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Volatility of Multiunit Uniform Price Auction: the Case of the Vehicle Quota System in Singapore Xinkai Cheng May 2011 1

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Volatility of Multiunit Uniform Price Auction: the Case of the Vehicle Quota System in Singapore Xinkai Cheng May 2011 1 Volatility of Multiunit Uniform Price Auction: The case of the Vehicle Quota System in Singapore XinKai Cheng May 2011 1 I am grateful to my thesis advisors Professor Ian Savage and Professor Robert Porter for their guidance, insights and encouragement. This work would not have been possible without them. I would also like to thank Sarah Muir and Professor Joseph Ferrie for their assistance and advice throughout the thesis writing process. 1. Introduction Urban transport management has always been a high priority for Singapore, one of the most densely populated countries in the world and widely admired for its rapid industrialization and modern efficient economy. Even in the early stages of nation building, the government recognized the pressing need to meet the transportation demands of the growing economy and increasingly affluent citizens, against the constraints of scarce land space in this city-state. Road traffic congestion was observed as early as late 1960s, and the government adopted proactive traffic management measures by the early 1970s. These include investments in public transportation and road infrastructure, and adoption of an integrated approach to transportation. In particular, draconian measures were adopted to curb automobile ownership and usage through consistently high import and road taxes, and registration fees. Despite the high costs, there were concerns by late 1980s that automobile ownership was increasing too rapidly. With rapid economic growth, increases in income were neutralizing the effects that fiscal instrument might have on automobile ownership (Phang and Chin, 1990). 8,000 1,000,000 7,000 900,000 800,000 6,000 700,000 5,000 600,000 4,000 500,000 3,000 400,000 300,000 2,000 200,000 1,000 100,000 0 0 1978 2000 1960 1962 1964 1966 1968 1970 1972 1974 1976 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2002 2004 2006 2008 2010 Population (in thousands) Population density (per km^2) Vehicle density (per km^2) Vehicle Population Fig.1: Population, Population Density, Vehicle and Vehicle Population from 1960 to 2010. Vehicle population on right axis In May 1990, the government implemented the Vehicle Quota System (VQS), a quantity rationing system of automobiles in Singapore: a car buyer who wishes to purchase a new car must first bid successfully for a Certificate of Entitlement (COE). The COEs are allocated through a public auction and the price that successful bidders pay is known as the COE premium. 1 Since the implementation of VQS, there had been many changes to the system and bidding format. After a review by a Parliamentary Committee in 1999, the bidding format was gradually changed from a sealed bid to open bid format in July 2001. It was argued that an open bid format will provide better access of information to auction bidders and result in smaller fluctuations of COE premiums and ultimately a better reflection of demand and supply. From the perspectives of policymakers, volatility in the COE premiums is seen as undesirable. Wild monthly fluctuations in COE premiums had been a constant source of frustration for car buyers and car dealers, as it created a lot of uncertainty for them. It is thus important for policy makers to understand and manage the volatility of COE premiums. The objective of this paper is to apply auction theory to analyze the impact on COE premium volatility after the change from a sealed bid to open bid auction format, and empirically investigate if the change resulted in lower volatility of COE premiums. The paper is structured as follows: Section two surveys the existing literature on the VQS and auction theory of multiunit uniform price auctions. Section three provides a brief overview of the VQS. Section four develops the theoretical framework to analyze the impact on volatility after the change in auction format. Section five describes the data and empirical model used in this study. Section six reports the empirical results. Lastly, section seven concludes with a discussion of theoretical analysis and empirical results. 2. Literature Review VQS is a unique transportation management policy that has been studied by many economic researchers. A rich literature on auctions had also been developed since the 1980s. A survey of studies that are relevant to the topic can be divided broadly into two categories: First, studies related directly to the VQS. Second, studies on auction theory, especially those on simultaneous multiunit uniform price auctions. Vehicle Quota System Many studies on VQS have focused on effectiveness and impact on social equity. Chin and Smith (1997) looked at the economic motivations behind the implementation of VQS, specifically the market failure of vehicle ownership and usage. In addition, they did an empirical assessment of VQS and concluded that VQS is indeed effective in controlling vehicle population, though they caution that the ultimate target of policy should be to avoid the harmful externalities associated with excessive vehicle usage. Koh and Lee (1994) applied auction theory to the VQS and discussed the optimal bidding strategies, for both transferable and non-transferable COEs. They also looked at the social equity and desirability of the uniform price format. In conclusion, they argued that COE auction should be made discriminatory, and that “a lowest successful percentage of vehicle value” pricing would be both more equitable and politically acceptable. Koh (2003) took an industrial economics approach and studied the impact of the VQS on the market structure of car dealers in Singapore. He developed an economic model and hypothesized that VQS had 2 increased the concentration of the car dealership industry. He then confirmed the hypothesis with an empirical assessment analyzing the populations and new registrations of different brands of automobiles. In his conclusions, he also suggested that the switch to online open-bidding format may “facilitate coordination among car distributors, so that they may collectively bid more conservatively and prevent the occurrence of bidding wars”. This implies that there would be less volatility in quota premiums if car distributors were successful in their collusion strategy. Chu, Koh and Tse (2004) hypothesized that car buyers use the public information available on past auctions to update their expectations on market demand. Their empirical analysis concludes that information on past bid distributions has good predictive power for the COE premiums. Koh, Mariano and Tse (2003) tested for revenue equivalence when the VQS was changed from the sealed bid format to the open bid format. They developed a regression model to estimate what COE prices would have been under the original sealed bid format and concluded that revenue equivalence did not hold. Quota premium would be on average about US$1,000 lower under the open bidding format. Chu (2010) conducted an empirical analysis of the impact on volatility of COE premiums since the change from sealed bid to open bid format. His study focused only on one category of COE premiums (CAT E) and concluded that the open bid format resulted in lower volatility for that category. I intend to build upon his work, by extending the empirical analysis to other categories. In addition, I will develop a separate regression model that will better estimate the volatility of COE premiums. Furthermore, I will apply auction theory to study the impact on volatility of COE premiums. Auction Theory Auction theory has traditionally focused on the case of single unit auctions. The literature on multiunit auctions is less developed, especially for cases where bidders demand more than a single unit each. As detailed in Klemperer (1999), homogenous units sold in multiunit auctions are allocated among bidders either simultaneously or sequentially. In the first case, all units are sold at the same time while in the latter case each unit is sold sequentially in repeated rounds of bidding. Under simultaneous allocation, there are two main pricing mechanisms: discriminatory and uniform price. Under discriminatory pricing, each bidder pays his own bid while under uniform price each bidder pays the same price, which is usually the lowest winning bid or highest losing bid. VQS is an example of a multiunit auction that has simultaneous allocation under a uniform price system, where bidders demand more than one unit each. As studies on single unit auctions are more developed, the studies on multiunit auctions build upon the works on single unit auctions. The best single unit analogue of the sealed bid version of VQS is called the second-price sealed bid auction or Vickrey auction. It is named after Vickrey (1961) who designed the auction for a single object, in which bidders submit sealed bids and the highest bidder wins the object but pays the second highest bid amount. He was the first to prove the revenue equivalence theorem, which was subsequently generalized by Riley and Sameulson (1981). The theorem implies that all 3 standard auctions are equivalent in terms of expected revenue, assuming that bidders are risk-neutral and the objects are allocated to the bidders with the highest values. In addition, under the Vickrey auction for single units, it is a weakly dominant strategy to bid one’s true value and the auction is efficient. One of the earliest studies on multiunit auctions is by Wilson (1979). He analyzed share auctions, where each bidder submits a bid similar to a demand schedule that states the bid for every possible quantity of the units in the auction. He showed that under uniform price auction, there are equilibrium strategies which support bid prices lower than that in the case where the units are sold individually. Ausubel and Cramton (2002) showed that multiunit auctions differ from single unit auctions in important ways. When bidders demand more than one unit, both discriminatory and uniform price auction formats lead to inefficient outcomes and the revenue equivalence theorem fails.
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