.14), and get the values of intercept (a + bµ) from CHAPTER 4. UNDERPRICING OF UNIFORM PRICE AUCTIONS 161

Table 4.6: Mean Slope and Intercept of Calibrated Bid Functions B = 1000

Auction K = 5 K = 10 K = 20 Number slope intercept slope intercept slope intercept 1 710.5 2837.4 693.3 2475.8 681.5 2294.1 (141.3) (445.9) (85.4) (230.3) (48.4) (118.9) 2 735.6 3347.3 713.3 3108.5 707.7 3005.3 (59.9) (177.2) (30.5) (83.3) (15.4) (40.4) 3 559.6 3102.3 544.5 2825.5 540.2 2697.5 (64.2) (224.9) (34.7) (108.7) (17.1) (49.6) 4 749.4 3678.6 738.6 3255.9 728.1 3033.6 (122.8) (433.1) (75.3) (227.1) (39.7) (108.2) 5 3854.5 11841 3510.0 9502.5 3394.7 8551.9 (1521.2) (4322.4) (888.1) (2145.7) (556.2) (1224.8) 6 4795.4 11214 4550.9 10186 4429.7 9689.8 (1046.2) (2264.3) (623.1) (1275.1) (395.5) (788.0) 7 5033.0 12597 4795.3 11411 4709.3 10912 (1121.8) (2524.5) (605.4) (1271.1) (367.2) (747.9) 8 4885.3 11394 4645.5 10375 4578.2 9995.6 (1344.9) (2893.9) (708.3) (1449.1) (406.0) (809.0) equation (4.18). Table (4.6) reports the mean slope and intercept of the calibrated bid functions, with their standard errors reported in the parentheses below the numbers of slope and intercept. These results are further visualized in two sets of ﬁgures. Figure (4.7) stacks the calibrated mean bid schedules for K = 5,10,20 together for each RGGI auction. As we can see that the curve for K = 5 is always on the top representing a higher mean value for owning allowances, while K = 20 curve lies lower than the others representing a lower mean value. Given the fact that the mean bid curves for different K values are all associated with the same auction clearing price, Figure (4.7) clearly shows that the fewer number of bids bidders submit, the more downward bias there is on the auction clearing price relative to what their continuous strategies would have generated, the more severe is the underpricing problem. Figure (4.8) illustrates the 95% conﬁdence interval of the mean bid schedule with K = 10. The dispersions between the upper and lower intervals are basically ranging from $0.05 CHAPTER 4. UNDERPRICING OF UNIFORM PRICE AUCTIONS 162

to $0.23 at the intercepts. Relative to the price level of $2.5 –$5, the estimated mean bid schedules are quite robust. The robustness becomes even better for the sampling case of K = 20. The second goal for the empirical procedure is to compare the calibrated mean bid schedule to the hypothetical bid curves of truthful bidding and no trading bidding. With the values of parameter c obtained, we only need to recover M and λ in order to do such comparisons. Note that

M Q M Q a + bµ = · + (c − b)µ + bµ = · + cµ 1 + M N 1 + M N

M N h = (a + bµ) − cµ 1 + M Q Given how we deﬁne c, we can next solve for λ

N − 2 − M λ = c(N − 1)(1 + M)

Table (4.7) lists the calibration results for M and λ.

4.4.4 Counterfactual Analysis

With the calibrated parameters of λ, we can get the hypothetical auction clearing price when there is no trading market exists. Under truthful bidding, bidder i’s demand curve is just his marginal value curve,

1 p = v − λq ⇒ q = (v − p), i i i λ i so the mean bid schedule is

1 Q q = (µ − p), E(ptruth) = µ − λ . λ N

In the case of strategic bidding with trading,

M Q q = · + (c − b)µ + bv − cp, i 1 + M N i CHAPTER 4. UNDERPRICING OF UNIFORM PRICE AUCTIONS 163

Table 4.7: Mean of Calibrated Parameters M and λ B = 1000

Auction K = 5 K = 10 K = 20 Number M λ M λ M λ (×10−4) (×10−4) (×10−4) 1 0.66 10 0.67 8.57 0.73 8.27 (0.48) (3.24) (0.07) (1.45) (0.03) (0.73) 2 8.02 2.75 9.42 2.76 7.32 1.73 (1.99) (0.75) (3.04) (0.55) (4.44) (0.57) 3 2.60 4.69 4.65 2.97 3.96 3.26 (0.23) (0.71) (0.84) (5.75) (0.36) (0.44) 4 2.01 4.30 4.33 2.47 4.28 5.52 (0.17) (0.72) (0.65) (0.67) (0.11) (0.42) 5 2.31 0.97 2.03 1.64 2.42 2.11 (0.91) (0.40) (0.43) (0.77) (0.15) (0.58) 6 2.07 1.68 1.82 1.14 1.02 1.17 (0.54) (0.17) (0.98) (0.22) (0.76) (0.27) 7 2.67 0.74 2.51 0.56 2.74 0.34 (0.13) (0.14) (0.30) (0.09) (0.17) (0.08) 8 2.73 0.53 3.24 0.24 5.73 0.30 (0.67) (0.10) (1.11) (0.09) (2.73) (0.09) CHAPTER 4. UNDERPRICING OF UNIFORM PRICE AUCTIONS 164

meaning that the mean bid schedule is

M Q N − 1 Q q = · + c(µ − p), E(ptrading) = µ − λ . 1 + M N N − 2 − M N

If there is no trading opportunity, ω = 0 thus ρ = 0 and equivalently M = 0, the equilibrium strategy is then N − 2 q = c(θ − p) = (θ − p), i i λ(N − 1) i so that the mean bid schedule is

N − 1 1 N − 2 Q q = · (µ − p), E(pno-trading) = µ − λ . N − 2 λ N − 1 N

Due to the fact that N − 2 N − 1 1 < < , N − 1 N − 2 − M if the same group of bidders compete in uniform auctions under these three scenarios, the underpricing will be the worst for the case of strategic bidding with trading. However, once trading is prohibited, non-compliance bidders will not participate in the auctions anymore because there is no speculative opportunities allowed. As a result, the number of participating bidders decreases, leading clearing price to decrease and underpricing to increase as the comparative statics in Section 4.3.3 have predicted. It means that the elimination of trading will have ambiguous effect on the underpricing. I therefore test whether the combination of these two opposite forces result in higher or lower clearing prices for each K value in each auction. Table (4.8) reports the results, where NC denotes the number of compliance bidders in each auction. We can see that compared to the real auction clearing prices the directions of the clearing price changes for the no trading scenario are mixed. In conclusion, the existence of the trading market won’t necessarily worsen the underpricing problem of uniform auctions as long as non-compliance bidders are active to enter auctions and reinforce the competition. CHAPTER 4. UNDERPRICING OF UNIFORM PRICE AUCTIONS 165

Table 4.8: Counterfactual Clearing Prices of the No Trading Case B = 1000

C Auction # N K = 5 K = 10 K = 20 bs with trading 1 33 3.87 3.92 3.93 3.07 (0.12) (0.05) (0.03) 2 42 3.49 3.49 3.56 3.38 (0.05) (0.04) (0.04) 3 31 3.24 3.41 3.38 3.51 (0.07) (0.57) (0.04) 4 36 3.01 3.16 2.91 3.23 (0.06) (0.06) (0.04) 5 34 2.59 2.54 2.50 2.19 (0.03) (0.06) (0.05) 6 43 2.03 2.07 2.06 2.05 (0.01) (0.01) (0.02) 7 37 2.02 2.04 2.06 2.07 (0.01) (0.01) (0.01) 8 35 1.95 1.98 1.98 1.88 (0.01) (0.01) (0.01) CHAPTER 4. UNDERPRICING OF UNIFORM PRICE AUCTIONS 166

4.5 Summary

In this chapter, I build an uniform price auction model to capture the particularity of emission permit auctions under a cap-and-trade system. The model allows for both private value and common value component so that it can well describe the fact that entities participating auctions of emission permits have both the private use value determined by their abatement technology and the common resale value intrinsically formed on the competitive trading market. The model predicts that the clearing price of allowances auction is usually underpriced in equilibrium compared to the secondary market prices. The magnitude of underpricing is positively affected by the liquidity of secondary market and the volatility of trading price, as well as how accurate bidders’ signals for resale value are. My empirical procedure builds on the theoretical model to analyze the summary statistics of the RGGI CO2 auctions and the futures trading price time series on CCFE. I show the recovered mean bid schedules for each of the eight RGGI auctions, and conduct counterfactual analyses to compute the hypothetical auction clearing price when there is no resale market affecting bidder’s strategy. The results conclude that although there is an inherent underpricing problem associated with the uniform price auction, the presence of a liquid and competitive secondary trading market won’t necessarily exacerbate the degree of underpricing. However, by encouraging bidders to submit more number of bids and allowing non-compliance bidders to participate the auctions may help mitigate the underpricing issue. The future extension of this chapter lies in the potentiality of introducing a dynamic model for the uniform price auction to characterize bidder’s behavior on the secondary market before or after the auctions. I currently assume a static environment. Although bidders collect information before the auctions to get signals for resale value and to determine their bid schedules accordingly, the auction is conducted as a static game. However, since the auctions can happen frequently (e.g., quarterly), the identical emission permits are actually sold in a sequence of auctions, in which bidders who participate in more than one auction may have a dynamic strategic response. Also, after the auction, if bidders decide to resell the allowances, or buy more allowances as they have reduced their demand in the auction, a dynamic model may better capture the strategic substitution between the two CHAPTER 4. UNDERPRICING OF UNIFORM PRICE AUCTIONS 167

markets. In conclusion, even with the static perspective, this chapter provides important insights to evaluate the performance of the RGGI auctions. It provides empirical evidence to support several auction design features for future cap-and-trade programs, which will be discussed detailedly in Chapter 5. CHAPTER 4. UNDERPRICING OF UNIFORM PRICE AUCTIONS 168

Figure 4.6: Downward Bias of Discrete Bid Price Statistics

(a) Bidder i’s Bids (b) Bidder j’s Bids

Figure 4.7: Calibrated Mean Bid Schedules CHAPTER 4. UNDERPRICING OF UNIFORM PRICE AUCTIONS 170

Figure 4.8: Conﬁdence Interval of Mean Bid Schedules Chapter 5

Policy Implications and Emission Auction Designs

5.1 Pricing Scheme – Enhance Allocative Efﬁciency

There is a broad consensus among economists specializing in auction design that a discriminatory auction is not best-suited for emission permits (Lopomo et al. (2011)). Among the several disadvantages of this auction format, perhaps the most unfavorable one is that even in an idealized “perfect competition” setting in which all bidders lack market power, the discriminatory auction will not lead to an asymptotically efficient distribution of emission permits. In Chapter 3, I have shown that there have been significant efficiency loss present in the EPA’s SO2 allowance auctions. Looking at existing nationwide and regional cap-and- trade programs, they are always large scale programs with a large number of compliance firms. Even though the program participants vary in sizes, the market of emission permits have never been dominated by only a few large players who can unilaterally manipulate the auction or the trading market as a monopoly or oligopoly. Under such circumstance, the multi-unit auction models developed in Wilson (1979), Ausubel and Cramton (2002), Hortacsu (2002a, 2002b) and Kastl (2011) provide a framework to understand bidders’ strategic incentives under different auction formats, and to evaluate the efficiency-revenue tradeoff associated with an auction design.

171 CHAPTER 5. POLICY IMPLICATIONS AND EMISSION AUCTION DESIGNS 172

Under the above structural framework, we can safely conclude that if the marginal abatement cost for the regulated gas emissions changes moderately by abatement quantity, bidders have relatively flat marginal valuations in the emission permit auction, thus the discriminatory auction will result in an outcome with uncertainty in raising higher revenue than uniform price auction but with a certainty in efficiency loss. For the purpose of a better chance in achieving allocative efficiency, uniform pricing rule should be adopted rather than discriminatory pricing rule. Under the uniform pricing rule, the auction format could be either sealed-bid uniform price auction or (English) clock auction. Another important advantage of the uniform pricing rule, cited by many economists, is that it invites wider participation since all winning bidders pay the same price and hence do not need to invest in predicting the market-clearing price. As Friedman (1991) argued, by contrast, “[the discriminatory auction] tends to limit the market to specialists who may also be more likely to collude.” Many bidders dislike the price variation associated with the discriminatory price auction format in sales of homogeneous items. For example, in spectrum auctions like the RCA auction, executive officers bid on their companies’ behalf. The highest bidders are uncomfortable having to explain to their superiors or shareholders why others get to pay less for an identical transponder or license. Even individual bidders may care more about “paying too much” than about the chance of getting a bargain. An advantage of uniform price auctions is that they insulate bidders (and perhaps their bosses too) from price risk of this kind. Porter et al. (2009) comments that “Auctions that use discriminatory pricing pose an ex post problem to participants, particularly those who are bidding agents for firms. Specifi- cally, nearly all participants who are included in the final allocation realize that they could have bid less and still obtained the same set of units. Furthermore, since discriminatory pricing encourages strategic bidding below value, there is often a set of bidders who could have made it into the final allocation by submitting a bid that more truthfully revealed their willingness to pay for the good, but failed to do so in their pursuit of extra profits. Thus, discriminatory auctions pose a sort of catch-22 to bidders: a bidder who wins has paid too much; a bidder who loses has bid too little. Auctions that use a uniform pricing rule avoid CHAPTER 5. POLICY IMPLICATIONS AND EMISSION AUCTION DESIGNS 173

this problem: all bidders pay one price, so no winning bidding agents appears to have se- cured a poorer contract for his principal than any other winning agent. More over, uniform pricing rules can encourage more revelation of bidders’ willingness to pay.” On a side note, uniform pricing creates a new problem for the government seller. The bidding information that is used to determine the price is available to the public, who may be disturbed by what they perceive as excessive surplus left in the bidders pockets. The auctioneer could potentially be second-guessed by the tax payers or end consumers for not extracting maximal revenue from the auction bidders. Keeping the bidding information secret could resolve this problem, but (English) clock auction can also excel in this context since ascending clock stops when auction clears and no bidding at prices higher than the clearing price will happen. There will be no information showing any market participants have higher willingness-to-pay for the allowances.

5.2 Reserve Price – Combat Underpricing

As seen in many legislation proposals, the single-round sealed-bid uniform price auction format is likely to be adopted in most future emissions cap-and-trade programs because of the simplicity of implementation, the equality in cost bearing, and the provision of a single price signal for trading market. Should a uniform price format be chosen to auctioning emission permits in a cap-and-trade program, the auction design must address the issue of underpricing in uniform price auction. Several policy instruments can be helpful in alle- viating underpricing and improving auction performance, among which setting a reserve price is particularly powerful. “A reserve price is an auction price below which the seller chooses to retrain ownership of the item rather than sell it.” If the reserve price is triggered, the reserve price becomes the auction clearing price, and only bids at or above that level are accepted. From the empirical analysis in Chapter 4, we have noticed that in the RGGI CO2 auctions, the minimum bids are always at the reserve price level, meaning that the reserve price has been binding all the time. If the number of bids submitted by bidders is usually stable regardless the level of the reserve price, removing the reserve price will make the price points even more sparse when auctioneer aggregates the projected demand. In that case, the downward bias of the CHAPTER 5. POLICY IMPLICATIONS AND EMISSION AUCTION DESIGNS 174

step function bids on the clearing price will be larger due to the wider steps. So setting a proper reserve price can help reduce the underpricing in auctions. The reserve price are is especially important where the bidders have very asymmetric willingness to pay for an item or asymmetric information or when participation in the auction is low. Reserve prices are also very important in reducing the potential damage from collusion because they reduce the profitability of collusion. This is true whether the collusion is tacit or explicit. The importance of reserve prices in limiting collusion is strongly supported in the theoretical literature and in empirical examinations of auction performance (Ausubel and Cramton (2002)). The academic literature and numerous notorious examples of failed auctions point to a credible and efficient reserve price as one of the most important aspects of auction design. Although it is desirable to find out the optimal reserve price at least theoretically, research on multi-unit auctions has not been able to tackle the task. Since for whatever multi- unit auction formats there might be multiple Bayesian Nash equilibria of auction outcomes and usually there is no closed-form solution of bidding strategy for auction models, it is very difficult to prove the existence of an optimal reserve price, let alone determine its price level. However, there are several practical methods to set a proper reserve price for emission permit auctions. One method of setting the reserve price for an emission permit auction would be to set it at a level close to but below the expected clearing price for the auction, which is likely to be very close to the current price for allowances in the secondary market. Based on this idea, Shobe (2010) extensively discussed the current market reserve price (CMRP). An alternative method for setting the reserve price would be to set it to a level that would maintain a minimum rate of progress in reducing emissions below business as usual and to maintain the value of investments in new technologies. In this case the reserve price would not be directly linked to market prices, but instead would grow at a constant rate, such as the rate of interest. For example, the proposed California cap-and-trade program rules specifies that the allowance reserve price will be $10 per metric ton for vintage 2012 allowances and $11.58 per metric ton for 2015 allowances in the 2012 auctions. The auction reserve price for both current and future vintage allowances will increase by 5 percent plus the rate inflation each year.” Similarly, the American Clean Energy and Security Act of 2009 CHAPTER 5. POLICY IMPLICATIONS AND EMISSION AUCTION DESIGNS 175

passed out of the House Committee on Energy and Commerce on May 21, 2009 includes the auction price provision, which imposes a minimum price for auctioned allowances of $10 in 2012, escalating by the rate of inﬂation plus 5% per annum. Besides the determination of an appropriate level for the reserve price, there are some other implementation details should be emphasized:

1. The reserve price has to be strictly binding even if the aggregate demand above reserve price is insufﬁcient for the total supply;

2. In order to maintain the integrity of the reserve price, the unsold allowances may be retired, may be rolled forward to the next auction, or may be placed in a “contingency bank” to be kept out of circulation temporarily;

3. Set a ceiling for auction clearing price, and infuse stored “contingent permits” back into circulation once the clearing price hits the ceiling, until the added supply can satisfy the excessive demand.

Last but not the least, the reserve price should be pre-announced. Due to the transparency requirement of auction implementation, as well as the reality of how bidders respond to auction design features, it makes more sense to disclose and commit to an announced reserve price before the auction.1

5.3 Minimize Friction of Entry and Bidding Costs

As discussed in section 3.2.3 and section 4.4,2, bidders in emission permit auctions only submit a limited number of bidpoints even though there is no restriction on the maximal

1In regular repeated auctions by a government, it may be difﬁcult to prevent bidders from learning the reserve price. An agency must have a rule for setting the reserve. Over time, smart bidders will be able to infer the rule for the setting of the reserve and will be able to bid on the basis of this information. Even if the reserve is set with randomness, over time it will likely be possible to infer the distribution of the randomization method. Thus, many bidders will have a reasonable estimate of the reserve price even thought the government agency is operating on the assumption that the reserve price is not known. The RGGI auction design experts conclude that it is not a good strategy to have undisclosed reserve price, since it cannot be assumed that the strategy for selecting the reserve will not become known to the bidders. It is better design to assume that bidders will be able to obtain any information reasonably available and hence make the reserve price public from the outset. CHAPTER 5. POLICY IMPLICATIONS AND EMISSION AUCTION DESIGNS 176

bidpoints allowed. Kang and Puller (2008) suggest several possible interpretations of the fact that a bidder does not submit a bid at every possible price point. One possibility is that there is some (unmodeled) cost to adding a bidpoint, and that cost outweighs the expected benefits of “fine tuning” the bid function.2 Kastl (2008) derives a model of bidding in step functions that explicitly models the cost of submitting bidpoints, and he estimates bounds on the marginal cost using bid data in the Czech treasury auctions. The estimates suggest that the costs of going from 1 to 2 bidpoints can total as little as $2 and as much as $150, while the upper bound on costs of the second bidpoint is as low as $13 and as high as $360. Intuitively, adding an additional bidpoint at some locations may yield only a small amount of additional expected profit, and a bidder may not find it worthwhile to compute and submit that bidpoint. McAdams (2008), Chapman, McAdams and Paarsch (2006) find that the additional benefit for bidders to use finer bids is very small. I have shown in Section 4.4.3 that if bidders each submit too few bidpoints in an emission permit auction, the low bid resolution can potentially magnify the underpricing problem as the lower bid resolution3 casts a downward bias on the auction clearing price. Be- sides this, it should also be in auctioneer’s interest to see a higher bid resolution due to several reasons. For example, by receiving more bidpoints from each bidder, the auctioneer (regulatory authority) can collect better information regarding market participants marginal abatement cost in reducing emissions. This is very useful in setting an appropriate reserve price for upcoming auctions in the same cap-and-trade program. Even more, such information can help evaluate whether the secondary trading market is in a healthy condition. Another reason that a higher bid resolution is desirable lies in the fact that the incremental bid quantities between a bidder’s bidpoints will be smaller if he submits more bidpoints, and it helps prevent that one or two bidders end up winning a large amount of allowances. Combining higher bid resolution with setting an upper limit of allowed cumulative bid quantity, bidders tend to bid more aggressively and competitively in the auction. Bidders are willing to submit more bids only if the cost of submitting bids are low. In the past, some programs have relied on paper submission of bids for the purpose of authenticity in submission, low risk of mistaken bids and so on. For example, the EPA auctions for SO2 2Another interpretation, suggested by Nautz (1995) and Hortacsu (2002), is that the monotonicity constraint is binding at the unobserved bidpoints. 3The bid resolution here means how many bidpoints a bidder submit to auctioneer in his demand schedule. CHAPTER 5. POLICY IMPLICATIONS AND EMISSION AUCTION DESIGNS 177

allowances required bidders to mail or fax in their bids one week ahead of the auction date. This method was used all the way from 1993 till 2009 in EPA annual auctions. But the inflexibility in adjusting bids and the time cost of compiling and submitting the bids strongly discourage bidders to submit large number of bids. As a result, the average number of bids in each EPA SO2 auction range around 4 - 6 bids. For the future cap-and- trade auctions, it is suggested to adopt online platform like the RGGI COATS system. With a friendly user interface and a real-time response algorithm checking whether the bids input are abiding the minimum bid number rule as well as other rules, it can motivate bidders to submit more bid points at very low cost. In Section 4.2.1, I have discussed that one possible factor leading to the inefficiency of emission permit auctions is the partial participation. If those compliance firms that enter the auction are only a small portion of all program participants, they may not provide good representation for the distribution of abatement cost in the allowance market. If they tend to all have lower abatement costs, the auction outcome will be very inefficient with the perspective of the allocative efficiency in the entire cap-and-trade system. An unfavorable consequence of this circumstance is that the auction clearing will be systematically lower than a market equilibrium. If the participation is only partial, i.e. many compliance facilities choose not enter auctions, it likely implies high friction of entry or high transaction costs. Linking the auction platform and trading platform together can create a synergy for the emission permit market participants, because they are most likely already have accounts set up in the trading platforms with their financial assurance constantly monitored. This can significantly reduce the operation costs, transaction costs, as well as entry costs, such as the liquidity friction imposed by requiring financial deposits much in advance or in certain payment forms that are not preferred by bidders. This has been experimented in the EU ETS auctions. Germany, Lithuania, Netherlands, and Austria all hold their auctions through the European Energy Exchange (EEX), which is a leading operator of regulated global futures exchanges, clearing houses and over-the-counter (OTC) markets. Therefore, it is important for the cap-and-trade programs to emphasize policies that facilitate the growth of a liquid secondary market. CHAPTER 5. POLICY IMPLICATIONS AND EMISSION AUCTION DESIGNS 178

5.4 Prevent Collusion and Market Manipulation

As we have discussed in Section 2.5, transparency in bidding is a common objective of federal auctions and procurements, but pre-auction transparency in the form of transparent registration, and real-time transparency in the form of revealing the identities of bidders can have unintended pro-collusive effects. Presumably, a primary motivation for transparency in bidding is the need to allay fears about corruption. In this case, however, the remedy is simple – post-auction transparency. Enough information regarding auction outcomes should be made available after the auction (at least to a monitoring authority) to detect any illicit activity. However, collusion in emission permit auctions can also be tactic rather than explicit. In uniform price auction, bidders exercise their monopsonistic power over the residual supply is acting out on their own interests without communicating or conspiring with other bidders. Such tactic collusion usually roots in the presence of market power. The ﬁrst step to tackle this issue calls for setting maximum bid capacity (sum of bid quantity from all bidpoints from one bidder) to limit the exercise of unilateral market power. To minimize collusion and other forms of market manipulation is an indirect method to reduce inefﬁ- ciency. Therefore, it is suggested that regulatory authority monitors each auction closely and retains the possibility to slightly modify auction rules for collusion prevention from time to time. Chapter 6

Conclusions

Starting off from the main idea that a carefully designed allowance auction can help maximize the beneﬁts of the cap and trade program, this dissertation tries to empirically analyze several key criteria for a well-designed allowance auction include:

1. Allocatively efﬁcient – getting allowances to those who value them the most;

2. Raising reasonable revenues from the sales of a valuable public asset;

3. Providing accurate price signals and helping to minimize price volatility;

4. Perceived as fair, transparent, and understandable to participants and the public;

5. Avoid collusive behavior by bidders and providing good signals about market prices;

6. Low administrative costs, low transaction costs for bidders;

7. Compatible with existing electricity and energy markets.

One major contribution of this work is that it introduces a “revealed preference” type of econometric method from the Industrial Organization literature into Environmental Eco- nomics study. Unlike most previous research on emission permit auctions that uses laboratory experiments to compare auction formats, I use actual auction data to conduct empirical analyses. In Chapter 3, I follow the econometric model of sealed-bid discriminatory multi- unit auction ﬁrst proposed by Hortacsu (2002b) and later improved by Kastl (2011) that use

179 CHAPTER 6. CONCLUSIONS 180

a structural approach to estimate bidders’ marginal valuations of emission allowances and compare counterfactual auction revenue under hypothetical auction format with uniform pricing scheme. My results show that the discriminatory auction adopted by EPA to sell

SO2 emission permits under the Acid Rain Program has suffered from an average efﬁciency loss of 7.14%, while it could not overwhelmingly outperform other auction formats with respect to extracting revenue either. To a degree, my study in Chapter 3 revisits the heated debate on the effectiveness of

SO2 allowance auction back in the late 1990s (Cason (1993), Cason (1995), Cason and Plott (1996), Joskow et al. (1996), Joskow et al. (1998), Ellerman et al. (2000)). At the time, the controversy seemed to be resolved by the fact that auction price close tracked the secondary market price and the price of SO2 allowances remained stable during Phase I of the ARP. However, there has not been any further research looking at the performance of SO2 allowance auction since the start of Phase II in 2000, after which the regulation scope enlarged from covering only 263 dirtiest entities to all electricity generating facilities in the United States. My analysis in Chapter 3 tries to get a more holistic view of the effectiveness of SO2 allowance auction over the entire period from 1993 to 2009. Re- evaluating this market after almost a decade is necessary and important, because not only the affected firms include the entire power industry, but also the stringency of emission cap is tightened significantly during Phase II, which could be a real stress test for the policy design in the cap-and-trade program of SO2. Another contribution of this paper, which is reflected in my study in Chapter 4, lies in the construction of a new model of emission permit auctions that can better characterize the particular information structure of emission permit market. I take into account that emission permits have both private use value and common resale value, so that my model link allowance auctions with the secondary trading market, which is crucial for a cap-and-trade program. More importantly, my model enables a structural analysis to econometrically analyze the limited auction data available for the RGGI CO2 allowance auctions. More often than not, like the RGGI program, detailed bidding data are required to be confidential. I come up with a statistical procedure based on my model to test the effect of secondary market interaction and speculators’ participation with only the summary statistics of auction data for as few as eight auctions. By my knowledge, this is the first structural study on CHAPTER 6. CONCLUSIONS 181

the RGGI auctions with actual RGGI data. I pointed out the underpricing issues related to uniform price format adopted in the RGGI auctions, and provided policy suggestions in Chapter 5 regarding how to improve the auction designs for emission trading programs. It should be point out that the analyses in this dissertation have been done under a framework of symmetric strategic equilibrium of multi-unit auctions, which are built on several assumptions. For example, the compliance facilities that participate the auctions are relatively similar. Even though the models allow them to vary in sizes to an extent, the framework will not work well if there exist one or two very large ﬁrms dominating the market. Also, the observed auction outcomes from released auction data is assumed to be the results of rational bidders exercising their equilibrium strategies according to auction theory. In reality, the current market status and auction outcomes may not necessarily be the equilibria. In addition, the conclusions drawn from the empirical results are based on the comparisons of actual auction data to the hypothetical best-case scenarios of using alternative auction formats, which may not necessarily be realized if the alternative auction formats are adopted in practice. The analyses in this dissertation aim to provide a perspective of empirical examination, which has been a gap in the past literature. However, it requires caution to apply the conclusions from each chapter. It will not be appropriate to generalize these results to other contexts without being aware of above limitations. To ensure the robustness of the major conclusions and recommendations in this dissertation, further research and improvement is very necessary. And we also need to wait for more cap-and-trade programs to incorporate emission permit auctions in their operation, so that we have more empirical data in a few years. A lot of the issues addressed in the previous chapters await to be revisited once more data are available. Nonetheless, it is important for us to start paying attention to these issues now, and to keep these issues in mind when designing future emission permit auctions. Appendix A

Appendix

A.1 Appendix to Chapter 1

Table A.1: Summary of Cap-and-Trade Programs in Chapter 1

Target Emissions Programs CFCs CFC Trading under Montreal Protocol Acid Rain Program (ARP) Clean Air Interstate Rule (CAIR) SO 2 Cross-State Air Pollution Rule (CSAPR) Regional Clean Air Incentives Market (RECLAIM) NOx Budget Trading Program (NBP) Clean Air Interstate Rule (CAIR) Cross-State Air Pollution Rule (CSAPR) NOx Regional Clean Air Incentives Market (RECLAIM) Texas Ozone Emission Cap-and-Trade Programs Illinois Emissions Reductions Market System United Kingdom Emission Trading Scheme (UK ETS) European Union Emission Trading Scheme (EU ETS) U.S. Regional Greenhouse Gas Initiative (RGGI) CO2 * New Zealand Emissions Trading Scheme (NZ ETS) * California AB-32 and Western Climate Initiative * American Clean Energy and Security Act, 2009 * Australia Clean Energy Bill, 2011 * Programs still in plan or without the emission cap.

182 APPENDIX A. APPENDIX 183

A.2 Appendix to Chapter 2

Table A.2: List of Business Type Bidders in SO2 Spot Auctions

Bidder Name Times Bidder Name Times ABN AMRO 3 AEPI 1 AES Corp. 1 AIG Trading Corp. 1 Alabama Power Co. 2 Allegheny Energy Supply Co. 1 Allegheny Power System 5 Allowance Holding Corp. 4 Alpha 3 Alvin Kaplan 1 Ameren Energy Generating Co. 1 American Electric Power 8 American Municipal Power-Ohio 2 Aquila Energy 4 ARPA 2 Avista Corp. 1 AYP Energy 1 Baltimore Gas and Electric Co. 3 Banc One Capital Markets 1 Bear Energy 1 BP Energy 1 Brian Utting 1 Buckeye Power 1 Canterbury Coal Co. 2 Cantor Fitzgerald 12 Carolina Power & Light Co. 4 CATEX Vitol Electric 2 Cedar Falls Utilities 3 Centaurus Energy 1 Centerior Energy Corp. 2 Central Illinois Power Service Co. 1 CEPO 1 CF Environmental 1 Champion Clean Energy 1 Cinergy Services 2 City of Springﬁeld, Illinois 1 City Utilities of Springﬁeld 1 Cleveland Electric Illuminating Co. 1 Coaltrade 1 Colorado Springs Utilities 2 Constellation Power Source 6 Coral Energy Holding 1 Credit Suisse Energy 1 Dayton Power & Light Co. 4 Denver City Energy Associates 1 Detroit Edison Co. 2 DigiLog Global Environmental 1 Dominion Energy Marketing 1 Duke Power 1 Duke Power Co. 5 ED & F Man International 1 Edison Mission Energy 3 Electric Energy 1 Element Markets 1 Emissions Trading 1 EMMT 1 Energy Planning Tools 1 Enron 6 Evolution Markets 1 Fortis Energy Marketing & Trading 1 Georgia Power Co. 1 Gilbert Leistner 1 Continued on next page APPENDIX A. APPENDIX 184

Table A.2 : Business Type Bidders in SO2 Spot Auctions (continued) Bidder Name Times Bidder Name Times Granite Ridge Energy 2 Grey K Environmental 1 Gulf Power Co. 2 H. Ted Santo 1 Hoosier Energy REC. 3 Illinois Power 7 Indiana Municipal Power Agency 1 Indianapolis Power & Light Co. 2 Innovative Business Engineering 1 Iowa Electric Light and Power 1 James Maltman 1 Jemison Investment Co. 1 JP Morgan 2 Kentucky Utilities Co. 1 Kerr-McGee Coal Corp. 2 Koch Carbon 1 KS&T 2 KUA Cane Island Unit 1 LG & E Energy Marketing 1 Louis Dreyfus Energy Services 2 LUME 2 Macquarie Cook Power 1 Man Financial 2 Marine Coal Sale Co. 3 Mark Battaglia 1 Massey Energy Co. 1 Merrill Lynch Commodities 2 MET 1 Milton R. Young Station 2 Mirant 2 Mississippi Power & Light Co. 2 Morgan Stanley 6 MPA 1 Muscatine Power and Water 1 Neil Benjamin 1 Northeast Utilities Service Co. 1 NRG Power Marketing 1 Ohio Power Co. (AEP) 1 Ohio Valley Electric Corp. 1 Olduvai Gorge 1 Omaha Public Power District 1 Patriot 1 PECO Energy Co. 2 PG&E Energy Trading - Power 2 Phibro 1 Phil Jensen 1 Potomac Electric Power Co. 3 PPL Generation 2 PSEG Energy Resources and Trade 4 PSI Energy 1 Public Service Co. of New Hampshire 1 Public Service Electric and Gas Co. 2 Reliant Energy 2 Richmond Power and Light 1 RMP 1 Rochester Gas & Electric Corp. 2 Roger Lessly 1 Sacramento Municipal Utility District 2 Saracen Energy 2 Savannah Electric and Power Co. 1 SCANA Corp. 1 Shell Energy North America (US) 1 South Carolina Electric & Gas Co. 2 South Carolina Fuel Co. 2 South Carolina Public Service Authority 2 Southern Illinois Power Cooperative 1 Southern Indiana Gas & Electric Co. 3 Southwest Public Service Co. 1 St. Joseph Light & Power Co. 3 Stephanie Pearce 1 Continued on next page APPENDIX A. APPENDIX 185

Table A.2 : Business Type Bidders in SO2 Spot Auctions (continued) Bidder Name Times Bidder Name Times SUEZ Energy Marketing NA 2 Sunbury Generation 1 Tampa Electric Co. 3 Tennessee Valley Authority 2 The Cincinnati Gas & Electric Co. 2 The Dayton Power & Light Co. 7 The Detroit Edison Co. 5 Transalta Energy Marketing U.S. 2 TVA 1 TXU Portfolio Management Co. 1 UGI Development Co. 1 United Engineers & Constructors 1 Virginia Electric Power Service Co. 1 Virginia Power 1 Wholesale Power Services 2 Wisconsin Electric Power Co. 1 WPS Power Development 3 APPENDIX A. APPENDIX 186

Table A.3: List of Potential Bidders in RGGI CO2 Auctions

Bidder Name Times Bidder Name Times Adirondack Council. 6 Aeolus Fund II Master Fund 2 AES Eastern Energy 11 Aircraft Services Corp. 8 Algonquin Windsor Locks 4 Allegheny Energy Supply Company 4 ANP Funding I 10 Astoria Energy 7 Astoria Generating Company 10 Barclays Bank 9 Basil P. Bourque 1 BG Dighton Power 1 Boston Generating 8 Brick Power Holding 11 Bridgeport Energy 4 Brookﬁeld Energy Marketing 7 Brooklyn Navy Yard Cogen Partners 7 Burlington Electric Department 1 Caithness Long Island 9 Calpine Energy Services 11 Carbon Lighthouse Association 1 Cargill Power Markets 3 Castleton Power 6 CE2 Carbon Capital 2 CE2 Environmental Markets 3 CE2 Environmental Opportunities I 3 Chambers Cogeneration 8 Clean Air Conservancy 1 Clean Air Gardening 1 Conectiv Energy Supply 7 Conn. Municipal Electric Energy Coop. 7 ConocoPhillips Co. 8 Consolidated Edison Comp. of NY. 11 Constellation Energy Commodities Group 10 CP Energy Marketing (US) 2 C-Quest Capital 3 Craig Hart 1 DC Energy Marketing 1 Delaware Municipal Electric Corp. 5 DigiLog Global Environmental Master Fund 3 Dominion Energy Marketing 11 DTE Carbon 7 Dynegy Marketing and Trade 11 E.ON Energy Trading SE 2 Eco-Energy 1 Element Markets 5 Empire Generating Co. 3 Energy America 1 Energy Echelon 2 EquiPower Resources 4 Evolution Markets 2 FES Fund I 2 FirstLight Power Resources Mgmt 1 Five Rings Capital 1 Four Oaks Interests 2 FPL Energy Power Marketing 2 GDF SUEZ Energy Marketing NA 7 GenOn Energy Management 2 Global Inv. Alternatives Group 1 Granite Ridge Energy 4 Green Fund Partners 1 Green Mountain Power Corp. 3 H.Q. Energy Services (US) 8 Hawkeye Energy Greenport 1 Hess Corp. 11 ICAP United 1 Continued on next page APPENDIX A. APPENDIX 187

Table A.3 : Potential Bidders in RGGI CO2 Auctions (continued) Bidder Name Times Bidder Name Times Indeck Energy Services of Silver Springs 3 Indeck-Corinth Limited Partnership 7 Indeck-Olean Limited Partnership 6 Indeck-Oswego Limited Partnership 6 Indeck-Yerkes Limited Partnership 6 Index Capital Group 1 Integrys Energy Services 3 J. Aron & Co. 3 James S. Burrell II 2 Jamestown Board of Public Utilities 3 JP Morgan Ventures Energy Corp. 5 J-Power USA Development Co. 9 Koch Supply & Trading 4 Lake Road Generating Company 6 Laurence DeWitt 1 Logan Generating Company 7 Louis Dreyfus Energy Services 7 Macquarie Cook Power 3 Macquarie Energy 2 Massachusetts Bay Transportation Auth. 1 Massachusetts Muni. Wholesale Elec. Co. 11 Massachusetts Water Resources Authority 3 Masspower 1 Maxim Power Corp. 1 Mercuria Energy Trading 2 Merrill Lynch Commodities 7 Michael Forlini 1 Milford Power Company 5 Millennium Power Partners 10 Mirant Energy Trading 9 Morgan Stanley Capital Group 8 National Grid Gen. dba National Grid 11 New Athens Generating Company 10 NextEra Energy Power Marketing 7 North American Energy Alliance 10 NRG Power Marketing 11 Old Dominion Electric Cooperative 8 ORBEO 2 Panda Brandywine 1 Power Authority of the State of New York 9 PPL EnergyPlus 9 PSEG Energy Resources & Trade 11 Public Service Co. of New Hampshire 11 RBC 11 RC Cape May Holdings 1 Rochester Gas and Electric Corp. 8 RPL Holdings 1 Saranac Power Partners 2 Selkirk Cogen Partners 11 Sempra Energy Trading 5 Seventh Generation Advisors 1 Shell Energy North America (US) 2 Statkraft Markets GmbH 5 Sterling Planet. 1 Stonyﬁeld Farm 2 SUEZ Energy Marketing NA 2 Sunoco Power Generation 3 TAQA Gen X 9 Tauber Oil Co. 1 The William & Flora Hewlett Foundation 1 Tradax Green Energy 5 TransCanada Power Marketing 8 Universal Carbon 2 Verso Paper Corp. 9 Village of Freeport 3 Vitol 10 William P Short III 1 Wing Fuel 2 APPENDIX A. APPENDIX 188

Table A.4: EU ETS Allowance Auctions in Phase II

Date Member State Auction Platform Quantity Weekly Tuesdays Germany EEX 300,000 spot Weekly Wednesdays Germany EEX 570,000 futures (Jan-Oct) Jul 5, 2012 UK UK DMO 4.0 million Jun 14, 2012 Netherlands EEX 1 million Jun 7, 2012 UK UK DMO 4.0 million May 10, 2012 UK UK DMO 4.0 million Apr 19, 2012 Netherlands EEX 1 million Apr 16, 2012 Austria Climex 300,000 CA + 100,000 NCA Mar 22, 2012 Netherlands EEX 1 million Mar 15, 2012 Lithuania EEX 850,000 Mar 8, 2012 UK UK DMO 3.5 million Feb 23, 2012 Netherlands EEX 1 million Feb 9, 2012 UK UK DMO 3.5 million Jan 26, 2012 Lithuania EEX 850,000 Dec 13, 2011 Lithuania EEX 850,000 Nov 28, 2011 Austria Climex 200,000 (competitive only) Nov 24, 2011 Netherlands EEX 2 million Nov 10, 2011 UK UK DMO 3.5 million Oct 27, 2011 Netherlands EEX 2 million Oct 6, 2011 UK UK DMO 3.5 million Sep 8, 2011 UK UK DMO 3.5 million Jul 7, 2011 UK UK DMO 3.5 million Jun 9, 2011 UK UK DMO 3.5 million Apr 11, 2011 Austria Climex 200,000 CA + 100,000 NCA Mar 10, 2011 UK UK DMO 4.4 million Feb 22, 2011 Germany∗ EEX 600,000∗ Feb 10, 2011 UK UK DMO 4.4 million Jan 13, 2011 UK UK DMO 4.4 million Nov 18, 2010 Netherlands Climex 2 million Nov 8, 2010 Austria Climex 200,000 (competitive only) Nov 4, 2010 UK UK DMO 4.4 million Oct 27, 2010 Netherlands Climex 2 million Continued on next page APPENDIX A. APPENDIX 189

Table A.4 : EU ETS Allowance Auctions in Phase II (continued) Date Member State Auction Platform Quantity Oct 7, 2010 UK UK DMO 4.4 million Sep 9, 2010 UK UK DMO 4.4 million Jul 8, 2010 UK UK DMO 4.4 million Jun 19, 2010 UK UK DMO 4.4 million Apr 15, 2010 Netherlands DSTA 4 million Mar 23, 2010 Austria Climex 200,000 CA + 100,000 NCA Mar 18, 2010 UK UK DMO 4.4 million CA + 100K NCA Feb 4, 2010 UK UK DMO 4.4 million Jan 7, 2010 UK UK DMO 4.4 million CA + 500K NCA Nov 5, 2009 UK UK DMO 4.2 million Oct 13, 2009 Austria Climex 200,000 (competitive only) Oct 8, 2009 UK UK DMO 4.2 million Sep 10, 2009 UK UK DMO 4.2 million Jul 9, 2009 UK UK DMO 4.2 million Jun 4, 2009 UK UK DMO 4.2 million Mar 24, 2009 UK UK DMO 4 million Mar 16, 2009 Austria Climex 200,000 CA + 100,000 NCA Nov 19, 2008 UK UK DMO Appr. 4 million

∗Quantity was increased by 300,000 EUAs, because the auction scheduled on Feb 1, 2011 was canceled due to suspension of CITL transactions. APPENDIX A. APPENDIX 190

A.3 Appendix to Chapter 3

Table A.5: Details of Bidders - SO2 Spot Auctions

All Types Environmental Type Business Type Spot Total No. Avg. No. No. Avg. No. No. Avg. No. Max No. Auction Bids Bidders Bids Bidders Bids Bidders Bids Bids 2009 77 21 3.67 6 1.67 15 4.67 8 2008 96 19 5.05 6 1 13 6.92 15 2007 72 17 4.24 5 1 12 5.58 10 2006 78 22 3.55 5 2.4 17 3.88 10 2005 115 30 3.83 8 1 22 4.86 15 2004 64 21 3.05 10 1 11 4.91 14 2003 82 36 2.28 25 1.08 11 5 15 2002 53 25 2.12 16 1.13 9 3.89 12 2001 85 27 3.15 11 1.18 16 4.5 13 2000 85 30 2.83 13 1.17 17 3.94 12 1999 77 23 3.35 9 1.22 14 4.71 26 1998 109 35 3.11 17 1.35 18 4.78 31 1997 159 32 4.97 12 3 20 6.15 20 1996 139 36 3.86 17 2.12 19 5.42 19 1995 89 33 2.7 16 1.63 17 3.71 17 1994 103 26 3.96 7 1.29 19 4.95 25 1993 106 44 2.41 12 1.58 32 2.72 12 APPENDIX A. APPENDIX 191

Table A.6: CO2 Spot Auctions Details

Auction Clearing Cover No. of Winning Revenue Envir. Year Price Ratio Bidders Bidders (mil $) Demand 2009 62.00 7.14 21 11 8.72 25 2008 380.01 4.79 19 17 48.74 32 2007 433.25 2.43 17 14 55.55 25 2006 860.07 2.94 22 14 110.39 12 2005 690.00 3.95 30 17 87.81 11 2004 260.00 2.31 21 14 34.11 30 2003 171.80 4.95 36 20 21.48 29 2002 160.50 2.42 25 21 21.37 47 2001 175.00 3.85 27 12 22.36 32 2000 126.21 2.55 30 23 16.78 51 1999 200.55 3.34 23 11 31.06 31 1998 115.01 5.11 35 11 17.54 59 1997 106.75 8.16 32 23 257 1996 66.05 6.08 36 29 730 1995 130.00 5.11 33 26 287 1994 150.00 5.89 26 17 48 1993 131.00 6.43 44 21 8576 APPENDIX A. APPENDIX 192

A.4 Appendix to Chapter 4

A.4.1 Derivation of Conditional Expectation of ti by Ollikka (2011)

Deﬁne a multivariate normal variable,

Xi = (X1,X2,1,X2,2) = (ti,vi,Ii) with a mean vector,       µ1 E[ti] µ       µ =  µ ,  =  E[vi]  =  µ   2 1      µ2,2 E[Ii] (N − 1)µ and a covariance matrix, ! Σ11 Σ12 Σ = . Σ21 Σ22

Note that Cov[ti,Ii] = Cov[ti,∑ j6=i vi] and

2 Σ11 = Var[vi] = δ T T T ! 2 ! ! Cov[ti,vi] δ η1 Σ = Σ = = ≡ 12 21 2 Cov[ti,Ii] (N − 1)ρδ η2 ! Var[vi] Cov[vi,Ii] Σ22 = Cov[vi,Ii] Var[Ii] ! δ2 + τ2 (N − 1)ρδ2 = (N − 1)ρδ2 (N − 1)[(δ2 + τ2) + (N − 2)ρδ2] ! ∆ ∆ = 11 12 ∆21 ∆22

Inverse of Σ22 is, ! −1 1 det(∆11) −det(∆12) Σ22 = det(Σ22) −det(∆21) det(∆22) ! 1 ∆ −∆ = 22 12 . ∆11∆22 − ∆12∆21 −∆21 ∆11 APPENDIX A. APPENDIX 193

The conditional distribution of the random variable {ti vi,Ii} has an expected value,

! −1 vi − µ2,1 E[ti vi,Ii] = µ1 + Σ12Σ22 Ii − µ2,2 !T ! 1 η ∆ − η ∆ v − µ = µ + 1 22 2 12 i det(Σ22) −η1∆21 + η2∆11 Ii − (N − 1)µ " # η ∆ − η ∆ + (N − 1)(η ∆ − η ∆ ) = 1 − 1 22 2 12 2 11 1 21 µ ∆11∆22 − ∆12∆21

η1∆22 − η2∆12 η2∆11 − η1∆21 + vi + Ii ∆11∆22 − ∆12∆21 ∆11∆22 − ∆12∆21 and a variance, −1 Σ = Σ11 − Σ12Σ22 Σ21 . {ti vi,Ii}

Substitute above equations into the following expression of the conditional expectation of ti,

E[ti vi,Ii] = Aµ + Bvi +CIi , where

τ2 A = τ2 + (1 − ρ + Nρ)δ2 δ2[τ2 + (1 − ρ)(1 − ρ + Nρ)δ2] B = [τ2 + (1 − ρ)δ2][τ2 + (1 − ρ + Nρ)δ2] ρτ2δ2 C = [τ2 + (1 − ρ)δ2][τ2 + (1 − ρ + Nρ)δ2]

A.4.2 Vives (2011) Solution of the Uniform Price Auction Equilibrium

We have the ﬁrst order condition,

1 E[ti vi,Ii] = + λ qi + p (A.1) (N − 1)c and the conditional expectation,

E[ti vi,Ii] = Aµ + Bvi +CIi (A.2)

1 h i where Ii = b Q − (N − 1)a + (N − 1)cp − qi . As equation (A.1) and (A.2) must be equal,

h 1 i C h i + λ q + p = Aµ + Bv + Q − (N − 1)a + (N − 1)cp − q (A.3) (N − 1)c i i b i APPENDIX A. APPENDIX 194

1 Write the equilibrium strategy in the form of vi = b (cp − a + qi)], plug it into equation (A.3) to get

h 1 i Bh i C h i + λ q + p = Aµ + cp − a + q + Q − (N − 1)a + (N − 1)cp − q (N − 1)c i b i b i 1h i 1h i c h i = Aµ + CQ − aB − (N − 1)aC + B −C q + B + (N − 1)C p b b i b

Equating the coefﬁcients of qi and p on both sides, we need to solve three simultaneous equations:

 h i Aµ + 1 CQ − aB − (N − )aC =  b 1 0  1 1 b (B −C) = (N−1)c + λ   c b (B + (N − 1)C) = 1  h h i−1 i. a = CQ + 1 + A(B −C)µ B + (N − 1)C  (N−1)c λ  =⇒ 1 −1 b = (N−1)c + λ (B −C)  .  1 −1 c = (N−1)c + λ (B −C) B + (N − 1)C

To further solve the parameters, let’s write out the expressions for (B −C) and [B + (N − 1)C] in the form of,

δ2[τ2 + (1 − ρ)(1 − ρ + Nρ)δ2] − ρτ2δ2 B −C = [τ2 + (1 − ρ)δ2][τ2 + (1 − ρ + Nρ)δ2] δ2(1 − ρ)[τ2 + (1 − ρ + Nρ)δ2] = [τ2 + (1 − ρ)δ2][τ2 + (1 − ρ + Nρ)δ2] δ2(1 − ρ) = [τ2 + (1 − ρ)δ2]

δ2[τ2 + (1 − ρ)(1 − ρ + Nρ)δ2] + (N − 1)ρτ2δ2 B + (N − 1)C = [τ2 + (1 − ρ)δ2][τ2 + (1 − ρ + Nρ)δ2] δ2(1 − ρ + Nρ)[τ2 + (1 − ρ)δ2] = [τ2 + (1 − ρ)δ2][τ2 + (1 − ρ + Nρ)δ2] δ2(1 − ρ + Nρ) = τ2 + (1 − ρ + Nρ)δ2 APPENDIX A. APPENDIX 195

Dividing (B −C) by [B + (N − 1)C], we get

B −C (1 − ρ)[τ2 + (1 − ρ + Nρ)δ2] = B + (N − 1)C (1 − ρ + Nρ)[τ2 + (1 − ρ)δ2] (1 − ρ)[τ2 + (1 − ρ + Nρ)δ2] = (1 − ρ)[τ2 + (1 − ρ + Nρ)δ2] + Nρτ2 1 = 2 1 + Nρτ (1−ρ)[τ2+(1−ρ+Nρ)δ2] 1 = 1 + M or equivalently, [B + (N − 1)C] = (1 + M)(B −C) .

Dividing C by [B + (N − 1)C], we get

C ρτ2 = B + (N − 1)C (1 − ρ + Nρ)[τ2 + (1 − ρ)δ2] ρτ2 = (1 − ρ)[τ2 + (1 − ρ + Nρ)δ2] + Nρτ2 (1 − ρ)[τ2 + (1 − ρ + Nρδ2] Nρτ2 1 = · · (1 − ρ)[τ2 + (1 − ρ + Nρ)δ2] + Nρτ2 (1 − ρ)[τ2 + (1 − ρ + Nρ)δ2] N Nρτ2 (1−ρ)[τ2+(1−ρ+Nρ)δ2] 1 = 2 · 1 + Nρτ N (1−ρ)[τ2+(1−ρ+Nρ)δ2] M 1 = · 1 + M N

1 −1 . Solving for c from c = (N−1)c + λ (B −C) B + (N − 1)C gives,

1 B −C cλ + = N − 1 B + (N − 1)C

1 1 1 c = − (A.4) λ 1 + M N − 1 N − 2 − M = λ(N − 1)(1 + M) APPENDIX A. APPENDIX 196

and solving for b,

1 −1 b = + λ (B −C) (N − 1)c = c[B + (N − 1)C] = c(1 + M)(B −C) N − 2 − M (1 − ρ)δ2 = (1 + M) λ(N − 1)(1 + M) τ2 + (1 − ρ)δ2 (1 − ρ)δ2 N − 2 − M = · τ2 + (1 − ρ)δ2 λ(N − 1) so we have

N − 2 − M (1 − ρ)δ2 c − b = 1 − (1 + M) λ(N − 1)(1 + M) τ2 + (1 − ρ)δ2 (1 − ρ)δ2 (1 − ρ + Nρ)[τ2 + (1 − ρ)δ2] = c 1 − · τ2 + (1 − ρ)δ2 (1 − ρ)[τ2 + (1 − ρ + Nρ)δ2] (1 − ρ + Nρ)δ2 = c 1 − τ2 + (1 − ρ + Nρ)δ2 τ2 = c − 1 = cA . τ2 + (1 − ρ + Nρ)δ2

Solving for a then gives

C 1 −1 B −C a = Q + + λ Aµ B + (N − 1)C (N − 1)c B + (N − 1)C M Q = · + cAµ 1 + M N M Q = · + (c − b)µ . 1 + M N

A.4.3 Comparative Statics

Given the way that parameter M is deﬁned,

ρτ2N M = (A.5) (1 − ρ)[τ2 + (1 − ρ + Nρ)δ2]

2 2 2 I compute its partial derivatives with respect to ω, σV , σθ, and σε in detailed steps as follows. APPENDIX A. APPENDIX 197

∂M A.4.3.1 (i) Derivation of ∂ω > 0 According to the total differentiation and the chain rule of partial derivative,

∂M ∂M ∂ρ ∂M ∂δ2 ∂M ∂τ2 = + + (A.6) ∂ω ∂ρ ∂ω ∂δ2 ∂ω ∂τ2 ∂ω

Denote D ≡ τ2 + (1 − ρ + Nρ)δ2,

∂M τ2Nρ(1 − ρ)(1 − ρ + Nρ) = − (A.7) ∂δ2 (1 − ρ)2D2 ∂M Nρ(1 − ρ)D − τ2Nρ(1 − ρ) Nρ(1 − ρ)(1 − ρ + Nρ)δ2 = = (A.8) ∂τ2 (1 − ρ)2D2 (1 − ρ)2D2 ∂M τ2N(1 − ρ)D + τ2NρD − τ2Nρ(1 − ρ)(N − 1)δ2 = ∂ρ (1 − ρ)2D2 τ2N τ2Nρ(1 − ρ)(N − 1)δ2 = − (A.9) (1 − ρ)2D (1 − ρ)2D2

Recall that the parameters δ2, τ2, and ρ are deﬁned as

2 2 2 2 2 δ = (1 − ω) σθ + ω σV (A.10) 2 2 2 τ = ω σε (A.11) ω2σ2 ρ = V (A.12) 2 2 2 2 (1 − ω) σθ + ω σV

Their partial derivatives over ω are respectively

∂δ2 = 2[ωσ2 − (1 − ω)σ2] (A.13) ∂ω V θ ∂τ2 = 2ωσ2 (A.14) ∂ω ε ∂ρ 2ωσ2 2ω2σ2 [ωσ2 − (1 − ω)σ2] = V − V V θ ∂ω δ2 δ4 2ω(1 − ω)σ2σ2 = θ V (A.15) δ4 APPENDIX A. APPENDIX 198

Combine above equations together to plug into equation (A.6), we then get

∂M h τ2N τ2Nρ(1 − ρ)(N − 1)δ2 i 2ω(1 − ω)σ2σ2 = − · θ V ∂ω (1 − ρ)2D (1 − ρ)2D2 δ4 τ2Nρ(1 − ρ)(1 − ρ + Nρ)δ2 2[ωσ2 − (1 − ω)σ2] − · V θ (1 − ρ)2D2 δ4 Nρ(1 − ρ)(1 − ρ + Nρ)δ2 + · 2ωσ2 (A.16) (1 − ρ)2D2 ε

Re-organize the items on the right hand side of equation (A.16), we can group them into two parts:

∂M τ2N h ρ(1 − ρ)(N − 1)δ2 i 2ω(1 − ω)σ2σ2 = 1 − · θ V ∂ω (1 − ρ)2D D δ4 2Nρ(1 − ρ)(1 − ρ + Nρ)δ2 h τ2[ωσ2 − (1 − ω)σ2] i + − V θ + 2ωσ2 (A.17) (1 − ρ)2D2 δ2 ε

Note that ρ(1 − ρ)(N − 1) < (1 − ρ + Nρ), the fraction term in the ﬁrst bracket of equation (A.17) is

ρ(1 − ρ)(N − 1)δ2 ρ(1 − ρ)(N − 1)δ2 = < 1 , (A.18) D τ2 + (1 − ρ + Nρ)δ2 hence the ﬁrst part of equation (A.17) is positive. Also, the term in the second bracket of equation (A.17) is

τ2[ωσ2 − (1 − ω)σ2] ωσ2 h i − V θ + 2ωσ2 = ε (1 − ω)σ2 − ωσ2 + (1 − ω)2σ2 + ω2σ2 δ2 ε δ2 θ V θ V ωσ2 = ε (1 − ω)[(2 − ω)σ2 + ωσ2 ] δ2 θ V so the second part of equation (A.17) is positive too. The sum of two positive parts shows that

∂M > 0 . ∂ω

∂M A.4.3.2 (ii) Derivation of 2 > 0 ∂σV Similarly as before, use total differentiation and the chain rule of partial derivative,

∂M ∂M ∂ρ ∂M ∂δ2 ∂M ∂τ2 2 = 2 + 2 2 + 2 2 (A.19) ∂σV ∂ρ ∂σV ∂δ ∂σV ∂τ ∂σV APPENDIX A. APPENDIX 199

2 2 2 The partial derivatives of δ , τ , and ρ over σV are respectively

2 ∂δ 2 2 = ω (A.20) ∂σV ∂τ2 2 = 0 (A.21) ∂σV 2 2 4 2 2 2 2 ∂ρ ω δ − ω σV ω (1 − ω) σV 2 = 4 = 4 (A.22) ∂σV δ δ

Combine equation (A.7), (A.8) and (A.9) together with equation (A.20), (A.21) and (A.22), and plug them into equation (A.19), we then get

2 2 2 2 2 2 ∂M h τ N τ Nρ(1 − ρ)(N − 1)δ i ω (1 − ω )σV 2 = 2 − 2 2 · 4 ∂σV (1 − ρ) D (1 − ρ) D δ τ2Nρ(1 − ρ)(1 − ρ + Nρ)δ2 − · ω2 (A.23) (1 − ρ)2D2

Re-organize the items on the right hand side of equation (A.23), we have:

2 ∂M τ N h 2 2 2 2 2 2 2 2 = 2 2 4 · ω (1 − ω) σθD − ρ(1 − ρ)(N − 1)δ ω (1 − ω) σθ ∂σV (1 − ρ) D δ i − ρ(1 − ρ)(1 − ρ + Nρ)δ4ω2 (A.24)

2 2 2 2 2 2 Note that ρδ = ω σV and (1 − ρ)δ = (1 − ω) σθ. Equation (A.24) can be rewritten as

∂M (1 − ρ)2D2δ4 2 · 2 ∂σV τ N 2 2 2 4 2 2 2 4 2 2 2 = ω (1 − ω) σθD − ω σV (1 − ω) σθ(1 − ρ)(N − 1) − ω σV (1 − ω) σθ(1 − ρ + Nρ) 2 2 2 2 2 2 2 = τ + δ + (N − 1)ρδ − ω σV (1 − ρ)(N − 1) − ω σV (1 − ρ + Nρ) 2 2 2 2 = τ + δ + ω σV [(N − 1) − (1 − ρ)(N − 1) − (1 − ρ + Nρ)] 2 2 2 2 = τ + δ − ω σV 2 2 2 = τ + (1 − ω) σθ (A.25)

Equation (A.25) apparently shows that ∂M 2 > 0 . ∂σV APPENDIX A. APPENDIX 200

∂M A.4.3.3 (iii) Derivation of 2 < 0 ∂σθ Similarly as before, use total differentiation and the chain rule of partial derivative,

∂M ∂M ∂ρ ∂M ∂δ2 ∂M ∂τ2 2 = 2 + 2 2 + 2 2 (A.26) ∂σθ ∂ρ ∂σθ ∂δ ∂σθ ∂τ ∂σθ

2 2 2 The partial derivatives of δ , τ , and ρ over σθ are respectively

2 ∂δ 2 2 = (1 − ω) > 0 (A.27) ∂σθ ∂τ2 2 = 0 (A.28) ∂σθ 2 2 2 ∂ρ ω (1 − ω) σV 2 = − 4 < 0 (A.29) ∂σθ δ

Recall that we discussed in equation (A.17) and (A.18) that

∂M τ2N h ρ(1 − ρ)(N − 1)δ2 i = 1 − > 0 , ∂ρ (1 − ρ)2D D as well as showed in equation (A.7) that

∂M τ2Nρ(1 − ρ)(1 − ρ + Nρ) = − < 0 . ∂δ2 (1 − ρ)2D2

∂M ∂M ∂ρ ∂M ∂δ2 2 = 2 + 2 2 (A.30) ∂σθ ∂ρ ∂σθ ∂δ ∂σθ |{z}|{z} |{z}|{z} (+) (−) (−) (+) This shows that ∂M 2 < 0 . ∂σθ

∂M A.4.3.4 (iv) Derivation of 2 > 0 ∂σε Similarly as before, use total differentiation and the chain rule of partial derivative,

∂M ∂M ∂ρ ∂M ∂δ2 ∂M ∂τ2 2 = 2 + 2 2 + 2 2 (A.31) ∂σε ∂ρ ∂σε ∂δ ∂σε ∂τ ∂σε APPENDIX A. APPENDIX 201

2 2 2 The partial derivatives of δ , τ , and ρ over σε are respectively

∂δ2 2 = 0 (A.32) ∂σε 2 ∂τ 2 2 = ω (A.33) ∂σε ∂ρ 2 = 0 (A.34) ∂σε

Plug equation (A.8) and (A.33) into equation (A.31), we have

2 2 2 ∂M Nρ(1 − ρ + Nρ)δ 2 N(1 − ρ + Nρ)ω σV 2 = 2 ω = 2 (A.35) ∂σε (1 − ρ)D (1 − ρ)D

Equation (A.35) shows that ∂M 2 > 0 . ∂σε APPENDIX A. APPENDIX 202

A.4.4 RGGI Auctions Summary Table

Table A.7: CO2 Spot Auctions Details

Auction Auction Vintage # Potential # Active # Winning Number Date Bidders Bidders Bidders 1 9/25/2008 2009 82 59 44 2 12/17/2008 2009 84 69 46 3 3/18/2009 2009 63 50 42 4 6/17/2009 2009 67 54 48 5 9/9/2009 2009 59 46 34 6 12/2/2009 2009 74 62 40 7 3/10/2010 2010 61 51 40 8 6/9/2010 2010 53 43 42 Auction Total Demand/Supply HHI Compliance Compliance Number Supply Ratio Index Demand % Won % 1 12,565,387 4.1 446 80 82 2 31,505,898 3.5 459 76 87 3 31,513,765 2.5 602 84 78 4 30,887,620 2.6 578 80 85 5 28,408,945 2.5 584 78 77 6 28,591,698 2.6 587 70 65 7 40,612,408 2.3 710 82 85 8 40,685,585 1.33 992 90 92 Auction Clearing Min Bid ($) Max Bid Median Bid Mean Bid Number Price Reserve Price ($) ($) ($) 1 3.07 1.86 12.00 2.51 2.77 2 3.38 1.86 7.20 3.00 3.03 3 3.51 1.86 10.00 3.33 3.24 4 3.23 1.86 12.00 2.89 2.83 5 2.19 1.86 12.00 2.10 2.30 6 2.05 1.86 5.00 2.00 2.05 7 2.07 1.86 5.00 2.06 2.07 8 1.88 1.86 4.00 2.00 2.01 Bibliography

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