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The Review of Economic Studies
, Volume Advance Article – Nov 17, 2017

40 pages

/lp/ou_press/better-lucky-than-rich-welfare-analysis-of-automobile-licence-fzxdLVquDs

- Publisher
- Oxford University Press
- Copyright
- © The Author 2017. Published by Oxford University Press on behalf of The Review of Economic Studies Limited.
- ISSN
- 0034-6527
- eISSN
- 1467-937X
- D.O.I.
- 10.1093/restud/rdx067
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- See Article on Publisher Site

Abstract Economists often favour market-based mechanisms over non-market based mechanisms to allocate scarce public resources on grounds of economic efficiency and revenue generation. When the usage of the resources in question generates type-dependent negative externalities, the welfare comparison can become ambiguous. Both types of allocation mechanisms are being implemented in China's major cities to distribute limited vehicle licences as a measure to combat worsening traffic congestion and air pollution. While Beijing employs non-transferable lotteries, Shanghai uses an auction system. This article empirically quantifies the welfare consequences of the two mechanisms by taking into account both allocation efficiency and automobile externalities post-allocation. Our analysis shows that different allocation mechanisms lead to dramatic differences in social welfare. Although Beijing's lottery system has a large advantage in reducing automobile externalities over auction, the advantage is offset by the significant allocative cost from misallocation. The lottery system in Beijing resulted in a social welfare loss of 30 billion Yuan (nearly $5 billion) in 2012 alone. A uniform-price auction would have generated nearly 20 billion Yuan to Beijing municipal government, more than covering all its subsidies to the local public transit system. 1. Introduction Market-based mechanisms (e.g. auction) have often been advocated for allocating scarce public resources on grounds of economic efficiency and revenue generation, as opposed to non-market based mechanisms (e.g. lottery). Both have been used widely in practice, often for different types of resources. For example, auctions are routinely used to sell mineral rights, timber, and radio spectrum while lotteries are employed in distributing hunting licences, charter school admissions, and jury duty.1 Market-based mechanisms have the potential to achieve efficiency by using price signals to distribute the scarce resource to those with the highest willingness to pay (WTP), whereas lotteries with no-transferability can lead to misallocation and welfare loss. However, when the usage of the resources generates negative externalities that are increasing in WTP, the welfare comparison between the two mechanisms can become ambiguous. In this case, the social benefit (consumer welfare net of externalities), the basis for measuring social welfare, diverges from and may even be decreasing with WTP, the basis for resource allocation under the market-based mechanisms. The resource in question here is a licence or permit to register a vehicle. Major cities in China have been experiencing the world's worst traffic congestion and air pollution as a result of rapid economic growth as well as vehicle ownership outpacing transport infrastructure and environmental regulation.2 Beijing, the second largest city in China, has been routinely ranked as one of the cities with the worst traffic condition in the world, with the average traffic speed during peak hours below 15 miles per hour. The daily concentration of PM2.5, a key measure of air quality, frequently reaches over ten times of the daily health limit recommended by the World Health Organization (WHO). To ease gridlock and improve air quality, Beijing municipal government introduced a quota system for vehicle licences in 2011 to limit the growth of vehicle ownership. About 20,000 new licences are distributed each month through non-transferable lotteries during 2011 and 2013 and the monthly quota was reduced to about 12,000 after 2013. Winning the lottery has become increasingly difficult: the odds decreased from 1:10 in January 2011 to 1:100 by the end of 2013 and further to less than 1/700 in August 2016. Shanghai, the largest city in China, also has a vehicle licence quota system but its licence allocation is through an auction system instead of lotteries. In fact, an auction system has been in place since 1994 but the goal of reducing vehicle ownership did not emerge until much more recently. In 2008, Shanghai government adopted a form of multi-unit, discriminatory and dynamic auction held monthly online to distribute about 10,000 licences. In 2012, the auction system generated over 6.7 billion Yuan (over $1 billion) to Shanghai municipal government.3 The average bid for a licence reached over 92,000 Yuan in March 2013, higher than the price of many entry-level vehicle models. The main objective of this study is to empirically quantify the welfare consequences of the two allocation mechanisms in distributing vehicle licences taking into account both allocation efficiency and externalities associated with vehicle usage. This is an important question for at least two reasons. First, traffic congestion and air pollution impose major costs to the society (Parry et al., 2007). Creutzig and He (2008) estimate that the external costs from automobile usage in Beijing amount to over 7.5% of its GDP. Under the endorsement of the central government, many large cities in China are adopting the licence quota system and employing different allocation mechanisms.4 However, the impacts and welfare consequences of these policies are unknown. Second, there is theoretical ambiguity a priori in welfare comparison between the two mechanisms because the usage of licence (registering and ultimately driving a vehicle) is associated with negative externalities such as congestion and pollution. These type-dependent externalities are likely to be increasing in consumers' WTP for a licence in that consumers with high WTP tend to have high income. At the same time, high-income households on average buy less fuel-efficient vehicles and drive more than low-income households as household travel survey data from both China and U.S. show (see Table 1 and discussion in Section 2). Whether the lottery or the auction system leads to higher social welfare depends critically on the level of consumer heterogeneity in WTP and its relationship with automobile externalities. Therefore, the efficiency comparison and the magnitude of welfare impacts are ultimately empirical questions. Table 1. Household income, engine size and annual travel Annual income Engine size(litre) Annual VMT(km) Number of observations (Yuan) Mean S.D. Mean S.D. ≤50k 1.58 0.38 13,907 8,499 4,827 50–100k 1.68 0.38 14,922 8,813 5,379 100–150k 1.78 0.42 16,554 9,478 1,327 150–200k 1.83 0.43 17,882 9,937 417 200–250k 1.87 0.39 17,661 9,348 133 250–300k 1.94 0.48 18,923 9,328 70 ≥ 300k 2.18 0.63 20,382 12,480 98 Full sample 1.67 0.40 14,896 8,927 12,251 Annual income Engine size(litre) Annual VMT(km) Number of observations (Yuan) Mean S.D. Mean S.D. ≤50k 1.58 0.38 13,907 8,499 4,827 50–100k 1.68 0.38 14,922 8,813 5,379 100–150k 1.78 0.42 16,554 9,478 1,327 150–200k 1.83 0.43 17,882 9,937 417 200–250k 1.87 0.39 17,661 9,348 133 250–300k 1.94 0.48 18,923 9,328 70 ≥ 300k 2.18 0.63 20,382 12,480 98 Full sample 1.67 0.40 14,896 8,927 12,251 Notes: The data source is 2010 Beijing Household Travel Survey. There are 12,251 vehicles surveyed from 10,577 households. In all, 1,440 households own two vehicles while 93 households own three vehicles. Table 1. Household income, engine size and annual travel Annual income Engine size(litre) Annual VMT(km) Number of observations (Yuan) Mean S.D. Mean S.D. ≤50k 1.58 0.38 13,907 8,499 4,827 50–100k 1.68 0.38 14,922 8,813 5,379 100–150k 1.78 0.42 16,554 9,478 1,327 150–200k 1.83 0.43 17,882 9,937 417 200–250k 1.87 0.39 17,661 9,348 133 250–300k 1.94 0.48 18,923 9,328 70 ≥ 300k 2.18 0.63 20,382 12,480 98 Full sample 1.67 0.40 14,896 8,927 12,251 Annual income Engine size(litre) Annual VMT(km) Number of observations (Yuan) Mean S.D. Mean S.D. ≤50k 1.58 0.38 13,907 8,499 4,827 50–100k 1.68 0.38 14,922 8,813 5,379 100–150k 1.78 0.42 16,554 9,478 1,327 150–200k 1.83 0.43 17,882 9,937 417 200–250k 1.87 0.39 17,661 9,348 133 250–300k 1.94 0.48 18,923 9,328 70 ≥ 300k 2.18 0.63 20,382 12,480 98 Full sample 1.67 0.40 14,896 8,927 12,251 Notes: The data source is 2010 Beijing Household Travel Survey. There are 12,251 vehicles surveyed from 10,577 households. In all, 1,440 households own two vehicles while 93 households own three vehicles. Since licences are allocated through lotteries and trade is not allowed in Beijing, we do not observe consumers' WTP. In Shanghai, licences are auctioned in a non-standard format where the bids may not reflect value and the equilibrium bidding function is difficult to characterize as shown in an experimental study by Liao and Holt (2013). To recover consumers' WTP for a licence, we recognize that consumer surplus from owning a vehicle should inform WTP for a licence, the additional cost that consumers have to bear to own a vehicle. To estimate consumer surplus from vehicle ownership, we estimate a random coefficients discrete choice model of vehicle demand that takes into account consumer preference heterogeneity and unobserved product attributes developed by Berry et al. (1995) (henceforth BLP). Similar to Petrin (2002), our estimation strategy employs both aggregate market-level data and information from household surveys to form moment conditions. From household surveys on new vehicle buyers, we obtain the share of buyers among different income groups. We use them to form (micro-) moment conditions and they are critical in identifying consumer preference heterogeneity. An important departure in our identification strategy from the literature is that we do not rely on the maintained exogeneity assumption that unobserved product attributes are uncorrelated with observed product attributes. Taking advantage of the multi-market nature of the data, we include vehicle model fixed effects to control for unobserved product attributes. In addition, we explicitly employ the common-trend assumption implicit in the difference-in-differences (DID) framework to better isolate the effect of the policy shock from unobserved demand shocks: the specification without the common trend assumption tends to attribute the large sales drop in 2011 as coming from a large (unobserved) negative demand shock. Our market-level data include data for four cities: Beijing, Nanjing, Shanghai, and Tianjin. Nanjing and Tianjin are two large cities next to Shanghai and Beijing, respectively. They did not have the licence quota system during the data period and as we show through graphs and regressions, the automobile markets in these two cities exhibit similar trends to Beijing and Shanghai in the absence of the policies. Several important findings emerge from our analysis. First, both policies in Beijing and Shanghai significantly limited new vehicle sales: the lottery system in Beijing reduced new vehicle sales by over 1.2 million in 2011 and 2012 while the Shanghai auction reduced sales by nearly two million from 2008 to 2012. These reductions are substantial and a reflection of the stringency of the quota system. Second, the welfare consequences of different allocation mechanisms are huge in magnitude. While Beijing's lottery system has a non-trivial advantage of three billion Yuan over an auction system in reducing automobile externalities, its allocative cost due to misallocation is over 33 billion Yuan in 2012, implying a welfare loss of nearly 30 billion in Beijing in 2012 alone. The significant allocative cost from the lottery system is driven by the large consumer heterogeneity in WTP for licences. Third, a uniform price auction would have generated nearly 20 billion revenue to Beijing municipal government in 2012, more than enough to cover all its subsidies to the local public transit system. Fourth, based on a range of plausible assumptions, the optimal level of quota in Beijing was lower than the quota used in 2012 and further reducing the quota would increase net social welfare. This study contributes to the literature in the following aspects. First, although theoretical literature on allocation mechanisms are abundant, there are very few empirical studies on quantifying welfare outcomes of different mechanisms. Glaeser and Luttmer (2003) study housing market rationing under the rent control in New York city and provide evidence of significant misallocation of houses, without explicitly estimating the allocative cost. Davis and Kilian (2011) find significant allocative costs from misallocation under the price ceiling in the U.S. residential market for natural gas. In the context of a quantity regulation, this article empirically examines allocative outcomes by exploring a rare opportunity where both market-based and non-market mechanisms are used for the same type of resources.5 Second, as discussed further above, in the presence of type-dependent externalities that is increasing in WTP, the efficiency comparison between the lottery and auction systems could be ambiguous due to the fact that externalities introduce a wedge between net social benefit, the basis for measuring social welfare, and the private benefit, the basis of resource allocation under auction. The implication of type-dependent externalities on optimal allocation mechanisms has been examined in several theoretical studies in the context of firm competition.6 Our analysis empirically highlights type-dependent externalities in the context of consumer goods and showcases the advantage of the lottery system in reducing externalities. Third, our analysis adds to the emerging literature on China's environmental and energy policies. China is by far the largest emitter of greenhouse gases, accounting for nearly 30% of world emissions in 2013. It is the largest energy consumer and is also the top importer of crude oil in the world. China's domestic policies could have global impacts but our understanding on the impacts of these policies is very limited.7 Before we proceed, it is helpful to further clarify the scope of our welfare analysis. First, our analysis focuses on the welfare consequences of different allocation mechanisms within the policy framework of a quota system. Automobile usage generates multiple types of externalities including congestion, air pollution, traffic accidents, and noise. A vehicle licence quota system in theory is not the first-best instrument to internalize these externalities since it does not directly address the source of externalities such as driving.8 Second, our analysis focuses on welfare impacts in the short run. The allocation of vehicle licences are likely to have impacts on household location, job decision and schooling choices, all of which could have important welfare implications in the long term. Although part of these welfare impacts such as the desire to live in a large apartment outside of the city center and hence the need to have a vehicle are captured by the WTP that we estimate, we are not investigating the policy impacts in these dimensions. The broader welfare comparisons between the quota system with other potentially more efficient policies such as congestion pricing and fuel taxes as well as long-run analysis will necessitate additional information and modelling efforts. 2. Allocation Mechanisms and Externalities The purpose of this section is to offer an illustration on the welfare comparison between lottery and auction systems in the presence of type-dependent negative externalities. In allocating scarce public resources, governments or resource managers have relied on both market-based mechanisms and non-market based mechanisms often for different types of goods. Market-based mechanisms such as a well-designed auction can allocate the resource to those with the highest value and hence achieve efficiency while non-market based mechanisms such as an administration process or lottery do not. It is argued that non-market based mechanisms such as a lottery are chosen often out of concern of fairness or for political convenience (Taylor et al., 2003). However, when the usage of resources generates market failures such as externalities, market-based mechanisms such as an auction may not yield efficient allocation because the private value and the social benefit diverge. We illustrate this point within the context of allocating vehicle licences using lotteries and auctions. Consider the following environment: (1) there are Q_ licences to be allocated; (2) there are N(N>Q_) agents, each demanding at most one licence; (3) each agent i has a private value (or WTP) Vi and the value is independent and identically distributed with a support of [0,V¯]; (4) the usage of the licence imposes an external cost of Ei, which is increasing in Vi. The fourth assumption of type-dependent externalities is a key departure from a standard model of resource allocation. As we document below, consumers with high WTP for a licence tend to have higher income. On average, they drive larger and less fuel-efficient vehicles and they drive more relative to those with a low WTP. So the usage of licences by those with a higher WTP is likely to generate larger external costs. Our estimates below show that neither the magnitude of external costs nor the difference in external costs across households is trivial. That is, the discussion below does have empirical relevance in our context. We compare two allocation mechanisms: a non-transferable lottery where all agents can participate and have an equal chance of winning (random allocation); and a uniform price auction where the Q_ highest bidders each gets one licence and pays a price equal to the highest rejected bid. Harris and Raviv (1981) show that each agent bids her value in this auction and therefore the licences will be allocated to the Q_ agents with the highest value. We use the uniform price auction for exposition and the point is not lost with other types of auctions such as discriminatory auctions that can achieve the same allocation outcome. We start with a simple case of allocation mechanisms with constant external costs from the usage of the licence and ultimately automobiles as depicted in the top panel of Figure 1. To ease exposition, we focus on a linear WTP schedule. Line Q(p) is the (smoothed) WTP schedule. Line EC is the external cost for the agents with the corresponding WTP and it is constant in this case. Assuming the quota Q_ is lower than the optimal cap Q*, the area BCD is the conventional deadweight loss (DWL) from quantity constraint. Total consumer surplus from the auction system is given by the area ABQ_O but the lottery system can only realize Q_/Q1 of consumer surplus from the random allocation, which is given by AQ_O. Therefore, the allocative cost, that is, welfare loss from misallocation, of the lottery system is ABQ_, which could even be larger than the DWL from quantity constraint. The empirical importance of allocative cost from random allocation is highlighted in Davis and Kilian (2011) in the context of price ceiling in the U.S. residential natural gas market. Figure 1. View largeDownload slide Welfare comparison of lottery and auction with externalities. Figure 1. View largeDownload slide Welfare comparison of lottery and auction with externalities. The middle panel in Figure 1 shows a case where the external costs are positively correlated with WTP. As in the top panel, BCD is the DWL from quantity constraint and ABQ_ is the allocative cost from the lottery system. However, the presence of type-dependent external costs implies that the lottery system leads to a reduction in external costs depicted by EDF, offsetting part of the allocative cost. The net welfare loss from lottery (versus auction) is given by the area ABQ_−EDF, which is positive in this case. The advantage in reducing externalities from the lottery system is dominated by the welfare loss from misallocation, implying that the auction system still produces a better welfare outcome. The welfare comparison between the two systems is reversed in the bottom panel where the external costs are “strongly” increasing in WTP. To ease exposition, we assume that the quota Q_ is at the intersection of the WTP schedule and the corresponding external cost curve. In this case, the reduction in external costs from the lottery given by EBQ_Q3 dominates the allocative cost given by ABQ_. Since agents with the highest private value generate the smallest social value, the auction will allocate the licences to the wrong hands from the efficiency perspective. This result is driven by the fact that the wedge introduced by the external costs between the private value and the social value leads to a negative correlation between the two. Note that the external cost line does not have to surpass the WTP schedule as shown in the graph to make the point. The result could still hold if the EC line is below the WTP schedule but is steeper. Which of the two scenarios is playing out in reality depends on the WTP schedule as well as its relationship with the external cost curve. Although one can get a good sense on the external costs from driving from different households based on household survey data, the WTP schedule is not readily available. The empirical goal is to develop a method to estimate the WTP schedule and conduct welfare comparison taking into account the external costs. The latent nature of WTP prevents me from showing the relationship between WTP and externalities from automobile usage directly off of the data. Supplementary Appendix Table 2 based on household surveys for new vehicle buyers (to be discussed in the data section) clearly shows that high-income households account for a disproportionally large share of new vehicle buyers, suggesting a positive correlation between income and WTP for a new vehicle. Because of these two reasons (not observing WTP directly and the positive correlation between WTP and income), we use income as a proxy for WTP in showing the potential relationship between WTP and externalities to motivate our analysis. Table 1 shows the average engine size, and annual vehicle miles travelled (VMT) by seven income groups from 2010 Beijing Household Travel Survey. For vehicle owners, the survey has information on household income (by group), engine size, and annual VMT by vehicle.9 The table shows that high-income households own vehicles with larger engines and drive more on average. These positive correlations are consistent with evidence of vehicle ownership and travel behaviour in the U.S. (Small and Van Dender, 2007; Li et al., 2009, 2014).10 Since the major part of externalities from automobile usage in urban areas comes from congestion and air pollution and these externalities are directly linked to travel distance and gasoline usage (Parry et al., 2007). This implies that households with a higher income are likely to produce larger externalities from automobile usage than households with a lower income. The welfare analysis will return to this point and provide estimates of externalities for different households with different WTP. 3. Policy and Data Description In this section, we first describe the background for the quota systems. We then discuss the lottery and auction policies in Beijing and Shanghai and present our data thereafter. 3.1. Background During the past three decades, China has embarked on an extraordinary journey of economic growth with its GDP growing at about 10% a year. As household income grows, luxury good consumption such as automobiles started to pick up dramatically at the turn of the century. Annual sales of new passenger vehicles increased from 2.4 million units in 2001 to nearly 22 million in 2013 as shown in Supplementary Appendix Figure 1. China surpassed the U.S. to become the largest auto market in 2009 and in 2013, it accounted for 26% of world's total new auto sales. Large cities in China are ahead of the curve in both economic growth and vehicle ownership. Beijing with about seven million households has gone from a city on bikes to a city on cars during this period: the stock of passenger vehicles increased from 1.6 million units to nearly 5 million units as shown in Supplementary Appendix Figure 1.11 The rapid growth in vehicle ownership leads to serious traffic congestion, despite significant efforts in expanding roads and public transit systems and a whole range of other traffic management policies such as driving restrictions and reducing public transit fares. The city is often ranked as one of the worst cities in traffic conditions. The traffic speed on arterial roads within the 5th ring road during morning peak hours (7:00–9:00) on work days averaged 14.7 miles/hour (MPH) in 2011, reduced from 22.8 MPH in 2005. The average speed was 13.4 MPH during afternoon peak hours (17:00–19:00) in 2011, compared with 20.2 MPH in 2005. During the same period, air quality has worsened dramatically, and the air quality index is frequently above the level above which the U.S. EPA recommends that everyone should avoid all outdoor physical activities.12 Shanghai, with 8.5 million households, has slightly better traffic conditions, on par with those in Los Angeles. The traffic speed on arterial roads averages 21.2 MPH and 22.3 MPH during morning and evening peak. As shown in the bottom panel of Supplementary Appendix Figure 1, the total number of vehicles in Shanghai is less than half of that in Beijing, despite having more households and higher household income. This is largely due to vehicle purchase restrictions put in place before vehicle ownership took off as we discuss below. The air quality in Beijing is consistently worse than Shanghai due to more vehicles, worse traffic, and winter heating coupled with unfavourable topography. In a ranking of air quality among 28 major cities on the east coast, Beijing ranked at the bottom with an annual average PM10 concentration of 121 micrograms per cubic meter while Shanghai ranked at 8th with an average PM10 concentration of 79 in 2010, still significantly higher than the WHO's health limit. 3.2. Policy description To address traffic congestion and air pollution, Beijing municipal government announced the policy of capping new vehicle licences which are necessary to register a vehicle, on December 23, 2010. Since January 2011, lotteries have been used to allocate about 20,000 licences each month during 2011–13 and the annual quota was reduced to 150,000 after 2013. A licence is needed for first-time buyers, and those who purchase an old vehicle, accept a gifted vehicle, or transfer out-of-state registration to Beijing. Vehicle owners who scrap the used vehicle can transfer the old licence to the new vehicle and do not need a new licence. The eligible participants include Beijing residents and non-residents who have been paying income tax for at least five years in Beijing. The licences are assigned to winners through random drawings. The winners can then use the licence to register their vehicles. Transferring a licence from a winner to other people is prohibited. Although there is anecdotal evidence that some transferring occurred by having vehicle registered under the winner but paid and used by another person, this is not known to be widespread because the legal owner (the winner) not only has the liabilities in paying annual registration fee, traffic fines and emission inspections, but also is liable for damages and injuries in accidents. In addition, barriers are in place to prevent Beijing residents from registering vehicles in neighbouring provinces. First, a temporary driving permit is needed to be able to drive an out-of-state vehicle in Beijing. More importantly, these vehicles are banned from entering the 5th ring road (within which the vast majority of business and population are located) during rush hours. So this avoidance behaviour is also not likely to be widespread. Among all the licences allocated, about 88% (or 17,600 each month) are for private vehicles and the rest are for institutions. The winners are determined in two different pools for these two categories. While the private licences are allocated monthly, the institutional licences are done bi-monthly. The first lottery was held on 26th, January 2011 and 17,600 private licences were allocated among 187,420 participants. The winning odds reduced to 1:100 by the end of 2013 and further to 1/725 in August 2016, due to the cumulation of pent-up demand over time as well as future buyers entering into the lottery pool.13 The top panel of Supplementary Appendix Figure 2 shows monthly licences allocated and new vehicle sales. The dramatic decrease in vehicle sales since the start of the policy reflects the stringency of the policy relative to the demand for new vehicles. The difference between vehicle sales and the number of licences allocated is due to the sales that do not need a licence (vehicle replacement after scrappage). The winners have six months to register a new vehicle before the winning certificates become expired. Once expired, the licence quota recycles back for distribution in future lotteries. The winners who allow their licences to expire will not be permitted to participate in the lottery within the next three years. Shanghai is the first city to implement a vehicle licence quota system in China and it auctioned its first licence in 1986. Although the market for private vehicles was very small at that time, traffic congestion was a big problem due to insufficient road infrastructure. In fact, Shanghai experimented with vehicle driving restrictions even before 1995. The auction system has evolved over time. Initially, it was a sealed-bid auction where reservation prices and quota levels varied across vehicles produced in Shanghai, non-Shanghai produced vehicles, and imports.14 In 2003, a unified auction system without a reservation price was put in place for domestic vehicles and imports. The online auction format during 2008 to 2012 can be characterized as a multi-unit, discriminatory (pay as you bid), and dynamic auction. The auction is held monthly during a 90-minute period and bidders observe the current lowest accepted bid prior to submitting a bid. In the first hour, bidders can submit a single initial bid and in the last 30 minutes, each bidder can revise their bids up to two times. The revised bid however has to be within a window of 300 Yuan below and above the current lowest accepted bid. The purpose of the bid revision period and the restriction on bid revisions is to reduce price volatility.15 The bottom panel in Supplementary Appendix Figure 2 shows the average and lowest accepted bid in each month from 2008 to 2012. The average bid price increased from 23,370 to 69,346 Yuan during this period. The plot shows that the average and the lowest winning bids are very close: the difference is usually less than 500 Yuan or 1–2% of the average bid.16 The winners are required to purchase a new vehicle within three months before the licence expires. The vehicle and the licence cannot be transferred within the first year of registration. Similar to Beijing, vehicles registered outside of Shanghai are not allowed to use the major roads during rush hours. Although there is anecdotal evidence that some households choose to register their vehicles in neighbouring provinces due to high licence prices, this phenomenon is not believed to be widespread. 3.3. Data description Our analysis focuses on policies in Beijing and Shanghai and we bring two nearby cities, Nanjing and Tianjin into analysis to facilitate identification. Nanjing is about 300 km away from Shanghai and is the capital city of Jiangsu province that shares boarder with Shanghai. Tianjin is about 150 km from Beijing. The characteristics of these four cities are shown in Supplementary Appendix Table 1. Shanghai and Beijing are the two largest cities in China by population. Tianjin is the sixth and Nanjing is the 11th.17 Shanghai has the highest average household income while Tianjin has the lowest. Supplementary Appendix Table 1 shows that Beijing has the smallest increase in average nominal income of 42% during the five-year period while Shanghai has the largest increase of 57%, with the inflation being 13.7% during this period. We rely on four main data sets together with a variety of auxiliary data for our analysis. The first main data set contains monthly vehicle sales by model (vintage-nameplate) in each city from 2008 to 2012. There are 84,912 observations (city-model-year-month) with 1,769 distinct models.18Figure 2 plots monthly sales (in log) in each city and displays two important features. First, sales in all four cities grew over time and tracked each other well before 2011 and the trend is more consistent across Beijing, Nanjing and Tianjin, reflecting the fact that Shanghai has an auction policy in place throughout the data period. Second, there was strong seasonality which is largely driven by holidays. The sales in December 2010 went up dramatically in all cities but then dropped significantly in February 2011. This is due to the fact that Chinese New Year was on February 3rd in 2011.19 Third, the sales increase in December 2011 appeared to be stronger in Beijing than in other cities. This is due to the anticipation and more importantly the fact that the quota policy was announced in December 23, 2010. Very little if any discussion on the policy was made public before the announcement. However, once the policy was announced, many who planned to buy a vehicle in the near future moved their purchase forward into the last week of December. In the main specification of our analysis, we remove the last two months in 2010 and the first two months in 2011 in Beijing to deal with the anticipation and more importantly announcement effects. Figure 2. View largeDownload slide New vehicle monthly sales (in logarithm) in the four cities. Figure 2. View largeDownload slide New vehicle monthly sales (in logarithm) in the four cities. The second data set contains vehicle characteristics of each model in the sales data. These characteristics include price, fuel economy (litres/100 km), vehicle size, engine size, vehicle type, and vehicle segment. The summary statistics are presented in Table 2. Vehicle prices are computed based on the Manufacturer Suggested Retail Prices (MSRPs) and the sales tax.20 The sales tax is normally set at 10% but was reduced to 5% and 7.5% for vehicles with engine displacement no more than 1.6 litre in 2009 and 2010, respectively. The average MSRP in the sample is over 300,000 Yuan and the median price is over 190,000, both significantly higher than the average household income in these cities. During the data period, the quality-adjusted prices have been decreasing by 3% each during year.21 Table 2. Summary statistics of vehicle sales and characteristics Variable Mean Median S.D. Min Max Price (in 2012 Yuan) 311.31 193.92 277.75 36.49 1148.38 Monthly sales by model in Beijing 125.93 31.00 240.66 1.00 3464.00 Monthly sales by model in Nanjing 34.71 9.00 65.36 1.00 964.00 Monthly sales by model in Shanghai 57.01 11.00 131.23 1.00 3036.00 Monthly sales by model in Tianjin 57.33 12.00 125.75 1.00 2295.00 Vehicle size ( m2) 8.01 8.09 1.01 4.20 10.97 Displacement (liter) 2.09 1.87 0.77 0.90 5.70 Liters per 100 kilometers 9.10 8.80 2.09 2.90 17.20 Yuan per 100 kilometers 66.17 63.62 16.10 20.61 129.95 Passenger car dummy 0.63 1.00 0.48 0.00 1.00 SUV dummy 0.22 0.00 0.41 0.00 1.00 Minivan dummy 0.15 0.00 0.36 0.00 1.00 Large dummy 0.14 0.00 0.35 0.00 1.00 Luxury dummy 0.02 0.00 0.16 0.00 1.00 Medium dummy 0.35 0.00 0.48 0.00 1.00 Mini dummy 0.03 0.00 0.17 0.00 1.00 Small dummy 0.21 0.00 0.41 0.00 1.00 Upper medium dummy 0.24 0.00 0.43 0.00 1.00 Variable Mean Median S.D. Min Max Price (in 2012 Yuan) 311.31 193.92 277.75 36.49 1148.38 Monthly sales by model in Beijing 125.93 31.00 240.66 1.00 3464.00 Monthly sales by model in Nanjing 34.71 9.00 65.36 1.00 964.00 Monthly sales by model in Shanghai 57.01 11.00 131.23 1.00 3036.00 Monthly sales by model in Tianjin 57.33 12.00 125.75 1.00 2295.00 Vehicle size ( m2) 8.01 8.09 1.01 4.20 10.97 Displacement (liter) 2.09 1.87 0.77 0.90 5.70 Liters per 100 kilometers 9.10 8.80 2.09 2.90 17.20 Yuan per 100 kilometers 66.17 63.62 16.10 20.61 129.95 Passenger car dummy 0.63 1.00 0.48 0.00 1.00 SUV dummy 0.22 0.00 0.41 0.00 1.00 Minivan dummy 0.15 0.00 0.36 0.00 1.00 Large dummy 0.14 0.00 0.35 0.00 1.00 Luxury dummy 0.02 0.00 0.16 0.00 1.00 Medium dummy 0.35 0.00 0.48 0.00 1.00 Mini dummy 0.03 0.00 0.17 0.00 1.00 Small dummy 0.21 0.00 0.41 0.00 1.00 Upper medium dummy 0.24 0.00 0.43 0.00 1.00 Notes: The observation is at the vehicle model-year-month level. Prices include vehicle sales tax which is 10% in 2008, 2011, and 2012. The tax varied across vehicles with different engine size in 2009 and 2010. There are 21,228 observations from 2008 to 2012 with 1,769 models (vintage-nameplate) in the data set. Table 2. Summary statistics of vehicle sales and characteristics Variable Mean Median S.D. Min Max Price (in 2012 Yuan) 311.31 193.92 277.75 36.49 1148.38 Monthly sales by model in Beijing 125.93 31.00 240.66 1.00 3464.00 Monthly sales by model in Nanjing 34.71 9.00 65.36 1.00 964.00 Monthly sales by model in Shanghai 57.01 11.00 131.23 1.00 3036.00 Monthly sales by model in Tianjin 57.33 12.00 125.75 1.00 2295.00 Vehicle size ( m2) 8.01 8.09 1.01 4.20 10.97 Displacement (liter) 2.09 1.87 0.77 0.90 5.70 Liters per 100 kilometers 9.10 8.80 2.09 2.90 17.20 Yuan per 100 kilometers 66.17 63.62 16.10 20.61 129.95 Passenger car dummy 0.63 1.00 0.48 0.00 1.00 SUV dummy 0.22 0.00 0.41 0.00 1.00 Minivan dummy 0.15 0.00 0.36 0.00 1.00 Large dummy 0.14 0.00 0.35 0.00 1.00 Luxury dummy 0.02 0.00 0.16 0.00 1.00 Medium dummy 0.35 0.00 0.48 0.00 1.00 Mini dummy 0.03 0.00 0.17 0.00 1.00 Small dummy 0.21 0.00 0.41 0.00 1.00 Upper medium dummy 0.24 0.00 0.43 0.00 1.00 Variable Mean Median S.D. Min Max Price (in 2012 Yuan) 311.31 193.92 277.75 36.49 1148.38 Monthly sales by model in Beijing 125.93 31.00 240.66 1.00 3464.00 Monthly sales by model in Nanjing 34.71 9.00 65.36 1.00 964.00 Monthly sales by model in Shanghai 57.01 11.00 131.23 1.00 3036.00 Monthly sales by model in Tianjin 57.33 12.00 125.75 1.00 2295.00 Vehicle size ( m2) 8.01 8.09 1.01 4.20 10.97 Displacement (liter) 2.09 1.87 0.77 0.90 5.70 Liters per 100 kilometers 9.10 8.80 2.09 2.90 17.20 Yuan per 100 kilometers 66.17 63.62 16.10 20.61 129.95 Passenger car dummy 0.63 1.00 0.48 0.00 1.00 SUV dummy 0.22 0.00 0.41 0.00 1.00 Minivan dummy 0.15 0.00 0.36 0.00 1.00 Large dummy 0.14 0.00 0.35 0.00 1.00 Luxury dummy 0.02 0.00 0.16 0.00 1.00 Medium dummy 0.35 0.00 0.48 0.00 1.00 Mini dummy 0.03 0.00 0.17 0.00 1.00 Small dummy 0.21 0.00 0.41 0.00 1.00 Upper medium dummy 0.24 0.00 0.43 0.00 1.00 Notes: The observation is at the vehicle model-year-month level. Prices include vehicle sales tax which is 10% in 2008, 2011, and 2012. The tax varied across vehicles with different engine size in 2009 and 2010. There are 21,228 observations from 2008 to 2012 with 1,769 models (vintage-nameplate) in the data set. MSRPs are set by manufacturers and are generally constant across locations and within a model year. There could be potential pitfalls in using MSRPs when they are different from the transaction prices due to promotions. Different from the promotion-heavy environment in the U.S., China's auto market has infrequent promotions from manufactures or dealers and retail prices are often very close to or the same as MSRPs, a phenomenon commonly seen for luxury products in China. Our analysis uses MSRPs with the implicit assumption that the allocation mechanisms in Shanghai and Beijing are not likely to affect firms price-setting behavior or local dealer incentives. This assumption should not be a driving factor in our results given the small market shares of these two cities and the marketing environment for automobiles in China.22 The third data set is income distributions by city by year. Income is arguably the most important determinant in vehicle purchase decisions. China's National Bureau of Statistics conducts a census every 10 years but the income data at the household level are not publicly available. Instead, we obtain the average income by income quantiles in each city in each year from the statistical yearbooks of each city. We construct household income distribution based on these aggregate information together with Chinese Household Income Survey (2002), a national representative survey, conducted by researchers at the University of Michigan. We adjust the income in the household survey (14,971 observations) proportionally and separately for each of the quantiles so that the interpolated income distributions in a given year are consistent with the annual income statistics from the yearbooks. The fourth set of data contains aggregate information from an annual national representative household survey among new vehicle buyers from Ford Motor Company. We were provided household shares by four income groups among new vehicles buyers in each city in each year. Supplementary Appendix Table 2 presents these shares along with the shares of different income group among all households, which are constructed based on the income distributions from each city. The table shows that high income groups account for a disproportionally large share of vehicle buyers. While the highest income group (annual household income over 144,000) accounts for only 4% of all households in 2008 in Beijing, this group accounts for over 20% of new vehicle buyers. These information will be used to form additional moment conditions that are crucial to identify consumer preference parameters. 4. Empirical model of vehicle demand To conduct welfare analysis, we need to recover consumers' WTP schedule for vehicle licences. As shown in Section 2, the efficiency outcomes under different allocation mechanisms hinge on the heterogeneity of consumer WTP: different mechanisms would have the same allocation efficiency in the absence of any heterogeneity. We do not observe licence prices in Beijing since the licences are allocated through lottery for free and transfers are not allowed. Our strategy to recover consumers' WTP for a licence is to recognize that the WTP for a licence reflects the additional cost a consumer is willing to bear to own a vehicle. Therefore, consumer surplus from owning a vehicle, that is, the WTP for the vehicle minus the market price of the vehicle, should inform the WTP for the licence itself. In particular, the WTP for the licence itself should be equal to the consumer surplus from the most preferred vehicle if the licence lasts as long as the vehicle (10–15 years).23 To estimate consumer surplus for different vehicles models, we set up and estimate a random coefficient discrete choice model of vehicle demand. In this section, we first specify the utility function, the basis of individual choices. We then discuss the aggregation process to obtain the market demand. We focus on the mechanism of the model in this section and leave the discussion on model estimation and identification to the next section. 4.1. Utility function specification Let m={1,2,3,4} denote a market (i.e. Beijing, Nanjing, Shanghai, Tianjin) and a year-month by t from 2008 to 2012. Let i denote a household and j∈J denote a model (i.e. vintage-nameplate) where J is the choice set. Household i's utility from product j is a function of household demographics and product characteristics. A household chooses one product from a total of J models and an outside alternative in a given month. The outside alternative captures the decision of not purchasing any new vehicle in the current month. The indirect utility of household i from product j in market m at time t is defined as umtij=u¯(pj,bmti,Xj,ξmtj,ymti,Zmti)+ϵmtij, (1) where the first term on the right, u¯(.), denotes the deterministic component of the utility as a function of vehicle attributes and consumer characteristics. pj is the tax-inclusive price of product j and it does not vary across markets and months within a year as we discussed in the data section. In Shanghai, for consumers who need to obtain a licence through auction, bmti is the price paid (i.e. the bid); and it is zero for consumers who do not need a new licence (e.g. after scraping a used vehicle).24 In other cities, bmti is always zero for everyone. The importance of variation in bmti for identification is discussed in Section 5.2. As shown above, the winning bids in the discriminatory multi-unit auction in Shanghai have very small spread. Given that we do not observe the distribution of the bids, we use the average bid as the price paid by all the winners. The effect of this measurement error on our results should be small since the difference between the average winning bid and the lowest winning bid is generally less than 2% of the average bid. Xj is a vector of observed product attributes (other than price) including a constant term, vehicle size, engine size and fuel cost. ξmtj includes unobserved product attributes such as product quality and unobserved demand shocks to be specified below. ymti is the income of household i and Zmti is a vector of (unobserved) household demographics. ϵmtij is an i.i.d. random taste shock and is assumed to follow the type I extreme value distribution. The utility from the outside good is defined as umti0=ϵmti0, where ϵmti0 also follows the type I extreme value distribution. Following the literature, we specify the first part of umtij, the deterministic utility to be: u¯mtij=αmtiln(pj+bmti)+∑k=1KXmtjkβ˜mtik+ξj. (2) αmti measures consumer i's preference or distaste for price and it is defined as: αmti=α0+α1lnymti+σνmti, where αi will be negatively related to income if α1 is negative. One would expect high income households to be less sensitive to price due to diminishing marginal utility of income. αi is also affected by unobserved household attributes captured by νmti. We assume that νmti has a standard normal distribution in the benchmark specification and σ is the standard deviation of a normal distribution. A note on the functional form of consumer preference on price is in order. The literature on vehicle demand has used different specifications for the price and income interactions. BLP and Petrin (2002) use ln( yi−pj) and the term has a natural explanation as the utility from the composite good. As discussed above, the median vehicle price in China are higher than the average income of most households, hence this specification does not lend itself well to our context.25 One might argue that we should use the current payment on the vehicle rather than vehicle price in the utility function. However, nearly 90% of vehicle buyers make full cash payment upfront on their purchases in China. Goldberg (1995) specifies the price and income interactions as αi( yi−pj) where αi varies across income categories. She argues that one can view the price and income variables to be proxies for vehicle capital cost and the lifetime wealth of the household, respectively. Berry et al. (1999) specify αi pj where αi is inversely related to income. In our context, both of these specifications do not lead to the intuitive pattern of price elasticity where more expensive products have less elastic demand. To generate that pattern, these specifications require that the increase in household income among the buyers has to be faster than the price increase if we compare two products with different prices. The current specification is chosen so as to allow income to affect consumer preference on price in a way that leads to the intuitive patter of price elasticity. In obtaining consumer surplus and welfare analysis, we rely on the price variable rather than the income variable because of the difficulty in directly interpreting the income variable in our context.26 Xmtjk is the kth attribute of product j. β˜ik is the random taste parameter of household i over product attribute k. It is a function of unobserved household demographics captured by νik, which is assumed to have a standard normal distribution. β˜mtik=β¯k+σkuνmtik. (3) The preference parameters defined above underscore consumer heterogeneity that our model tries to capture. The heterogeneity will translate into heterogeneity in consumers' WTP for a new vehicle, which is crucial for our welfare analysis. With all the components defined above, the utility function can be fully written out as the following: umtij=(α0+α1lnymti+σνmti)ln(pj+bmti)+∑k=1KXmtjk(β¯k+σkuνmtik)+ξmtj+ϵmtij. (4) 4.2. Choice probabilities and aggregate demand Based on the i.i.d. type I extreme value distribution of ϵmtij and ϵmti0, the choice probability of household i for product j is Prmtij(pj,bmti,Xj,ξmtj,ymti,Zmti)=exp(u¯mtij)1+∑hexp(u¯mtih). (5) When there is no quantity constraint, bmti=0. Zmti includes unobserved household demographics νmti that affects consumer preference on price and νmtik that affects consumer preference on other vehicle attributes such as size and fuel cost. This equation can be used directly to generate aggregate sales in the market when there is no quantity constraint such as in Nanjing and Tianjin as well as in pre-policy Beijing. Without quantity constraint, the market share of product j in market m at time t is: Smtj=∫Prmtij(pj,Xj,ξmtj,ymti,Zmti)dF(ymti,Zmti). (6) In the case of quantity constraint, the aggregation needs to take into account the allocation mechanisms. There are two types of households: those who need to acquire a new licence to register a vehicle and those who do not. Under both lottery and auction policies, households who scrap a used vehicle can use the old licence to register a new vehicle. We do not have household level data and therefore do not observe the type of households in this regard. Instead, we explicitly model the type probabilities as a function of vehicle ownership rate in Beijing and Shanghai. Denote Lmt as the probability that a household in city m and time t would need to obtain a new licence to register a vehicle. We parameterize Lmt as a logistic function of observed vehicle ownership rate across markets and over time, omt: Lmt=11+exp(γ0+omt*γ1). (7) A positive coefficient γ1 would imply that as vehicle ownership rate rises, the probability of a household needing a new licence will decrease.27 In theory, we could allow the function Lmt to be individual specific by allowing it to depend on household income ymti. The separate identification of the two income coefficients (one in this function and the other in the utility function) comes from two sources. First, Nanjing and Tianjin do not have a quota system and the income coefficient in the utility function can be identified solely based on the sales data and the micro-moments to be discussed below from these two cities. Second, there is a difference between total new vehicle sales and the number of permits allocated in Beijing and Shanghai. The difference is driven by the consumers who buy a new vehicle to replace a used vehicle hence do not need a new licence. The variation in this difference over time and across Beijing and Shanghai helps identify the Lmt function. When both omt and ymti are included in the Lmt function in a robustness check, neither is statistically significant though the preference parameters in the utility function barely change. This suggests that the separate identification of the coefficients of omt and ymti in the Lmt function would necessitate more detailed household-level data than what we have such as income differences among those who purchase to replace a used vehicle and other buyers. In Beijing, the households who need a new licence must obtain it through the lottery system. Denote the odds of winning a lottery in Beijing in a given month among all potential buyers from 2011 ( t>36) as ρ. Denote cmt as a random draw from a Bernoulli distribution with probability of Lmt being 1. The market share of product j in Beijing ( m=1) is: S1tj[t>36]=∫1(c1t=1)Pr1tij(⋅)*ρ+1(c1t=0)Pr1tij(⋅)dF(y1ti,Z1ti,c1t), (8) where 1(.) is the indicator function. The choice probability Pr1tij is defined by equation (5) where the winning bid bmti=0 since Beijing uses a lottery system. The first part of the integrand defines the case of buyers needing a new licence and hence participating the lottery and the second part of the integrand for the case of buyers who do not need a new licence (e.g. buy a new vehicle to replace a used one). In Shanghai, vehicle buyers who need a new licence have to pay the winning bid bmti through auction while those who buy a new vehicle to replace a used one do not need to pay ( bmti=0). The market share of product j in Shanghai ( m=3) is defined as: S3tj=∫1(c3t=1)Pr3tij(bmti>0,⋅)+1(c3t=0)Pr3tij(bmti=0,⋅)dF(y3ti,Z3ti,c3t), (9) where the choice probability Pr3tij(bmti>0,⋅) is defined by equation (5) where the winning bid bmti is positive for those who need a new licence. The static model above follows closely with the BLP demand literature on automobiles but ignoring dynamics could be an important limitation given that automobiles are durable goods and transaction costs could be non-trivial. Recent literature has tried to estimate the demand for durable goods in a dynamic setting where dynamically optimizing consumers can choose among a set of available vehicle models or wait to purchase in the future by taking into account changes in product attributes, the choice set and the industry structure. To address the issue of large state space in this type of settings, Gowrisankaran and Rysman (2012) propose an empirical strategy based on the assumption that the logit-inclusive values (i.e. ex-ante discounted lifetime utility of buying a preferred product) are sufficient statistics for capturing the evolution of state variables that affect consumers' dynamic decision. This alleviates the need to track a large set of state variables and makes the computation more tractable.28 Adopting this approach in my context is challenging for at least two reasons. First, our data spans only five years and estimating the process of the logit-inclusive value (e.g. a AR(1) process) based on the short time-series is unlikely to yield credible results, which is a crucial piece in this approach. Second, the approach does not lend itself well when there is a need to include a large set of fixed effects as this will essentially increase the state space. In our BLP framework, our analysis shows that it is important to include year-month fixed effects as well as city-vehicle segment fixed effects to control for the national trend in vehicle sales and city-specific demand for different types of vehicles.29 The BLP literature typically assumes that for each time period, a set of potential consumers from the same population arrive at the market to make choices. This assumption is strong in our context where vehicle ownership increases dramatically over time and the majority of vehicle owners are first-time buyers. In addition, the quota policy could also affect the pool of potential buyers from one period to another. In our main analysis, we allow the pool of the potential buyers to evolve over time by drawing them from the population without replacement. In estimation, consumers who are more likely to make a purchase in one period are less likely to appear in the pool of potential buyers in the next period.30 Equation (7) and the simulation of consumer pool without replacement over time capture two different aspects of the market. Equation (7) captures vehicle replacement where the (second-time) buyers replace their used vehicles and are not subject to the quota system. The simulation of consumer pool without replacement over time allows the pool of new buyers (who are subject to the quota system) to evolve due to the impact of the quota policy. If we had household level data on vehicle ownership such as the age of the vehicle and vehicle purchase decisions, these two aspects of the market could be modelled to incorporate household-level heterogeneity in the simulation of potential buyers. For example, one could structure the simulation of consumer pool such that: (1) households who own vehicles say age 10 years or older have a low probability of needing a licence when buying a new vehicle; and (2) households who recently bought a new vehicle have a low probability of being a buyer. Without detailed household-level information on vehicle ownership, we instead model the first aspect using vehicle ownership data at the city level through Equation (7). We define the market size Nmt to be half of the number of households in the city in a given year in the benchmark specification. To check the sensitivity of the result to this definition, we estimate a model where the market size is the total number of households as has been traditionally done in the literature for the U.S. market.31 The results do not differ in any significant way as we will show below. Furthermore, we make the conceptual distinction between the market size and the lottery pool. The market is composed of all potential buyers who first make lottery participation decisions. Those who decide to participate form the lottery pool and the winners then make vehicle purchase decisions. Our specification and aggregation method lump these two decisions together. The parameter ρ in equation (8) captures both participation decisions and the winning odds of the lottery. Therefore, it should not be compared against the observed odds in the data. That is, our specification does not explicitly model the increase of the lottery pool due to the cumulation of unmet demand as well as strategic participation behavior, which explains the drop of the winning odds over time. As one of the robustness checks, we estimate the model without using the post-policy data in Beijing (2011–2012) and equation (8). The analysis shows that this simplified modelling choice does not have qualitative impacts on the welfare outcomes. 5. Identification and Estimation 5.1. Constructing moment conditions Our goal is to recover the preference parameters in equation (4) to estimate consumers' WTP for a licence. The identification challenge comes from the fact that there are unobserved product attributes as well as demand shocks ξmtj in the utility function. The unobserved product attributes such as product quality are likely to be correlated with prices. Previous studies show that ignoring these unobserved product attributes biases the price coefficient towards zero and leads to wrong welfare calculations. This challenge in fact motivated the methodology in BLP. An additional issue in our context is that unobserved demand shocks in Shanghai are likely to be correlated with average bids and hence render them endogenous. Ignoring this can also bias the price coefficient towards zero. To facilitate the discussion on identification and estimation below, notice that the utility function in equation (4) contains terms that vary by households as well as terms that do not. We separate these two categories and rewrite the utility function as the following: umtij=δmtj+μmtij+ϵmtij, (10) where δmtj is the household-invariant utility or the mean utility of product j in market m at time t. Based on equation (4), it is specified as follows δmtj(θ1)=Xjβ¯+ξmtj=Xjβ¯+ξj+ηt+1(m=3)η′t+ζms+κmyrt+emtj=δj+ηt+1(m=3)η′t+ζms+κmyrt+emtj, (11) where we write ξmtj into several terms in the second line. ξj is unobserved product attributes such as quality and safety features that do not vary over time and across markets. ηt captures time (year-month) fixed effects that control for common demand shocks and seasonalities across cities. 1(m=3)η′t captures Shanghai-specific time effects. ζms is city-specific preferences for different vehicle segments where s is an index for segments. yrt is year (1 to 5) and κmyrt captures city-specific time trend. emtj is time-varying and city-specific demand shocks. The last line combines Xjβ¯+ξj into product dummies δj, absorbing the utility that is constant for all households across the markets. The parameters in the mean utility function are denoted as θ1={δj,ηt,η′t,ζms,κm}. The second part in equation (10), μmtij, is household-specific utility defined as: μmtij(θ2)=[α0+α1lnymti+σνmti]ln(pmtj+bmti)+∑kxmjkνmtikσku. (12) The parameters in the household-specific utility are denoted as θ2={α0,α1,σ,σu}. With this specification, we can rewrite the choice probabilities in equation (5) as follows Prmtij(pj,bmti,Xj,ξmtj,ymti,Zmti)=exp[δmtj(θ1)+μmtij(θ2)]1+∑h{exp[δmth(θ1)+μmtih(θ2)]}. (13) The market shares can be written as Smtj(δmtj,θ2,θ3), where θ3={γ0,γ1,ρ} which characterizes the licence allocation processes described above. In the choice probabilities, unobserved product attributes and demand shocks are absorbed in δmtj while the price and bid variables are in μmtij. If we could include market-time-product fixed effects subsuming δmtj, we can control for unobserved product attributes and demand shocks. However, this is impractical in this nonlinear model. BLP develop a methodology to back out δmtj. Under mild regularity conditions, for given vectors of θ2 and θ3, a unique vector of δmt for each market that equalizes the predicted market shares with observed market shares can be recovered through a contraction mapping algorithm: δmtn+1=δmtn+ln(Smto)−ln[S^(δmtn,θ2,θ3)], (14) where n is the number of iterations. So is a vector of observed market shares while S^() is predicted market share. With the recovered δmt for given vectors of θ2 and θ3, θ1 can be estimated using a linear framework following equation (11). To estimate the model, we follow BLP by using simulated GMM with the nested contraction mapping. The GMM is based on three sets of moment conditions. The first set is formed based on the city-year specific demand shocks in equation (11). The identification assumption is that these demand shocks are mean independent of city-year dummy variables, that is, having zero mean at the city-year level: E[emtj(θ2,θ3)|dmt]=0, (15) where dmt are city-year dummies. This assumption amounts to that time-varying demand shocks have a common trend across cities and the common trend is controlled by time fixed effects. What is left from the time trend emtj is not systematically different across cities. Note that we have also included city-segment fixed effects and these control for difference in levels in demand shocks. Since Beijing implemented the lottery in 2011 and 2012, this assumption implies that the lottery policy is exogenous to the time-varying demand-shocks in Beijing. This common trend assumption (in the absence of the policy) is motivated by the graphical evidence in Figure 2 and it is a key assumption needed in the DID analysis for policy evaluation. Although one cannot test this assumption directly given that we do not observe the counterfactual of no policy for the treatment group (Beijing in our case), we have three years of data before the policy and we can examine if the pre-policy time trends are the same across the cities in a reduced-form framework. If they are the same before the policy, we would be more comfortable with the assumption (Heckman and Hotz, 1989). Since Shanghai implements an auction system throughout our data period, we do not have a pre-policy period for comparison. To allow for the possibility of different time trend between Shanghai and other cities, we include Shanghai-specific time effects in equation (11) in the benchmark specification as a conservative measure.32 Recall we have city-segment dummies (which swaps city fixed effects) and time fixed effects in the equation. This leaves us eight exclusion restrictions in the first set including city-year dummy variables for Beijing and Nanjing from 2009 to 2012 (Tianjin is the base group and year 2008 is the base year). The second set of moment conditions is constructed based on the aggregate information from the household survey presented in the right panel of Supplementary Appendix Table 2. We match the predicted shares of households by income group by city among new vehicle buyers to those in the table. We use the fourth group as the base group and this gives us twelve moment conditions (four cities each with three income groups): Et[S˜mgt|buyers(θ2,θ3)−Smgt|buyers]=0, (16) where g is a income group and S˜mgt|buyers is the predicted share of income group g among vehicle buyers while Smgt|buyers is the observed counterpart. The former is calculated as: S˜mgt|buyers(θ2,θ3)=∑i=1Nmtd(ymti∈INCg)∑j=1JPrmtij∑i=1Nmt∑j=1JPrmtij, (17) where d(.) is an indicator function being 1 for household i whose income ( ymti) falls into the income range of group g, INCg. Nmt is the market size, the number of potential buyers. These moment conditions turn out to be crucial in recovering the curvature of the WTP schedule (i.e. heterogeneity in WTP). The third set of moment conditions matches the predicted quantity of licences to the observed quota in each month.33 Et[Q˜mt(θ2,θ3)−Qmt]=0, (18) where Q˜mt is predicted quantity of licences and it is calculated for Beijing ( m=1 and t>36) and Shanghai ( m=3) as the following: Q˜1t=∑i∑j=1J[1(c1t=1)Pr1tij(⋅)*ρ],Q˜3t=∑i∑j=1J[1(c3t=1)Pr3tij(b3ti>0,⋅)], (19) where 1(.) is the indicator function and cmt are random draws from a Bernoulli distribution as discussed in Section 4.2. There could be a time gap between winning a licence and purchasing a vehicle. In Beijing, winners have six months to purchase a new vehicle while in Shanghai, winners have three months before the licence expires. Many consumers indeed take their time to purchase their vehicles. In the estimation, Qmt is not the quota observed in that particular month; rather it is the average of the last six months and three months for Beijing and Shanghai, respectively. We form the objective function by stacking these three sets of moment conditions. The procedure involves iteratively updating θ2 and θ3 and then δmj from the inner loop of contraction mapping to minimize the objective function. The estimation starts with an initial weighted matrix to obtain consistent initial estimates of the parameters and optimal weighting matrix. The model is then re-estimated using the new weighting matrix. 5.2. Identification sources and strategy To address the potential endogeneity in vehicle prices due to unobserved product attributes, the maintained identification assumption in the BLP literature is that unobserved product attributes are mean independent of those observed ones. This allows researchers to use the exclusion restrictions given by the product attributes of other products within the firm and outside the firm to form moment conditions (macro-moments). This identification assumption could be violated if firms choose product attributes (observed and unobserved) jointly (Klier and Linn, 2012). Although our empirical setup follows closely the BLP literature, our identification strategy does not rely on this assumption. Because we have data from four cities, we include vehicle model fixed effects which would subsume both unobserved product attributes and household-invariant observed product attributes in the mean utility function in equation (11). Our identification strategy is made possible by the fact that different households are paying different effective prices (price plus bid) for the same vehicle in Shanghai depending on whether they need a new licence or not. This allows us to have all the price variables in the household-specific utility and be isolated from unobserved product and demand shocks. To understand this, imagine if we do not have data for Shanghai, we would have α0ln(pj) entering the mean-utility term. We would then need to estimate α0 for welfare analysis. Since the price variable and the unobserved product attributes would both appear in the mean utility, one would need to evoke some type of exogeneity assumption such as the one maintained in the literature to deal with price endogeneity.34 The identification of the WTP schedule critically hinges on the coefficients on the price and income variables in equation (4). Because the price variables enter the household-specific utility, both cross-model and within model variation in prices are helpful for identification. There are several important sources of price variation. First, during our data period, MSRPs range from 36,000 to over 1.1 million Yuan with the quality-adjusted average price decreases by about 3% each year. Second, the sales tax, which affects consumer prices, reduced from 10% to 5% and 7.5% for vehicles with engine displacement no more than 1.6 Liter in 2009 and 2010, respectively. For other vehicles, the sales tax was kept at 10%. Third, there is considerable variation over time in average winning bids in Shanghai auction. The average winning bid ranges from 23,370 to 69,346 during the data period. This then affects effective price (price + winning bid) for consumers who need a licence in Shanghai (for vehicle replacement, no licence is needed). Intuitively, the discontinuity in purchase costs (prices plus bids) between Shanghai and other cities due to the auction policy helps identify the price coefficient. Higher purchase costs for buyers who need a new licence in Shanghai lead to lower vehicle sales than in other cities, due to consumer disutility from high prices. The magnitude in sales reduction regulates the magnitude of the price coefficient. The micro-moments on the share of different income groups among new vehicle buyers help identify heterogeneity in consumer price sensitivity and WTP. These micro-moments in Supplementary Appendix Table 2 show that high income groups account for disproportionally larger shares among new vehicle buyers, suggesting that households with higher income are less price sensitive. The disproportionality is more salient in Shanghai. This can be explained by the fact that higher purchase costs in Shanghai make new vehicle purchase more out of reach for low income households. These micro-moments help pin down the coefficient on the income variable and hence the curvature of the WTP schedule. We will come back to this when we present our WTP estimates in Section 7.2. Another source of heterogeneity in consumer WTP is captured by the random coefficient on the price variable and the coefficient estimate turns out to be small in magnitude, suggesting that the heterogeneity in WTP is largely driven by income. Our sensitivity analysis below shows that the large heterogeneity in the WTP schedule is not driven by the infinite support of the normal distribution used to characterize the unobserved heterogeneity. 5.3. Further discussions on computation Before concluding this section, we offer some additional details for estimation. First, the estimation starts from generating a set of households in each year-month and in each market. Each of the households is defined by a vector of household demographics including income from the income distribution and unobserved household attributes from the standard normal. When generating the random draws, we use randomized Halton sequences to improve efficiency (Train, 2003). Our results below are all based on 250 households in each year-month and market.35 Second, we speed up the estimation process through a combination of two techniques. The first technique is to parallelize the computation across the four markets. The time savings from the parallel process more than offset the additional overhead time. The second technique is to modify equation (14) for the contraction mapping by employing Newton's method where the update is based on the derivate of the market share with respect to the mean utility δmt: δmtn+1=δmtn+[∂ln[S^(δmtn,θ2,θ3)]∂δmtn]−1{ln(Smto)−ln[S^(δmtn,θ2,θ3)]}. (20) Although additional time is needed to calculate the derivatives, there is still considerable savings from fewer iterations due to the quadratic convergence rate of Newton's method. 6. Estimation Results In this section, we first present evidence from the reduced-form regressions on the common trend assumption and the sales impact of the lottery policy in Beijing. Then we discuss the parameter estimates from the random coefficients discrete choice model. 6.1. Evidence from reduced-form regressions To examine the validity of the common trend assumption across the cities, we estimate the following regression based on data from 2008 to 2010 (pre-policy period). ln(Smtj)=αln(pj+bmt)+δj+λmt+ηt+1(m=3)η′t+ζms+emtj, (21) where the dependent variable is the log market shares. bmt is the average monthly winning bid in Shanghai and zero for other cities (i.e. m≠3).36 δj is model (vintage-nameplate) dummies. λmt is city-year fixed effects to capture city-specific and time-varying demand shocks. The common trend assumption assumes that these shocks are the same across cities in a given year. The other terms are defined the same as in equation (11): we include time (year-month) fixed effects, Shanghai-specific time effects and city-segment fixed effects. Table 3 presents the regression results for three specifications. The first two use all observations while the third one drops the data in the last two months of 2010 in Beijing to remove the anticipation effect and more importantly the announcement effect in December 2010. In all specifications, the base group is Tianjin and the base year is 2008. The first specification does not include Shanghai-specific time fixed effects but include Shanghai-year fixed effects. The coefficient estimate on ln(price + bid) suggests a price elasticity of −4.33, which is a plausible magnitude. All the city–year interactions are small in magnitude and not statistically different from zero, suggesting a similar time trend across the four cities. Note that the income variable, arguably the most important determinant of vehicle purchase is only controlled for through fixed effects. A model with more flexible specification of income heterogeneity such as our demand model should be able to better control for the effect of more subtle changes in income (such as different rate of change among different income groups) on vehicle demand. Table 3. Pre-policy trend analysis Specification 1 Specification 2 Specification 3 Variables Coef. S.E. Coef. S.E. Coef. S.E. Ln(price + bid) −4.329 0.310 −4.530 0.320 −4.522 0.322 Beijing*2009 −0.033 0.085 −0.033 0.085 −0.032 0.085 Beijing*2010 0.021 0.080 0.021 0.080 −0.027 0.082 Nanjing*2009 0.056 0.071 0.056 0.071 0.056 0.071 Nanjing*2010 0.081 0.069 0.081 0.069 0.081 0.069 Shanghai*2009 −0.062 0.095 No No Shanghai*2010 −0.105 0.088 No No Vintage-model fixed effects Yes Yes Yes City-segment fixed effects Yes Yes Yes Year-month fixed effects Yes Yes Yes Shanghai year-month fixed effects No Yes Yes Specification 1 Specification 2 Specification 3 Variables Coef. S.E. Coef. S.E. Coef. S.E. Ln(price + bid) −4.329 0.310 −4.530 0.320 −4.522 0.322 Beijing*2009 −0.033 0.085 −0.033 0.085 −0.032 0.085 Beijing*2010 0.021 0.080 0.021 0.080 −0.027 0.082 Nanjing*2009 0.056 0.071 0.056 0.071 0.056 0.071 Nanjing*2010 0.081 0.069 0.081 0.069 0.081 0.069 Shanghai*2009 −0.062 0.095 No No Shanghai*2010 −0.105 0.088 No No Vintage-model fixed effects Yes Yes Yes City-segment fixed effects Yes Yes Yes Year-month fixed effects Yes Yes Yes Shanghai year-month fixed effects No Yes Yes Notes: The dependent variable is ln(market shares). Specifications 1 and 2 use all the 47,232 observations from 2008 to 2010. Specification 3 drops observations in November and December of 2010 in Beiijing to remove anticipation effect and has 46,462 observations. Tianjin is the base group and 2008 is the base year. The standard errors are clustered at the model level. Table 3. Pre-policy trend analysis Specification 1 Specification 2 Specification 3 Variables Coef. S.E. Coef. S.E. Coef. S.E. Ln(price + bid) −4.329 0.310 −4.530 0.320 −4.522 0.322 Beijing*2009 −0.033 0.085 −0.033 0.085 −0.032 0.085 Beijing*2010 0.021 0.080 0.021 0.080 −0.027 0.082 Nanjing*2009 0.056 0.071 0.056 0.071 0.056 0.071 Nanjing*2010 0.081 0.069 0.081 0.069 0.081 0.069 Shanghai*2009 −0.062 0.095 No No Shanghai*2010 −0.105 0.088 No No Vintage-model fixed effects Yes Yes Yes City-segment fixed effects Yes Yes Yes Year-month fixed effects Yes Yes Yes Shanghai year-month fixed effects No Yes Yes Specification 1 Specification 2 Specification 3 Variables Coef. S.E. Coef. S.E. Coef. S.E. Ln(price + bid) −4.329 0.310 −4.530 0.320 −4.522 0.322 Beijing*2009 −0.033 0.085 −0.033 0.085 −0.032 0.085 Beijing*2010 0.021 0.080 0.021 0.080 −0.027 0.082 Nanjing*2009 0.056 0.071 0.056 0.071 0.056 0.071 Nanjing*2010 0.081 0.069 0.081 0.069 0.081 0.069 Shanghai*2009 −0.062 0.095 No No Shanghai*2010 −0.105 0.088 No No Vintage-model fixed effects Yes Yes Yes City-segment fixed effects Yes Yes Yes Year-month fixed effects Yes Yes Yes Shanghai year-month fixed effects No Yes Yes Notes: The dependent variable is ln(market shares). Specifications 1 and 2 use all the 47,232 observations from 2008 to 2010. Specification 3 drops observations in November and December of 2010 in Beiijing to remove anticipation effect and has 46,462 observations. Tianjin is the base group and 2008 is the base year. The standard errors are clustered at the model level. The second specification include Shanghai-specific time fixed effects to control for monthly demand shocks in Shanghai that are different from the base group and could be correlated with the average bid. The price coefficient reduces to −4.53, consistent with the conjecture that unobserved demand shocks that are correlated with the average bid can bias the price coefficient towards zero. Nevertheless, the difference in the price coefficient estimates is quite small. The city–year interactions again have small and insignificant coefficient estimates. The third specification produces very similar results to the second one, suggesting that the anticipation and announcement effects are not large enough perhaps due to the short notice. The evidence from Figure 2 and these results support the common trend assumption, the basis of our first set of moment conditions in the structural estimation. We next use a DID framework to examine the sales impact of the lottery policy. These results will be compared with those from the structural demand model. The equation for DID is very similar to equation (21) except replacing city-year fixed effects with lottery policy dummies for Beijing in 2011 and 2012. The results are presented in Supplementary Appendix Table 3. The first specification uses all observations while the other two drop observations in the last two months in 2010 and the first two months in 2011 in Beijing. While the first two specifications include city-specific time trend (up to second-order polynomials), the third one does not. Using the full data set, the lottery policy is estimated to have reduced sales by 60.6% in 2011 and 50.7% in 2012. This implies that without the policy, the sales would have been 847,000 units in 2011 and 1.05 million units in 2012, compared with a pre-policy sales of 804,000 in 2010. The second specification produces slightly smaller sales impacts: 54.1% and 40.4% in 2011 and 2012, respectively. This is intuitive since we drop the last two months in 2010 where the increase in sales was partly due to the fact that people moved their purchase forward from the future. So without the policy, the sales would have been smaller in 2010. The sales impacts of the policy would have been smaller in 2011 and 2012 to be consistent with growth in other cities. These estimates imply that the sales would have been about 728,000 and 873,000 in the absence of the policy in 2011 and 2012. The third specification leads to slightly larger sales impacts than those from Specification 2. We will come back to these estimates for comparison once we obtain estimates from the structural model. 6.2. Parameter estimates from the demand system Table 4 shows parameter estimates from the GMM estimation for five specifications. The first panel represent parameters in θ2 which appear in the household-specific utility function in equation (12). The three parameters in the second panel are the auxiliary parameters θ3 that are needed to incorporate the policies into the calculation of market shares as shown in equations (8) and (9). We do not present parameter estimates for θ1 since they are not needed to perform our policy simulations and welfare analysis: θ2, θ3, and δmtj, the mean utilities from equation (20) suffice. Table 4. Parameter estimates from GMM Variables Specification 1 Specification 2 Specification 3 Specification 4 Specification 5 Coef. S.E. Coef. S.E. Coef. S.E. Coef. S.E. Coef. S.E. Parameters in the household-specific utility ( θ2) Ln(price + bid) −16.810 0.225 −17.080 0.200 −14.515 0.185 −17.323 0.173 −16.571 0.173 Ln(price + bid)*Ln(income) 1.620 0.033 1.888 0.031 1.443 0.054 1.620 0.026 1.620 0.037 Ln(income) −6.394 0.366 −7.619 0.352 −5.807 0.409 −6.404 0.301 −6.418 0.287 σ for Ln(price + bid) 0.067 0.014 0.073 0.026 0.073 0.016 0.069 0.012 0.067 0.027 σ for constant 0.655 0.133 0.698 0.415 0.714 0.152 0.583 0.184 0.643 0.304 σ for engine displacement 0.645 0.289 0.708 0.041 0.708 0.250 0.671 0.276 0.648 0.347 Auxiliary parameters for allocation mechanism ( θ3) ρ 0.229 0.030 0.384 0.087 0.236 0.039 0.220 0.034 0.231 0.030 γ0 −1.426 0.203 −1.111 0.406 −1.422 0.262 −1.428 0.185 −1.429 0.179 γ1 0.259 0.020 0.139 0.061 0.250 0.026 0.259 0.035 0.260 0.038 Variables Specification 1 Specification 2 Specification 3 Specification 4 Specification 5 Coef. S.E. Coef. S.E. Coef. S.E. Coef. S.E. Coef. S.E. Parameters in the household-specific utility ( θ2) Ln(price + bid) −16.810 0.225 −17.080 0.200 −14.515 0.185 −17.323 0.173 −16.571 0.173 Ln(price + bid)*Ln(income) 1.620 0.033 1.888 0.031 1.443 0.054 1.620 0.026 1.620 0.037 Ln(income) −6.394 0.366 −7.619 0.352 −5.807 0.409 −6.404 0.301 −6.418 0.287 σ for Ln(price + bid) 0.067 0.014 0.073 0.026 0.073 0.016 0.069 0.012 0.067 0.027 σ for constant 0.655 0.133 0.698 0.415 0.714 0.152 0.583 0.184 0.643 0.304 σ for engine displacement 0.645 0.289 0.708 0.041 0.708 0.250 0.671 0.276 0.648 0.347 Auxiliary parameters for allocation mechanism ( θ3) ρ 0.229 0.030 0.384 0.087 0.236 0.039 0.220 0.034 0.231 0.030 γ0 −1.426 0.203 −1.111 0.406 −1.422 0.262 −1.428 0.185 −1.429 0.179 γ1 0.259 0.020 0.139 0.061 0.250 0.026 0.259 0.035 0.260 0.038 Notes: Specification 1 is the benchmark and the preferred model. Specification 2 does not include the first set of moment conditions (common-trend moments). Specification 3 assumes all the households as the potential buyers in a year so the market size in each month is the total number of households divided by 12. Specification 4 assumes a certain percentage of licences are used to buy used vehicles: 15% in Beijing and 5% in Shanghai. Specification 5 takes the random draws for unobserved household attributes from a standard normal distribution removing draws below 2.5 and above 97.5 percentiles. Table 4. Parameter estimates from GMM Variables Specification 1 Specification 2 Specification 3 Specification 4 Specification 5 Coef. S.E. Coef. S.E. Coef. S.E. Coef. S.E. Coef. S.E. Parameters in the household-specific utility ( θ2) Ln(price + bid) −16.810 0.225 −17.080 0.200 −14.515 0.185 −17.323 0.173 −16.571 0.173 Ln(price + bid)*Ln(income) 1.620 0.033 1.888 0.031 1.443 0.054 1.620 0.026 1.620 0.037 Ln(income) −6.394 0.366 −7.619 0.352 −5.807 0.409 −6.404 0.301 −6.418 0.287 σ for Ln(price + bid) 0.067 0.014 0.073 0.026 0.073 0.016 0.069 0.012 0.067 0.027 σ for constant 0.655 0.133 0.698 0.415 0.714 0.152 0.583 0.184 0.643 0.304 σ for engine displacement 0.645 0.289 0.708 0.041 0.708 0.250 0.671 0.276 0.648 0.347 Auxiliary parameters for allocation mechanism ( θ3) ρ 0.229 0.030 0.384 0.087 0.236 0.039 0.220 0.034 0.231 0.030 γ0 −1.426 0.203 −1.111 0.406 −1.422 0.262 −1.428 0.185 −1.429 0.179 γ1 0.259 0.020 0.139 0.061 0.250 0.026 0.259 0.035 0.260 0.038 Variables Specification 1 Specification 2 Specification 3 Specification 4 Specification 5 Coef. S.E. Coef. S.E. Coef. S.E. Coef. S.E. Coef. S.E. Parameters in the household-specific utility ( θ2) Ln(price + bid) −16.810 0.225 −17.080 0.200 −14.515 0.185 −17.323 0.173 −16.571 0.173 Ln(price + bid)*Ln(income) 1.620 0.033 1.888 0.031 1.443 0.054 1.620 0.026 1.620 0.037 Ln(income) −6.394 0.366 −7.619 0.352 −5.807 0.409 −6.404 0.301 −6.418 0.287 σ for Ln(price + bid) 0.067 0.014 0.073 0.026 0.073 0.016 0.069 0.012 0.067 0.027 σ for constant 0.655 0.133 0.698 0.415 0.714 0.152 0.583 0.184 0.643 0.304 σ for engine displacement 0.645 0.289 0.708 0.041 0.708 0.250 0.671 0.276 0.648 0.347 Auxiliary parameters for allocation mechanism ( θ3) ρ 0.229 0.030 0.384 0.087 0.236 0.039 0.220 0.034 0.231 0.030 γ0 −1.426 0.203 −1.111 0.406 −1.422 0.262 −1.428 0.185 −1.429 0.179 γ1 0.259 0.020 0.139 0.061 0.250 0.026 0.259 0.035 0.260 0.038 Notes: Specification 1 is the benchmark and the preferred model. Specification 2 does not include the first set of moment conditions (common-trend moments). Specification 3 assumes all the households as the potential buyers in a year so the market size in each month is the total number of households divided by 12. Specification 4 assumes a certain percentage of licences are used to buy used vehicles: 15% in Beijing and 5% in Shanghai. Specification 5 takes the random draws for unobserved household attributes from a standard normal distribution removing draws below 2.5 and above 97.5 percentiles. The first specification is the benchmark model and our preferred specification. Before we discuss the coefficient estimates and compare results across different specifications, we note that the magnitude of the preference parameters by themselves are hard to interpret and we defer much of the discussion on the comparison across specifications to the next two sections where we simulate sales and conduct welfare analysis using these parameters. In the benchmark specification, the coefficient estimate on ln(price + bid) is negative while that on the interaction between this price variable and ln(income) is positive. This suggests that households with a higher income are less price sensitive. Given the range of ln(income) from 0.55 to 6.72, the first two coefficient estimates suggest that all households dislike high prices. The variable ln(income) in the specification is to capture the fact that the utility difference between a new vehicle and the outside good varies by income. The second and third coefficient estimates imply the partial effect of ln(income) is positive for about 95% of the vehicle models, suggesting that the utility difference increases with income. The next three coefficients are random coefficients, representing the standard deviation estimates of the normal distribution for preferences on each vehicle characteristics. The random coefficient on constant captures the variation (due to unobserved household demographics) in the utility difference between a new vehicle and the outside good. The random coefficients are statistically significant, adding consumer heterogeneity to what is implied by income heterogeneity. To get a sense of the magnitude of coefficient estimates on price variables, we calculate price elasticities based on model estimates. The average own price elasticity is −9.49 with a range of −7.80 to −14.53. Models with a higher price tend to have a smaller elasticity in magnitude (see Supplementary Appendix Figure 3) as buyers of more expensive vehicles tend to be of higher income and less price sensitive. The average elasticity is somewhat larger in magnitude than the estimates obtained for the U.S. market which range from −3 to −8.4 (BLP, Goldberg, 1995; Petrin, 2002; Beresteanu and Li, 2011).37 We believe our estimates are reasonable and the difference could be attributed to at least the following two reasons. First, the income level in these four cities in China is less than one half of the U.S. income level during the data period of 1981 to 1993 used in Petrin (2002). To the extent that higher income would reduce price sensitivity, the differences in income could lead to the differences in price elasticities. Second, vehicle prices in our data are much higher than MSPRs in the U.S. for the same brand.38 For example, a Hyundai Sonata GLS Sedan with 2.4 Liter engine with base options had a MSRP of $19,695 in the U.S., and a similar model produced in China had an MSPR of 178,800 Yuan (over $28,000). That is, one needs to adjust our price elasticities downward (in magnitude) to compare them with the elasticities in the U.S. market.39 The first auxiliary parameter ρ is the ratio of total licence allocated over the number of potential vehicle buyers (without the quota constraint) that would need a new licence (e.g. fist-time buyers) under the quota system. It measures the stringency of the quota system: the smaller it is, the more stringent the quota is. It is a very important parameter in estimating the counterfactual sales under the policy. The parameter is estimated to be 0.229 in the benchmark specification, implying that only one out of five potential buyers that need a licence are able to obtain a licence through the lottery. As discussed above, this should not be compared with the observed odds because the observed lottery pool includes not only those who enter the market for a new vehicle in the current month but also unmet demand in the past months and future buyers. Our empirical model lumps lottery participation decision and vehicle choices together. Nevertheless, as we show below, the estimate of 0.229 (together with other parameters) leads to reasonable counterfactual sales without the policy. The second and third auxiliary parameters define the probability of a buyer needing a new licence given by equation (7). The positive coefficient γ1 suggests that as vehicle ownership goes up, the share of potential buyers who need a new licence decreases. This is intuitive since as vehicle ownership increases, more and more households would need to replace their old vehicles with new vehicles and hence do not need a new licence. These two parameter estimates imply that about 80% of potential buyers in Shanghai and 78% in Beijing in 2012 would need a licence should they decide to buy a vehicle. 6.3. Robustness checks To examine the importance of the first set of moment conditions based on the common trend assumption, we estimate the model without these moment conditions under Specification 2. The coefficient estimates on ln(price+bid) and its interaction with income are both larger in magnitude. The average own price elasticity is −8.44 with a range from −6.40 to −13.11. These are similar to the estimates from the benchmark specification in magnitude. A key difference is that the estimate of ρ is almost twice as large as that from the benchmark model. This estimate implies that the quota is much less stringent and as we show below, the model estimates from this specification predict unreasonably small sales under the counterfactual scenario of no policy and under-estimate consumers WTP for licences as discussed below. In another robustness check not shown in the table, the estimation does not utilize the second set of moment conditions (micro-moments) that are based on shares of new vehicle purchases by income group. These moment conditions are important in recovering the heterogeneity in WTP for a new car and price sensitivity across income groups. Without these moments, the parameter estimates imply that high income households are more price sensitive, running against our intuition as well as the results from the benchmark model. In addition, price elasticity estimates are larger in magnitude for more expensive vehicles, opposite to the results from the first two specifications. This highlights the importance of the micro-moments in identifying price coefficients and WTP schedule. Table 4 also presents results from three additional specifications as further robustness checks. These robustness checks show that our estimation results are robust to: (1) the definition of market size; (2) the usage of licences for buying used vehicles; and (3) the distribution of the random coefficients. Specification 3 examines the sensitivity of the results to the definition of market size. In the benchmark model, we assume half of the households in a city participate in the market for new vehicles, implying the market size of a month is the number of households divided by 24. Specification 3 assumes the market size to be the number of all households as is often done in the studies on the U.S. market. The coefficients by and large are very similar to those in the benchmark specification. This implies that the mean utilities must be smaller in this specification to generate the same number of new vehicle sales as in the benchmark specification. Specification 4 assumes that 85% of the lottery winners use the licence to purchase new vehicles instead of used vehicles in Beijing and the number in Shanghai is 95%. As specified by the policy, buyers of used vehicles need a licence if they do not already have one (i.e. from scrapping an old vehicle). We do not have detailed statistics on the ultimate usage of the licences and we use these two numbers as the upper bound. We choose a lower number for Shanghai because the buyers there tend to have higher income than in Beijing.40 In the first four specifications, draws for random coefficients are from the standard normal distribution which is unbounded. To remove the impacts of extreme values, Specification 5 uses random draws from a truncated normal distribution by removing the draws below 2.5 percentile and above 97.5 percentile. The results are again close to the benchmark specification and so are the simulation results and welfare analysis shown below. 6.4. Impacts on vehicle sales Table 5 presents the simulated sales under the counterfactual of no policy for various specifications. Under the benchmark specification, the counterfactual sales in Beijing are 833,431 and 1,274,954 in 2011 and 2012 (with standard errors 144,810 and 136,000), relative to observed sales of 334,308 and 520,442 under the policy. This suggests that the lottery policy reduced sales by 60% and 59%, respectively in 2011 and 2012. The estimated sales impact in 2011 is very close to those from the DID analysis in Supplementary Appendix Table 3. The sales impact in 2012 from the structural model is somewhat larger than those from the DID\break analysis. Table 5. Policy impacts on sales in Beijing and Shanghai Year Observed Counterfactural sales without licence quotas in Beijing and Shanghai Sales Specification 1 Specification 2 Specification 3 Specification 4 Specification 5 Beijing 2011 334,308 833,431 612,655 843,796 848,434 830,453 2012 520,442 1,274,954 940,851 1,289,578 1,297,333 1,269,863 Shanghai 2008 165,298 373,569 319,957 356,631 385,944 369,692 2009 208,570 482,096 413,194 461,496 498,211 478,276 2010 264,232 662,500 567,299 635,184 684,922 659,805 2011 277,119 744,558 629,219 715,686 769,095 739,892 2012 295,047 869,915 723,721 830,736 897,528 865,674 Year Observed Counterfactural sales without licence quotas in Beijing and Shanghai Sales Specification 1 Specification 2 Specification 3 Specification 4 Specification 5 Beijing 2011 334,308 833,431 612,655 843,796 848,434 830,453 2012 520,442 1,274,954 940,851 1,289,578 1,297,333 1,269,863 Shanghai 2008 165,298 373,569 319,957 356,631 385,944 369,692 2009 208,570 482,096 413,194 461,496 498,211 478,276 2010 264,232 662,500 567,299 635,184 684,922 659,805 2011 277,119 744,558 629,219 715,686 769,095 739,892 2012 295,047 869,915 723,721 830,736 897,528 865,674 Notes: The five counterfactual outcomes correspond to the five specifications in Table 4. Specification 1 is the benchmark and preferred model. Specification 2 does not include the first set of moment conditions (common-trend moments). Specification 3 assumes all the households as the potential buyers in a year so the market size in each month is the total number of households divided by 12. Specification 4 assumes a certain percentage of licences are used to buy used vehicles: 15% in Beijing and 5% in Shanghai. Specification 5 takes the random draws for unobserved household attributes from a standard normal distribution removing draws below 2.5 and above 97.5 percentiles. The sales in Beijing from 2008 to 2010 were 411,936, 602,219, and 804,355, respectively. Table 5. Policy impacts on sales in Beijing and Shanghai Year Observed Counterfactural sales without licence quotas in Beijing and Shanghai Sales Specification 1 Specification 2 Specification 3 Specification 4 Specification 5 Beijing 2011 334,308 833,431 612,655 843,796 848,434 830,453 2012 520,442 1,274,954 940,851 1,289,578 1,297,333 1,269,863 Shanghai 2008 165,298 373,569 319,957 356,631 385,944 369,692 2009 208,570 482,096 413,194 461,496 498,211 478,276 2010 264,232 662,500 567,299 635,184 684,922 659,805 2011 277,119 744,558 629,219 715,686 769,095 739,892 2012 295,047 869,915 723,721 830,736 897,528 865,674 Year Observed Counterfactural sales without licence quotas in Beijing and Shanghai Sales Specification 1 Specification 2 Specification 3 Specification 4 Specification 5 Beijing 2011 334,308 833,431 612,655 843,796 848,434 830,453 2012 520,442 1,274,954 940,851 1,289,578 1,297,333 1,269,863 Shanghai 2008 165,298 373,569 319,957 356,631 385,944 369,692 2009 208,570 482,096 413,194 461,496 498,211 478,276 2010 264,232 662,500 567,299 635,184 684,922 659,805 2011 277,119 744,558 629,219 715,686 769,095 739,892 2012 295,047 869,915 723,721 830,736 897,528 865,674 Notes: The five counterfactual outcomes correspond to the five specifications in Table 4. Specification 1 is the benchmark and preferred model. Specification 2 does not include the first set of moment conditions (common-trend moments). Specification 3 assumes all the households as the potential buyers in a year so the market size in each month is the total number of households divided by 12. Specification 4 assumes a certain percentage of licences are used to buy used vehicles: 15% in Beijing and 5% in Shanghai. Specification 5 takes the random draws for unobserved household attributes from a standard normal distribution removing draws below 2.5 and above 97.5 percentiles. The sales in Beijing from 2008 to 2010 were 411,936, 602,219, and 804,355, respectively. The model estimates predict the sales would have increased by 53% from 2011 to 2012 in Beijing without the quota system. This is quite a bit larger than what was observed in Tianjin and Nanjing (13% and 5%), our control groups. This larger uptake in sales, relative to other cities, could be due to the combination of the following two reasons. First, the number of households in Beijing increased by 2.8% from 2011 to 2012, compared to 0.6% in Nanjing, 1.4% in Shanghai, and 4.3% in Tianjin. Second, the average income of the top quantile increased from 158,233 to 189,213 from 2011 to 2012 in Beijing, a 19.6% growth. This is much larger than the other three cities: 6.5%, 10.9% and 7.9% in Nanjing, Shanghai and Tianjin, respectively. Given that the high-income group contributes disproportionally more to new vehicle purchases as shown in Supplementary Appendix Table 2, the larger income growth in this group could lead to a larger increase in vehicle sales. Under Specification 2 without the first set of moment conditions, the counterfactual sales in Beijing without the policy are 612,654 and 940,851 in 2011 and 2012, respectively. The 31% drop in sales in 2011 from 804,355 in 2010 without the policy is hard to explain given that the sales decrease during the same period in Nanjing and Tianjin was 6.6% and 0.02%. Since the common trend assumption is not enforced, this specification attributes part of the large sales drop from 2010 to 2011 from the quota system to a negative demand shock in 2011 in Beijing relative to other cities. This then leads to a larger estimate on ρ (i.e. less stringent quota) and predicts a large decrease in sales without the policy. It is interesting to note that although Specification 2 without the micro-moments does not provide sensible pattern of price elasticities, the simulated sales impacts (not shown in Table 5) are close to those from the benchmark model. This is because the policy impacts are mainly identified through the first set of moment conditions that utilize common trend assumption, just as in a DID analysis. The micro-moment conditions, on the other hand, are very important for identifying consumer WTP and subsequent welfare comparisons. The bottom panel of Table 5 shows the counterfactual sales without the auction policy from 2008 to 2012 in Shanghai. The results from the benchmark specification suggest that the policy reduced the sales by 50–70% during this period. Interestingly, although Specification 2 leads to unreasonably low pr