Economics of Environmental and Sustainable Choices: Plastics

ECONOMICS OF ENVIRONMENTAL AND SUSTAINABLE CHOICES: PLASTICS

AND BIODEGRADABLE PRODUCTS

JINGZE JIANG

A dissertation submitted in partial fulfillment of the requirements for the degree of

DOCTOR OF PHILOSOPHY

WASHINGTON STATE UNIVERSITY School of Economic Sciences

July 2013

To the Faculty of Washington State University:

The members of the Committee appointed to examine the dissertation of JINGZE

JIANG find it satisfactory and recommend that it be accepted.

______Thomas L. Marsh, Ph.D., Co-Chair

______Jill J. McCluskey, Ph.D., Co-Chair

______Ana Espinola-Arredondo, Ph.D.

ACKNOWLEDGMENTS

I would like to express my gratitude to faculty, friends and family members for their support and assistance. Without them, I could not have completed this dissertation with peace and joy. Because of space limitations, I can only refer to a small list of individuals to whom I owe a great debt of gratitude. Most of all, I would thank to my

Ph.D. committee co-chair Dr. Thomas L. Marsh, who is the most important person to help me realize my dream. He has taught me how to be a good teacher and how to think about economic problems as a scientist. He has always taken the time to introduce me to people within the discipline. He has also provided me with financial support and the opportunity to work with experts in other fields. I would also like to thank my co-chair

Dr. Jill J. McCluskey for her unconditional support as a mentor to help me to finish the second chapter of this dissertation and for her strong encouragement to pursue my career.

She has always been a steadfast advocate for me. I also extend appreciation to my committee member Dr. Ana Espinola-Arredondo. She has always given the best and most constructive comments on my work. Her guidance has made my four years a thoughtful and rewarding journey. I also want to thank Dr. Eric J. Belasco and Dr. Peter R. Tozer, whose comments and suggestions benefit the last two chapters. I am grateful to Sarah

Reifel, Sarah Pollock and Laura Girardeau for their willingness to help edit my work.

I also want to extend thanks to the High Tunnel and Biodegradable Mulch Special

Crop Research Initiative (SCRI) Project team, especially Dr. Debra Ann Inglis, Dr. Carol

iii

Miles, Dr. Douglas G. Hayes, Dr. Andrew Corbin, Terry Phillips and Suzette Galinato, for providing data, extension information and for their recognition of my work.

I would like to thank my greatest colleagues and friends, Max St. Brown, Charles

James, Peter Gray, Yingzi Li, Xin Zhao, Huixin Li, Yunfei Zhao, Xiaojiao Jiang, Wooten

Jadrian and Lyliana Gayoso-Gomez; my officemates, Andey Zaikin, Lilian Carrillo-

Rodriguez and Pratikshya Sapkota Bastola for making my Ph.D. study unforgettable and full of fun. To a the wonderful people I met in Pullman, including Connie Cooley, Ralph

Cooley, Yueqi Hu, Heather Skurdal, Peter Skurdal, and Anna Montgomery, thank you for making Pullman my second hometown.

Finally, my deepest appreciation goes to my parents, grandparents, aunt, uncles and niece for their patient, support and encouragement. Thank you all!

ECONOMICS OF ENVIRONMENTAL AND SUSTAINABLE CHOICES: PLASTICS

AND BIODEGRADABLE PRODUCTS

ABSTRACT

by Jingze Jiang, Ph.D. Washington State University July 2013

Co-Chairs: Thomas L. Marsh and Jill J. McCluskey

This dissertation discusses the optimal choices for plastic products end-user and manufacturers in the context of environmental and sustainable development concerns.

This research helps us understand the formation of environmentally friendly norms, the adoption of environmentally friendly biodegradable plastics and effective risk management in the plastics industry. Three independent yet related papers make up this dissertation.

The first study examines consumers and retailers’ use of plastic shopping bags. I developed a theoretical model to establish a context for analysis of stores’ voluntary rewards programs. These programs encourage consumers to use reusable bags instead of plastic bags. This research characterizes the behavior of stores and consumers, especially the external effect of participation, as well as economic environments for broader

v application of the model. Results show that voluntary reward programs can increase store profits and reduce the use of plastic bags, providing policy makers with an alternative to bans and taxation.

The second paper explores the use of agricultural plastics. We developed a growers’ decision model to investigate the adoption of conventional (polyethylene) and biodegradable plastic mulches, as well as their long-term environmental consequences for sustainable agriculture. Results suggest that when growers integrate plastic waste management into their decision making process, they achieve a stable, regarding long- term figure for on-site plastic mulch residuals. We found that increasing landfill tipping fees and decreasing tomato market prices can result in cessation of the use of polyethylene plastic mulches. However, it only makes economic sense to switch one of three biodegradable plastic mulch brands to replace polyethylene plastic mulches for tomato production in Washington.

The third paper explores the long-term price linkage and price volatility transmission among plastics, their conventional feedstock (crude oil) and newly- developed feedstock (corn) markets in the United States. We confirm the causal relationship from the crude oil futures market to the corn futures and plastics markets, and reveal significant volatility spillovers from the crude oil futures market to the corn futures and plastics markets as well as the importance of the Energy Independence and

Security Act of 2007.

TABLE OF CONTENTS

Page

ACKNOWLEDGMENTS ...... iii

ABSTRACT ...... v

LIST OF TABLES ...... ix

LIST OF FIGURES ...... xi

CHAPTER

1. INTRODUCTION ...... 1

Overview of Bittersweet Plastics ...... 1

Research Objectives ...... 4

Dissertation Format ...... 4

Summary of Findings ...... 6

References ...... 8

2. BANDWAGON EFFECTS ON PARTICIPATION IN VOLUNTARY

ENVIRONMENTAL PROGRAMS: A CASE OF PLASTIC BAG REDUCTION .. 12

Introduction ...... 12

Background ...... 13

Literature Review ...... 14

Model ...... 17

Discussion ...... 18

Conclusions ...... 23

vii

References ...... 44

3. SUSTAINABLE PLASTIC MULCH USE AND DISPOSAL DECISIONS IN

AGRICULTURE ...... 56

Introduction ...... 57

Literature Review ...... 57

Methodology and Framework ...... 60

Case Study Using Washington Tomatoes ...... 62

Conclusions ...... 78

References ...... 87

4. VOLATILITY SPILLOVER EFFECTS IN THE U.S. CRUDE OIL, CORN AND

PLASTIC MARKETS ...... 105

Introduction ...... 105

Data and Methodology ...... 106

Empirical Results ...... 110

Conclusions ...... 118

References ...... 126

APPENDIX ...... 147

A. Chapter Two ...... 147

B. Chapter Three ...... 158

viii

LIST OF TABLES

Page

Chapter 2

Table 2.1 Parameter Values ...... 48

Table 2.2 Total Profit Difference Change with More Reusable Bag Users in Store H .... 49

Table 2.3 Total Profit Difference Change with More Reusable Bag Users in Store L..... 50

Chapter 3

Table 3.1 Parameter Values for the Simulation Model ...... 94

Table 3.2 Statistics Summary for Washington State Tomato Production, 1995-2009 ..... 95

Table 3.3 Physical and Mechanical Properties of Plastic Mulches ...... 96

Table 3.4 Parameter Description and Values in a Case Study of Washington Tomatoes 97

Table 3.5 GRT for Washington State Tomato Growers, 1995-2009 ...... 98

Chapter 4

Table 4.1 Augmented Dickey-Fuller Tests ...... 132

Table 4.2 Descriptive Statistics and Diagnostics Results ...... 133

Table 4.3 Granger-Causality Wald Test ...... 134

Table 4.4 Weak Exogeneity Test ...... 135

Table 4.5 Cointegration Rank Test ...... 136

Table 4.6 Univariate GARCH (1,1) for Crude Oil Futures Prices ...... 137

Table 4.7 Error Correction Model for Plastic and Corn Futures Prices ...... 138

Table 4.8 Constant Spillover Multivariate ARCH (1) Model ...... 139

Table 4.9 Statistics Summary for Spillover Ratios in the Constant Spillover Model ..... 140

Table 4.10 Event-Dummy Spillover Multivariate ARCH (1) Model ...... 141

LIST OF FIGURES

Page

Chapter 1

Figure 1.1 Connection among Sections ...... 11

Chapter 2

Figure 2.1 Market Segmentation in the Baseline ...... 51

Figure 2.2 Market Segmentation in the Voluntary Reward Scenario ...... 52

Figure 2.3 Profit Comparison in Period One, When c

Figure 2.4 Total Profit Difference Change with More Reusable Bag Users in Store H ... 54

Figure 2.5 Total Profit Difference Change with More Reusable Bag Users in Store L ... 55

Chapter 3

Figure 3.1 Stability Analysis under Minimum Disposal Fee Equal to $20/ton ...... 99

Figure 3.2 Stability Analysis under Minimum Disposal Fee Equal to $100/ton ...... 100

Figure 3.3 Stability Analysis under Minimum Disposal Fee Equal to $310/ton ...... 101

Figure 3.4 Tomato Prices and GRT for Plastic Mulches in Washington State, 1995-2009

...... 102

Figure 3.5 Effect of Landfill Tipping Fees on GRT for Plastic Mulches in Washington

State, 1995-2009 ...... 103

Figure 3.6 Evaluation of Various Biodegradable Mulches by the Relative Growth Rate

Threshold (RGRT) for Tomato Growth in Washington, 1995-2009 ...... 104

Chapter 4

Figure 4.1 United States Monthly Plastic Prices, Corn and Crude Oil Futures Price

Indices, February 1993 - May 2013 ...... 142

Figure 4.2 Predicted Errors for Plastic Prices in the Vector Error Correction Model .... 143

Figure 4.3 Predicted Errors for Corn Future Prices in the Vector Error Correction Model

...... 144

Figure 4.4 Spillover Ratios for Plastic Prices in the Constant Spillovers Model ...... 145

Figure 4.5 Spillover Ratios for Corn Futures Prices in the Constant Spillovers Model . 146

xii

Dedication

To Hongying Zhao and Bing Jiang, my parents and my foundation.

To Guizhi Zhu, Kegang Zhao and Xiulian li, Sizhu Jiang my grandparents and my

spiritual guides.

To Hongmei Zhao, Yong Chen and Hongbo Zhao, my beloved aunt and uncles.

To Haolan Chen, my little niece and my wonder of wonders.

Thank you for all of the love, support, encouragement and dedication. This is a tribute to

the ten of you.

xiii

CHAPTER ONE

INTRODUCTION

Overview of Bittersweet Plastics

Although plastics have long been highly valued for their utility and practicality, more voices have been raised recently that link plastics to environmental problems and the energy crisis. Plastics are popular because they provide things people want, with less economic cost (Stevens, 2002). For instance, for two thirds of the price of a metal zipper, a consumer can buy a plastic zipper, which works just as well. Reasons for the cost advantage of plastics include the ease of production and the reduction in required manpower (Andrady, 2003). In addition, plastics have many competitive properties, since they are lightweight, durable, and have excellent electrical insulation properties. These characteristics make them ideal for use in packaging, building supplies, electrical products, consumer products, furniture, vehicles and agriculture (Andrady, 2003).

However, consumers have recently become more concerned and knowledgeable about the environmental problems caused by plastics. The major environmental concern is plastic waste, including litter and managed waste. Without proper disposal, plastic waste harms wild life and agricultural productivity. Dee (2002) found that 143 species have been injured or killed by plastic waste through suffocation, ingestion, or entanglement. Farmers who use disposable plastic tools, such as greenhouses and mulch film, but do not dispose of them properly contribute to plastic litter, which leads to a

1 decrease in soil permeability and productivity (Cao, 2011; Jiang, et al., 1998; Yan, et al.,

2006). Furthermore, even properly managed plastic waste can causes problems. For instance, the dumping process takes a great deal of time and space, and incineration releases pollutants into the air.

Consumers’ decisions to use plastics as well as how they dispose of the waste are the direct factors causing plastic’s environmental effects. Little, if any, research has examined whether people consider disposal methods and cost in choosing which plastic products to buy. Therefore, policy recommendations for plastic waste reduction based on existing research are not appropriate. For instance, plastic shopping bag bans and levies, overlook the inconvenience, monetary cost and environmental damage of the plastic alternatives. This results in long-term ineffectiveness (APEnvEcon, 2008) and cause even more environmental problems (Lewis,Verghese and Fitzpatrick, 2010; Villarreal and

Feigenbaum, 2012). Our study fills a gap in the literature by combining, from an individual and social perspective, analyses of the optimal choice of plastics use and disposal methods with an assessment of long-term environmental consequences.

Another concern related to plastics use is the raw materials from which plastics are produced. Plastic is a primary petrochemical product, which utilizes oil and natural gas as major feedstock and fuel (Speight, 2010). In 2010, about 3% of the petroleum used in the United States, or 190 million barrels of liquid petroleum gases (LPG) and natural gas liquids (NGL), was for the production of plastic products. Of those 190 million

2 barrels, around 99% is used as feedstock and the rest is consumed as fuel (Energy

Information Administration, 2013). More than 40% of plastic manufacturing costs are for hydrocarbon feedstock (Vickner, 2013). Therefore, the crude oil market is closely linked to the plastics industry, which is the third largest manufacturing industry in the United

States, directly creating 900,000 jobs (Plastics Industry Trade Association [SPI], 2013).

Increasing uncertainty in the crude oil market may seriously disrupt the plastics industry, which can, in turn, affect the economy.

Environmental concerns have spurred a small revolution in the plastics industry.

An increasing number of plastic manufacturers have begun to invest in biodegradable plastics that counter the undesirable aspects of conventional plastics. However, two new problems have arisen. First is the adoption problem. The substantial price premiums for biodegradable plastics are a primary reason that consumers have been driven away

(Social and Economic Sciences Research Center, 2012). In addition, the public may not possess enough technical information on the capability and safety of biodegradable plastics (Klemchuk, 1990). Furthermore, many of industries using plastics do not have access to the economic research to help guide them in choosing profitable biodegradable plastics.

Another problem is related to risk emission among markets. This risk figures prominently into agricultural commodities pricing, (Apergis and Rezitis, 2003;

Buguk,Hudson and Hanson, 2003; Wu,Guan and Myers, 2011), industrial operations

(Elyasiani,Mansur and Odusami, 2011) and public policy decisions (Ray, et al., 1998), due to the high costs of risk management procedures (Trujillo-Barrera,Mallory and

Garcia, 2011). Currently, most biodegradable plastics are made from corn. This necessitates a direct link between the corn market and the plastics industry. In addition, the rapid expansion of biofuel production, especially corn based ethanol, is likely to increase the use of corn based energy to fuel the plastics industry. To avoid inefficient risk management procedures, it is necessary for stakeholders in the plastic, corn and crude oil markets to understand risk emission through vertical market chains (Apergis and Rezitis, 2003; Buguk,Hudson and Hanson, 2003).

Research Objectives

The objectives of this study are to investigate the optimal choices for plastic products users and manufactures in the context of environmental and sustainable development concerns. In addition, it is important for us to understand the formation of environmentally friendly norms, the adoption of environmentally friendly biodegradable plastics and effective risk management in the plastics industry.

Dissertation Format

Three independent, yet related papers comprise this dissertation. Figure 1.1 shows the connection between these papers. The first paper focuses on the downstream of plastics industry, by examining consumers and retailers’ use of plastic shopping bags. We

4 evaluate the effect of voluntary rewards for consumers’ environmentally friendly behavior on store profits, identify optimal reward programs and assess the effectiveness of reward programs to encourage consumers to exhibit environmentally friendly behavior in the long-term. We develop a theoretical model to establish a context for analysis of stores’ voluntary reward programs, encouraging consumers to use reusable instead of plastic bags. This research characterizes the behavior of stores and consumers, especially the external effects of participation, as well as economic environments for the broader application of the model.

The second paper also discusses the downstream of plastics industry but focuses on the use of agricultural plastics. We examine the adoption of conventional

(polyethylene) and biodegradable plastic mulches and the long-term environmental consequences on sustainable agriculture by modeling farmers’ production choices. This section characterizes grower’s optimal decision rules for plastic mulch usage and remnant disposal, finds the plastic mulch adoption threshold and analyzes socially optimal choices. The model further predicts that in the long-run, on-site plastic mulch residue can reach a steady state. The necessary condition for the optimum of the intertemporal model is empirically applied to tomato production in Washington.

The third paper studies the upstream of plastics industry based on crude oil and corn as feedstock and fuel. This study examines price transmission in the U.S. crude oil, corn and plastic markets, especially price volatility spillover effects. The vector error

5 correction model (VECM) is used to proxy the mean equations for the autoregressive conditional heteroskedasticity (ARCH) process. By considering vertical market chains, this paper fills a gap in the literature by examining the plastic market within the energy- corn market system. We also explore the long-term relationship between plastic, corn futures, and crude oil futures prices.

Summary of Findings

In the first paper, results show that voluntary reward programs, which encourage consumers to use reusable bags, can increase store profits. Furthermore, these rewards help reduce the use of plastic bags, providing policy makers with an alternative to bans and taxation.

In the second paper, we theoretically predict the long-term on-site plastic mulch residual, showing that this can reach the steady state. This occurs, when the amount of residue either approach zero or reach the value equal to the ratio of the mulch ruminant to the decay rate underground. We also empirically find that increasing landfill tipping fees and decreasing tomato market prices would result in the growers’ cease to use polyethylene plastic mulches. However, we find that it only makes economic sense to switch one of three biodegradable plastic mulch brands to replace polyethylene plastic mulches for tomato production in Washington.

In the third paper, we apply the Granger causality test to determine the causality among crude oil futures, corn futures and plastics prices. We confirm other scholars’ findings of a causal relationship from the crude oil futures market to the corn futures and plastics markets. Results also indicate significant volatility spillovers from the crude oil futures market to the corn futures and plastics markets with the constant spillover model.

In the event-dummy spillover model, the corn futures and plastics market were found to be linked more closely to the crude oil futures market after the introduction of the Energy

Independence and Security Act of 2007 (EISA).

References

Andrady, A.L. 2003. Plastics and the Environment. Wiley-Interscience.

APEnvEcon. 2008. "Regulatory Impact Analysis on Proposed Legislation to Increase Levies on Plastic Shopping Bags and Certain Waste Facilities." In AP EnvEcon. Available at www.environ.ie/en/Legislation/Environment/Waste/WasteManagement/FileDown Load,21599,en.pdf,pp. 96.

Apergis, N., and A. Rezitis. 2003. "Agricultural price volatility spillover effects: the case of Greece." European Review of Agricultural Economics 30:389-406.

Buguk, C., D. Hudson, and T. Hanson. 2003. "Price volatility spillover in agricultural markets: An examination of US catfish markets." Journal of Agricultural and Resource Economics:86-99.

Cao, Z.. 2011. "Gansu "White Revolution"--the worry of mulch remnant disposal." Available at http://gansu.gansudaily.com.cn/system/2011/11/02/012249320_02.shtml.

Dee, J. 2002. "A Bag Habit We Need to Break." Sydney, Australia: Planet Ark.

Elyasiani, E., I. Mansur, and B. Odusami. 2011. "Oil price shocks and industry stock returns." Energy Economics 33:966-974.

Energy Information Administration. 2013. "How much oil is used to make plastic?" In Energy Information Administration. Available at http://www.eia.gov/tools/faqs/faq.cfm?id=34&t=6.

Jiang, L., Y. Ma, B. Li, and L. Zhang. 1998. "Effect of Plastic Mulches Residue on Tomatoes Growth and Yeild." Fujian Agricultural Sciences and Technology:12- 15.

Klemchuk, P.P. 1990. "Degradable plastics: A critical review." Polymer Degradation and Stability:183-202.

Lewis, H., K. Verghese, and L. Fitzpatrick. 2010. "Evaluating the Sustainability Impacts of Packaging: the Plastic Carry Bag Dilemma." Packaging Technology and Science 23:145-160.

Plastics Industry Trade Association (SPI) (2013) "A Few Fast Facts on Plastics and the Economy." Available at http://www.plasticsindustry.org/AboutPlastics/content. cfm?ItemNumber =787&navItemNumber=1280.

Ray, D.E., J.W. Richardson, D.G. De La Torre Ugarte, and K.H. Tiller. 1998. "Estimating price variability in agriculture: Implications for decision makers." Journal of agricultural and applied economics 30:21-34.

Social and Economic Sciences Research Center. 2012. "Biodegradable Mulches: Experimences and Opinions of Intermediaries." Available at http://mtvernon.wsu.edu /hightunnels/Content/SCRI-CRIS-2012.pdf. Washington State University.

Speight, J.G. 2010. The Refinery of the Future. In. Burlington, MA, Elsevier.

Stevens, E.S. 2002. Green Plastics: an Introduction to the New Science of Biodegradable Plastics: Princeton University Press.

Trujillo-Barrera, A., M. Mallory, and P. Garcia. 2011. "Volatility spillovers in the US crude oil, corn, and ethanol markets." In Proceedings of the NCCC-134 Conference on Applied Commodity Price Analysis, Forecasting, and Market Risk Management. St. Louis, MO.

Vickner, S.S. 2013. "A USDA-Certified Biobased Product Introduction." American Journal of Agricultural Economics 95:512-518.

Villarreal, P., and B. Feigenbaum. 2012. "A Survey on the Economic Effects of Los Angeles County’s Plastic Bag Ban." In National Center for Policy Analysis. Available at www.ncpa.org/pdfs/st340.pdf.

Wu, F., Z. Guan, and R.J. Myers. 2011. "Volatility spillover effects and cross hedging in corn and crude oil futures." Journal of Futures Markets 31:1052-1075.

Yan, C., X. Mei, W. He, and S. Zheng. 2006. "Present Stuation of Residue Pollution of Mulching Plastic Film and Controlling Measures." Transactions of the CSAE 22:269-272.

Figure 1.1 Connection among Sections

CHAPTER TWO

BANDWAGON EFFECTS ON PARTICIPATION IN VOLUNTARY

ENVIRONMENTAL PROGRAMS: A CASE OF PLASTIC BAG REDUCTION

Abstract

This study evaluates the effect of voluntary rewards for consumers’ environmentally friendly behavior on stores’ profits, finds optimal reward programs and assesses the effectiveness of reward programs on encouraging consumers to exhibit environmentally friendly behavior in the long-term. The author develops a theoretical model to establish a concrete context for analysis of stores’ voluntary reward programs, which encourage consumers to use reusable bags instead of plastic bags. This research characterizes the behavior of stores and consumers, especially the external effect of participation, as well as economic environments for the broader application of the model. Results show that voluntary reward programs, which encourage consumers to use reusable bags, can increase store profits. Furthermore, the rewards also help reduce the use of plastic bags, providing policy makers with an alternative to bans and taxation.

Key words: voluntary reward program, bandwagon effect, plastic shopping bag, reusable bag, duopoly market

1. Introduction

An increasing number of firms have started offering consumers rewards for environmentally friendly behavior. For example, in order to reduce waste, coffee shops give discounts to consumers who bring their own cups and soft drink companies give rewards to consumers who return bottles and cans to recycling bins. Hotels offer gift cards to consumers who decline housekeeping services to save water and grocery stores give monetary rewards to shoppers who use reusable cloth bags to reduce plastic waste.

However, these behaviors cannot be explained by previous research, who suggest that firms cater to consumers who are already environmentally friendly rather than prompting consumers to become environmentally friendly [1-3].

Research also shows that government bans or taxes to force consumers into changing their behavior to fit environmentally friendly standards are ineffective in the long-run. This has increased the public’s interest in the effectiveness of firms’ voluntary reward programs to encourage consumers’ green behavior. Scholars argue that both bans and taxes overlook the opportunity costs that are imposed on consumer. Therefore, consumers respond only passively to these policies [4-6]. This is the main hindrance to government intervention. Although voluntary rewards programs have received increasing public attention, our literature search found that no economic research has assessed the effectiveness of these programs in promoting the formation of environmentally friendly behavior.

Therefore, this work addresses the need by identifying alternatives to bans and taxes in order to promote the formation of environmentally friendly social norms. By considering the external effects of green program participation, this study evaluates the effects of voluntary rewards on stores’ profits, identifies optimal reward programs and assesses the effectiveness of reward programs on encouraging consumers to exhibit environmentally friendly behavior in the long-run. In this work, the author develops a theoretical model in order to create a concrete context for analyzing the voluntary reward programs reducing plastic shopping bags. Finally, this research characterizes the behavior of stores and consumers, as well as economic environments they operate in, for the broader application of the model.

Results of this study show that rewards are effective for controlling plastic bag use, since the number of reusable bag users increases after a reward is put in place. We also find that, compared with the offer of no rewards, voluntary reward programs increase store profits, which can be used to attract more consumers to participate in these environmental programs.

2. Background

Public concern for the environment and the problems caused by plastic shopping bags has recently increased. Dikgang and Visser [7] report that 143 different species are routinely injured and killed by plastic bags through suffocation, ingestion, or entanglement. In sub-

Saharan Africa, plastic bags play a role in spreading disease, since they are frequently

14 used as toilets before they are discarded [8]. In addition, the dumping process for plastic bag waste takes a great deal of time and space and the incineration of plastic bags releases pollutants into the air.

Although regulators have imposed levies on plastic bags or banned them in some locations, these types of policies are not popular worldwide. In Europe, Ireland set a

“plastax” as 0.15 euros per bag in 2002, which was increased to 0.22 euros in 2007 [9,

10]. Among African nations, South Africa, Kenya, Rwanda, Tanzania, Uganda, Ghana,

Ethiopia and Lesotho enacted a ban on thin plastic bags [11-13]. In Asia, China banned all supermarkets, department stores and other retailers from providing customers with free plastic bags in 2008 [14].

However, most countries still hesitate to take such actions [15]. The main argument against bans or levies is related to welfare loss for both consumers and grocery stores. In fact, these types of policies overlook the inconvenience, monetary cost and environmental damage of the alternatives to plastic. Therefore, bans and taxes may cause even more problems [6, 16]. In addition, surveys carried on in Ireland after six-year plastax implementation reveals that in the long-run, only increasing the bag levy can ensure that plastic bag use does not increase. Moreover, the marginal effect of the bag levy to reduce plastic bag use is decreasing [9]. Therefore, the effectiveness of levies on controlling plastic bag usage is questionable.

One alternative to bag levies and bans is the retailer rewards program. Several stores in regions with no bag levies or bans have voluntarily developed programs in which they reward those consumers who do not use plastic bags. Some set up plastic bag recycling bins; others give rewards or discounts to consumers for bringing in reusable bags. For example, Target stores, the drugstore giant Consumer Value Stores Pharmacy

(CVS Pharmacy) and Whole Foods Market in United States are pioneers of this type of action. Business for Social Responsibility reports that stores’ voluntary behavior provides the push that changes the consumers’ shopping behavior permanently [17].

Stores’ goodwill cannot be separated from their profit maximization objective.

Bowles [18] argues that the incentive itself can convey the designers’ preference, since they select the incentive based on their objectives and beliefs on the agents’ response under each possible incentive. However, reward programs do offer a potential profit increase, such as saving the cost of packaging and increasing market share.

Consumers’ environmental behavior is costly, especially when switching from traditional shopping habits to others with a higher opportunity cost. For example, consumers using cloth reusable bags experience an opportunity cost which is absent when the plastic bag provided by the store. However, studies show that when many consumers behave in environmentally friendly ways, more consumers decide to “go green”.

3. Literature Review

Early studies on the control of polybag usage, most of which are empirical in nature, focus on the role of the government [7, 10, 12]. Main findings show that taxation can address the problem of polybag overuse, but effectiveness decreases over time.

Therefore, this study aims to assess the effectiveness of alternative methods, such as voluntary reward programs, to examine whether the “invisible hand” has potential to solve environment problems caused by plastic bags in the long-term.

Firms and stores tend to be overly compliant with environmental protection regulations, which have existed for many years in green product markets. Several studies have found that anticipated government regulations motivate firms to take voluntary action [19, 20]. However, without the needs of strict government policy, some stores still want to go green, especially in terms of developing programs that increase consumers’ environmental friendly behavior. Therefore, this study aims to identify why stores decide to go green without government regulation.

Although a consumers’ environmental awareness affects his/her choice of whether to switch to use reusable cloth bags, externality generated by other participating consumers can significantly affect the adoption of the new social norm. Several behavioral economics scholars suggest that prevailing societal behaviors are more effective at influencing consumers to choose the environmentally friendly behavior [21-

24]. They also point out that even consumers who are not environmentally active actually behave in an environmentally friendly manner when a large group of consumers also

17 chooses to do so. This is because they feel guilty not complying with group norm, and complying with the group increases their self-esteem [22]. This consumer behavior is defined by Leibenstein [25] as the bandwagon effect as people’s valuations for an item increase when they observe others consuming that item. However, little or no research on consumers’ participation in environmental protection programs has considered this effect.

Therefore, this research fills this gap by assessing how the bandwagon effect encourages consumers’ participation in such programs. In this research, the author introduces the bandwagon effect into consumers’ utility function, and considers store programs as a trigger that starts this bandwagon effect.

4. Model

This study examines a duopoly retail grocery market. A basket of groceries, x, is homogeneous in all other respects except for a difference in quality a. Two levels of quality are considered in the market: low quality ( ) and high quality ( ), where

. Two stores differ in terms of the quality of their groceries. Specifically, store L sells low quality groceries, while store H offers high quality products. Moreover, the author assumes that the cost of groceries is positively related to the groceries’ quality.

For simplicity, the author assumes that the per basket cost of low quality is , and that

represents the basket cost of high quality, where c is the marginal cost of a good.

Hence, a basket of groceries in store L has a price , which is lower than the same

18 basket in store H, . Finally, stores provide rewards to those customers using a reusable bag and for the low and high store respectively.

In each of two periods, stores play a two-stage game. At each period, each store first chooses the monetary reward, , . In the second stage, stores compete in prices. This study assumes that when stores start to offer rewards at period one, no reusable bag users exist. However, at period two, some consumers have used reusable bags in each store, due to the implementation of rewards in period one.

The notations follow this rule: the superscripts specify periods and scenarios, and subscripts distinguish consumer choices and stores.

4.1. Utility

The author normalizes the total population of consumers to unity, and follows Mussa and

Rosen [26] to assume that each consumer only shops at one store, purchases just one basket of groceries and uses either one plastic shopping bag or one reusable cloth bag.

Consumers have homogenous preferences; however, their income levels differ.

The consumer’s income in monetary terms is denoted with y, while consumer type is

denoted with ( ), which is a function of income y. Moreover, represents the ( ) marginal utility of money. This reflects the relationship that as income level goes down, the evaluation of any goods in terms of money rises [27]. y is uniformly distributed

19 between to ̅, and therefore it implies that is also uniformly distributed between and ̅, where ( ) and ( ̅) ̅.

A consumer maximizes the utility function, ( ), represented as equation (2.1), which depends on consuming a basket x measured in terms of money,

, experiencing the quality of the basket of groceries she/he brought at a store and using a reusable bag or plastic bag.

Use a reusable bag ̅

( ) ( ) ( ) ( ) ( )

(2.1) { ( ) Use a plastic bag where represents the monetary rewards given by a store i, where i= L, H, for using a reusable cloth bag, which is no less than zero ( ), is the set of consumers who

have used reusable bags. The non-negative ( ) is the number of ̅ consumers who have already participated by using the reusable cloth bags in the store.

This is evaluated by the imputed value in terms of money . When the imputed value is larger than zero, the consumer values belonging to the reusable-bag-user group more than the non-reusable-bag-user group, and vice versa. The author assumes that the former case

20 holds ( ), since consumers feel appreciated for people’s environmentally friendly behavior.

measures the bandwagon effect. The author assumes that the bandwagon ̅ effect only has an effect within a store. For example, the number of reusable bag users in store L will not generate a positive externality on consumers shopping at store H. After

multiplying by the marginal utility of money, , one can get the individual utility of ̅

̅ bandwagon effect .

is the relative individual opportunity cost of bringing a reusable cloth bag to using a plastic bag (e.g. effort to remember bring the bag), which measures the best alternative forgone, such as time. This study assumes is larger than zero, which means that the individual opportunity cost for using a reusable bag is higher than for a plastic bag, given that the plastic bag is provided by the store.

The consumer faces a budget constraint, , where is the price for quality . For the utility maximization problem, this constraint should be bounded, because of local nonsatiation. Therefore, one can rewrite the utility function as follows:

Use a reusable bag ̅ ( ) ( )

(2.2) { Use a plastic bag

The consumer’s utility function indicates that besides the tradeoff between product quality and price, a consumer should consider the potential utility increase by using a reusable bag. Although the opportunity cost, reduces the utility, she/he gains the reward, and experience the utility increase from involving in the environmentally

friendly shopping group . ̅

4.2. Market Share

The market share of each store and the share of reusable bag users or plastic bag users at a store are related to the consumers’ type . Equation (2.2) shows that consumer’s utility is a function of consumer type . Moreover, the unity population with uniformly distributed consumer type results in the fact that the market share of each store is the percentage of consumers shopping at that store, and the share of reusable bag (plastic bag) users at a store is the percentage of consumers using reusable bag (plastic bag) at that store. Let a consumer shopping at store i with a reusable bag have utility ( ), or with a plastic bag have utility ( ) , where, i=L,H . Let be the set of consumers shopping at store i, be the set of consumers shopping at store i with reusable bags

22 and be the set of consumers shopping at store i with plastic bags, and

. Therefore,

{ }

(2.3)

{ }

(2.4) where

The author assumes that two stores serve the whole market and focuses on the case of non-full participation of reusable bag at both stores. Therefore ( ) and

( ) are always satisfied. The market share of store i is denoted with , satisfying equation (2.5). Hence, there is a population of consumers using reusable bags.

( ) ( ), where i=L,H (2.5)

5. Discussion

This section discusses the scenario in which no stores offer rewards as the baseline. Next, the author studies the scenario in which both stores offer rewards, and compare profits in the voluntary reward scenario with that in the baseline case.

5.1. Baseline

Consumers do not use reusable bags in this scenario, since the opportunity cost of using reusable bag is not compensated with a store reward program, rendering the utility of

using a reusable bag smaller than using a plastic bag ( ).

Hence the bandwagon effect is absent in period two.

The cutoff in which consumers are indifferent regarding the two stores

determines the market share. From setting , this study

characterizes the type of consumer who is indifferent regarding the two grocery stores,

, such that

（2.6） where .

Therefore, the set of consumers shopping at store L is

{ } { } , and the set of

consumers shopping at store H is {

} { ̅} . Figure 2.1 illustrates the market segmentation

characterized by the consumer types in a consumer-type--utility diagram by taking the value in table 2.1. Therefore the market share for stores L and H are

( ) (2.7) ̅

̅ ( ) (2.8) ̅

Let be the profit of store i in baseline scenario, where i=L, H, and is the plastic shopping bag’s cost for stores,

( ) ∫ ( ) (2.9)

( ) ∫ ( ) (2.10)

Since is uniformly distributed over [ , ̅], from equations (2.7) to (2.10), then

( ) (2.11) ( )( ̅ ) ̅

( )( ) (2.12) ( ̅ ) ( )( ̅ )

The stores’ optimal prices are solved by differentiating function (2.11) and (2.12) in terms of and respectively, and setting them to zero. In this way, one can find an

optimal price for stores L and H at the baseline scenario, denoted as

and respectively,

( ̅ ) ( ̅ )

(2.13) ( ̅ ) ( ̅ )

(2.14)

( ̅ ) ( ̅ ) where (Proof in appendix A), and

for achieving the fully covered market.

By plugging the optimal prices into function (2.11) and (2.12), one can get optimal profits in the baseline scenario,

̅ ( ) ( ) (2.15) ( ̅ ) ̅ ( ) ( ) (2.16) ( ̅ )

The optimal price represented in equation (2.13) and (2.14) include the plastic shopping bag’s cost. Therefore, the optimal profits shown in equation (2.15) and (2.16) are not affected by . This result indicates that the so-called free plastic bag is not free for consumers.

5.2. Voluntary Rewards

This case represents the setting in which stores offer rewards to consumers for using the reusable bags. The reward program generates different market segmentation than the baseline.

5.2.1. Market Segmentations Based on Consumers’ Behavior

First of all, let us consider the type of consumers who are indifferent as to whether they use a plastic bag or a reusable bag at store i, i=L,H, in both periods. At period one in the voluntary reward scenario, there is no bandwagon effect, and a consumer who is indifferent as to whether to use or not use a reusable bag at store i is characterized by

satisfying ( ) . At period two, there is

the bandwagon effect, and she/he is characterized by satisfying

( ) . Therefore, and are solved,

(2.17)

(2.18)

( )

(2.19)

( )

(2.20)

where .

Characterizing the cutoff consumers helps to find the set of consumers shopping at store i, i= L,H, with either a plastic bag or a reusable bag in both periods. First, an individual store is studied, and the set of consumers using either a plastic or a reusable

27 bag within a store is characterized. Analyzing the relationship between the consumer types and utility gained, results show that the cutoff type of consumer characterized in equations (2.17-2.20) is the minimum type to shop in a store with a plastic bag, but the highest type to shop with a reusable bag. For instance, let us consider store L at period

one and the cutoff type of consumer is . Therefore, consumers who are the type

within ) choose to shop in store L with a reusable bag, and remainder of

consumers shopping at store L whose type is higher than use a plastic bag (See

Appendix A for detail). Before fully characterizing market segmentation, one needs to know the relationship among cutoff consumer types across stores.

Lemma 1. Let be the type of consumers indifferent between two stores and be the type of consumers indifferent between using and not using a reusable bag at store i in period t, which satisfies one of the equations (2.17) to (2.20), where i=L,H and t =1, 2, then,

must be satisfied due to the non-full participation at both stores.

Proof. See Appendix A.

The lemma above indicates the market segmentation based on consumers’

behavior at period t. Consumers belonging to the set [ ) [ ) )

shop at store L, where [ ) is the set of consumer type using a reusable bag at store L

denoted as and ) is the set of type using a plastic bag at store L, denoted

as . The ones belonging to the set

[ ] = ) [ ] shop at store H.

Figure 2.2 illustrates the segmentation in a two-dimension graph, with a horizontal axis representing the consumer type, and a vertical axis denoting the

consumer’s utility. The set is the interval [ ), is the interval

), is the interval ) and is the interval ]. For all

below , the utility is greatest from shopping at store L with a reusable bag. For all

consumers in the set , shopping at store L with a plastic bag gains their greatest

utility. For all in the range ), consumers gains their largest utility by

shopping at store H with a reusable bag. For the rest of consumers in set , their highest utility is achieved from shopping at store H with a plastic bag. Note that

are characterized in equation (2.17) to (2.18). The and who is indifferent between two stores at period one and two, respectively, are obtained from

setting ( ) and

( ) ( ). Therefore, and are solved as

(2.21)

( )

(2.22)

where and ensuring the existence of a duopoly market.

The author now examines the stores’ models. In either period, each store first chooses its own rewards, and then competes in prices. A standard way to solve this is to solve the second stage in period two first. In this method, the optimal prices in period two are solved given the rewards, and the number of reusable bag users is determined in period one. Adopting backward induction to solve the model ensures that the solution of the model is sub-game perfect.

5.2.2. Choice of prices at period two

The store i’s profit at second stage in period two is denoted as , where i= L,H,

given store’s rewards in period two and the set of reusable bag user formed in period

one , then

( ) ∫ ( ) ( ) ∫ ( )

(2.23) ̅

( ) ∫ ( ) ( ) ∫ ( )

(2.24)

The optimal prices in terms of and are obtained by plugging the

characterized , and into equation (2.19), (2.20) and (2.22), differentiating

30 profit functions with respect to prices, then setting equal to zero. The optimal prices at

period two , are

̅ ̅ ( ̅ ) ( ) ( ) ( )

(2.25)

̅ ( ̅ ) ( ̅ ) ( ) ( )

(2.26)

5.2.3. Choice of rewards at period two

At the first stage in period two, stores choose the optimal rewards. Using equation (2.25),

(2.26), the profit functions for either store are in terms of rewards. By differentiating the profit function with respect to rewards, one can obtain the optimal rewards

in the second period.

( )

(2.27)

̅ ( )

(2.28)

The bandwagon effect occurs in period two. All optimal prices and rewards in period two

are affected by the bandwagon effect of reusable bag users, ( ).

5.2.4. Choice of prices in period one

Let be the store i’s profit at the second stage in period one, where i=

L,H, given the store’s rewards in period one , then

( ) ∫ ( ) ( ) ∫ ( )

(2.29)

( ) ∫ ( ) ( ) ∫ ( )

(2.30)

One can plug the characterized , and in equation (2.17), (2.18) and (2.21), differentiating profit functions with respect to prices, then setting equal to zero. The

optimal prices in period one , are

( ̅ ) ( ̅ ) ( ̅ )

(2.31)

( ̅ ) ( ̅ ) ( ̅ )

(2.32)

5.2.5. Choice of rewards at period one

Again, at the first stage in period one, stores choose the optimal rewards. By substituting prices in equation (2.31), (2.32) into the profit function (2.29), (2.30), the profit functions for either store are in terms of rewards. By differentiating the profit function with respect

to rewards, and setting to zero, one can solve the optimal rewards in period one as

(2.33)

(2.34)

It is interesting to note the difference of the number of reusable bag users in period one and two. This is important because much of the argument against a plastic bag taxation or ban is long-run ineffectiveness, which means that the number of reusable bag users decreases over time. Therefore, the author examines whether the number of reusable bag users increased in period two if stores implement voluntary rewards to control plastic bag usage.

Recall that the number of consumers using reusable bags at store L in period t is

( ) , and the number of consumers using reusable bags at store H in ( ̅ )

period t is ( ) where t=1, 2. In this paper, using the optimal solutions for ( ̅ ) prices and rewards in equations (2.25-2.28) and equations (2.31-2.34), the author expresses the number of reusable bag users in period two in terms of the number of reusable bag users in period one as (Proof in appendix A),

∫ ( ) ( ) ∫ ( ) (2.35) ( ̅ )

∫ ( ) ( ) ∫ ( ) ( ̅ ) (2.36) ( ̅ ) ( )

Since ̅ , , both ( ̅ ) and ( ̅ ( ) ( ̅ ) ( ) ( ) ( )

) are larger than one. Therefore the number of reusable users increases in ( ̅ ) ( ) either store at period two, and one can conclude that:

Lemma 2. The number of reusable-bag users increases at both stores in period two, if stores voluntarily reward reusable bag users in period one.

One can summarize the game solution for the case in which the stores offer rewards to consumers for using the reusable bag as,

Proposition 1. Under the assumptions of the model, a subgame perfect Nash equilibrium, if it exists, under stores rewarding consumers using reusable bags can be characterized as

̅ 1) Period one: stores’ rewards are and for store L and H,

( ̅ ) ( ̅ ) ( ̅ ) respectively. Store L charges and

( ̅ ) ( ̅ ) ( ̅ ) store H sets a price . The number of

consumers using reusable bags in store L and H are ( ) and ( ̅ )

̅ ̅ ( ) ( ) , respectively; ( ̅ ) ( ̅ ) ( ̅ )( )

( ) 2). Period two: store L and H’s rewards are and

̅ ( ) ( ̅ ) ( ̅ ) respectively. Store L charges

( ̅ ) ( ) ( ̅ ) and store H sets a price

( ̅ ) ( ̅ ) ( ) . The number of consumers using reusable

bags in store L and H is ̅ , and ̅ timse greater ( ) ( ) ( ̅ ) ( ) than they in period 1, respectively;

The author also notices that the difference between optimal rewards in period one and

they are in period two are related to bandwagon effects, ( ) and ,

( ). By rewriting the optimal rewards in period two as a function of the

optimal rewards in period one, one can find the influence of bandwagon effects on the stores’ reward program.

Corollary 1. The larger the bandwagon effect, the fewer rewards that stores offer in period two.

Proof. 1). The optimal rewards offered by the store L at period one and two are

( ) ( ) and is respectively, hence .

( ) Moreover, is the bandwagon effect in the period two. Therefore, given , ( ̅ )

( ) the larger is, the smaller is. ( ̅ )

2).The optimal rewards offered by the store H at period one and two are

̅ ( ) ̅ ( ) and is respectively, hence .

Moreover, ( ) is the bandwagon effect in the period two. Therefore, given

, the larger ( ) is, the smaller is. □

The above corollary indicates that the bandwagon effect makes reward programs less necessary. Intuitively, stores offer the rewards in order to incentivize a certain number of reusable bag users, and expect the group of reusable bag users to generate an externality to attract more consumers using reusable bags in order to achieve the optimal amount of reusable bag users.

Furthermore, one may ask how large the bandwagon effects should be to result

( ) the zero optimal rewards in period two. By setting and

( ) ( ) no larger than zero, this study finds that ( ̅ )

( ) and result zero rewards given by store L and store H respectively at

period two, hence

Lemma 3. Stores choose not to give rewards in period two, if the bandwagon effect in period two is at least twice the rewards given in period one.

5.3. Profits in the Voluntary Reward Scenario versus Profits in the Baseline

The profit function can be separated into four parts, namely the marginal profit with respect to reusable bag users, the share of reusable bag users, the marginal profit with respect to consumers using plastic bag users, and the share of plastic bag users. In

equation (2.29), for example, ( ) represents the marginal profit with

respect to consumers using a reusable bag at store L in period one, ( ) is the

share of reusable bag users in store L, ( ) is the marginal profit with respect

to consumers using a plastic bag at store L, and ( ) is the share of plastic bag

users in store L in period one. Comparing the marginal profits in voluntary reward scenario in period one with them in the baseline case, one can conclude that:

Lemma 4. In period one, the marginal profit from the voluntary rewards programs is smaller than in the baseline. In the voluntary reward scenario, store L gains more profits

37 from a reusable bag user than a plastic bag user, but store H gains more profit from a plastic bag user.

Proof. See Appendix A

The above lemma indicates that compared with the scenario of reward program absent, the implementation of reward programs decreases the profit that stores can get from each consumer. In addition, store L loses more profit from a plastic bag user than from a reusable bag user. On the contrary, store H loses more from a reusable bag user.

Lemma 5. Compared with the baseline case, in period one, if , store L takes the share away from store H in the voluntary reward scenario; if , store H takes the share away from store L in the voluntary reward scenario; if , the market shares do not change in the voluntary reward scenario.

Proof. See Appendix A

Lemma 4 and 5 together implies that if , store H earns less profit in the reward scenario than it in the baseline case; if , store L earns less profit in the reward scenario than in baseline; if , the profits of the two stores are less in the reward scenario than they are in baseline.

Figure 2.3 illustrates the profits differences in the baseline and in the voluntary reward scenario, when .The horizontal axis is the market share measured by the

38 number of consumers, and the vertical axis is the marginal profits. Hence the square area measures profits. Since , store H takes away share from store L. Therefore, store

L loses market share in the voluntary reward scenario. In addition,

marginal profits with respect to consumers using either plastic bags or reusable bags decreased. Hence store L loses profit in reward scenarios in period one.

Although store H gains market share, which contributes to the profit increase, labeled by area C, profit gains cannot offset profit loss caused by marginal profit decrease

(area B). This study finds that store H’s market share increase is , but the

( ) marginal profit decrease in store H is no less than . should be much

larger than , since the non-full participation requires an extremely large and small .

Hence, the store H gains market share, but still loses profit in reward scenario at period one. Thus,

Lemma 6. Compared with profits in the baseline case, profits of both stores decrease in period one in the voluntary reward scenario.

Profits in period one decrease compared to the baseline case. However, if profits in period two increase and can offset the loss in period one, the Total Profit (profit in period one plus it in period two) for a store increase in the voluntarily reward scenario.

Therefore, the author compares the profits between two periods in the voluntarily reward

39 scenario, finding that the differences occur in period two, when the optimal profits

introduce the bandwagon effect ( ), i=L,H (See Appendix A). Therefore,

using optimal profits at period two to do comparative statics, one can show that,

( ) ( ) (2.37)

( ) ( ) (2.38)

Corollary 2. Under the voluntary reward scenario, compared with profits in period one, the bandwagon effect in store i increases store i’s profit in period two, where i=L,H, but the bandwagon effect in store H hinders the profit increase in store L in period two.

Although in period one profits decrease for both stores compared with the no rewards scenario, in period two the bandwagon effect would increase profits. Therefore, one would ask whether the increased profit in period two can offset the lost amount in period one (proved in Lemma 6), resulting in the Total Profit increase. To address this question, the author carries on a simulation given the parameters values in table 2.1 to study how the bandwagon effect affects the stores’ Total Profits.

The bandwagon effect is positively related to two elements, the number of

reusable bag users at period one ( ( )) triggering the bandwagon effect and the

imputed value. The first element, ( ), is endogenously determined, but not

affected by the imputed value . Using the parameters value in table 2.1, this study finds that the number of reusable bag user in store H is around three times as large as it in store

L. Hence, this represents our first scenario, in which store H has more reusable bag users than store L does at period one. Next, the author simulates the scenario that store H has fewer plastic bag users than store H by changing the parameter ’s value to seven, so that the number of reusable bag users in store L is one and half times as large as it in store H.

In each scenario, the author attempts fifteen different imputed values of , since the larger of is, the larger the bandwagon effect.

In this study, the author is concerned with examining the Total Profit difference between the baseline and the voluntary reward scenarios. Hence, the author uses the Total

Profit in the voluntary reward case subtracting it in the baseline to get the Total Profit

Difference in figure 2.4, figure 2.5, table 2.2 and table 2.3. In addition, table 2.2 and figure 2.4 represent results for the scenario in which store H has more reusable bag users in period one than store L, and table 2.3 and figure 2.5 shows the results for the scenario where store L has more reusable bag user in period one than store H dose. In both figure

2.4 and 2.5, one can observe that the store that is able to attract more reusable bag users in period one (i.e. store H in figure 2.4, and store L in figure 2.5) increases their Total

Profit difference as the imputed value increases. However, the one that is able to incentivize fewer reusable bag users at period one (i.e. store L in figure 2.4, and store H

41 in figure 2.5) decrease the Total Profit deference as the imputed value increases.

Furthermore, in figure 2.4 and 2.5, one can observe that as the imputed value increase, the store with the ability to draw more reusable bag users at period one begins to have a positive Total Profit Difference value. Therefore, one can conclude that

Proposition 2. When consumers value belonging to the group using reusable bags, the store can incentivize more consumers to use reusable bags relative to its competitors in period one can achieve a total profit increase, compared with the baseline case.

6. Conclusions

This study develops a theoretical model to establish a concrete context for analysis of stores’ voluntary reward programs, which encourage consumers to use reusable instead of plastic bags. Considering the bandwagon effect from the group of reusable bag users, which has already been confirmed by experimental studies [21-25], the author demonstrates the effectiveness of reward programs and discusses the stores’ profit change caused by implementing reward programs.

Results show that rewards, starting the bandwagon effect of using reusable bags in period one, are effective in controlling the plastic bag usage, since they increase the number of reusable bags in period two. Moreover, this study compares the results with the case in which rewards are absent. The author finds that the implementation of voluntary reward programs can increase the profits of stores that are able to generate

42 greater bandwagon effect of using reusable bags in period one. These findings show that the voluntary reward program can be a good alternative to bag levies and bans that have been proved the long-term ineffectiveness in reducing plastic bags usage [6, 9, 16].

More research is needed to analyze consumers’ surplus change produced by rewards. Therefore, future studies can focus on evaluating the social welfare changes generated by voluntary reward programs in order to fully assess the impact of reward programs and compare them with government bans and taxes.

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Table 2.1 Parameter Values

Parameters Description Value

Lowest type 1

̅ Highest type 15

Marginal cost of a good 4

Relative individual opportunity cost of bringing a reusable cloth 1 bag

Low quality 5

High quality 10

200 Income over consumer type

Imputed value for belonging to the reusable-bag-user group 40

Cost of a plastic shopping bag 2

Table 2.2 Total Profit Difference Change with More Reusable Bag User in Store H

Store L Store H

0 -3.46 -13.43

1 -3.51 -5.44

2 -3.56 -5.43

5 -3.98 -5.3

50 -5.91 -3.5

60 -6.36 -2.75

70 -6.79 -1.88

80 -7.21 -0.9

90 -8.35 8.06

100 -9.1 10.62

110 -9.85 13.36

120 -10.6 16.28

130 -11.32 19.4

140 -12.03 22.71

150 -12.71 26.23

Table 2.3 Total Profit Difference Change with More Reusable Bag User in Store L

Store L Store H

0 -1.55 -5.38

1 -1.58 -2.21

2 -1.61 -2.21

5 -1.7 -2.2

50 1.08 -3.91

60 1.85 -4.19

70 2.71 -4.51

80 3.66 -4.87

90 4.71 -5.27

100 5.85 -5.71

110 7.11 -6.18

120 8.46 -6.68

130 9.93 -7.21

140 11.52 -7.76

150 13.21 -8.33

Figure 2.1 Market Segmentation in the Baseline

Figure 2.2 Market Segmentation in the Voluntary Reward Scenario

Figure 2.3 Profit Comparison in Period One, When c

Figure 2.4 Total Profit Difference Change with More Reusable Bag Users in Store H

Figure 2.5 Total Profit Difference Change with More Reusable Bag Users in Store L

CHAPTER THREE

SUSTAINABLE PLASTIC MULCH USE AND DISPOSAL DECISIONS IN AGRICULTURE

Abstract

This paper studies the adoption of conventional (polyethylene) and biodegradable plastic mulches and the long-term environmental consequences in sustainable agriculture by modeling farmers’ production choices. We characterize the grower’s optimal decision rules for plastic mulch usage and remnant disposal, find the plastic mulch adoption threshold and analyze the socially optimal choices. The model further predicts that in the long-run, the on-site plastic mulch residue can reach steady state, where the amount of residue is either approaching zero or the ratio of the mulch ruminant to the decay rate underground. The necessary condition for the optimum of the intertemporal model is empirically applied to tomatoes production in Washington. This study shows that increasing landfill tipping fees and decreasing tomato market prices would result in the growers’ cease to use polyethylene plastic mulches, but only one among three biodegradable plastic mulch brands is worth switching.

Key words: biodegradable residue, plastic mulch, disposal method, threshold, tomatoes

1. Introduction

Mulches increase the productivity of vegetable and fruit crops by controlling weeds, conserving moisture and modifying temperature (Ricotta and Masiunas, 1991; Schonbeck and Evanylo, 1998) Conventional plastic mulches1 made from polyethylene (PE) are widely used in agricultural production in the United States. In fact, by 2006, approximately 400,000 acres of the United States were covered with PE plastic mulch

(Miles et al., 2010)

As sustainable agriculture grows, farmers and other stakeholders have begun to consider the long-term impacts of PE plastic mulches on production and the environment.

Although PE plastic mulches lack degradability, they deteriorate with ultraviolet (UV) radiation and are therefore used for one only growing season. In addition, due to the high cost of collecting, sorting, cleaning and transporting, few growers recycle the used mulches (Cameron and Dudek, 2009)Some growers discard used mulches on site by plowing or burying PE under the soil, leading to a decrease in soil permeability and productivity (Cao, 2011; Jiang et al., 1998; Yan et al., 2006) Accumulated plastic waste also poses a risk to wildlife and livestock that ingest or become entangled in the waste

(Dikgang and Visser, 2012).

Most growers implementing waste management into their crop production dispose of used PE mulches in landfills; however, environmental consequences still exist (Garthe and Kowal, 2010). Non-degradable PE mulch waste in the landfill increases the total

57 waste volume of the landfill in the long-run, which negatively affects society (Huhtala,

1997). The negative externality of larger volumes of waste in landfills is reflected in the real estate market (Havlicek et al., 1971; Seok Lim and Missios, 2007). Moreover, waste handling fees in disposal facilities continue to rise (Repa, 2005). If the monitoring of disposal regulation is lax in the long-run, growers may choose to burn the mulch waste, thereby exacerbating environmental consequences (Miller et al., 2002; Ready and Ready,

1995; Repa, 2005).

These environmental concerns also affect the adoption of plastic mulches in the long-run. Due to the increasing cost of using PE plastic mulches, growers may choose stop using them, sacrificing the increased production efficiency. As a result, more plastic manufacturers have begun to invest in biodegradable plastic mulches to counter the undesirable aspects of PE plastic mulches. However, growers have resisted adoption

(Growcom, 2010; Hemphill, 1993) mainly due to substantial price premiums for biodegradable plastics (Social and Economic Sciences Research Center, 2012).

Furthermore, growers may not have enough technical information on how biodegradable plastic mulches affect crop production (Klemchuk, 1990) nor do they have access to economic research to them choose profitable biodegradable mulches. With little or no research in this area, this paper leads the way in developing economic adoption criteria for these types of mulches.

Growers’ choices to use plastic mulch2, as well as how to dispose of remnants, are direct factors that lead to environmental effects. Little, or no research has examined how growers choose among various plastic mulch types with different degradation abilities and disposal methods. Studies on the physical and chemical properties of plastic mulches and plastic waste demonstrate the environmental consequences of on-site PE plastic mulch waste (Yan et al., 2006; Zhao et al., 2011) and plastic waste disposal (Hemphill,

1993; Lament, 1993). But, without considering growers’ economic activities, the total amount of on-site mulch residue and disposed mulch waste is unknown, so the environmental impact of applying plastic mulch usage is not assessable, and policy recommendations of plastic mulch waste reduction based on existing research are not appropriate.

This study fills a gap in the literature by combining the analysis of the grower’s optimal choice of plastic mulch use and disposal method with the assessment of environmental consequences in the long-run. In this work, we constructed an intertemporal model to analyze growers’ optimal choice of plastic mulch use and various disposal methods, based on the environmental management model (Conrad and Clark,

1987). Since the individual grower does not fully internalize the negative environmental impact related to plastic mulch usage and other inputs, we extend the model to a social planner’s optimal choice between plastic mulch and other inputs (e.g. herbicide) at an aggregate level. We carried out simulations to predict the effects of the grower’s optimal choice on on-site plastic mulch residue accumulation in the long-term.

Results show that the starting point and the disposal costs are important factors in determining the amount of accumulated plastic residue on-site. However, on-site mulch residue always achieves the steady state, in which the residue either approaches zero or is equal to the ratio of plastic mulch remnants to the plastic mulch decay rate underground.

This means the grower’s plastic mulch waste management is effective in terms of on-site mulch waste control. Finally, we applied the necessary conditions for the optimum empirically in order to determine the plastic mulch adoption threshold for tomato growers in Washington.

Our study demonstrates how the economic environment (i.e. landfill tipping fees and tomato market prices) changes would affect PE plastic mulch adoption for tomato growers in Washington. We constructed an economic criterion is constructed for switching from PE plastic mulches to alternative biodegradable plastic mulches, and applied this criterion to assess three brands of biodegradable plastic mulch.

2. Literature Review

Several studies have been conducted on controlling agricultural pollution while considering economic effect. Most of these studies focus on the impact of herbicide, pesticide and fertilizer application and livestock production on water quality (Aftab et al.,

2007; Ashraf and Christensen, 1974; Conrad and Olson, 1992; Forster, 1975; Johnson et al., 1991; Kaplan et al., 2004; Keith, 1977; Ribaudo et al., 2001; Swinton and King, 1994;

Taheripour et al., 2008; Wu, 1999; Yadav, 1997). These studies concentrate on the

60 government intervention to control pollution. Their research shows that the high implementation costs of regulation as well as a lack of knowledge about pollution and economic activity are the main hindrance to government intervention. For example, Keith studied improper policies and found that the regulation of the Colorado River Basin was intended to meet pollution level requirements, but may cause growers to cease irrigation due to the economic infeasibility of meeting the requirement. Few studies have investigated agricultural production involving plastic mulches and the growers’ disposal management. Hence, this study analyze grower’s decisions and related environmental impacts to provide a reference point for policy making related to agricultural plastic mulch.

Static spatial models and dynamic models have been developed for normative analysis of agricultural pollution control policies, but the latter is more appropriate for environmental management with pollutant stocks. One major limitation of a static model is the assumption that the amount of a pollutant does not change over time (Braden et al.,

1989; Griffin and Bromley, 1982; Innes, 2000; Jacobs and Timmons, 1974). To overcome this shortcoming Conrad and Clark (1987) developed a dynamic pollution control model that has been applied to evaluate nitrogen control (Martínez and Albiac,

2004) and pesticide mitigation (Anderson et al., 1985; Conrad and Olson, 1992).Their models reveal the fundamental notion of agricultural pollutant stock evolution: pollutant stock naturally decays over time and the emission of new pollution adds to pollution stock. Studies focusing on aggregated polluters outside of agriculture confirm such

61 notions (Germain et al., 2006); Jørgensen and Zaccour (2001). Our framework builds on this literature and applies the dynamic model to evaluate plastic mulch pollution.

3. Methodology and Framework

3.1. Decision Model

Growers tend to consider profit when deciding whether to use plastic mulches and balancing mulch disposal cost decisions. Plastic mulches have been shown to increase productive capacity and product quality. However, cumulated plastic mulch residue underground lowers soil quality, which in turn decreases productivity (Zhang, 2012).

We developed a model that describes the representative grower k producing a single crop j on a homogeneous farm under an infinite planning horizon. The grower simultaneously chooses production inputs and disposal methods for mulch remnants and can use one of i=1, …, N types of plastic mulch with different decay rates to grow crop j.

The chosen amount of plastic mulch i input at time t is indicated by where

or a zero amount of means that grower k does not use plastic mulch i at time t.

Besides mulch input, , other crop production inputs , such as labor, machinery, seeds, and pesticides, are represented by .

These additional crop production inputs can be partitioned into two subcategories:

( ) . One subcategory provides mechanical services to plastic mulch i, which are complementary inputs for the plastic mulch (e.g. trained labor and

62 specific machines to install and remove plastic mulch i). Previous empirical research shows that including these complementary service flows in the production function causes their estimated coefficients to be very small, since the summed effects of all service flows are captured by the input stock variables they serve (i.e. mulch input in our study). Hence, the service flow variables should be omitted in the production function

(Doll, 1974). However, the cost function should include the service flow variables and the stock variable (Heady, 1952). These service flow variables are denoted as ( ), which is a function of and not included in the crop j production function. The remaining crop production inputs, , are denoted as .

There are four options to dispose of plastic mulches after harvesting, recycling, landfill, illegal burning or leaving the remnants on site and waiting for the tillage. The choice variables related to the plastic mulch i remnants disposal are

, which represent the portion of plastic mulch i remnants handled by recycling, landfill and illegal burning respectively. The sum of these three

choice variables is between zero and one. Moreover, ∑ represents the portion of plastic mulch i remnants left on site after one growing season time t. The dynamic state variable is , representing the accumulated on-site plastic mulch i residue related to plastic mulch i at time t. The price parameters include the market price

of the crop j, , and mulch remnants handling cost, . The mulch remnant handling

3 cost includes recycling fee ( ), landfill tipping fee ( ) and

63 expected illegal burning fine ( ) at time t. The illegal burning fine, , has a known probability that the grower will be caught by a regulator. Thus, the expected fine is

Bastioli and Limited (2005) generalize the life-cycle of plastic into four phases: the materials processing phase, the transportation phase, the use phase and the waste phase. The plastic mulch i remnants occur at the end of third phase and the plastic mulch i residue is at the last phase in the life-cycle of plastic mulch i. The plastic mulch i is employed during one crop growing season. During this phase, a majority of the plastic mulch i is exposed to the sun and degrades due to the long-wave length ultraviolet light

(Briassoulis, 2007). The average decay rate at this phase is denoted by . After harvest,

the plastic mulch i remnants function is ( ), where .

The amount of plastic mulch i remnants left on site will be buried in the soil after tillage, which contributes to the stock of on-site plastic mulch i residue . The plastic mulch i residue that is tilled underground after the growing season is then exposed to a different environment. Microorganisms are the main factor causing degradation during the underground phase (Briassoulis, 2007). is used to represent the average decay rate during the underground phase.

Consider a concave production function ( ) for crop j and

convex total cost function ( ). ( ) is a continuously

differentiable functions for and . The output of crop ( ) is

64 positively related with the input and ( ), but is negatively

related to the on-site plastic mulch residue ( ). The grower k is assumed to

sell all of the crops at market price, . Hence, ( ) represents the revenue of grower k’s farm at time t. Following previous literature, the discount factor

, indicates that the grower values the current profit more than the future profit

(Conrad and Olson, 1992; Martínez and Albiac, 2004).

Given the initial on-site plastic mulch i residue ̅̅ ̅̅ ̅ ̅ , the grower k’s objective function is specified as

(3.1) {∑ ( ) ( ) }.

{ }

The objective function is subject to the equation of motion for plastic mulch i residue, which models the plastic mulch i residue accumulation process on-site. Following

(Germain et al., 2006; Jørgensen and Zaccour, 2001) the stock pollutant constraints related to the mulch in the last phase are modeled as follows:

(3.2) ( ) ( ∑ ) ( ) where the first component on the right-hand side of the equation (2) is on-site plastic mulch i residue left from last period after underground degradation (( ) ). The second component represents the new in-flow of undisposed plastic mulch i remnants.

The total cost ( ) can be further specified into two parts: disposal costs and other production related costs. The disposal cost, ( )

( ) ( ) ( ) is comprised of the portions of plastic mulch i remnants recycled, landfilled and illegally burned respectively. The other production related costs for crop j at time t are represented by

(3.3) ( ) ( ) ( )

To solve this discrete-time dynamic optimal problem, equations (3.1) - (3.3) are combined to form the discrete current value Hamiltonian (Shone, 2003):

(3.4) ( ) ( )

( ∑ ) ( )

where can be interpreted as the shadow price whose value is negative. The shadow price measures the loss in future profit due to additional mulch put on the residue stock . The negative shadow price ( ) can also be interpreted as the imputed opportunity cost of plastic mulch i residue change. The residue change is determined by the degradability which is exogenous to the growers’ disposal decision.

Hence, the negative shadow price also represents the imputed value of plastic mulch i remnants disposal.

The terminal or transversality condition in this model is given by

(3.5)

Equation (3.5) plays a role as an important condition to help search the optimal choice, and can be satisfied, if the present value of imputed opportunity cost of plastic mulch i

residue change has fallen to zero ( ). It can also be satisfied if the plastic mulch i residue change has a positive imputed opportunity, but no mulch residue remains

( ).

The first-order-conditions of the discrete current value Hamiltonian listed below

(equations 3.6 to 3.10) and the transversality condition (equation 3.5) are the necessary and sufficient conditions for the optimal choices and states.

(3.6)

(3.7)

( ) ( ∑ )

(3.8)

(3.9)

[ ( )]

(3.10) ( ) ( ∑ ) ( )

Equations (3.6) - (3.8) maximize the Hamiltonian function by the choice of the control variables at each point along the optimum trajectory. Equation (3.6) implies the optimal rule for using the crop production inputs (e.g. seed, pesticide, water). is the

marginal production of input . Thus, the marginal production multiplied by the market price for crop j is the value of marginal production. Therefore, equation (3.6) indicates the optimum when the value of marginal production for inputs equals the

marginal cost of inputs , . The optimal amount of inputs can be found by solving equation (3.6).

After finding the optimal input level for , we consider the condition (3.7).

combined with gives us the marginal cost for using plastic mulch i.

is the handling costs for the portion of mulch i remnants chosen to be

disposed of. ( ∑ ) valued by the imputed opportunity cost of plastic mulch i residue change , , is the cost for the portion of mulch i remnants chosen to leave on-site. Therefore, the LHS of equation (3.7) describes the marginal total cost of

using plastic mulch i while the RHS, , is the value of marginal production. The

68 inequality in condition (3.7) implies that the marginal cost for using the plastic mulch i is greater than the value of marginal production.

Thus, the optimal choice is not to adopt the mulch i. When the equality holds, the grower chooses to use mulch i at optimal level. The complementary condition for condition (3.7), where marginal cost is lower than the value of marginal production for adopting the plastic mulch i, assures the grower that increasing the level of the plastic mulch i use will increase profit. Hence the equality in condition (3.7) also can be interpreted as the threshold for the plastic mulch i adoption, or the Mulch Production

Constraint (MPC).

To summarize the above analysis, the grower’s rule for using plastic mulch i is as follows:

(3.11)

{

Conditions in equation (3.8) describes the optimal rule for the grower choosing the portion of plastic mulch i remnants to be recycled, landfilled and illegal burnt respectively. Given that the MPC is satisfied, the optimal choice among the three mulch remnants handling methods follows the rules below (see proof in Appendix B)

{ }

(3.12)

{ { }

Considering the optimal input level of in equation (3.6), the optimal decision rule for the plastic mulch i adoption in condition (3.11) and the optimal decision rule of handling the mulch i remnants listed in condition (3.12) together, result in the condition for the optimal decision rule for the plastic mulch i adoption by either disposing of remnants (condition 3.13) or leaving remnants on-site (condition 3.14).

{ } (3.13)

( ) (3.14)

Condition (3.9) is the portfolio balance (PB) condition, when the on-site plastic mulch i residue exists ( >0), and it is the Hamiltonian function with respect to the corresponding sate variable. The PB condition implies that the evolution of imputed opportunity cost of the undisposed mulch i remnants equals to the value loss of marginal production of plastic mulch i residue increment. The equality reflects the optimal evolution under residue existence.

Condition (3.10) is the dynamic constraint (DC). It describes the evolution of the on-site plastic mulch i residue. The equation (3.10) is simplified as

(3.15) { ( )

3.2. Social Optimal Choice

Although growers try to manage the plastic mulch remnants to avoid productivity reduction caused by accumulated plastic mulch residues, they may not fully consider the environmental damage or effects on social welfare. For example, besides compromising soil quality, PE plastic mulch residues may kill terrestrial animals (Dreyer et al., 1999;

Lgbokwe et al., 2003; Omidi et al., 2012) and increase marine debris, which also threatens marine animals (Derraik, 2002; Gautam, 2009; Joyner and Frew, 1991).

Other disposal methods, such as burning, convert carbon from petroleum deposits into atmospheric carbon. The carbon dioxide discharged from the disposed plastic differs from that of degraded biodegradable materials. The former removes carbon from a carbon sink and increases greenhouse gases, but the latter simply cycles the greenhouse gases from plants to the air (Ellis et al., 2005; Gautam, 2009). Research shows that greenhouse gas emissions from PE plastics are higher than from biodegradable plastics

(European Plastic Film, 2002).

Plastic mulch does carry some environmental benefits. By using these plastic mulches, growers reduce environmental damage caused by herbicide usage and increase water use efficiency (Mukherjee et al., 2012). Therefore, the socially environmental damage minimization problem is integrated into the aggregated profit maximization

71 problem in order to analyze the trade-off between the amount of mulch i input, , and the other inputs, .

The socially optimal problem is to maximize the difference between the summation of all growers’ profit and the environmental damage outside farms,

( ).The damage function caused by growing crop j, ( ), is an non-

concave function of the aggregated amount of plastic mulch i, ∑ and

other inputs such, as pesticide, denoted as ∑ . Furthermore, the damage function is an increasing function of both inputs, . The marginal rate of

damage (MRD) of input to input is expressed as:

(3.16)

The MRD measures how much environmental damage increases if the input increases by one marginal unit relative to the case in which the input increases by one marginal unit. In production theory, the marginal rate of technical substitution (MRTS) of input to input at certain production level analyzes the trade-off among inputs without considering the production externality on environments (Mas-Colell et al., 1995).

However, by analyzing MRD, one can better understand how the environment damage would affect the optimal choice between the mulch i and the other substitutable inputs by mulch i (e.g. herbicide). In addition, is used to denote MRD of input to input

72 for reaching individual grower’s maximum profit to produce crop

j, ( ).

The constraints and transversality condition are the same as the private optimal problem. The discrete current value Hamiltonian is as follows:

(3.17) ∑ { ( ) ( )

( ∑ ) ( )} ( )

By solving the first-order conditions of discrete current value Hamiltonian, the optimal amount of other inputs (e.g. herbicide), and plastic mulch i 4 satisfy the following equations,

(3.18)

(3.19)

The static analysis for equation (3.18) and (3.19) are represented in equation (3.20),

(3.20)

[ ] [ ]

[ ]

Applying Cramer’s rule and solving for and , we find that and

(see Appendix B for derivations), implying the larger value of is, less input and more input are used at optimal level. As a result, social planners would encourage growers to use plastic mulches, which cause less environmental damage while maintaining production yields and overall input costs.

3.3. On-Site Plastic Mulch Residue Prediction for Private Control

Private residue control does not fully consider the social costs related to plastic mulch usage; however, the higher rate the plastic mulch residue left on-site, the lower quality the soil is in the long-run (Cao, 2011). Hence, it is important for on-site plastic mulch pollution control. If the scenario that the on-site mulch residue steady state cannot be achieved, the mulch residue should keep accumulating in the long-turn continuously intensifying the soil damage. However, if a sustainable level of residue is feasible, the damage will be fixed in the long-term. To analyze the steady state for the on-site plastic mulch residue, a simulation is discussed below.

The on-site mulch i residue ( ) steady state is affected by the grower’s imputed value for mulch i remnants disposal ( ) and the minimum disposal fee in the long-run. When the steady state of the on-site plastic mulch residue is achieved, the evolution of the residue stops. However, the evolution of the residue is affected by the plastic mulch remnants handling rule (equation 3.15), which is determined by the relative

74 value of and the minimum disposal fee (equation 3.12). Therefore, the key functions for simulation are the evolution of the grower’s imputed opportunity cost

( ) represented by equation (3.9) and the evolution of the mulch i residue expressed by equation (3.15).

Before we conducted a qualitative analysis of the steady state is conducted, we specified the relationship between the mulch i residue and crop j’s production. In the general formulation, the analysis yields ambiguous results. To derive the solution, we keep the general functional form of the production function and mulch residue evolution function, but specify the negative relationship between the mulch residue and production.

Although such specification is considered an approximation, the essence of the relationships of the system is captured. Therefore, the unequivocalness makes up for the loss of generality.

Our specification follows that of Jiang et al. (1998). They show the relationship between plastic mulch residue and crop production as:

(3.22) ( ) ( )

This study uses the same function form to get the analytical optima. The marginal effect of increasing mulch pollutant stock for crop j production is represented by equation

(3.23).

(3.23)

Knowing the specific expression for equation (3.9) can be written as

(3.24) ( ) ( ( ))( )

It is also assumed that the other exogenous price variables (e.g. ) are stable over time and denote and ( ) as and respectively.

Analysis of the phase diagram in the ( ) space under three scenarios with different minimum disposal fees: $ 20/ton (Low), $ 100/ton (Medium) and $ 310/ton

(High) is conducted by simulation. Figures (3.1) to (3.3) are the specified phase diagram by using the parameter values in table (3.1). The minimum disposal fee partitions the diagrams into two areas: the upper area represents the grower’s choice not to dispose, and the lower area represents the grower’s choice to dispose. Different starting points have been used to find the long-run optimal plastic mulch residue. Simulation results suggest that the on-site plastic mulch residue under private control always achieves the steady state where the residue is either approaching zero or the ratio of plastic mulch remnants,

( ) to the plastic mulch decay rate underground, .

There is one approximating saddle point A (0, 305.08) under $ 20/ton (Low) minimum disposal fee (figure 3.1) and a saddle point B (10, 27.73) under $ 310/ton (High) minimum disposal fee (figure 3.3), where 10 is the ratio of plastic mulch remnants to the

76 plastic mulch decay rate underground (see Appendix B for the mathematical proof). Both scenarios imply that only the starting points, (11, 58.117) in figure (3.1) and starting point

(40, 12.22) in figure (3.3) located on the unique trajectories can approach or achieve the

(approximating) saddle points. However, if the starting points are above the unique trajectory, the on-site mulch residue is approaching zero at the steady state. If they are under the unique trajectory, the residue is equal to the ratio of plastic mulch remnants to the plastic mulch decay rate underground.

The results in the scenario where the minimum disposal fee is at the medium level, $100/ton, combine the results in the earlier two extreme scenarios. We find both the approximating saddle point A (0, 305.08) in the upper area and the saddle point B (10,

27.73) in the lower area (figure 3.2). If the starting point is below the lower area stable trajectory, such as (1, 56) and (40, 12), the mulch residue reach the steady state where the amount of the residue is the ratio of plastic mulch i remnants to the decay rate underground. If the starting point is above the upper area stable trajectory, such as(10,

110), the on-site mulch residue approaches zero at the steady state. For the starting points located above the lower area stable trajectory and below the upper area stable trajectory, such as (4, 110), (4, 109) and (1, 70), the steady amount of on-site plastic mulch residue can either be approaching zero or the mulch remnants to the underground decay rate ratio.

Results indicate that growers’ plastic mulch waste management is effective in controlling on-site plastic waste accumulation. Results also point to the importance of

77 decay rates aboveground and underground in determining the mulch on-site residue in the long-run. Once growers make optimal choices on plastic mulch use and disposal method, decay rate aboveground and decay rate underground related to mulch material properties are the only two parameters affecting the steady amount of plastic mulch residue. However, most experiments by material experts have overlooked the underground decay rate.

4. Case Study Using Washington Tomatoes

In this case study, the theoretical model described above is employed to evaluate the mulch adoption threshold for tomato growers using PE plastic mulches in Washington

State. The case study had two main goals. First, we examined the change of growers’ standards for adoption regarding PE plastic mulches’ ability to enhance productivity in

Washington while considering the changes in economic environments, namely changing the tomato market price and increasing remnant disposal fees. Secondly, we conducted a sensitivity analysis to determine the amount of enhanced production growth that would incentivize tomato growers to switch from PE plastic to biodegradable plastic mulches.

We collect time series data for tomato prices and waste disposal fee from 1995 to

2009. For simplicity, a one-acre farm and normalize all input and output variables on a per acre basis is assumed. Tomato prices ($/lb) in the western US are collected from

USDA Economics, Statistics and Market Information System (ESMIS) (USDA, 2010).

Tomato yield data (lb/acre) in Washington are generated from historical yield data5.

Linear low-density PE plastic (LLDPE) film price data is used to represent the price of plastic mulches ($/lb)6 (PlasticsNews, 1999). Local landfill tipping fee data are collected from Department of Ecology State of Washington (Washington State Department of

Ecology, 1999)and the National Solid Waste Management Association (NSWMA)’s

2005 Tipping Fee Survey (Repa, 2005). Summary statistics are listed in table 3.27.

A field survey is also conducted to characterize tomato growers’ plastic mulch choices in Washington by Mount Vernon Northwestern Washington Research and

Extension Center’ Specialty Crop Research Initiative (SCRI) project team from 2010 to

2012. Research shows that the majority of vegetable growers choose to send all PE plastic remnants to landfill facilities (Baameur, 2009), which is the cheapest way to handle the remnants of plastic mulch89 However, between 1995 and 2002 the average landfill tipping fee in Washington nearly doubled, increasing from $32.19 per ton to

$ 62.09 dollar (Washington State Department of Ecology, 1999). This landfill tipping fee increases the marginal cost (MC) of using PE plastic mulches. Per equation (3.7), which describes the growers’ mulch choice rule, the increase in MC could result in growers not adopting PE plastic mulches. However, if such increases can be offset by the value of marginal production of PE plastic mulches, the growers keep using plastic mulches.

Due to the historical increase in landfill tipping fees, fully biodegradable plastic mulches present a good alternative to PE plastic mulches. However, the ability of these mulches to enhance productivity is still in question. If biodegradable plastic mulches can

79 optimize cost savings as well as enhance productivity, growers would likely switch from

PE plastic mulches to biodegradable mulches. Hence, we develop economic criteria for biodegradable mulches adoption and apply it to three biodegradable mulches brands.

Brand 1 and 2 are commercially-available starch-based mulch, and Brand 3 is experimental poly-lactic acid (PLA) mulch. Although the comparison of physical properties with PE plastic mulch are listed in table 3.3, it may be difficult for growers to make decisions on plastic mulch adoption based on these facts.

4.1. Empirical Model

Assuming that PE plastic mulches (i= h)’ decay rates below and above ground are approximately approaching zero, , ( ) , then the necessary condition for the optimum, equation (3.13), is rearranged to analyze the minimal marginal production rate for adoption of PE plastic mulches by Washington tomato growers as follows:

(3.25)

where is the tomato production growth rate (%) enhanced by the PE plastic

mulch for grower k’s farm at time t. is the grower k’s tomato production (lb/acre)

with the PE plastic mulch at time t. Therefore, is the corresponding

expression for in equation (3.13) (see Appendix B for the detailed linkage). is the

80 price of PE plastic mulches ($/lb). The costs associated with mechanical services for using PE plastic mulches (denoted as in equation 3.13) are represented by

and , which include the cost ($/acre) of hiring labor to remove PE plastic mulch and using machinery to remove PE plastic mulch respectively. is the landfill tipping

fee ($/lb) at time t. is the amount of the PE plastic mulch (lb/acre) applied to grow

tomatoes in grower k’s farm at time t. Hence, is equivalent to in equation

7 (3.13). , similar to in equation (3.13), is the amount of the PE plastic mulch

(lb/acre) remaining in the soil and attached the soil absorbing the water after harvesting,

which is heavier than . is the tomato market price ($/lb) at time t.

When the equality in equation (3.25) holds, the value for is also the minimum production growth rate for the adoptation of plastic mulches, based on the equation (3.7). This is termed the tomato Growth Rate Threshold (GRT). Besides time series data, other parameter values in equation (3.25) are listed in tables (3.2) and (3.3).

A sensitivity analysis of the GRT to the changes in tomato prices and the landfill tipping fee allows one to assess the sensitivity of adoption. The evaluation of optimal thresholds for switching from PE plastic mulches to alternative biodegradable plastic mulches offers a method to assess the substitutability of fully biodegradable plastic mulches.

4.2. Change in Tomato Prices

Our results indicate that tomato prices are inversely related to GRT (figure 3.4). This is because when the tomato price is high, the value for each unit of tomatoes is high. Even if the PE plastic mulches increase production slightly, the higher tomato price magnifies such increases by increasing revenue. In this situation, the GRT is lower. However, if tomato prices are low, a significant increase in production would be necessary to increase revenue.

4.3. Increasing Landfill Tipping Fees

This study examines the effect of increasing landfill tipping fees on GRT. Figure (3.5) represents the GRT yearly value for tomato growing from 1995 to 2009. The landfill tipping fee increases by $0.1 and $1 per pound in scenarios 1 and 2, respectively. table

(3.5) reports the outcomes of the simulations from these increases in the landfill tipping fee. Figure (3.6) and table (3.4) indicate that the GRT in scenario 2 shifts to higher level than scenario 1.

The average landfill tipping fee elasticity of GRT measures how responsive GRT is to a change in landfill tipping fee. The elasticity in scenario 1 is 0.011 and in scenario 2 is 0.012 (see Appendix B). Although the elasticity values are less than one, we cannot simply conclude that the GRT is not sensitive to the increasing landfill tipping fee. Since the techniques of applying PE plastic mulches have been fully developed, it is hard to increase their contribution to tomato yield by 0.001% or 0.011% more to offset the losses from the increased landfill tipping fee. Therefore, the increasing landfill tipping fee

82 discourages tomato growers to adopt PE plastic mulches, sacrificing the increased production efficiency from using plastic mulches.

4.4. Switching to Biodegradable Plastic Mulch

Although biodegradable plastic mulches are gaining ground in the industry, there is no standard to evaluate the decision to switch from plastic to biodegradable mulches.

Therefore, this study evaluates which factors or determinants cause growers to make this switch.

The switching determinant includes the grower’s main concern for the biodegradable plastic mulch and possesses the property to compare the biodegradable plastic mulch with PE plastic mulch. The biggest concerns held by growers regarding biodegradable plastic mulch are whether it has the ability to enhance crop production and whether the price to buy it is higher. The GRT studied above is the synthesized growth rate involving the mulch price and disposal cost to reveal the grower’s concern of plastic mulch application. Therefore, we conduct a simulation of the GRT for biodegradable plastic mulch by increasing the mulch price and eliminating the disposal related cost. The ratio of the biodegradable plastic mulches’ GRT to the plastic mulches’ GRT , called

Relative Growth Rate Threshold (RGRT), implies that the relative growth rate expected by the grower to switch to biodegradable plastic mulch. Therefore, RGRT is the switching determinant. If biodegradable plastic mulches do have a higher relative growth

83 rate than RGRT, then using biodegradable plastic mulches brings additional benefits to the grower.

Although the physical properties in table 3.3 cannot guide growers to make decision, the RGRT does access the switching decision for tomato growers in

Washington. Figure 3.6 implies that brand 2 is a good alternative for PE plastic mulches, since the relative growth rate line of brand 2 is above RGRT. However, the other two mulches selected are not good alternatives.

5. Conclusions

Despite the prevalence of PE plastic mulch pollution, few studies have investigated its effects. Pollution caused by PE plastic mulch has already become a serious problem in many developing countries, and could cause serious problems in developed countries as well.

In this study crop growers’ sustainable choice of plastic mulch use evaluates decisions regarding disposal methods. This provides insights into growers’ decision- making process in the adoption of PE and biodegradable plastic mulch as well as the long-run environmental consequences. Results may be used to help growers choose a profitable plastic mulch, support the plastics industry to better understand market demand, and assist regulators in making policies to control plastic mulch waste pollution.

We developed a general dynamic optimization model to study representative grower’s profit maximization problem, characterize the optimal choice of plastic mulches and disposal methods for plastic mulch remnants. Furthermore, we analyze the trade-off between plastic mulch inputs and other inputs (e.g. herbicide) by utilizing the social planner’s problem when considering the aggregate profit maximization problem and environmental damage function. We evaluated the effect of the changes in the marginal rate of damage of other inputs to plastic mulch input on optimal choices among inputs.

Results show that the socially optimal choice is to adopt plastic mulches that cause less environmental damage while maintaining production yields and overall input costs.

Results of the simulation conducted for evaluating on-site plastic mulch residue under private mulch waste control in the long-run indicates that the residue achieves a steady state when the sustainable level of residue either approaches zero or is equal to the ratio of plastic mulch remnants to the decay rate underground. Therefore, growers’ plastic mulch waste management is effective in terms of on-site residue control. Furthermore, if the material properties making plastic mulches, decay rates aboveground and underground are known, one can predict the long-term plastic mulch residue on-site based on our model.

We apply the solution from the general dynamic optimization model to tomato growers in Washington State. Results suggest that an increase in landfill tipping fees and a decrease in tomato market prices would result in an increase in the PE plastic mulch

85 adoption threshold. In other words, growers are more likely to cease using plastic mulches under this scenario. By applying optimal adoption thresholds, which are criteria for switching from PE plastic mulches to alternative biodegradable plastic mulches, we find that only one of three biodegradable plastic mulch brands is expected to be preferred by tomato growers. This pioneering study may assist Washington tomato growers in choosing the profitable plastic mulch.

Limitation of the study are related to the difficulty in finding data on the decay rates of biodegradable plastic mulches due to the lack of experimental studies to base this work upon. Therefore, further research is needed in order to directly evaluate the benefits of switching from PE plastic to biodegradable plastic mulches.

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Table 3.1 Parameter Values for Simulation Model

Parameter Description Value

Crop j market price 36

( ) Plastic mulch i remnants 1 Slop in crop production 1 function Plastic mulch i decay rate 0.1 underground Discount factor 0.98

Table 3.2 Statistics Summary for Washington State Tomato Production, 1995-2009

Variables Min Max Mean Std.

($/lb) 0.88 2.20 1.37 0.29

(lb/acre) 28902.82 37081.29 32041.40 2128.74

($/lb) 0.31 1.03 0.54 0.19

a ($/ton) 32.19 62.09 47.04 7.50 a in the calculation, it is converted to $/lb

Table 3.3 Physical and Mechanical Properties of Plastic Mulches

Type of Thickness Weight Tensile strength b Tearing Much strength Machine Transverse Direction Direction Brand 1 Thick Very light Very weak Weak Weak Brand 2 Very thin Light Weak Very Weak Very Weak Brand 3 Very thick Very heavy Strong Strong Strong PE Thin Heavy Very strong Very strong Very strong bthe maximum stress that a material can withstand while being stretched or pulled before failing or breaking (De Garmo,Black and Kohser, 2011).

Data collected by Mount Vernon Northwestern Washington Research and Extension

Center’ Specialty Crop Research Initiative (SCRI) Project from 2010 to 2012

Table 3.4 Parameter Description and Values for a Case Study of Washington Tomatoes

Parameter Description Value t (year) Time period 1 Cost for hiring labor to remove the ($/acre) 342c plastic mulch Cost for purchasing machines to remove ($/acre) 2800c the plastic mulch c,d (lb/acre) Amount of plastic mulch sent to landfill 1829.52 c Based on data collected by Mount Vernon Northwestern Washington Research and

Extension Center’ Specialty Crop Research Initiative (SCRI) Project from 2010 to 2012. d The original amount of applied plastic mulch is 609.84 lb/acre, but the amount sent to landfill facilities is heavier, since it is combined with soil and water.

Table 3.5 GRT for Washington State Tomato Growers, 1995-2009

Year 1995 1996 1997 1998 1999 2000 2001 2002 Baseline Analysis 12.8 12.3 10.1 8.38 10.1 10.2 10.8 10.1

Scenario 1e 13.5 12.9 10.6 8.83 10.7 10.7 11.4 10.7

Scenario 2 f 19.6 18.7 15.4 12.9 15.5 15.6 16.6 15.6 Year 2003 2004 2005 2006 2007 2008 2009 Average Baseline Analysis 8.97 8.27 6.85 6.28 7.01 7.99 9.44 9.3

Scenario 1e 9.44 8.7 7.2 6.6 7.36 8.39 9.91 9.79

f 98 Scenario 2 13.7 12.5 10.3 9.44 10.4 11.9 14.2 14.2

e Landfill Tipping Fee Increase $0.1/lb. f Landfill Tipping Fee Increase $1/lb.

Figure 3.1 Stability Analysis under Minimum Disposal Fee Equal to $20/ton

Figure 3.2 Stability Analysis under Minimum Disposal Fee Equal to $100/ton

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Figure 3.3 Stability Analysis under Minimum Disposal Fee Equal to $310/ton

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Figure 3.4 Tomato Prices and GRT for Plastic Mulches in Washington State, 1995-2009

*Note: GRT stands for the Growth Rate Threshold. This is the minimum mulch enhanced growth rate ensuring that growers adopt the mulch.

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Figure 3.5 Effect of Landfill Tipping Fees on GRT for Plastic Mulches in Washington

State, 1995-2009

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Figure 3.6 Evaluation of Various Biodegradable Mulches by the Relative Growth Rate

Threshold (RGRT) for Tomato Growth in Washington, 1995-2009

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CHAPTER FOUR

VOLATILITY SPILLOVER EFFECTS IN THE U.S. CRUDE OIL, CORN AND PLASTIC MARKETS

Abstract

This article examines price linkages in the U.S. crude oil, corn and plastics markets, especially price volatility spillover effects. The vector error correction model (VECM) is used to proxy the mean equations for the autoregressive conditional heteroskedasticity

(ARCH) process. By considering the interaction of vertical market chains, this work fills a gap in the literature by examining the plastics market within the energy-corn market system. We also explore the long-term relationship between plastic and corn futures prices. The Granger causality test was used to determine the causal relationship from the crude oil futures market to the corn futures and plastics market. Results indicate significant volatility spillover from the crude oil futures market to the corn futures and plastics market with the constant spillover model. In the event-dummy spillover model, the corn futures and plastics market were found to be linked more closely to the crude oil futures market after the introduction of the Energy Independence and Security Act of

2007 (EISA).

Key words: volatility spillover, plastics price, crude oil futures, corn futures, ARCH,

VECM

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1. Introduction

It is important to assess market linkages, because it can assist the stakeholders in those markets to increase pricing efficiency and to better understand the assimilation of market signals and structural rigidities of prices (Apergis and Rezitis, 2003). Recently, the search for sustainable development and the evolution of technology have strengthened the linkages among markets. The plastics industry is a representative industry facing challenges from both the conventional and newly-developed feedstock markets which increase the impact on those markets.

The plastics market10 is strongly linked to the crude oil market, generating considerable economic interest. Plastics are a primary petrochemical product that utilize oil and natural gas as major feedstock and fuel (Speight, 2010). In 2010, about 3% of the petroleum used in the United States, or 190 million barrels of liquid petroleum gases

(LPG) and natural gas liquids (NGL), was used in the production of plastic products. Of those 190 million barrels, around 99% was used as feedstock and the rest is consumed as fuel (Energy Information Administration, 2013). More than 40% of plastic manufacturing costs are for hydrocarbon feedstock (Vickner, 2013). Therefore, as crude oil prices rise, plastics producers necessarily raise prices to protect profit margins from rising costs

(Chang, 2013). However, few studies have examined price transmission between these two markets (Masih et al., 2010; Vickner, 2013), and instead had focused on average price level analysis.

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The corn market is linked to the plastics market through biofuel production and biotechnology development. The rapid expansion of biofuel production, especially corn- based ethanol in the U.S., is a response to high crude oil prices and the strong dependence of the U.S. on international energy markets (Tyner, 2008). Naturally, the rising importance of corn in energy production is likely to increase the use of corn-based energy to fuel the plastic industry. In addition, the use of starch-based biodegradable plastics is increasing due to increasing concern about oil-based plastic pollution and the energy crisis (Begemann, 1997; Vickner, 2013). However, there is little or no economic research on the empirical links between plastic prices and corn prices, nor on the links between crude oil, corn, and plastic prices. Therefore, this analysis fills in important gap in the research.

Another important issue of linkage among markets is price volatility transmission, or volatility spillover. Price volatility represents the risks to the economic activities of participants. This figures prominently in agricultural commodities pricing, (Apergis and

Rezitis, 2003; Buguk et al., 2003; Wu et al., 2011), industrial operation (Elyasiani et al.,

2011) and public policy decisions (Ray et al., 1998), because increased price volatility results in greater costs for risk management procedures (Trujillo-Barrera et al., 2011).

However, overlooking the existence of volatility spillover through vertical market chains would decrease the efficiency of the risk management procedures (Apergis and Rezitis,

2003; Buguk et al., 2003).

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In this study, we investigate the long-term equilibrium relationships between crude oil, corn, and plastic prices in the United States. We also evaluate the price volatility spillover effects across markets. In addition, we examine the effect of the

Energy Independence and Security Act of 2007 (EISA), which provides many opportunities to expand the development of biofuel production in the United States.

In order to model the long-term relationship of conditional means, we examine the cointegration relationship among the three markets, applying the vector error correction model (VECM). We find that plastic prices measured by the United States

ICIS Petrochemical Index (IPEX) and corn futures prices are moving together in the long run. The results also reveal that crude oil futures prices are exogenous with respect to other prices, especially corn futures. This corresponds to many studies on the dynamics of price transmissions between energy and agricultural commodity markets (Alghalith,

2009; Chang and Su, 2010; Harri et al., 2009; Mueller et al., 2011).

The autoregressive conditional heteroskedasticity (ARCH) model first introduced by Engle (1982) is widely applied to study volatility (Brooks, 2008; Greene, 2003;

Hamilton, 1994). Because of the interest of volatility spillover effects, we construct a vector ARCH model with two different parameterizations for volatility spillover parameters: constant and event-dummy (Christiansen, 2007; Ng, 2000; Wu et al., 2011).

Results from the constant spillover model show that positive volatility spillover from crude oil futures prices to corn futures and plastic prices are statistically significant at the

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5% level. This accounts for a relatively larger proportion in the corn futures market than in the plastics market throughout the entire sample period. In addition, price volatility transmissions between corn futures market and the plastics market are significant in both directions, but are not symmetric.

In this study, we analyzed the effect of the Energy Independence and Security Act of 2007 (EISA) on the change in spillover in order to compare and extend the literature.

The EISA follows the Energy Policy Act of 2005 and emphasizes the importance of developing clean renewable fuels. However, most scholars analyzed the Energy Policy

Act of 2005, but not EISA (McPhail, 2011; McPhail and Babcock, 2012; Natanelov et al.,

2011; Wu et al., 2011). We found that the crude oil futures market became more closely linked to the other two markets after the introduction of EISA. Furthermore, results reveal that the crude oil futures market adds volatility to the corn futures market, but reduced volatility in the plastics market after the act was signed into law.

Much economic research has analyzed the long-term relationship between crude oil and corn prices, and has identified links between oil, ethanol, and corn prices (Birur et al., 2009; Mueller et al., 2011; Saghaian, 2010; Serra et al., 2011; Timmer, 2008). Several scholars have analyzed volatility transmission between these two markets (Du et al.,

2011; Wu et al., 2011) and all of them identified volatility transmission from crude oil prices to corn prices. Therefore, in our research, we extended the volatility transmission analysis to include a downstream market, namely, the plastics market.

109

Evidence of volatility spillover in the financial market is well-documented (Baele,

2005; Bekaert and Harvey, 1997; Christiansen, 2007; Glosten et al., 1993; Ng, 2000).

These studies have examined the international stock and bond markets, and demonstrate that ARCH is suitable for modeling volatility spillover. For instance, Christiansen (2007) estimated the generalized ARCH (GARCH) model for US bonds, regional European bonds and local European bonds markets found statistical evidence of risk transmission in the United States and European bond markets. However, that study made strong assumptions about the causal relationship among markets. Ng (2000) developed a bivariate GARCH model, which estimated the equations simultaneously. The multivariate ARCH/ GARCH model performed well when the causality among markets was weak.

Therefore, in this study, we first examine the causality among the crude oil futures, corn futures, and plastics markets and then fit the data with a multivariate ARCH model.

2. Data and Methodology

To investigate linkages between the crude oil futures, corn futures, and plastics markets in United States, we used monthly data from February, 1993 to May, 2013 and made 244

11 observations. The crude oil futures price , , is the weighted average price over a month of trading (settlement price) on the New York Mercantile Exchange (NYMEX).

12 Consistent with the crude oil futures, the corn futures price , , is the settlement price

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on the Chicago Board of Trade (CBOT). The monthly plastic price, , is measured with the United States ICIS Petrochemical Index (IPEX)13. The plastic industry produces various types of plastics, such as low-density-polyethylene (LDPE), high-density- polyethylene (HDPE). In order to consider the plastics industry as a whole, we chose

IPEX to proxy plastic prices to create a weighted measure of the average change in petrochemical prices over time. Since the price for plastics is an index, we further changed all prices as indices by setting the prices from February, 1993 as one (e.g.

), and we use lower-case letters for these transformed prices.

Figure 4.1 displays the three data series in this study. We can see that corn futures prices and plastic prices have a close relationship, which tend to move in the same pattern.

The fundamental assumption in time-series analysis is stationarity (Greene, 2003). We first used the augmented Dickey-Fuller (ADF) test in order to identify the unit root in the data (Dickey and Fuller, 1981)and the optimal lags in the ADF test based on Schwarz

Criterion (SBC) value (Schwarz, 1978). The results are presented in table 4.1.

Results suggest that all three series are non-stationary at the level, but stationary at the first difference. This is because after first differences were used, we rejected the hypothesis that the variables have a unit root problem at the 5% significance level for the data. Hence the variables are I(1) variables, requiring us to undertake the cointegration test to avoid potential spurious regressions (Hamilton, 1994). Table 4.2 presents the

111

summary statistics of the prices as well as the prices with the first differences of three markets. The skewness and kurtosis coefficients for I (1) prices are negatively skewed and leptokurtic compared with the normal distribution. The Jarque-Bera test results indicate non-normality, and the Ljung-Box Q test results imply that the serial correlation, which strongly supports an ARCH-type model (Elyasiani et al., 2011).

2.1. Conditional Mean Specification

We first performed the causality and weak exogeneity test for prices with first differences on the three markets (Hendry, 2004). Results in table 4.3 indicate that crude oil prices are exogenous, generating external shocks that affect the other two markets. In addition, our cointegration test suggests a long-run equilibrium relationship between plastic and corn futures prices (tables 4.4 and 4.5). Combining the optimal lags chosen in the previous section with cointegration test results, we developed a vector error correction autoregressive model (VECM) to fit the plastic-corn market system as:

∑ ∑

[ ] [ ] [ ] [ ]

∑ ∑ (4.1) [ ] [ ]

(4.2)

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where is the first-difference operator, is the lagged value of the error correction

term satisfying the long-run relationship equation (4.2). and are random shocks in the plastics and corn futures markets, respectively.

SBC suggests that the best model for conditional means of crude oil futures prices should not include lags at the first differences, and many scholars also suggest that the crude oil futures price follows a random model without the drift process (Alquist and

Kilian, 2010; Crowder and Hamed, 1993; Hamilton, 2008; Wu et al., 2011). Therefore, crude oil futures prices are specified as equation (4.3). In addition, the conditional mean for is zero.

(4.3)

Although the VECM with multivariate ARCH models contain many parameters for estimation, Ng (2000), Wu et al. (2011), Baele (2005) and Bekaert and Harvey (1997) use a two-step procedure. First, random shocks are estimated from the conditional mean

equations. Next, the estimated residual, [ ], from the previous step is used to estimate

the volatility spillover model through a maximum likelihood estimation method. The next step is to construct the volatility spillover models.

2.2. Conditional Variance Equation

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Considering the causal relationships among the three markets, we followed Wu et al.

(2011) and Ng (2000) to identify and measure volatility spillover among the three markets. The model is specified as：

(4.4)

( ) [ ] [ ] [ ] (4.5) ( )

[ ] [ ] [ ] (4.6) where

(4.7) ( )

(4.8)

[ ] ( ) (4.9)

(4.10) where represents the information available at time t-1. Therefore, the conditional

prices, namely ( ) and ( ). [ ] are defined as the crude oil

futures market volatility spillover parameters, which are related to the volatility spillover from the oil market to the other two markets. Shocks in the crude oil futures market follow a conditional normal distribution (equation 4.7), with the mean zero and variance characterized by GARCH (1,1) process (equation 4.8). Therefore, crude oil futures prices,

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which lie outside the cointegration prices system, follow the GARCH (1,1) process, and we estimate the model in one step.

The idiosyncratic shocks in the plastic and corn futures markets are [ ],

which follow a conditional normal distribution ( equation 4.9) with mean zero and covariance . { } is the conditional covariance matrix parameterized to fit

the Baba-Engel-Kraft-Kroner (BEKK) model (Engle and Kroner, 1995), which follows a multivariate ARCH process (equation 4.10). The major advantage of the BEKK model is the assurance of a positive definite matrix (Brooks, 2008). In our model specification, the idiosyncratic crude oil market shock, , causes volatility spillover from the crude oil market to both plastic and corn futures markets. We assume that the idiosyncratic crude oil market shock is not correlated with the idiosyncratic shocks in the other two markets.

2.3. Volatility Spillovers Evaluation

To understand the volatility spillover between the plastic and corn futures markets, which move together in the long run, we further specify matrix , equation (4.10) as:

(4.11) [ ] [ ] [ ]

The matrixes B captures the ARCH effects and the elements measures the degree of innovation from market i to market j, where i, j = P,C (Apergis and Rezitis, 2003).

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We constructed the equations to assess the volatility spillover from the crude oil futures market to the plastic and corn futures market by understanding the conditional variance of plastic prices and corn futures prices, which can be expressed as:

(4.12) ( | )

(4.13) ( | )

Following Wu et al. (2011), Christiansen (2007) and Ng (2000), we constructed a volatility spillover ratio to measure the volatility spillover effect from outside the cointegrated price system to each variable within the system. The ratio measures the portion of volatility in either the plastic or corn futures market coming from the crude oil futures market, with a value range from zero to one. The two ratios are represented in equations (4.14) and (4.15).

(4.14)

(4.15)

In this research, the volatility spillover parameters, , is divided into two cases: the constant (equation 4.16) and event-dummy volatility models (equation 4.17). The constant volatility model analyzes the sample periods as a whole, but the event-dummy volatility model considers the intensity change of spillover in response to an important

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event. In this study, we considered the impact of the Energy Independence and Security

Act of 2007 (EISA).

[ ] [ ] (4.16)

[ ] [ ] [ ] (4.17)

On December, 2007, the EISA was signed into law. It aimed to change U.S. energy policy in many areas, including the development of biofuels. For instance, Title II in

EISA contains the requirement to create Biomass-based diesel fuel as the addition of renewable biofuels to diesel fuel. Furthermore, EISA encourages the use of non- cornstarch products (e.g. sugar or cellulose) to produce biofuel, which was not emphasized in energy acts previously (the U.S. Government Printing Office, 2007).

Although many scholars have studied the impact of the Energy Policy Act of 2005, they did not study the impact of the EISA. Wu et al. (2011)studied the crude oil and corn markets from 1992 to 2009, and McPhail (2011) analyzed it from 1994 to 2010. They concluded that the Energy Policy Act of 2005 strengthened the linkage between energy and commodity markets.

We extended the sample period to 2013, and analyze the impact of the EISA.

Since we are interested in the spillover effects from the crude oil market to the other two markets, we used a dummy variable, , in (equation 4.17), which is equal to 1 after

December 2007, and 0 otherwise.

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3. Empirical Results

First, we estimated the crude oil futures price following the univariate GARCH (1,1) process (equations 4.3, 4.4, 4.7 and 4.8). Results are presented in table 4.6.

3.1. Results in the Crude Oil Futures Market

There are three methods to check test the validity of this GARCH (1,1) model. For the unconditional variance, the normality assumption is not rejected (The p-value for Jarque-

Bera statistics is larger than the critical value at 5%) and the Ljung-Box Q statistics14 for autocorrelation do not fall in the rejection region for no autocorrelation as well. In addition, both ARCH and GARCH coefficients are statistically significant at the 1% level, and the sum is 0.9849 ( ). This indicates that shocks in the corn market have a persistent effect on conditional variance. It is important to have a model fit the crude oil futures market well, since we will use the estimated crude oil futures market idiosyncratic shock as one exogenous variable in the volatility spillover models to estimate the parameters of highest interest.

3.2. Conditional Means Estimation in the Plastic and Corn Futures Markets

We fitted the conditional means for plastic and corn futures prices using the VECM

(equations 4.1 and 4.2). The diagnostic tests for this model show evidence of ARCH effects, but not autocorrelation. Figures 4.2 and 4.3 show the estimated error based on

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the VECM model, and we can see obvious volatility clustering in both the plastics and crude oil markets, which is a sign of an ARCH model.

Table 4.7 presents the results of the model. We have shown the long-run relationship between plastic prices and corn futures prices through the cointegration test.

Normalizing in terms of the coefficient of plastic prices, the relationship is specified as:

(4.18)

The estimates in equation (4.18) are statistically significant at the 5% level. This indicates that plastic and corn futures prices measured by our indices are moving together in the long run, which also reveals a strong relationship between plastic and corn futures prices.

When the corn futures prices index increases (decreases) by 1 unit, the plastic price index is expected to increase (decrease) by 1.3093.

The estimation of VECM (2) model generates residuals that are used to jointly estimate equations (4.6), (4.9) and (4.10) with a quasi-maximum likelihood procedure in the following sections.

3.3. Constant Spillovers Model

In this section, we estimate the model restricting the spillover parameters as constant over time. Based on SBC and the estimability of the model, we chose one as the optimal lag in the multivariate ARCH model.15 Results are shown in table 4.8.

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We first found the volatility spillover between the corn futures market and the plastics market. We evaluated the spillover from the corn futures to the plastics markets are evaluated with , and from the plastic to the corn futures markets with . Both were found to be statistically significant at the 1% level. This indicates the existence of volatility spillover from the corn futures market the plastics market, and the opposite also holds. Furthermore, the corn futures market mitigates the volatility in plastics market, since the sign for is negative. However, the plastics market was found to increase the volatility in the corn futures market ( ).

This opposite effects can be explained by two reasons. First, the plastic prices index consists of a large portion of plastic spot prices and should have more volatility than corn futures prices (Kawai, 1983). Many finance studies show that the commodity futures can be used to hedge spot price volatility (Hodgson and Nicholls, 1991; Spyrou,

2005). Therefore, the closer the linkage between the plastic and corn futures markets, the more the corn futures market can reduce volatility in the plastics market, as well as increasing potential volatility from the plastics market to corn futures market. In addition, one of the main reasons for introducing corn-based biofuel can also explain the negative

. Wetzstein and Wetzstein (2011) point out that alternative energy sources are introduced in order to reduce energy price volatility, which retards economic growth.

Therefore, the negative volatility spillover effect from the corn futures markets to the plastics markets agrees with scholarly findings.

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We examined volatility spillover effects from crude oil futures prices to plastic and corn futures prices. The spillover parameters, and , for plastic and crude oil futures prices, respectively, are statistically significant at the 5% level, and the values are positive. Therefore, both the plastics and the corn futures market are exposed to an additional risk from the crude oil futures market. To measure the magnitude of this extra risk from the crude oil market, we used the estimated value for parameters into equation

(4.14) and (4.15) to measure volatility spillover ratios. The statistical summary for these ratios is presented in table 4.9, and the ratios for the plastics and corn futures markets are shown in figure 4.4 and 4.5, respectively.

On average, about 12.45% of the conditional variance of corn futures prices and only approximately 2.87% of the conditional variance of plastic prices are caused by the crude oil futures market. In addition, the lowest and highest values of this ratio are also larger for the corn futures market than they for the plastics market. Therefore, in the constant spillover model, we find that the crude oil market is a bigger risk contributor to in the corn market than in the plastics market. For corn farmers, their risk management focuses on mitigating risk from weather (Baele, 2005; Skees, 2001) and technological change (Hurley et al., 2004; Kim and Chavas, 2003), which are closely related to production, but overlooks the increasing risk from the energy market. On the contrary, the manufacturing industry including plastics manufacturers has long adopted a strategy to hedge risks from the energy market (Jenne and Cattell, 1983; Russell, 2005a, b).

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Therefore, the volatility effects contributed from the crude oil markets are more influential in the corn market than in the plastics market.

3.4. Event-Dummy Spillover Model

We also estimated a model considering the effect of EISA into the spillover parameters

(equation 4.18). Results are shown in table 4.10.

We examined volatility spillover between the corn futures market and the plastics market. We found that only the volatility emitted from the corn futures market to the plastics market was statistically significant at the 10% level, and the negative is consistant with the findings in the constant volatility model.

The volatility spillover effects from crude oil futures prices to plastic and corn futures prices differed from those reported in the previous model. The spillover parameters, and are for plastic prices before and after EISA was introduced, respectively. and are for corn futures prices before and after EISA was introduced, respectively. Results show that after the EISA was introduced, crude oil futures volatility spillover to the other two markets change was significant at the 1% level

( and ). This implies that EISA dramatically increases the linkage between the crude oil markets and the other two markets. Other scholars have found similar impacts of the U.S. Energy Policy Act of 2005 on risk spillover effects from the energy market to the commodities market (Birur et al., 2009; Glosten et al., 1993; Wu et al., 2011).

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However, is negative, which indicates that the crude oil market reduced volatility in the plastics market after EISA was introduced. The mitigated volatility caused by the crude oil market is also related to the purpose of EISA to reduce energy market risk by encouraging renewable energy usage. Furthermore, the positive coefficient for supports the argument that EISA encouraged the development of renewable energy that used corn as a feedstock. Therefore, it created a great opportunity for the energy market to penetrate the corn market, which in turn can increase the risk of spillover from the energy market to the corn futures market. Therefore, today’s corn farmers who are planning to buy corn futures as a financial tool to hedge production risk should consider impacts from the energy market.

4. Conclusions

In this research, we used the vector error correction model (VECM) to proxy the mean equation for the ARCH process in order to examine price transmission among the crude oil, corn and plastics markets in United States, especially price volatility spillover effects.

By considering vertical market chains, this work fills a gap in the literature by examining the plastics market within the energy-corn market system (Fischer et al., 2006; Masih et al., 2010; Saghaian, 2010; Wu et al., 2011).

We find that when the corn futures prices index increases, the plastic prices proxied by the United States ICIS Petrochemical Index (IPEX) also go up in the long term, and vice versa. In the short-term, the corn futures market reduces the volatility, or

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mitigates risk, in plastics market. On the contrary, the plastics market increases the volatility in corn markets.

Results also show that in the long-term the crude oil futures prices index is exogenous to the plastics and corn futures prices indices. This is consistent with previous findings on the causal relationship between the energy market and the commodities market (Chang and Su, 2010; Harri et al., 2009; Mueller et al., 2011). However, considering the volatility emission across markets, we find that the volatility emitted from crude oil futures prices to plastics and corn futures prices, which accounts for a relatively larger proportion of volatility in corn futures prices than in plastic prices. We argue that the existence and significance of volatility emissions from crude oil futures market are related to the development of bioenergy to reduce the risk in energy market, which is confirmed by our event dummy volatility model.

In the event dummy volatility model, we analyze the EISA of 2007 which encourages the widely application of bioenergy, especially biofuel. Results demonstrate that EISA had the same effect as the Energy Policy Act of 2005 in increasing the linkage between the corn and the crude oil futures markets. In addition, we found that the crude oil futures market reduced the volatility in the plastics market after EISA was introduced.

Our findings suggest that today’s corn farmers who are considering buying the corn futures as a financial tool to hedge the production risk should also consider the impacts from the energy market.

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The CME group is starting to collect data for plastic futures prices. Therefore, our models can be re-examined when more data for plastic prices are available. Because the corn market is just beginning to affect the plastics market, most of our results regarding corn futures and plastic prices are not statistically significant at the conventional level.

Therefore, our research may be advanced by simulating different scenarios in which corn-based plastic takes up a different market share on the plastics market. This would allow us to calculate and compare volatility spillover ratios under different scenarios.

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Table 4.1 Augmented Dickey-Fuller Tests

Variables Levels (Lags) First differences (Lags)

1.33 (3) 36.10 (2)**

1.30 (3) 31.49 (2)**

1.26 (1) 78.15 (0)**

Lags are selected by choosing the smallest Schwarz Criterion (SBC) value.

** Significant at 5%.

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Table 4.2 Descriptive Statistics and Diagnostics Results

Plastic Prices Corn Prices Crude Oil Prices

Level I (1) Level I (1) Level I (1)

Mean 1.8483 0.0084 1.4039 0.0054 2.2798 0.0141

Median 1.5107 0.0104 1.1190 0.0071 1.5107 0.0194

Std. error 0.7739 0.1086 0.5521 0.1170 1.5056 0.2503

Min 0.8930 -0.8887 0.9157 -0.6108 0.5447 -1.5937

Max 3.5486 0.2643 3.1870 0.5254 6.7961 0.7374

Skewness 0.5351 -3.0849 1.2886 -0.7828 0.7403 -1.2538

Kurtosis 1.8770 24.8380 3.3929 11.2331 2.2889 10.7876

J-B 24.465*** 2695.164*** 69.096*** 711.134*** 35.634*** 677.714***

Q (n) 0.0000 0.0000 0.0000 0.0000 0.0000 0.0010 (p value) *** Significant at 1%.

The normality test statistics J-B stands for Jarque-Bera with null hypothesis: normality.

Q (n) is the Ljung-Box Q statistic for testing autocorrelation with null hypothesis: The data are independently distributed.

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Table 4.3 Granger-Causality Wald Test

Degree of Freedom Chi-square P-value

Group 1: Group 2: 4 106.48 <0.0001

Group 1: Group 2: , 4 9.70 0.0458

Group 1: Group 2: , 4 1.03 <0.9057

The null hypothesis of the Granger causality test is that Group 1 is influenced only by itself, and not by Group 2.

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Table 4.4 Weak Exogeneity Test

Variables Chi-Square P-value

The price system: ,

5.50 0.0190

4.67 0.0308

The null hypothesis is that one variable is weakly exogenous for the others.

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Table 4.5 Cointegration Rank Test

Critical value 95%

Rank=0 Rank 0 11.3270** 11.2248

Rank 1 Rank 2 0.0194 4.1299

* *Significant at 5%.

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Table 4.6 Univariate GARCH (1,1) for Crude Oil Futures Price

( )

Variable 0.0002 (0.0001)

0.1713*** (0.0404)

0.8136*** (0.0414) J-B-oil 0.8321 J-B-oil p-value 0.6596 Q(n)-oil p-value >0.5 * Significant at 10%, ** Significant at 5%, ***Significant at 1%.

The normality test statistics J-B stands for Jarque-Bera with null hypothesis: normality.

Q (n) is the Ljung-Box Q statistic for testing autocorrelation with null hypothesis: The residuals from the model have no autocorrelation.

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Table 4.7 Error Correction Model for Plastic and Corn Futures Prices

∑ ∑

[ ] [ ] [ ] [ ]

∑ ∑ [ ] [ ]

Variabl Variab Variab Variabl

e le le e 0.0023 0.0036 (0.0050) (0.0068)

0.7460*** 0.0886* -0.1991* -0.0549 (0.0576) (0.0454) (0.0791) (0.0624)

-0.2047*** 0.2474*** 0.2199*** 0.2564*** (0.0594) (0.0452) (0.0815) (0.0621)

-0.0230*** 0.0392*** 0.0378** -0.0495** (0.0112) (0.0147) (0.0154) (0.0202)

1***1 -0.0300

-1.3093***2 0.0378 Q(n)- Q(n)- plastic corn >0.4 >0.2 p-value p- value * Significant at 10%, ** Significant at 5%, ***Significant at 1%.

1 the significance tested in weakly exogeneity test

2 the significance tested in cointegration test under restriction or not

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Table 4.8 Constant Spillovers Multivariate ARCH (1) Model

[ ] [ ] [ ]

[ ] ( )

Variable Variable 0.0606*** -0.0232 (0.0193) (0.1725)

0.1713*** -0.3633*** (0.0184) (0.0963)

0.0051*** 0.6586*** (0.0006) (0.1313)

0.0006 0.7038*** (0.0007) (0.1455)

0.0046*** (0.0010)

J-B-plastic 892.3056 J-B-corn 125.3082 J-B-plastic p-value 0.0000 J-B-corn p-value 0.0000 Q(n)-plastic p-value >0.2 Q(n)-corn p-value >0.4 * Significant at 10%, ** Significant at 5%, ***Significant at 1%.

The normality test statistics J-B stands for Jarque-Bera with null hypothesis: normality16.

Q (n) is the Ljung-Box Q statistic for testing autocorrelation with null hypothesis: The residuals from the model have no autocorrelation.

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Table 4.9 Statistics Summary for Spillover Ratios in the Constant Spillovers Model

Plastic Prices Corn Futures Prices Mean 0.0287 0.1245 Median 0.0121 0.0670 Std. error 0.0400 0.1399 Min 0.0011 0.0026 Max 0.2809 0.7769

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Table 4.10 Event-Dummy Spillover Multivariate ARCH (1) Model

[ ] {[ ] [ ] } [ ]

[ ] ( )

Variable Variable 0.00004 0.0015*** (0.01614) (0.0002)

-0.0026 0.9557*** (0.0088) (0.1037)

-0.1000** -0.1914* (0.0433) (0.1112)

1.0031*** -0.0306 (0.0222) (0.0515)

0.0024*** -0.7151*** (0.0003) (0.1179)

-0.0003* (0.0002)

J-B-plastic 1207.6990 J-B-corn 167.5619 J-B-plastic p-value 0.0000 J-B-corn p-value 0.0000 Q(n)-plastic p-value >0.4 Q(n)-corn p-value >0.2 * Significant at 10%, ** Significant at 5%, ***Significant at 1%.

The normality test statistics J-B stands for Jarque-Bera with null hypothesis: normality.

Q (n) is the Ljung-Box Q statistic for testing autocorrelation with null hypothesis: The residuals from the model have no autocorrelation.

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Figure 4.1 United States Monthly Plastic Prices, Corn and Crude Oil Futures Price Indices, February 1993 - May 2013

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Figure 4.2 Predicted Errors for Plastic Prices in the Vector Error Correction Model

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Figure 4.3 Predicted Errors for Corn Future Prices in the Vector Error Correction Model

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Figure 4.4 Spillover Ratios for Plastic Prices in the Constant Spillovers Model

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Figure 4.5 Spillover Ratios for Corn Futures Prices in the Constant Spillovers Model

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APPENDIX

A. Chapter Two

1). Proof .

( ̅ ) ( ̅ )

(A1) ( ̅ ) ( ̅ )

(A2) hence

( ̅ ) ( ) (A3) Then we have

(A4)

2) Considering store L in period one

̃ Let be the type of consumers shopping at store L in period one, be the type of consumers indifferent between two stores, then

The utility for consumer type is

( ) (A5) therefore

(A6)

̃ The utility for consumer type gains from using a reusable bag is

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̃ ( ) ̃ ̃ ̃ (A7)

̃ The utility for consumer type gains from using a plastic bag is

̃ ̃ (A8) therefore

̃ ̃ ̃ (A9)

̃ If , then we have

̃ ̃ ̃ (A10) or

(A11) ̃ ̃

̃ so the consumer type has larger utility for using a reusable bag.

̃ If , then we have

̃ ̃ ̃ (A12) or

(A13) ̃ ̃

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̃ so the consumer type has larger utility for using a plastic bag.

For store L in period two, and store H in both periods, we can get the similar conclusion through the similar proof.

3) Proof for Lemma 1

Lemma 1. Let be the type of consumers indifferent between two stores and be the type of consumers indifferent between using a reusable bag and not using a reusable bag at store i in period t, which satisfies one of equations (2.17) to (2.20), where i=L,H and t

=1, 2, then, must be satisfied due to the non-full participation at both stores.

First of all, and should be in the interval [ ], since [ ] is the set of possible consumer types.

Consumers with a type smaller than shop at store L, and those with type larger than

shop at store H; therefore, consumers’ type indifferent between using a reusable bag

and not using a reusable bag at store L must be no larger than , and consumers’ type indifferent between using a reusable bag and not using a reusable bag at store L must be no smaller than . Then we have

(A14)

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Moreover, appendix 2) shows that in store i, consumers with type smaller than choose

to use a reusable bag and those with a larger than choose to use a plastic bag,

therefore cannot be equal to either or or as to satisfy the existence of reusable bag users and plastic bag users. We conclude that

(A15)

4) Proof for the number of reusable bag users in period two in terms of the number of reusable bag users in period one.

4.1) Store L

The number of reusable bag users in period two is

∫ ( ) (A16) ( ̅ ) where

( )

(A17)

And optimal reward in period two is

( )

(A18)

Then we plug A17 and into A16, and we obtain

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∫ ( ) ( ) ∫ ( ) (A19) ( ̅ )

4.1) Store H

The number of reusable bag users in period two is

∫ ( ) (A20) ( ̅ ) where

( )

(A21)

And the optimal reward in period two is

̅ ( )

(A22)

The consumer type indifferent between two stores in period two is

̅ ( )( ) ( ) ( )

(A23) ( )

Then we plug A21, A22 and A23 into A20, and obtain

∫ ( ) ( ) ∫ ( ) ( ̅ ) (A24) ( ̅ ) ( )

5) Proof for Lemma 2

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i. The marginal profits with respect to reusable bag users at store L in period one

( ̅ )( ) Baseline: (A25)

( ̅ )( ) ( ) Reward: (A26)

( ) The difference between A25 and A26 is A26 has one more part, . Moreover,

( ) ( ) , where ( ) Since we show

̅ ( ) in lemma 2, , or . Therefore , and we

conclude that A25 is larger than A26, or the marginal profit with respect to reusable bag users at store L in period one is larger in the baseline.

ii. The marginal profits with respect to plastic bag users at store L in period one

( ̅ )( ) Baseline: (A27)

( ̅ )( ) ( ) Reward: (A28)

( ) The difference between A27 and A28 is A28 has one more part, . Moreover,

( ) ( ) , where ( ) Since we show

( ) in lemma 2, , or . Therefore , and we

conclude that A27 is larger than A 28, or the marginal profit with respect to plastic bag users at store L in period one is larger in the baseline.

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In addition, we subtract A28 from A26 and get , so A26 is larger than A28. We

conclude that, in the voluntary reward scenario, store L gains more profit from a reusable bag user than a plastic bag user at period one. iii. The marginal profits with respect to reusable bag users at store H in period one

( ̅ )( ) Baseline: (A29)

( ̅ )( ) ( ) Reward: (A30)

( ) The difference between A29 and A30 is A30 has one more part, . We’ve

( ) ( ) proved in the first part, hence . We conclude that A29 is

larger than A30, or the marginal profit with respect to reusable bag users at store H in period one is larger in the baseline. iv. The marginal profits with respect to plastic bag users at store H in period one

( ̅ )( ) Baseline: (A31)

( ̅ )( ) ( ) Reward: (A32)

( ) The difference between A 31 and A 32 is A 32 has one more part . We’ve

( ) ( ) proved in the first part, hence . We conclude that A 31 is

larger than A32, or the marginal profit with respect to plastic bag users at store H in period one is larger in the baseline.

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In addition, we subtract A32 from A30 and get , so A32 is larger than A30. We

conclude that, in voluntary reward scenario, store H gains more profit from a plastic bag user than a reusable bag user at period one.

6) Proof for Lemma 3

The type of consumers indifferent between to store is , and we plug in the optimal prices and rewards,

(A33)

Therefore the store L’s market share in the baseline is

(A34)

The store H’s market share in the baseline is

(A35)

The type of consumers indifferent between to store is , and we plug in the optimal prices and rewards,

(A36) ( )

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Therefore the store L’s market share in the baseline is

(A37) ( )

The store H’s market share in the baseline is

(A38) ( ) if , A 37 is larger than A34 and A38 is smaller than A35, hence the store L takes share away from store H in the voluntary reward scenario, compared with the baseline; if

, A37 is smaller than A34 and A38 is larger than A35; hence, store H takes shares away from store L in voluntary reward scenario, compared with the baseline; if

, A37 is equal to A34 and A38 is equal to A35; hence, the market shares do not change in the voluntary reward scenario compared with the baseline.

7) Comparison of optimal profits at two periods in the voluntary reward scenario

The profits in period one in the voluntary reward scenario are

̅ [( )( ) ( ) ] ( )

(A39) ( ̅ )( ) ( ̅ )

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̅ [( )( ) ( ) ] ( )

( ̅ )( ) ( ̅ )

( ̅ )

( ) ( ̅ )( ) ( ) [ ] (A40) ( ̅ )( )

The profits in period two in the voluntary reward scenario are

̅ [( )( ) ( ) ( )]

( ̅ )( )

( ( ) )

( ̅ )

(A41)

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̅ [( )( ) ( ) ( )]

( ̅ )( )

( ( ) ) ̅ ( )

( ̅ ) ( ̅ )

( ( ) )

[

̅ ( ) ( )( ) ( ) ] ( ̅ )( ) (A42)

We compare A29 with A41, A40 with A42, and we find that the differences are in period

two the optimal profits introduce the bandwagon effect ( ), i=L,H

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B. Chapter Three

1). Private Optimal Disposal Rule

We first conduct analyses using equation (3.8), since this may result in corner solutions.

1). If and are all larger than , then

2). If and at least one is smaller than – , then

A ). if { }

B ). if { }

C ). if { }

We conclude from 1) to 2) that if { } , the optimal choice is to dispose of all mulch i remnants by the lowest disposal cost method; If

{ } , the optimal choice is to leave all mulch i remnants on site.

2). Social Optimal-First-Order-Conditions and derivation of equation (3.18) and (3.19)

(B1)

(B2)

( ) ( ∑ )

(B3) ( )

( )

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(B4) [ ( )]

(B5) ( ) ( ∑ ) ( )

When the equality holds, condition (B2) can be expressed as,

(B6)

Since , and at the optimal inputs level.

Therefore, we rewrite equations (B1) and (B6) we get equations (3.18) and (3.19) as

3). Solution for equation (3.20)

(3.20)

[ ] [ ]

[ ]

First, we note that , and .

159

Let [ ]

[ ]

Because convex cost function , non-concave damage function and concave production function , we can show that determinant of is larger than zero,|

|= . In addition, , and .

Applying the Cramer’s rule we have

| |

Because of , and , we show that , and .

4). Saddle, Stable and Unstable Point Proof

1. Approximate Saddle Point A

When { } and

1). Since ( ) ,

160

( ) 2). Since , ( ) ( ) ( )

[ ] [ ]

In order to find the properties for optimal point

( )

[ ]

( ) ( ) ( )

[ ]

The characteristic roots for A is and . Since ( )

the system is dynamically unstable. If we found the proper starting

point, this will converge to a fixed point (saddle point) (Shone, 2003).

However, the , as the time goes to infinity, the residue cannot attain zero, but approach zero, . The critical point A is the approximate saddle point.

2. Saddle Point B

When { } and

1). Since ( ) ( ) ,

( ) 2). Since , ( ) ( ) ( )

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[ ] [ ]

In order to find the properties for optimal point

( )

[ ]

( ) ( ) ( )

and

( ) [ ]

The characteristic roots for A is and . Since ( )

the system is dynamically unstable. However, if we found the

proper starting point, this converges to a fixed point (saddle point) (Shone, 2002).

5). Optimal Theoretical Solution Equation (3.13) and Empirical Application

Equation (3.25)

Since tomato growers in Washington choose the landfill to dispose of PE plastic mulch remnant, equation (3.13) is simplified as

(B7)

The change of the cost directly related to PE plastic mulches is , and its empirical correspondence is the price of PE plastic mulches times the amount of PE plastic mulches

applied in one-acre farm, .

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The change of the cost indirectly related to PE plastic mulches is , and the

empirical expression is the cost of hiring new labor and buying the mulch installation

machine for one-acre farm, .

The PE plastic mulch remnant handling cost is the landfill waste disposal cost,

, which is equal to the landfill tipping fee times the amount of PE plastic mulch

sent to landfill, .

The tomato production before using PE plastic mulches is , and the

tomato market price in Washington is .The marginal production is equal to the

production growth after using PE plastic mulch, which is equal to ,

where is the growth rate of tomato production by using PE plastic mulch.

Therefore, the empirical correspondence of equation (B7) is

(B8)

Rearranging equation (B8) we get equation (3.25):

6). Elasticity of GRT to the Landfill Tipping Fee

( )

163

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Footnote

1 Mulch is a layer of material for plant protection and weed control, which is spread on the top of the soil (USDA, 2012)

2 For the purposes of this article, the term plastic mulch includes all types of plastic mulches with different decay rates, such as PE plastic mulch and fully biodegradable plastic mulch.

3 Disposal fees include not only the fee charged from the disposal facility, but also the labor and machinery costs to move the mulch remnants.

4 We do not consider the case that no plastic mulches are used.

5 The available data for Washington (WA) tomato yield is from 1960 to 1975. However, we regress WA tomato yield onto the US yield, and then used the US yield to predict the

WA yield from 1995 to 2009.

6 PE plastic mulches are one of LLDPE film.

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7 Data related to tomato growing with different brand of biodegradable plastic mulches were collected by the Washington State University Extension SCRI group.

8 Many media sources show that the recycling always costs twice higher much as landfill waste disposal.

9 Ecy.wa.gov lists the case of illegal open burn, and shows the fines from $5000 to

$26,000.

10 The typical plastics are high molecular weight polymers, which mix with other substances for the purpose of performance improvement and cost reduction. The term

“plastic” defines a wide range of synthetic or semi synthetic organic amorphous solid materials that are used for the industrial products manufacture (Pandya, 2011).

11 Crude Oil Futures is continuous contract number 1. Raw futures data is collected from

New York Mercantile Exchange (NYMEX).

12 Corn Futures is continuous contract number 6. Raw futures data is collected from

Chicago Board of Trade (CBOT).

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13 The ICIS Petrochemical Index (IPEX) provides a capacity-weighted measure of average change in petrochemical prices over time. The index calculation includes spot and futures prices of 12 petrochemical grades: ethylene, propylene, benzene, toluene, par xylene, styrene, butadiene, methanol, polyvinyl chloride, polyethylene, polypropylene and polystyrene.

14 The Ljung-Box Q-statistic is used to test the null hypothesis that the model is correctly specified, or equally that the noise terms are random.

15 Although it is common to use the GARCH (1,1) model that most of time assure scholars not to spend time to choose lags, GARCH (1,1) is not suitable for this study.

Because of the limited number of observations, but too many parameters in GARCH

(1,1), the quasi maximum likelihood procedure cannot converge.

16 Although the normality assumption is not satisfied, the quasi-maximum likelihood estimators are consistent and asymptotic normal (Lumsdaine,1996).

167