An Empirical Investigation of Durability in the U.S. Automobile Market

An Empirical Investigation of Durability in the U.S. Automobile Market Yijia Wang y New York University November, 2007 Abstract The durability of motor vehicles is an important variable in understanding the U.S. automobile market. This paper is among the rst to empirically model the oligopolistic automakers durability choices. A dynamic random coe cient discrete choice model is developed and estimated using micro-level data from Consumer Expenditure Survey. The demand model captures the two opposing e ects of durability on automobile demand: competition e ect and holding time e ect. The results indicate while a 10% improvement in durability draws 12.31% more consumers, the overall demand only increases by 9.55% due to the fact that consumers replace their vehicles less often. Firms optimization conditions with respect to price and durability are utilized to retrieve production costs and marginal costs of improving durability. A welfare experiment of improving durability by 10% for all rms results in a drop in consumer welfare of 1.09%, which indicates that consumers do not necessarily bene t if the privately optimal durability choices are forced to go up. The model also enables the rst attempt to systematically investigate whether cost di erences in improving durability lie behind the durability discrepancy across brands. The results indicate that cost di erences do not appear to be signi cant in explaining the variation. Keywords: e ects of durability, random coe cient, dynamic discrete choice model, duration analysis, automobile market, welfare analysis, durability discrepancy. I am deeply grateful to my committee members, Alessandro Lizzeri, Allan Collard-Wexler, and Daniel Xu, for their continuous guidance and encouragement. I have greatly bene ted from discussions with Heski Bar- Isaac, Mark Dean, Fei Deng, Jonathan Eaton, Chris Flinn, Alessandro Gavazza, Zhiguo He, Donghoon Lee, Elizabeth Potamites, Ariell Reshef, Matt Wiswall, Ali Yurukoglu and seminar participants at NYU Applied Microeconomics seminar. All errors are my own. y Department of Economics, New York University. Email: yw317@nyu.edu. 1

1 Introduction Durable goods account for 34% of the manufacturing production in 2007. 1 One of the most important dimensions of any durable goods market is durability, the speed at which quality depreciates. As a signi cant determinant in consumers purchase decisions, durability is utilized by manufacturers as a critical characteristic to compete in the market. An accurate model of durability is therefore essential in understanding the behaviors of both the consumer and producer side of the market. It is also the basis to answer the question whether durability is e ciently provided, a big question for consumer and social welfare. The U.S. automobile market is an ideal industry to study these issues due to its size and availability of data. In this $110 billion business, vehicle durability has long been under close watch. 2 Since 1962, the Consumer Reports annual car issue gives a relative reliability rating for almost every model in the market up to 6 years old 3. J. D. Power and Associates (JDPA) publishes a problem-per-100-vehicle measure for each vehicle make in its annual Vehicle Dependability Study starting from 1990. 4 Despite their importance in understanding the auto market and close attention from the industry, rms durability decisions have been remarkably little studied. Theoretical literature has mainly focused on a monopolistic setting. Early work by Swan (1970, 1971) suggested that a monopolist would provide the socially optimal level of durability. However, Waldman (1996) shows that Swan s well-known independence result is sensitive to its assumption that used goods and news goods are perfect substitutes. When this assumption is relaxed, durability is provided below the socially optimal level. Hendel and Lizzeri (1999a) add quantity to the monopolist s choice variables and show when the production is distorted durability can be over-provided by the monopolist. Unfortunately, this theoretical literature provides little guidance on whether durability will be e ciently provided in an oligopolistic market. Although the auto market is one of the most-studied in the empirical literature, (Bresnahan (1987), Berry, Levinsohn and Pakes (1995), henceforth BLP, Goldberg (1995), Petrin (2002) ), the research has mostly ignored the dynamic consideration in this market. Consumers choose which vehicles to buy not only based on the prices and characteristics at the time of the purchase but also the expected conditions of the vehicles in the future and the resale prices they will get in the secondary market. This is a fundamental feature of the auto market, which cannot be captured by a static model. 1 From Bureau of Economic Analysis website, http://www.bea.gov/national/nipaweb. 2 From Bureau of Economic Analysis website, http://www.bea.gov/industry/gpotables. 3 The reliability ratings were expanded for vehicles going back to 8 years in 1995. 4 Because vehicles maintain quality well only if their owners experience little problem, a closely related concept is reliability. I will use these two interchangeably in this paper. 2

One of the main di culties of modeling durability choices is to accurately evaluating the e ects of durability on demand. Higher durability attracts more consumers and provides a competition advantage for the rms. But, when the motor vehicles depreciate slower, consumer hold onto them longer and make replacement purchases less often. I call the rst e ect the competition e ect and the latter the holding time e ect. Since the holding time e ect may o set the rms incentive to improve durability, a dynamic model that can incorporate the multiple period holding behaviors and the holding time e ect is needed for understanding rms durability choices. In this paper I make three contributions to the current literature. First, I develop and estimate a dynamic random coe cient discrete choice demand model which incorporates both the competition e ect and the holding time e ect, so that I can quantitatively decompose the two opposing e ects and measure the rms incentives to build more durable cars. Second, I model durability decisions within an oligopolistic, rather than monopolistic setting. This generalization is clearly necessary to capture the richness of the U.S. auto market. The demand estimates and rms optimization conditions with respect to price and durability are then used to retrieve both the production cost and marginal cost of improving durability. Third, the equilibrium model enables the rst attempt to answer two important questions: how welfare would change with changes in durability provision, and whether di erences in marginal cost of improving durability lie behind durability discrepancy. Now, let me explain the three contributions in more detail. Because both the cost estimates and the welfare analysis depend on measuring demand sensitivities to durability, accurately and comprehensively modeling the e ects of durability on demand is the core step of the model. E ects of durability go in two opposing directions. The positive e ect is easy to recognize. Higher reliability boosts demand by bene ting the vehicle owners in reducing the rate of problem occurrence and repair cost caused by vehicle breakdowns. Higher reliability also leads to a higher resale price. Using the resale price data from National Automobile Dealers Association (N.A.D.A) O cial Used Car Guide, I nd that while a vehicle on average retains 84% of its value after one year, this percentage drops to 75.5% if the vehicle experiences one more problem per year. This positive e ect is termed as the competition e ect because higher reliability increases the producers competitive advantage in a di erentiated goods market. The other direction of the e ects comes from the fact that people hold vehicles across multiple periods. According to CNW marketing research, from 1980-2000 a new vehicle stays in a household for 7.6 years on average. 5 People hold on longer to more durable 5 Data comes from a sample table from CNWbyWEB service. http://cnwmr.com/nss- 3

vehicles. As a consequence, consumers of more durable cars come back to the market to buy new vehicles less often, repressing the overall demand. Why do consumers hold onto more durable vehicles longer? To explain that, rst we need to understand why people hold durable goods across multiple periods at all. A good s quality depreciates over time, resulting in used goods of various qualities, each an imperfect substitute for the new goods. A person who holds the same vehicle for multiple periods is essentially consuming vehicle of progressively lower quality. If there are no frictions in the market, a consumer would choose a quality that maximizes her utility in each period and have no incentive to hold it across multiple qualities. However, market is not perfect. One friction is transaction cost, which is searching cost and pecuniary loss in trading (for example, the lower resale value obtained when trading in a used vehicle). Consumers hold their durable goods over periods in order to economize on transaction cost. In other words, a consumer has a target quality level, but transaction cost prevents her from getting the preferred quality in each period. Instead, an optimizing consumer will wait for the quality to depreciate till it hits a threshold at which point paying the transaction cost to get the target quality becomes worthwhile. 6 Since the upgrading occurs when quality hits the threshold, a faster deprecation should shorten the time needed for the quality to reach that level. This e ect has been demonstrated both empirically and theoretically. Potter and Sattler (1999) study a random sample of Illinois registration data and nd the duration of ownership is signi cantly positively correlated with vehicle s reliability rating by Consumer Reports. Stolyarov (2002) sets up a stationary dynamic model of a homogenous durable goods and establishes that goods deteriorating faster have shorter holding intervals. Hendel and Lizzeri (1999b) also predict and con rm such a relationship. This is the holding time e ect. The two opposing e ects imply that rms may not have incentives to improve durability if the holding time e ect dominates the competition e ect, even without considering the associated higher production cost. This calls for a demand model that can integrate the two e ects. I achieve this goal by extending the standard random coe cient discrete choice model to incorporate multiple period holding patterns. I assume that once consumers make a purchase, they hold onto their vehicles for some time before going back to the market. The inactive holding duration is captured by a parametric distribution function which depends on both vehicle characteristics and consumer characteristics. By allowing the holding time distribution to be vehicle speci c, I allow the vehicles features, especially durability, to a ect the mean holding length. Consumers purchase decisions are based on expected utilities of folder/cnwbywebcontents/ 6 There is a literature in macroeconomics that uses transaction cost to explain the slow adjustment in duables stocks. See Caballero (1993), Eberly (1994), and Attanasio (2000). 4

the alternatives, with expectation taken over the holding time distributions. I use the micro-level data from Consumer Expenditure Survey for the analysis. A unique feature of the data, which has not been previously exploited, is that it records holding histories for each vehicle. I utilize this information to estimate the holding duration distributions, which are then substituted into utility functions to calculate the likelihood of each observed purchase. A stationary purchase assumption is imposed to make the estimation feasible: consumers have time-persistent preferences and take the choice sets and their characteristics as xed. The stationary assumption enables a closed-form utility function, so that the estimation becomes similar to a standard estimation by BLP. 7 While this assumption may seem restrictive, there are two reasons for its adoption. First, unlike consumer electronics which exhibit rapid product innovation and price decline, product attributes in automobile market are much more stable 8 and market suggested retail prices of new vehicles do not drop after introductions. Thus, the value of delaying purchase to wait for better and cheaper products should not be an major concern in the car market. Secondly, this assumption enables consistent modeling of the supply side, a point I return to in section two below. The demand estimates indicate that competition e ect plays a more important role in determining demand at the current durability levels than the holding time e ect. Though higher durability signi cantly reduces the purchase frequency, the increase in market shares from people switching brands dominates the adverse holding time e ect. These demand estimates, together with the optimization conditions from the oligopoly companies, are used to retrieve production costs and marginal costs of improving durability. The estimates indicate that the weighted-average production cost per vehicle is $12,415 and the production cost goes up by $670.8 if an average vehicle s durability improves by 10%. Finally, I use my model to answer two important questions. The rst is the welfare consequence of improving durability. While I am not trying to give a conclusive answer to whether the current durability is below or above the socially optimal level, my model can be used to determine the welfare e ects of various policy experiments. First, I increase durability by 10% and let rms reset the equilibrium prices optimally. Consumer welfare and rms pro ts are calculated before and after the change. Not surprisingly, rms su er a loss after the durability is forced to deviate from the original levels. Interestingly, consumer 7 This method of feeding a reduced-form distribution to convert the dynamic model to essentially a static one is similar in spirit to Carranza (2007) which estimates a reduced-form reservation utility of delaying the purchase. 8 Using the vehicle features data from Ward s Yearbook, from 1996-2003, changes in wheelbase, length, height, width and MPG for the same model are all less than 0.5%. Change in engine size is less than 2%; the biggest improvement is in horsepower, but only around 6%. 5

welfare also falls, by 1.09% after the change. The reason for the drop is that the higher equilibrium prices o set the bene ts from higher durability. The results are similar when the magnitude of improvement in durability is reset to 20%. These results provide evidence that it is not necessarily bene cial for consumers and the whole society if the rms durability is forced to deviate upward from the market-determined level. The second question is whether di erences in marginal cost of durability lie behind the durability discrepancy across brands. Toyota and Honda have long been recognized as producing highly reliable vehicles. Figure 1 shows the measure of problems per vehicle taken from Vehicle Dependability Study from JDPA. The numbers in the gure is the average problem measures for model-years 2000-2003 for ve manufacturers: GM, Ford, Chrysler, Toyota, and Honda. These measures should be inversely correlated with the reliability of the vehicles. From the gure, Toyota and Honda top the chart. On average, a Toyota model has about 30% less problems than a Chrysler, which is at the bottom of the chart. 9 of the reasons why the durability discrepancy needs attentions is the recent discussion of the shrinking market share of U.S. auto producers. 10 One The reliability discrepancy between some Japanese automakers and their American counterparts has been cited by the automobile industry analysts and academic researchers as one of the most important factors behind this trend. 11 If each rm faces the same marginal revenue curve for durability, controlling for vehicle characteristics, di erences in marginal cost of improving durability can lead to distinctive equilibrium durability levels. Using the model s estimates of marginal costs, this paper is the rst study on whether manufacturers systematically di er in their costs of improving durability. The results indicate that Toyota and Honda do not have signi cantly lower marginal costs. Thus, cost di erences cannot serve as an explanation for the durability discrepancy across manufacturers. 9 This di erence in reliability has been very consistent over the years. According to Consumer Reports, during 1986-2002, 98% of the three-year old Toyota models and 91% of the three-year old Honda models were granted an "above average" for the reliability ratings, while only 7% of Chrysler models received this rating. Depending on the publication years, Consumer Reports either used a three-scale verdict, "above average", "average", "below average", or a ve-scale measure, "well above average", "above average", "averge", "below average", "well below average". Toyota and Honda were usually rated as "well above average" when a ve-scale measure was used. 10 According to Automotive News Market Data Book (1970-2006), the market share of Detroit Big Three (GM, Ford and Chrysler) decreased from 87% in 1970 to 60% in 2006 in the light vehicle market, and their share declined from 86% to 50% in the passenger car market during the same period. 11 For example, see "The end of Detroit: How the Big Three Lost Grip on the American Car Market" by Micheline Maynard (2003) and :"Special Report: The Car Company in Front - Toyota" The Economist, vol. 374, iss. 8411, pg. 73. 6

Figure 1: Problem Per Vehicle by Vehicle Makes 1.1 Literature Review This paper is built on random coe cient discrete choice models, starting from the seminal paper by BLP, and a large literature that follows, for example, Nevo (2001), Petrin (2002), and Goolsbee and Petrin (2004). All of these models are static setups which cannot incorporate repeat purchases. Recent studies on demand estimation have increasingly stressed the dynamic feature of demand. A very active literature focuses on consumers timing decision of when to enter the market, for example, Melnikov (2001), and Gowrisankaran and Rysman (2007) 12. These models allow for entry and exit of the products and forward-looking consumers who have rational expectation about the value of purchasing in the future when the set of products and their characteristics and prices are uncertain. The timing decision is essentially an optimal stopping problem; thus these papers are in the spirit of Rust (1987). To make the estimation feasible, a major simplifying assumption is imposed on these models that a scalar inclusive future value represents the transition of a large set of state variables and the scalar follows a Markov process. Though an appealing approach, this assumption is di cult to be reconciled with any optimal rm behavior. Since one of my main goals is to explicitly model the supply side, it is di cult to incorporate such a modeling technique to the equilibrium model. 12 Although their model allows for repeat purchase, there is no depreciation for the owned products, so the repeat purchase decisions essentially depend on evolution of the choice set. 7

Two empirical papers stand out explicitly accounting for consumers replacement decisions in a fully dynamic context. Schiraldi (2006) analyzes the Italian automobile industry by estimating a dynamic random coe cient model in which consumers optimize the replacement cycles due to transaction cost. My paper shares the idea that transaction cost lies behind the multi-period holding behaviors, but I do not attempt to quantify the magnitude of transaction costs. 13 Gordon (2006) studies the PC processor industry by estimating a logit demand speci cation and allowing for repeat purchases. Neither of the two models explicitly model the producer side, mainly due to the incompatibility of rms optimal behaviors and the simplifying assumption that makes the demand estimation feasible. As mentioned before, theoretical literature on durability has mainly focused on a monopolist. See Waldman (2003) for a review on the theoretical literature on durability. The paper is also related to Gilbert (1992) and De Jong (1996) in modeling holding durations. Both papers estimate a parametric distribution for the holding time, with both vehicle and household characteristics as explanatory variables. The latter paper also models vehicle type choice using nested logit, but the type decision is completely independent of the holding durations. That is, consumers do not take the holding durations into account when they decide which product to buy. The remainder of the paper is structured as follows. Section 2 describe the demand and supply side of the model. Section 3 introduces the various data sets. Section 4 explains the estimation algorithm. Section 5 presents the results. Section 6 concludes. 2 Modeling 2.1 Demand Consumers have a single unit demand at any given time and have in nite horizons. Whenever facing the purchase decision, consumers choose from the available new products in the current period to maximize utility. Used vehicles and choosing not to buy are grouped into an outside option. The point where I depart from the static discrete choice model is that I allow consumers to hold onto their vehicles for some period of time before going back to the market to make a similar purchase decision. This inactive holding period is captured by a cumulative distribution function F (h jy i ; j );which is both individual and vehicle speci c. By specifying the distribution function to be vehicle speci c, I allow the vehicle characteristics, especially the durability, to a ect the speed of depreciation and thus the holding length. Individual 13 Transaction cost not only varies across products but is also individual speci c. People who are extremely hassle-averse could hold on to their vehicles till scrappage. 8

specialty captures the variation in consumers in transaction cost and preference for new cars. People have higher transaction cost tend to hold their vehicles longer; consumers who prefer driving brand new vehicles would have a shorter duration of holding. Finally, the randomness comes from the consideration that consumers cannot fully predict the holding length due to uncertainty in their lives. For example, being relocated to a di erent state may bring forward the upgrading time. Specifying a holding time distribution as above implicitly imposes a restriction on consumer behaviors. That is, once the purchase is made, the evolution of market does not a ect owners holding time. It means that I rule out the case where consumers cut short the holding time of currently owned vehicles when some brand new product is introduced into the market. Given the vehicle attributes are quite stable and the style of the cars are not changing dramatically over the years, this assumption may not be very restrictive. To be consistent with the continuous feature of holding time, future utilities are discounted by a continuous discount factor : The expected utility of buying product j by consumer i is then E(U ij ) = Z 1 0 Z h e t X j i + j + " ij dt Pj 0 e h Pj h 0 i + e h E(V i ) df (h jy i ; j ) where X j is vehicle characteristics vector, j is product j 0 s unobserved characteristics, " ij is error terms which is assumed to be extreme value distributed, Pj 0 is purchase price of new product j, and Pj h is the resale price at age h. Coe cients on vehicle features and prices, i and i, are individual speci c to allow various preferences and price-sensitivities across consumers. E(V i ) is the expected value of having the option of purchasing again after disposing of the current product. Note that " ij are not time speci c, which implies a persistent preference for the consumers. A major simpli cation of the model comes from the assumption that consumers do not have foresight about the evolvement of the market and do not know the set of future products and their characteristics and prices. This, together with the persistent preference shocks, implies a stationary purchase decision whenever upgrading happens. As explained in the introduction, estimation of a fully forward-looking dynamic model requires using a scalar and a Markov process for the scalar to approximate for the transition of the large set of state variables. This simpli cation is hard to be reconciled with any rm optimal behavior. Thus, to make the estimation feasible, we impose the stationary decision assumption. This enables us to replace the expected value of future purchase with the current value to get (1) 9

a closed-form of utility function for each product. Replacing E(V i ) with E(U ij ) in (1) and rearranging terms, we get E(U ij ) = 1 Z X H j i + j + " ij + D 1 ij 0 P 0 j e h P h j i df (h jy i ; j ) where D ij = 1 R 1 0 e h df (h jy i ; j ): 14 Because the scale of the utility in the discrete choice model does not matter, we can multiply each product s expected utility by and de ne EU ij = u ij : Let P ij = Dij 1 R H 0 Pj 0 e h Pj h df (h jy i ; j ) denote the present value of the prices paid in a life time given the expected holding time. Then, p ij = P ij can be thought as the price payment ow. Thus, the purchase decision can be thought of as being made based on the utility ow. u ij = X j i + j + " ij + p ij i (2) Note that the holding time enters the utility function through the price payment ow. Faster replacement cycles implies higher rental prices payment. To account for the heterogeneity among consumers, we follow Berry, Levinsohn and Pakes (1994) (henceforth BLP) to allow the preference parameters to depend on observed and unobserved consumer characteristics. That is, i = + z p i p + v p i p where z p i is the observed consumer characteristics which is interacted with price, p is the coe cient on this interaction term, v p i is an unobserved random term, which is assumed to be distributed according to a standard normal, p is the coe cient to be estimated, which captures the variance of the unobserved term. Similarly, we have the random coe cient for each of the element in i, ki = k + zi k k + vi k k 14 With time-speci c error terms, E(V i) = maxfeu i1; :::; EU ijg: Then, we can use the contraction mapping: V i = max j Z 1 Z h e t X j i + j + " ij dt Pj 0 e h Pj h 0 0 i df (h jy i; j ) + Z 1 0 e h df (h jy i; j )E(V i) to nd the xed point of E(V i) for each person for every possible value in the parameter set. This will signi cantly increase the computation burden. Extension to this complication is left for future research. 10

Then, the utility ow can be re-expressed as u ij = j + " ij + X k x jk z k i k + X k x jk v k i k + p ij + p ij z p i p + p ij v p i p where j being the mean utility of product j ; j = X k x jk k + j Denote the set of parameters to be estimated as! = f; ; ; g and let ij (!) = X k x jk z k i k + X k x jk v k i k + p ij + p ij z p i p + p ij v p i p be the individual speci c utility term. Note here, unlike the static BLP model, the price of any alternative is individual speci c. The reason is that individuals di er in their holding time and thus they pay di erent rental prices. This individual specialty enables the identi cation of price coe cient without using instrumental variables. 15 Assume f" ij g is i:i:d extreme value distributed, then the probability that consumer i chooses product j is given by the usual logit form: es ij (;!) = exp( j + ij (!)) 1 + P k exp( k + ik (!)) (3) We can also interpret it as the share of consumers of type i who purchase product j: But this is not the share of consumers of type i who would enter the market to make purchase of product j every period because of the multiple-period holding patterns. For example, suppose 10 consumers buy Toyota Camry but each holds for 5 years. If the consumers purchases happen uniformly over a ve-year period, then in one year we would only observe 2 Toyota Camry purchases on average. If, on the contrary, each consumer holds the vehicle for only half a year, then in one year we would observe an average of 20 Camry purchases. Thus, the share of consumers i buying product j in a unit period of time (a year) is the total share of consumer i who buys product j weighted by the frequency of purchasing and is given by 15 If the price of an alternative were constant across consumers, it wouldn t be separately estimated from the mean utilities. Instrumental variables have to be utilized when regressing the mean utilities on the vehicle characterisitics and price to recover the preference coe cients. 11

s ij (;!) = exp( j + ij (!)) 1 + P 1 k exp( k + ik (!)) E[h jz j ; y i ] X exp( l + il (!)) 1 + P 1 k exp( k + ik (!)) E[h jz j ; y i ] l! 1 which can simplify to s ij (;!) = exp( j + ij (!))=E[h jz j ; y i ] 1 + P l exp( l + il (!))=E[h jz l ; y i ] (4) The inverse of the expected holding time re ects the frequency of purchasing. (We will detail how to obtain the distribution function F (h jz j ; y i ) and expected holding time in the next subsection.) Note that by introducing the holding time, the individual share functions have to be adjusted to account for the di erence in frequency of purchasing. In a static model without consideration of holding time, function (4) collapses to the usual individual demand. 2.2 Supply Firms choose prices and durability to maximize their pro ts. There are F rms in the market and the set of products produced by rm f is z f : Then, rm f 0 s objective function is max M X k2z f s k (p; d)(p 0 k c k (d k ; w k )) (5) where M is the market size, and c k is product k 0 s marginal production cost, which is assumed to depend on its durability level d k and a vector of cost characteristics w k :For simplicity, we assume marginal cost is independent of the output levels. Assuming the prices and durability achieve inner solutions 16, the rst order conditions are given by X @s k (p; d) @P 0 (Pk 0 c k (d k ; w k )) + s j (p; d) = 0 (6) k2z f j 16 Corner solutions for prices and durabiltiy do not make sense, because we never observe zero prices, neither vehicles not depreciating at all. 12

X k2z f @s k (p; d) @d j (P 0 k c k (d k ; w k )) s j (p; d) @c j(d j ; w j ) @d j = 0 (7) for j = 1; :::; J The J rst-order conditions in (6) are the pricing equations, which imply the price-cost margins (Pj 0 is given by: c j ) for each good. To see this, de ne a J by J matrix, ; whose (i; j) element (i; j) = ( @si @P 0 j 0 if i and j are produced by the same rm; otherwise Then, (6) can be expressed in matrix notation as (P c) + s = 0 =) P c = 1 s (8) with P c being the vector of price-cost margins and s being the vector of market shares. Similarly, the J rst-order conditions in (7) imply the derivatives of marginal product cost with respect to durability evaluated at the current durability level. De ne as the J by J matrix as (i; j) = ( @si @d j 0 if i and j are produced by the same rm; otherwise Let Dc(d) denote the vector of derivatives of marginal cost with respect to durability, then (7) can be expressed as (P c) s: Dc(d) = 0 =) Dc(d) = (P c):=s (9) with : and := meaning element production and element division, respectively. The vectors in (8) and (9) depend only on the parameters of the demand system and the equilibrium price and durability vectors. 3 Data The main data source is the micro-level data from Consumer Expenditure Survey (CES) 1996-2002. In each quarter, about 7,800 consumer units (CU) are interviewed. Each CU is 13

interviewed for ve consecutive times in a 15-month period and then dropped from the survey. 17 The Information about family characteristics is collected: income, geographic region, family size, age of reference person, race, education, etc. From the 2 nd to 5 th interview, the respondents report all the vehicles owned during the past three months and vehicles disposed of in the same reference period. Information on each owned vehicle is obtained: make/model, model year, vehicle purchase year and month. Disposal year and month and reimbursement amount are reported if the vehicles are disposed of. 1819 There are two separate uses for this data set. Demand Data First, it provides me the consumer-level demand for new vehicles. New vehicles bought during the interviews are counted as new purchases in that given year. In the sample period, 6,286 new purchases are observed. In order to calculate market shares, market size needs to be determined. I use the number of vehicle stocks plus the number of CUs that do not own any vehicle as the market size for a given year. 20 This leads to an average of 7% of total market share of new purchases. In each year, about 100 out of the approximately 200 new models available that year are actually bought in the data set. Infrequently purchased models never appear in the sample. I treat the set of models that are actually bought as the choice set. 21 Demand data is supplemented by vehicle attributes data on the 1996-2002 new models from Ward s Automotive Yearbook 22. For each model, the following information is collected: list prices, length, width, wheelbase, weight, horsepower, engine size, miles per gallon, automatic transmission, and drive type (four-wheel drive or all-wheel drive). I also collect the market segmentation data from Consumer Reports (subcompact, compact, mid-size, large, luxury, sporty, SUV, van and pick-up truck).table 2 provides the summary 17 Approximately 20% of the CUs are new to the survey each month. 18 A disposal can be trading-in, selling to a private party, being stolen, giving away to someone outside the CU, or damaged beyond repair. I do not attempt to distinguish between these various ways of disposing of a vehicle. 19 Before 1996, the surveys did not have a vehicle number variable by which the disposal information could be matched with the main owned vehicle data. Since a CU owns two vehicles on average, I cannot pin down which vehicle was disposed. 20 Previous literature uses the number of households as the market size, see BLP (1995). Given the average number of vehicles a household owns is around 2, using the number of households would underestimate the market size of vehicles. 21 It is a common practice to exclude the options with small market shares from the choice set for demand estimation for di erentiated goods market. See Nevo (2001). As mentioned in Goldberg (1995), because the utility is derived from vehicle characteristics, the absence of some models from the choice set doesn not represent a problem for the demand estimation. 22 CES contains some characteristics information, but mainly on the options, such as number of doors, number of cylinders, whether it has a sunroof, etc. 14

statistics on the purchased models and the households that make the purchases. 23 After excluding the observations with missing variables, the sample size of new purchases is 3,114. About two thirds of the observations in my sample is American vehicles; products from Japan takes a share of 28%. The most common segment is mid-size vehicles (25%); light trucks (SUV, pickup-truck and van) have a 42% share. Durability is measured by the negative of problem-per-vehicle from Vehicle Dependability Study of JDPA for model-years 2000-2003. 2425 The measures are based on responses from about 50,000 owners annually. Table 1 provides the problem measure list by make. Although a higher problem measure approximates a lower durability on average, there are three caveats about using this measure. First, JDPA does not distinguish between severe problem and minor problem in calculating the measures. An engine replacement could be more expensive than xing the brake, thus should imply a lower durability measure 26. However, JDPA does not weight the problem symptoms by the corresponding cost and treat all trouble spots equally. This could be especially problematic for vehicles which constantly experience inexpensive troubles, but whose conditions can be restored after the minor x. European cars tend to have a more complicated electrical system and are more likely to be plagued with electrical troubles 27. This is probably why European vehicles have a reputation for quality but are ranked low in the problem measure table. I will add origin dummies in the estimation to partially control for this problem. But if the repair pattern is more make-speci c, rather than origin-speci c, then I would misspecify the durability for some makes. Another caveat about this measure is that JDPA only reports the make-average index, but not model-speci c. 28 Thus, I cannot capture the durability variation across models within the same make. This should be of less concern if one is willing to assume that durability 23 Half of the discarded observations do not have detailed information on the model. For example, the survey only speci es a purchase of Buick or GMC truck, but not the exact model. I adjust the market sizes accordingly to maintain the same total market shares calculated before discarding the purchase data. 24 Since 1990, JDPA has conducted surveys to collect problem symptoms experienced by the owners at 4 to 5 years of ownership. For example, in calendar year 2001, owners of 1997 model-year cars and trucks were surveyed. This was later changed to 3 years of ownership in 2003, when the owners of 2000 model-years were included in the survey. Prior to year 2003, problem measures for nameplates with ranking lower than the industry average were not publicly released. So, the complete ranking is only available for model-years 2000 and later. We take the average of problem measures for each nameplate for model-years 2000-2003. 25 Another source of reliability data is Consumer Reports. We compiled the reliability measures for modelyears 1990-2002 at 4 years old. The make-average reliability index is highly negatively correlated with the JDPA measure. 26 Using the repair cost data from CES, the most expensive repairs are body work/painting, clutch/transmission, and engine repair/replacement. 27 Electrical troubles: power accessories, wiring, wiper motor, radio and sound system, switches, horn, etc. 28 The reliability index from Consumer Reports provides model-speci c ratings. But, they ratings are relative measures. 15

variation is more between makes than within makes because, for example, models under the same make have access to the same production technology and managerial talents. Finally, note that problem measures are collected through JDPA s vehicle reliability and service surveys. The vehicle owners maintenance and usage patterns a ect how many problems would occur. Consumers who pay less to maintain their vehicles would expect a higher rate of repair down the road. This idiosyncrasy in maintenance and usage shouldn t cause concern if it is random across individuals. However, if buyers of a speci c make tend to maintain less and use more heavily, the problem measure wouldn t correctly capture the durability of that make. Basic warranty coverage comes from Automotive News. Consistent with the problem measure, I also use the average from 2000-2003 for each make. Duration data As described in the model, consumers make the purchase decisions based on the expected utilities, with expectation taken over holding duration. Thus, I need to specify a holding time distribution for each consumer and each model in her choice set. This step is done by separately estimating the holding distributions using the duration data in CES. For each vehicle in the sample, I have a holding history, starting from the time of the purchase, ending either at the time of disposal or at the end of the interviews if it is still kept by the owner. If it is still kept at the end of the interview, the holding time for that vehicle is right censored at that point. In addition to the right censoring, there is another data feature that requires attention. Vehicles that are bought before the start of the interviews enter the sample only if they are still owned when the households start being interviewed. I must take this into account, together with the right censoring, when studying the holding patterns. Again, after excluding the observations with incomplete information, I am left with 51,278 data points. 2930 Figure 2 shows the empirical distribution of holding time (including both censored and uncensored); the mean duration in the sample is 4 years. In Figure 3, I plot the average holding time against durability by makes. Though the positive relationship between the holding time and durability is quite interesting, care should be taken when attempting any interpretation because most of the durations are incomplete spells. 29 Original data points are 111,876. 30% can t be matched with price data. There are several reasons for the unmatching: (1) Vehicles with model-years earlier than 1979 are grouped together by CES, also for 1980-1982 and for 1983-1985. 10.5% of the data belongs to this case. (2) 19% of the vehicles do not have detailed information on models, eg. BMW but not BMW 3 series, or model years. (3) 1% are exotic models, like Bradley GT, which are not included in the N.A.D.A price data. 30 In order to use more data points, I include both new and used vehicles in the duration analysis. But, I 16

Figure 2: Distribution of Holding Time Figure 3: Average Holding Time and Durability by Makes 17

Table 3 provides the summary statistics on the duration data and the owners. 89% of the durations are right-censored. The mean age of a vehicle when purchased is 3.5 years. A consumer pays 11.36 thousand dollars for an average vehicle, which retains 58.5% of its value three years later. The rest of the variables are quite similar to those in Table 2, except two notable di erences. One is the lower proportion of SUV and pickup in the duration data. Remember that the duration data set covers the vehicle stocks in 1996-2002, while demand data are the new purchases. The changing vehicle composition re ects the growingpopularity of light trucks over the years. Mean income is higher in the demand data because I only include new vehicles in the demand data set. One disadvantage of the data is that I only observe the family characteristics at the time when the CUs are interviewed. Though some of the variables are constant during the holding period, such as, race of the household head, but others can evolve over time, for example, family size and income. The holding durations are speci ed as functions of consumer characteristics at the time of purchase, which can be di erent from those observed at the time of the interviews. I acknowledge this problem, but have no other option but using the current characteristics to approximate the relevant variables. 31 Resale Prices In the model consumers can sell their used vehicles at any age. It is the rental price that enters the utility function. Thus, I need to know the resale price for each model at each age. Potentially, I could use the transaction prices directly from CES. Unfortunately, the resale prices in the CES are far from being complete and desirable. 32 So, instead I use the price data obtained from National Automobile Dealers Association (N.A.D.A) O cial Used Car Guide from July 1996 to July 2006. In each of these calender years, I have retail price allow the duration distribution to di er by age. 31 Since my demand data only covers 7 years, it may not be controvertial to assume that the durability measures have not changed during this sample period. However, when coming to the duration data, the time trend of durability becomes a concern. As noted in Consumer Reports, the automotive reliability has been continually improving over the several decades. In the 1993 April issue of Consumer Reports, it says "In the 1980s alone, the average trouble rate of new American-made models dropped by two-thirds, approaching the reliability of Japanese models at the start of the decades. Meanwhile, Japanese automakers improved their products reliability by one-third." Ideally, I should use the year-speci c measues to re ect the yearly uctuations in durability and thus their e ects on holding durations. Good news is that across-brand di erence in durability is highly correlated over years. This can be veri ed by checking the relative ratings from CR across years. "In our experience, a model s past often fortells its future, for example, year after year, Toyota and Honda charts are lled with read and Hyundai and some Jeep charts with black." one editor of Consumer Reports also con rms. 32 58.7% of the model-vintage in the sample do not have purchase price; and because it could be di erent submodels with distinct conditions that contribute to the calculation of model-mean prices at di erent vintages, the model-mean prices from the sample have a substantial variation from one vintage to another. 18

for each model available in the market, up to 20 years old. For people who buy new vehicles in 2002, the future resale prices are needed to obtain rental price at each age. Since these future prices are nowhere to be available, I use a price regression to predict the values. Table 4 shows this pre-stage regression result. On average, a vehicle retains 84% of its value a year later. This ratio is signi cantly a ected by the vehicle s durability. A more durable car has a higher resale value controlling for other factors. The price depreciation slows down as vehicles age, implying a convex decreasing price schedule with age. The number of models of the same model-year and the number of models in the same calender year capture the competition in the market. The t is quite well, with a R 2 of 0.98. To be consistent, I use predicted resale prices for all the model-age in my sample. 33 34 4 Estimation 4.1 Demand Estimation The estimation strategy is to maximize the probability that each consumer in the data set makes the observed choice. The likelihood function is log L = X i I(c i = j) log(s ij (;!)) where I is the indicator function of consumer s observed purchase. R H 0 To calculate the individual speci c utility term ij (!);simulation method needs to be Pj 0 dg(h jy i ; j ): There are no closed- implemented. Remember p ij = Dij 1 e h Pj h form expectation for the price payment ow. We will use a simple frequency simulator to approximate the integrals, with the pseudo-random draws from the distributions of holding time obtained from the rst-step duration analysis, which depends on both consumer characteristics and vehicle features. One way to maximize the likelihood function is to search over the parameter! and the vector of mean utility levels j. These mean utilities are just the alternative-speci c xed e ects. However, since the large number of alternatives in the automobile market, searching 33 Ideally, the sales weighted average should be used. But, sales data available for public use are not detailed up to bodytypes.thus, simple average is taken with respect to bodytypes. 34 One caveat of the data is that retail prices are reported for less than 1% of the new vehicles. We have to use list price for the new vehicles, which creates a discrepancy between the new vehicle prices and the used vehicle prices, because the latter is transaction-based. 19

over the xed e ects and! simultaneously is too computation-costly. Instead, we use the method of Berry (1994) which shows that for any value of! there exists a unique vector such that the predicted market shares equal the observed market shares. This allows to be expressed as a function of!, (!);and the parameters that enter the likelihood function can be reduced to! only. The market share is just the sum of individual consumer s demand. market share of j is Z s j = s ij ((!);!)dg(y i ) y i The predicted where G(y i ) is the cumulative distribution function of consumer characteristics y i. Again, we don t have closed-form solution for this integral; evaluation has to be done numerically by simulation. For each possible!, we nd out the xed e ects such that s j = s 0 j for each j;where s0 j is the observed market share for product j:this is done by iteration 35 : 0 j(!) = j (!) + ln(s j ) ln(s 0 j) j = 1; :::; J Then,! is searched over to maximize the likelihood function. Finally, the xed e ects evaluated at the optimal! is regressed onto the space of vehicle characteristics to obtain the mean preference parameters. As in standard random coe cient models, the identi cation of preference parameters come from the variation in market shares across products and markets. The correlation of market shares among products with similar attributes identify the distribution of preference parameters across consumers. 4.2 Estimation of Duration The last piece in the model is to estimate the distribution of holding time to be fed into the demand estimation. We model the holding duration as Weibull distributed. Both vehicle characteristics and household characteristics are included in the covariates to allow the distribution of holding time to vary across models and across consumers. Maximum likelihood 35 It can be easily shown that all the conditions for the contraction mapping to work in Berry(1994) hold in this model. 20

is used for the estimation 36. The likelihood function has to integrate both the left truncation and right censoring and is given as follows: log L = NX JX i=1 j=1 I(v i = j) d i log f(h i jz j ; y i ) 1 F (h 0 i jz j; y i ) + (1 d i) log 1 F (h i jz j ; y i ) 1 F (h 0 i jz j; y i ) where h 0 i is the length of holding duration when the observation enters the sample, h i is consumer i 0 s length of holding when the vehicle is disposed-of or censored at the end of the interviews, d i is the dummy that indicates the vehicle is disposed of if it takes value one, zero if the duration is right censored, v i denote the vehicle consumer i owns, z j and y i are vectors of vehicle characteristics and household characteristics, respectively. The mean of the holding duration is speci ed as E(h jz j ; y i ) = exp( z j z + y i y ) (1 + 1 b b ) where b is the parameter that determines whether the hazard rate increases or decreases with time. Notice that a positive coe cient on z or y implies a negative e ect on expected holding time. The vehicle characteristics included as determinants of the mean are problem measure, basic warranty length, age at purchase, interaction between problem measure and age, purchase price, resale price after 3 years, number of cylinders, light truck dummy, origin dummies and vehicle category dummies. Household characteristics include family size, number of persons less than 18, income, age of household head, education, number of vehicles owned the household, region dummies, rural dummy, and race dummies. 5 Results 5.1 Duration Analysis Result Let s begin with the result of duration analysis because it serves as an input to the demand estimation. The result is reported in table 5. Marginal e ect column captures the average changes in expected holding time when the corresponding variables increase by 1. As expected in the holding time e ect, higher durability increases the number of years a consumer holds a 36 The estimation is done with simulated annealing in Matlab. As stressed in the numerical methods literature, we found that simulated annealing leads to much more robust estimates than both the simplex and gradient-based search methods. 21