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BEAUTIFUL LEMONS: ADVERSE SELECTION IN DURABLE-GOODS MARKETS WITH SORTING*
Jonathan R. Peterson Faculty of Management NRU Higher School of Economics
[email protected] Henry S. Schneider Johnson Graduate School of Management Cornell University
[email protected]
June 2014
Abstract We document a basic characteristic of adverse selection in secondhand markets for durable goods: goods with higher observed quality may have more adverse selection and hence lower unobserved quality. We provide a simple theoretical model to demonstrate this result, which is a consequence of the interaction of sorting over observed quality between drivers with different quality valuations and adverse selection over unobserved quality. We then offer empirical support using data on secondhand prices and repair rates of used cars from the Consumer Expenditure Survey, and discuss a number of implications for everyday advertising and consumer questions.
1. INTRODUCTION In this study, we make a simple but important point about adverse selection in secondhand markets: used goods with higher observed quality may have worse adverse selection and consequently lower unobserved quality. The intuition is as follows. When a used good has deteriorated such that it has low observed quality, there is often a gain from trade from sorting. This sorting arises because used-good sellers typically have a high valuation for quality, reflected in their initial decision to have purchased the good new, and used-good buyers typically have a lower valuation for quality, reflected in their preference for the used good and its combination of lower quality and lower price. However, when a used good has retained its high observed quality, this sorting motive is absent, and there must be another reason for the seller to put the good up for sale. An important reason may be hidden defects. In addition to representing a basic characteristic of durable-goods markets, recognition of this adverse selection/sorting interaction can shed light on a number of everyday advertising and consumer questions. First, it can explain why sellers of used goods often tout the high quality of an item while simultaneously attempting to justify why they would want to dispose of it. For example, the following listing on Craigslist for a 2005 Chevrolet Silverado truck states: “Runs great with no problems what so ever! Winter ready and needs absolutely nothing! … I am only getting rid of it because I am leaving for the winter and for who knows how long.”1 Second, it makes clear that high observed quality need not be an indication of high unobserved quality. While the quality of observed and unobserved parts may be positively correlated in the total population if owners generally divide into “careful” types who take care of the good, and “careless” types who do not, the selection of goods that end up on the secondhand market may not follow this pattern. Third, it provides practicable lessons to both sellers and buyers. For sellers, the lesson is to advertise credible reasons why the high observed-quality good is for sale (if such reasons exist), and it highlights the importance of warranties, refund policies, and reputation mechanisms 1
Other examples are for used aluminum-siding installation equipment, which mentions “Great condition!!!! Out of business & leaving state;” and for a laptop computer, which mentions, “Less than a year old. Perfect condition … Battery lasts as long as it did out of the box as I have never ran it off the battery, only the AC … This is a fast laptop! I am only selling it because my wife bought a touch screen laptop and so I inherited it.”
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for sellers of high observed-quality goods to address potential buyer concerns about low unobserved quality. For buyers, the lesson is to carefully assess the motives of sellers of high observed-quality items, and to seek contractual or other assurances about unobserved quality when such motives are absent. To formalize ideas, we provide a model of adverse selection and sorting in the used-car market, a large market for which detailed data are available. We model a car as an assemblage of parts where the conditions of some parts are observable to buyers and sellers (“observed” parts such as external vehicle body), while the conditions of other parts are observable to sellers only (“unobserved” parts, which might include engine and brakes). The model predicts more adverse selection over unobserved parts for cars with higher observed quality. We then provide empirical support for this result. Our measure of observed quality of a recentlytraded used car with a given set of characteristics (model, vintage, age, mileage, and attributes such as sunroof and engine size) is its price. If two cars with the same characteristics have different prices, we infer that the higher-price car has higher observed quality. To test the predictions of the model, we estimate the relationship between used price and post-purchase repair rate. Under pure symmetric information, the model predicts that the secondhand price is reduced to account for any observed defects and associated repair costs, and hence a higher car price corresponds to fewer post-purchase repairs. When there is asymmetric information, a higher price will correspond to more repairs due to the adverseselection/sorting interaction. Using data from the Consumer Expenditure Survey, we estimate the relationship between price and repairs shortly after purchase, and find that cars that are repaired within the year after purchase had a 3.8 percent higher price (p=.03). This positive relationship between price and repairs is hard to explain without asymmetric information because, as mentioned, the cost of anticipated repairs should be deducted from car price. We next split out the effect for vehicle body work, which is the one category we are confident has an observable component. The other categories such as engine are likely to have significant asymmetric information. Consistent with the theoretical predictions, we find that cars with more postpurchase body-work repairs have a lower price: Cars with body-work repairs have a 19.4 percent lower
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price (p=.02) compared to cars with other repairs, which had a 4.6 percent higher price (p=.01). The primary risk to the interpretation of the positive relationship between price and repairs is that there is an uncaptured buyer characteristic that co-determines prices and repairs. This would occur if the types of buyers who purchase high-price cars are more likely to conduct repairs conditional on a defect. We provide a number of checks that indicate that this story is very unlikely to be driving the results. In addition to the implications mentioned earlier, we note two further consequences of the adverse-selection/sorting interaction. First, used-car sellers may have a hard time using price to signal unobserved quality to potential buyers. Cai, Riley, and Ye (2007) demonstrated how sellers could credibly use high prices to signal high unobserved quality in secondhand markets. The idea is that sellers of high unobserved-quality goods have a lower internal cost of failing to sell the item because of the higher value of continuing to use it. The inverse relationship between observed and unobserved qualities would at a minimum complicate this price signaling. Second, the more severe adverse selection for high observed-quality goods implies that the market does not reward high observed quality as much as in the full-information case. Consequently, owners have less incentive to invest in observed quality (i.e., maintenance of observed parts) because the return to this investment is reduced due to the accompanying increase in adverse selection. A precursor to our study is the theoretical work is Hendel and Lizzeri (2002), which predicted that more reliable car models (i.e., models with a lower unobserved defect rate) have more adverse selection. Their model assumes a single dimension of quality that is observed by sellers but not buyers. We introduce multiple dimensions of quality with varying information properties, which permits us to directly model the relationship between observed and unobserved quality, obtain the predictions that we bring to the data, and arrive at the various implications about the secondhand market that we highlight. Also related is the literature on information in financial markets (e.g., Glosten and Milgrom 1985), which considers assets for which buyers do not know the value. Buyers face “informed” sellers who are aware of the value, and “liquidity” sellers who sell for reasons unrelated to the value. Informed sellers only sell if the asset has low unobserved value, and so adverse selection is increasing in the
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number of informed sellers. One can consider sellers of high observed-quality goods as akin to informed sellers in the sense that they only sell if unobserved quality is low, while sellers of low observed-quality goods are akin to liquidity traders in that their trade decision is less dependent on unobserved quality.2 Previous evidence on adverse selection in durable-goods markets is mixed. An incomplete list or previous work includes Bond (1982, 1984), which found no difference in repair rates between traded and non-traded young trucks, but a difference for old trucks. Adams, Hosken, and Newberry (2011) found no evidence of adverse selection among younger used cars based on trade prices. Emons and Sheldon (2009) and Engers, Hartmann, and Stern (2009) found evidence of adverse selection from turnover patterns, while Porter and Sattler (1999) did not. Gilligan (2004) found evidence of adverse selection among used airplanes, while Lewis (2011) found that information disclosures can limit adverse selection online. Peterson and Schneider (2014) found that used trade volume is decreasing and repair rate is increasing in the defect rate of unobserved parts but not observed parts, which is evidence of adverse selection. 3 The current study contributes to the literatures on durable goods and information economics by documenting a basic characteristic of adverse selection in durable-goods markets: higher observed-quality goods are more susceptible to adverse selection. We provide empirical support for this sorting/adverseselection interaction, and note that a positive relationship between used price and repair rate is hard to explain by either adverse selection or sorting in isolation, but arises naturally from their interaction. We have highlighted a number of real-world implications of this interaction. The results also bring new evidence to the literature on adverse selection. As mentioned, the previous literature found mixed results. However, much of the previous literature treated goods as having unidimensional quality, measuring trade patterns, prices, and repair rates as they relate to quality as a 2
Similarly, Rosenman and Wilson (1991), Genesove (1993), and Chezum and Wimmer (1997) examined used durable-goods markets and generally found more adverse selection among sellers who bring to market a smaller fraction of their assets (e.g., a smaller fraction of their inventory of used cars). These sellers are presumably more selective about which items to sell based on unobserved quality. 3 Theoretical work on adverse selection in Wilson (1980), Kim (1985), and Hendel, Lizzeri, and Siniscalchi (2005) examine mechanisms that may overcome the market failure identified in Akerlof (1970). Theoretical work on sorting for durable goods includes Swan (1970, 1971), Mussa and Rosen (1978), Anderson and Ginsburgh (1994), Waldman (1996a, 1996b), Hendel and Lizzeri (1999a), and Porter and Sattler (1999). Hendel and Lizzeri (1999b) is an important paper that examines both adverse selection and sorting.
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whole. The current results demonstrate that the observed and unobserved qualities of secondhand goods may be inversely related, which can lead to significantly attenuated estimates of the effects of adverse selection when the good is examined as a whole.
2. THE USED-CAR MARKET WITH ADVERSE SELECTION AND SORTING A. Asymmetric information We present a model of the used-car market where some aspects of car quality can be repaired and other aspects either cannot be repaired or are prohibitively expensive to repair. The non-repairable aspects of quality are observed by buyers and sellers and are items such as faded paint and rust, interior stains and smell, and other wear and tear. For a rough idea of how to think about the non-repairable aspects of quality, Table A1 of the Appendix provides the car-quality categories used by Kelley Blue Book. For aspects of quality that can be repaired, some parts have asymmetric information and others have symmetric information. The purpose of the model is to show how observed aspects of quality affect the level of adverse selection created by the unobserved aspects of quality. It will be useful to distinguish the aspects of observed quality that cannot be repaired (or are prohibitively expensive to repair) from the conditions of individual parts that can be repaired. We use the terms “sellers” and “buyers” to represent potential used-car sellers and potential usedcar buyers. Sellers have one used car each; buyers are not endowed with any cars. A seller has a taste for quality that is drawn from a uniform distribution on [1, 𝜃! ] with a total mass equal to one. The function 𝐹 𝜃 =
!!! !! !!
represents the fraction of sellers with a taste less than 𝜃. All used-car buyers have a taste
𝜃 = 1, and the distribution of used-car buyers has a mass greater than one.4 Let 𝑄 be the non-repairable aspect of quality (that is, the cost of repair exceeds the utility received by the highest-valuation driver for the repair), and let 𝑎 and 𝑏 represent two car parts that can have defects and be repaired. Part 𝑖 ∈ {𝑎, 𝑏} has a defect with probability 𝜆! ∈ (0,1), which costs 𝑐! > 0 4
The underlying reason why sellers have a higher taste of quality than buyers is that sellers originally purchased the car new, and are considering trading up to another new car (See Hendel and Lizzeri 1999b and others on this point).
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to repair. The probabilities of defects for the two parts are independent of each other.5 If a part has a defect, it must be repaired for the car to be driven. In practice, the assumption is that the defect must be repaired within a reasonable amount of time after purchasing the car (in our test we examine repairs within one year after purchase), which allows us to abstract away from a sorting motive in which sellers sell a car with a defect to buyers who do not mind driving the car without repairing the defect. We expect most defects to be of the kind that must be repaired within some reasonable amount of time to continue driving, such as worn-out brakes, a failing battery, or a defective catalytic converter that must be repaired to pass an emissions inspection. Also recall that the aspects of observed quality for which there are gains from trade are captured in 𝑄, which are not essential for the car to operate and for which drivers have heterogeneous tastes. We denote part 𝑖 = 1 if the part has a defect and part 𝑖 = 0 if not. 𝑄 and part 𝑎 are observed by sellers and buyers. Part 𝑏 is observed only by sellers. The total utility that a driver with taste 𝜃 receives from owning a car is 𝜃𝑄 − 𝑐! 𝑎 − 𝑐! 𝑏. Note that 𝜃 only applies to 𝑄, which assumes that drivers’ taste for car quality is unrelated to drivers’ taste for a functioning car. This restriction, along with the requirement that defects must be repaired, is equivalent to (i) all drivers having the same value for a car that is not repaired and therefore is not functional – namely, zero; and (ii) all drivers facing the same cost to conduct repairs (our empirical analysis will condition on car characteristics, so the assumption of the same repair costs is within very similar cars). Drivers receive zero value from owning a second car. Sellers have the option of replacing their used car with a new car. New cars have no defects and hence have overall quality 𝑄! > 𝑄. We assume that 𝑄 > (𝑐! + 𝑐! ) so that used cars with defects are worth repairing rather than scrapping. We also assume the new-car market is competitive and hence that 𝑃! and 𝑄! are exogenous, which allows us to
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Our empirical specifications will include controls for car model, vintage, age, and mileage so in practice this assumption is that the repair probabilities are independent conditional on car characteristics. This permits some car models to be more defect-prone than others (e.g., Fords incur more defects than Hondas), but abstracts away from the possibility that some drivers idiosyncratically care for their car at different levels than other drivers of similar cars. We expect most of the variation in defect rates across cars and car parts is associated with car characteristics (such as make and mileage) rather than driver. Introducing more robust defect correlations would be interesting, but complicates the model and is not central for understanding the phenomenon of interest.
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avoid considering interactions with the new-car market.6 We also assume that 𝜃! 𝑄! > 𝑃! > 𝑄! , which guarantees that it would be efficient for some but not all sellers to replace their used car with a new one. Because the number of used-car buyers exceeds the number of sellers, the market price is the reservation price (taste for quality) of the used-car buyers, which as mentioned is 𝜃 = 1. Hence, the market price is 𝑃 𝑄, 𝑎 = 𝑄 − 𝑐! 𝑎 − 𝑐! 𝑔 𝑄, 𝑎 , where 𝑔 𝑄, 𝑎
is the buyer’s inference about
unobserved condition given the observed quantities, 𝑄 and 𝑎, because a buyer cannot observed the condition of part 𝑏. Given rational expectations, 𝑔(𝑄, 𝑎) is the fraction of cars on the secondhand market with an unobserved defect. In the proof of Proposition 1 below we will find that 𝑔 𝑄, 𝑎 = 𝑔(𝑄), and so we will write 𝑔(𝑄) henceforth. A seller sells her car if the utility of driving a new car minus the price differential between a new and used car (the cost of upgrading) exceeds the utility of driving the used car. That is, a seller with taste 𝜃 sells her car if 𝜃𝑄! − (𝑃! − 𝑃 𝑄, 𝑎 ) > 𝜃𝑄 − 𝑐! 𝑎 − 𝑐! 𝑏. Substituting the expression for market price, 𝑃(𝑄, 𝑎), from above into this condition gives the following cutoff rule for sellers: A seller upgrades to a new car if her taste for quality is, [1]
𝜃≥
!! !!!!! !!!! ! ! !! !!
Equation [1] defines the lower bound on taste among sellers who sell their car. Let 𝜃′ and 𝜃′′ be the cutoff tastes when the car does and does not have an unobserved defect, respectively (i.e., 𝑏 = 1 or 𝑏 = 0). These cutoff rules determine the fractions of cars on the secondhand market with and without an unobserved defect, and consequently determine the probability that a car on the secondhand market has an unobserved defect, 𝑔 𝑄 . Using Bayes’ Rule, 𝑔 𝑄 is the number of cars sold with an unobserved defect divided by the total number of cars sold in equilibrium,
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Clearly the automobile market is not perfectly competitive but oligopoly and monopolistically competitive models would complicate the model, and evidence indicates that market power in the new-car market is limited, particularly in the US market, which is the focus of our empirical analysis: There is a low level of concentration (in 2011, seven producers in the US market had over an eight percent market share) and profit margins for the major sellers in the US market during the last ten years were typically in the low single digits.
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[2]
𝑔 𝑄 =
!! !!! ! ! !! !!! ! ! ! !!!! !!! ! !!
Our first result demonstrates that our model gives the basic adverse-selection outcome regarding the conditions of cars that end up on the secondhand market.
Proposition 1: The repair rate for unobserved parts is higher for traded cars than the overall population of cars (𝑔 𝑄 > 𝜆! ). In contrast, the repair rate for observed parts is the same for traded cars and the overall population of cars (𝑔 𝑄 = 𝜆! ).
Proof: Substituting 𝐹 𝜃 =
!!! !! !!
, 𝜃!! =
solving for 𝑔 𝑄 gives 𝑔 𝑄 = 𝜆! +
!! !!!!! !!! !(!) !! !!
!
!
!
!!
−
! ! !!
, and 𝜃!!! =
− 4𝜆! 1 − 𝜆!
!! !!!!! !(!) !! !!
into Equation [2] and
, where 𝐾 = 𝜃! 𝑄! − 𝑄 𝜃! − 1 −
𝑃! . Because this expression is greater than 𝜆! , traded cars have a higher repair rate for unobserved parts compared to the overall population. Notice that the expression for 𝑔 above does not depend on the condition of the observed part, 𝑎. Therefore, the seller’s decision in Equation [1] also does not depend on the condition of the observed part. This is because the repair cost for the observed part comes directly out of the sale price. ∎
The intuition for Proposition 1 is from the basic adverse-selection result in Akerlof (1970). Because unobserved quality is not reflected in the market price, drivers with high unobserved-quality cars are not rewarded for this quality and hence are more likely to keep their cars. In contrast, because the probabilities of observed and unobserved defects are independent, and because any defects in 𝑎 must be repaired regardless of whether the seller or buyer drives the car, there are no gains from trade over 𝑎. Hence, the trade decision is not affected by the condition of the observed part 𝑎. We now report our main result, which establishes the inverse relationship between observed car quality and the condition of the unobserved parts.
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Proposition 2: The repair rate for unobserved parts among traded cars (𝑔(𝑄)) is increasing in observed car quality (𝑄).
Proof: From the proof of Proposition 1, the closed-form solution for the fraction of traded cars with repairs of unobserved defects is, 𝑔 𝑄 = 𝜆! +
!
!
!
!!
−
! ! !!
− 4𝜆! 1 − 𝜆!
, where 𝐾 = 𝜃! 𝑄! −
𝑄 𝜃! − 1 − 𝑃! . Because the expression 𝑔 𝑄 is decreasing in 𝐾, 𝜃! > 1 implies that 𝐾 is decreasing in 𝑄. Therefore 𝑔 𝑄 is increasing in 𝑄. ∎
The reasoning behind Proposition 2 is as follows. An owner of a high observed-quality car only has reason to sell her car if it has an unobserved defect. Hence, there is adverse selection. However, an owner of a low observed-quality car may prefer to sell at the market price regardless of its unobserved condition, which causes a lower proportion of low observed-quality cars to have unobserved defects. Said another way, the sorting effect dilutes the adverse-selection effect. This implies that lower observedquality cars have fewer repairs of the unobserved part after purchase. Naturally, buyers are willing to pay more for cars with high observed quality and less for cars they expect to have unobserved defects. Because Proposition 2 indicates that high observed-quality cars have more unobserved defects, this implies that observed quality has a direct positive effect on used-car price, and an indirect negative effect on used-car price. This leads to the following results.
Lemma 1: For sufficient small uncertainty about the quality of unobserved parts in the population, the secondhand price is increasing in (a) the observed quality and (b) the repair rate of unobserved parts among traded car.
Proof: From the expression for used-car price, 𝑃 𝑄, 𝑎 = 𝑄 − 𝑐! 𝑎 − 𝑐! 𝑔 𝑄 , and the closed-form
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solution for 𝑔(𝑄) from the proof of Proposition 1, we have, 𝑃 𝑄, 𝑎 = 𝑄 − 𝑐! 𝑎 − 𝑐! 𝜆! − 𝐾 ! − 4𝜆! 1 − 𝜆! 𝑐!!
!" !,! !"
=1−
! !
,
! ! ! !!!! !!!! !!!
where
−1
𝐾 = 𝜃! 𝑄! − 𝑄 𝜃! − 1 − 𝑃! .
! !
𝐾−
Then,
𝜃! − 1 , which is positive when the variance of repair costs for
unobserved defects, 𝜆! 1 − 𝜆! 𝑐!! , is sufficiently small. The relationship between secondhand price and the repair rate of unobserved parts follows from above and Proposition 2 ∎
Lemma 1 indicates that adverse selection can generate a positive relationship between the price and the unobserved defect rate of traded cars. The intuition is that the positive effect of higher observed quality on price is larger (in absolute terms) than the negative effect of the expected unobserved defect rate on price as long as unobserved defects in the population are not too severe (the defect rate and/or the repair cost are not too large). Again, note that any defects that are observed would be deducted from the car price and hence would cause a negative correlation between price and repair rate. Hence, a positive relationship between price and repairs is consistent only with this adverse selection/sorting interaction. B. Full information Thus far the model has had both symmetric and asymmetric information. For completeness, we now examine the model under full information and present the formal predictions to which we can compare the results above. Under full information, the secondhand price is now a function of the actual conditions of both parts 𝑎 and 𝑏, such that, 𝑃 𝑄, 𝑎, 𝑏 = 𝑄 − 𝑐! 𝑎 − 𝑐! 𝑏. As before, used-car sellers will sell whenever 𝜃𝑄! − (𝑃! − 𝑃 𝑄, 𝑎, 𝑏 ) > 𝜃𝑄 − 𝑐! 𝑎 − 𝑐! 𝑏 . We can now write the full-information analogue of Propositions 1 and 2.
Proposition 3: Under full information, the repair rate among traded cars is (i) unrelated to the observed quality and (ii) decreasing in the secondhand price. Furthermore, the negative relationship between the
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repair rate and secondhand price does not depend on observed quality.
Proof: A seller with a car of observed quality 𝑄 and parts conditions 𝑎 and 𝑏 will sell if 𝜃𝑄! − 𝑃! + 𝑃 𝑄, 𝑎, 𝑏 > 𝜃𝑄 − 𝑐! 𝑎 − 𝑐! 𝑏. When 𝑄, 𝑎, and 𝑏 are observed, the market price is 𝑃 𝑄, 𝑎, 𝑏 = 𝑄 − 𝑐! 𝑎 − 𝑐! 𝑏. Substituting the price equation into the selling condition gives 𝜃𝑄! − 𝑃! > 𝜃 − 1 𝑄, which does not depend on the conditions of parts 𝑎 and 𝑏. Hence, the defect rates are unrelated to the decision to sell and therefore unrelated to observed quality 𝑄. The relationship between the defect rate and price does not depend on observed quality 𝑄 because buyers can observe the defects directly and hence will account for the repair cost for the defects fully in the secondhand price. ∎
Proposition 3 states that under full information, higher secondhand prices correspond to fewer defects, and that this relationship is unrelated to observed quality 𝑄. Therefore, the full-information predictions are distinct from the asymmetric-information predictions.
3. DATA AND EMPIRICAL MODEL A. Data We examine data from the interview portion of the CES, which is a rolling panel data set in which households enter and exit every five quarters, from the years 1991 through 2006.7 The unit of observation is a car in a specific quarter, and the data describe a detailed set of car and respondent characteristics. We start by limiting the sample to cars purchased used from a dealer or private party. Then, because the data on used car prices are most complete for cars purchased within the last year, and we are also most interested in repair rates shortly after used purchase, we limit the sample to cars
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Specifically, we use data from the Consumer Unit Characteristics and Income file (the FMLY file) and various Detailed Expenditure files (the LSD, OVB, OVC, VEQ, and VOT files). Up to four quarters of car expenditure data are available per household, with an average of 2.6 quarters per household due to non-responses in some quarters.
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purchased used within the last year (21 percent of the sample).8 The reported secondhand price is the amount paid after trade-in allowance (12 percent of used purchases involve a trade-in). We add back into the price the trade-in allowance to capture the full price of the car, and include an indicator for trade-in in our regression model in case pricing with trade-ins is systematically different. The CES also records repair expenditures by part category (e.g., air conditioning). Parts categories are described in Appendix Table A2. We adjust all expenditures to 2014 dollars, and exclude cars driven less than 100 miles per year and more than 50,000 mile per year (0.5 percent) to limit the influence of outliers. We also exclude cars up to four years old (33 percent) because they are likely to be off-lease, and previous work shows these cars to be less susceptible to adverse selection (see Hendel and Lizzeri 2002, Johnson and Waldman 2003, 2010, and Johnson, Schneider, and Waldman 2014), and additionally may be covered under warranty. Additionally, because car mileage is reported for the interview quarter, which is one to four quarters after the purchase quarter, we use a linear interpolation to infer the mileage at the time of transaction. This will have good accuracy because the cars in the sample are over four years old and therefore the mileage interpolation over one to four prior quarters is modest. The results are similar when un-interpolated mileage is used instead. Finally, we exclude a small number of observations where the respondent reports purchasing a service warranty because repair expenditures may not reflect actual repairs (0.4 percent). The CES does not identify specifically which cars received the recorded repairs, but only whether the expenditure was for a car or truck. We address this limitation by restricting the sample to vehiclequarters where the household had only one car and/or one truck, which allows us to match expenditures to individual cars or trucks.9 This restriction excludes 23 percent of households and 50 percent of vehicle-
8
For cars bought used within the last year, 74 percent contain the price, for cars purchased used between one and two years ago, 47 percent contain the price, and for cars purchased used more than two years ago, 16 percent contain the price. 9 If, for example, the household has one car and two trucks, then only the car is included in the data set because we do not know how maintenance expenditures are divided across the two trucks.
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quarters.10 Note that we use the term “car” to refer to both cars and trucks. Table 1 provides summary statistics for the estimation sample. Table 2 provides repair frequencies and repair costs by part category for the estimation sample. B. Empirical model Our primary analysis is to estimate the relationship between the secondhand car price and postpurchase repair rate. If a car has an observed defect, the buyer would anticipate repairs and the price will be lower to account for these repairs. This generates a negative relationship between secondhand price and post-purchase repair. In contrast, if the car has an unobserved defect, the price cannot directly reflect the repair cost because the buyer is not aware of the defect. However, from Lemma 1, the joint adverse selection/sorting effect is that cars with higher observed quality may have higher repair rates for unobserved parts, but the positive effect on prices from the higher observed quality is larger than the negative effect on prices from the expected increase in unobserved repairs, and the net effect may be a positive relationship between price and repair rate. Therefore, a finding of a positive relationship between prices and post-purchase repairs is evidence of this adverse selection/sorting interaction. The following regression equation provides a test of the relationship between price and repairs, [3]
log 𝑃 = 𝛽! 𝑅 + 𝑋𝛽! + 𝑒.
log (𝑃) is the natural log of secondhand price; 𝑅 = 1 if the car received a significant repair, which we define as a repair of at least $100, within the year after purchase, and 𝑅 = 0 otherwise; 𝑋 is a row vector of car and buyer characteristics, and an intercept term; and 𝑒 is a mean-zero random error. For our first analysis, we combine together all parts categories to create the indicator 𝑅;11 for the second analysis, we separate out the effect for body work, which is the one category we are confident has an observable 10
The fraction of excluded vehicle-quarters is larger than the fraction of excluded households because the restriction tends to exclude cars from households with many cars. Also, before 1996, the data only identify that the household disposed a car but not which car was disposed. For these years, we identify the disposed car by matching the disposal identifier to a car that appears in the data in one quarter but not the subsequent quarter. 11 This measure includes all categories in Table A1 except “Audio Equipment and Installation” and “Vehicle Accessories and Customization,” which are primarily discretionary expenditures unlikely to reflect car condition (e.g., roof rack), and “Other Vehicle Services, Parts, and Equipment,” which is an assortment of car expenditures not captured elsewhere, many of which are not repairs (car washes, gas cans, car jacks, tire/wheel combinations, etc.).
13
component; and for the third analysis, we show the results individually for each parts category. From Lemma 1, 𝛽! ≥ 0 is evidence of the adverse selection/sorting interaction for unobserved parts, and we expect 𝛽! < 0 for observed parts.12 Price appears on the left-hand side and repairs on the right-hand side, and so Equation [3] represents a hedonic pricing model. The repairs occur shortly after secondhand trade, and so we are using them as an indicator of a defect at the time of trade. Including repairs on the right-hand side also allows us to compare the effects of different parts in the same regression model. We include fixed effects for car groups according to what we expect are the most important predictors of price, which are car model, vintage, and mileage. To construct the groups, we define vintage in three-year age intervals and mileage in 30,000-mile intervals. An example of a group is one with Ford Taurus’s of vintages 1986-1988 with 60,000-89,999 miles. These group fixed effects are designed to permit a very flexible functional form yet contain sufficient within-group variation in repairs and prices to estimate the price-repair relationship. Figure A1 in the Appendix shows the number of car-quarters per group in the estimation sample, and that 90 percent of car-quarters are in groups with other car-quarters. Figure A2 shows the number of cars per group, and that 65 percent of groups have multiple cars. Figure A3 shows the variation in secondhand prices within groups, and that there is very meaningful variation. The regression models additionally include: linear terms for car mileage and vintage to allow these characteristics to affect prices within groups; car age; whether the car was purchased from a dealer or privately; involved a trade-in, as this may affect price; the geographic area of the respondent (Northeast, Midwest, South, West; the finest level of geographic area available) in case market characteristics vary by region; car attributes that vary within a car model, including air conditioning, sunroof, automatic transmission, number of engine cylinders, and four-wheel drive; and driver characteristics, including gender, race, buyer age as dummies in ten-year intervals, buyer income in 12
An alternative modeling assumption would include secondhand price as a linear term (instead of log) and repair rate as the actual repair cost. The problem with that specification is that we expect the control variables to have a proportional effect on price. For example, an increase in mileage reduces the price of a BMW versus a Honda by similar amounts in percentage terms, but clearly not in absolute amount. Including price in log format, along with the repair dummy, better captures this relationship.
14
deciles, and indicators for education ranges of less than high school, high school, some college, and at least a college degree.13
4. EMPIRICAL RESULTS A. Relationship between secondhand price and repair rate The estimated models with all parts together are reported in Table 3. Column (1) contains the base specification, column (2) includes the five additional car attributes and region, and column (3) includes the driver characteristics. Column (3) is the specification of interest, and indicates that a postpurchase repair is associated with a 3.8 percent higher price (p=.03), which is evidence of the adverse selection/sorting interaction for the car overall. In column (4), we split the repair effect by whether the car was purchased privately or from a dealer, which shows a modestly stronger effect for dealers, but the difference is not statistically meaningful. Note that the original driver’s decision to dispose of her car privately versus through a dealer may be endogenous to unobserved car condition, and so we do not dwell on this distinction further.14 In Table 4, we estimate the same sets of specifications but now split out the effect for body work, which as mentioned is the one parts category we expect to be (mostly) symmetrically observed, versus the other categories, which may have significant asymmetric information. (These specifications also include a discretionary expenditures indicator, which we discuss in the subsection below.) In the primary specification of interest in column (3), we find that body-work repairs correspond to a 19.4 percent lower price (p=.02), while the remaining repairs correspond to a 4.6 percent higher price (p=.01). The difference between the two is statistically significant at the one percent level. These results are consistent with the adverse selection/sorting mechanism from the theoretical model applying to most car parts, with the exception of body work, which is primarily symmetrically observed. B. Unobserved quality preferences 13
Note that the inclusion of car vintage and age effectively controls for any time effects. Given that we are considering cars that were over four years old at purchase, most of these dealers are unlikely to be franchised new-car dealers (which also sell some used cars), but rather smaller independent dealers. 14
15
In our theoretical model, we assume any defects must be repaired in order to operate the car, so that post-purchase repairs directly indicate the condition of the parts at the time of trade. However, if repairing defects is discretionary and the regression model does not adequately capture driver preferences for car quality, then there is a risk of an omitted-variable bias. Specifically, the positive relationship between secondhand price and post-purchase repairs could be due to some drivers preferring to buy nicer cars and also to conduct more repairs. This would be an alternative explanation for the positive relationship between price and repairs, and represents the most plausible identification risk. We provide qualitative and quantitative arguments below that we believe strongly suggest that such a story is not driving the results. In our regression model, in order to control for driver quality preferences, we have conditioned on a very large set of driver and car characteristics (described above). A reasonable explanation for the remaining (conditional) price variation is simply that search costs prevent drivers from obtaining the exact car or quality level that they desire. Instead, drivers are subject to the idiosyncratic inventories and availability of particular dealers and private sellers. For example, a driver seeking a used Honda Accord hoping to spend $10,000 may only find a slightly nicer Accord for $11,000, while another driver with the same preferences might find a slightly worse Accord for $9,000 – thus generating price variation conditional on observables. Additionally, car-purchase preferences may be independent of repair preferences conditional on the included regressors. We can provide empirical evidence against the potential omitted variable bias as well. As mentioned, this bias would occur if repairs are discretionary and the regression inadequately controls for quality preferences. In this case, the relationship between secondhand price and repair rate will be biased upward. Thus, for observed defects, the negative relationship between price and repair rate from the theoretical model will be less negative or positive, depending on the magnitude of the bias. For unobserved defects, the positive relationship between price and repair rate from the theoretical model will be more positive. Thus, a positive relationship between secondhand price and repair rate for observed defects identifies an omitted variable problem, while unobserved defects are not helpful for identifying an
16
omitted-variable problem because the relationship should be positive regardless of the bias. In the previous subsection, we argued that body work is the category we are most confident is symmetrically observed. Thus, a positive relationship between price and repairs for body work would indicate an omitted-variable problem. In fact, we found a strong negative relationship, providing no evidence of a problem. While this test allows for false negatives in the sense that a negative relationship does not rule out an omitted variable problem, it should identify more significant problems. A related and perhaps clearer test is to examine the relationship between secondhand price and car expenditures that are clearly discretionary and represent driver quality preferences directly and not car condition at the time of trade. The CES reports expenditures on car customization, accessories, and audio equipment, which fit these criteria. Table A2 in the Appendix describes these categories, which include items such as alarm systems, bike/ski racks, and stereo equipment. If the regression adequately controls for quality preferences, then there should be no relationship between secondhand price and these expenditures. The models in Table 4 include these expenditures (“Discretionary”). No relationship is apparent, which is consistent with no omitted-variable problem.15 We next test for unobserved quality preferences by splitting out the repair effects by whether the household is in the bottom or top half of the income distribution. If quality preferences are incompletely captured in the regression model and repairs are discretionary, then we would expect to see high-income households purchase higher-price cars and also conduct more repairs, and hence show a more positive repair effect compared to low-income households. In fact, the repair effect is smaller for high-income households for both the body-work category and the remaining parts categories (the discretionary category is about the same). Finally, we show the regression model where each part category enters individually. That is, each category is represented by an indicator variable for at least $100 of repairs in that category. We combine 15
Note that there are relatively few instances of discretionary expenditures in our data – Table 2 indicates 143 instances over $100 – and so the estimated coefficient for “Discretionary” is relatively imprecise. While the estimated coefficient is statistically different from that of “Repair excluding body work” in column 2 at the 8 percent level, the difference is not significant in column 3.
17
the “tire repair” with “tire purchases and mounting” categories because tire repair rarely has a cost of $100 or more. We combine “drive shaft or rear end,” “front end,” and “shocks” with “steering” because the first three categories also have very few instances in which costs are $100 or more, and all four relate to the vehicle suspension system. The estimates are in Table 5, sorted by magnitude. The specification is otherwise the same as in column (3) of Table 4. Note that disaggregating repairs by category reduces the precision of the estimates, and thus should be interpreted with caution. Nevertheless, “body work” has the most negative effect. The estimates for “air conditioning,” “other,” and “discretionary” are also consistent with our priors that these categories may have significant symmetrically observed and/or discretionary components. The negative estimates for “clutch/transmission” and “suspension” may simply be due to imprecision, or perhaps transmission and suspension problems are sometimes observed by buyers (e.g., perhaps the car fails to operate at all with some transmission problems), or because transmission and suspension problems are unobserved by both buyers and sellers at the time of trade. One might also consider “tires” to be partially observed and/or discretionary, and indeed the magnitude of this estimate is approximately zero. Note that “Motor tune-up” is less discretionary than the category name might imply; e.g., emissions control or a poorly running engine (misfiring) are problems that typically would not be postponed for long. Generally, the results of Table 5 agree with our priors of the observability and discretionary nature of the various parts categories and the predictions of the theoretical model.
5. CONCLUDING REMARKS Based on the relationship between used-car prices and repair rates, we have provided new evidence that there exists significant adverse selection in the used-car market. What is particularly new in this paper is that we have documented a basic characteristic of adverse selection in durable-goods markets – the possibility of an inverse relationship between observed unobserved qualities. This result can explain the initially paradoxical outcome that used cars with the same descriptive characteristics but that have a higher secondhand price have more post-purchase repairs. This relationship is hard to explain under
18
complete information because the cost of any anticipated repairs should be deducted from the secondhand price. With a simple theoretical model, we show how this pattern is easily explained by the interaction of sorting over observed quality and adverse selection over unobserved quality. The result is that the severity of adverse selection depends not only on the level of uncertainty over unobserved quality, but also centrally and in a positive direction on observed quality.
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Glosten, L., and P. Milgrom (1985) “Bid, Ask, and Transaction Prices in a Specialist Market with Heterogeneously Informed Traders.” Journal of Financial Economics, 14, 71-100. Hendel, I., and A. Lizzeri (1999a) “Interfering with Secondary Markets.” Rand Journal of Economics, 30, 1-21. Hendel, I., and A. Lizzeri (1999b) “Adverse Selection in Durable Goods Markets.” American Economic Review, 89, 1097-1115. Hendel, I., and A. Lizzeri (2002) “The Role of Leasing Under Adverse Selection.” Journal of Political Economy, 110, 113-143. Hendel, I., A. Lizzeri, and M. Siniscalchi (2005) “Efficient Sorting in a Dynamic Adverse-Selection Model.” Review of Economic Studies, 72, 467-497. Johnson, J., and M. Waldman (2003) “Leasing, Lemons, and Buybacks.” Rand Journal of Economics, 34, 247-265. Johnson, J., and M. Waldman (2010) “Leasing, Lemons, and Moral Hazard.” Journal of Law and Economics, 53, 307-328. Johnson, J., M. Waldman, and H. Schneider (2014) “The Role and Growth of New-Car Leasing: Theory and Evidence.” Journal of Law and Economics, 57. Kim, J. (1985) “The Market for ‘Lemons’ Reconsidered: A Model of the Used Car Market with Asymmetric Information.” American Economic Review, 75, 836-843. Lewis, G. (2011) “Asymmetric Information, Adverse Selection, and Online Disclosures: The Case of eBay Motors.” American Economic Review, 101(4), 1535-1546. Mussa, M., and S. Rosen (1978) “Monopoly and Product Quality.” Journal of Economic Theory, 18, 301. Peterson, J., and H. Schneider (2014) “Adverse Selection in the Used-Car Market: Evidence from Purchase and Repair Patterns in the Consumer Expenditure Survey.” Rand Journal of Economics, 45(1), 140-154. Porter, R., and P. Sattler (1999) “Patterns of Trade in the Market for Used Durables: Theory and Evidence.” NBER working paper, w7149. Rosenman, R., and W. Wilson. (1991) “Quality Differentials and Prices: Are Cherries Lemons?” Journal of Industrial Economics, 39(6): 649-658. Swan, P. (1970) “Durability of Consumption Goods.” American Economic Review, 60, 884-894.
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Swan, P. (1971) “The Durability of Goods and Regulation of Monopoly.” Bell Journal of Economics and Management Science, 2, 347-357. Waldman, M. (1996a) “Durable Goods Pricing When Quality Matters.” Journal of Business, 69, 489-510. Waldman, M. (1996b) “Planned Obsolescence and the R&D Decision.” Rand Journal of Economics, 27, 583-595. Wilson, C. (1980) “The Nature of Equilibrium in Markets with Adverse Selection.” Bell Journal of Economics, 11, 108-130.
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Table 1: Summary statistics for the estimation sample Number of nonStandard missing values Mean deviation Minimum Maximum Price 9538 5840 5848 1 98228 Vintage 9538 1989.9 5.1 1981 2001 Car age at purchase 9538 8.42 3.63 4 24 -4 Mileage at purchase (x10 ) 9538 8.3 4.1 0.1 44.7 Household income percentile 8900 0.47 0.26 0.00 1.00 Purchased from dealer 9538 0.53 0.50 0 1 Purchase with trade-in 9538 0.15 0.36 0 1 Driver age (years) 9538 39.5 14.3 16 94 Education less than HS 9538 0.40 0.49 0 1 Education HS 9538 0.23 0.42 0 1 Education some college 9538 0.25 0.43 0 1 Education college or more 9538 0.12 0.33 0 1 Female 9538 0.39 0.49 0 1 Black 9538 0.10 0.30 0 1 Northeast 9225 0.16 0.37 0 1 Midwest 9225 0.27 0.44 0 1 South 9225 0.30 0.46 0 1 West 9225 0.27 0.44 0 1 Air conditioning 9535 0.85 0.36 0 1 Sunroof 9535 0.11 0.32 0 1 Automatic transmission 9533 0.79 0.41 0 1 Number of cylinders 9538 5.60 1.44 4 8 Four wheel drive 9537 0.15 0.36 0 1 Notes: The unit of observation is a car in a quarter. The sample consists of observations used in the regression analysis. See the text for additional information about the sample.
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Table 2: Repair rates and expenditures by part for the estimation sample Expenditure conditional on repair Number of Number of car-quarters car-quarters with repairs Standard with repairs over $100 Mean ($) deviation ($) Air conditioning 97 72 293 427 Battery 340 90 90 65 Body work 138 116 468 496 Brakes 591 401 209 209 Clutch or transmission 237 201 643 927 Drive shaft or rear end 39 33 359 665 Electrical 414 303 213 210 Engine cooling 321 212 206 241 Engine repair 394 337 579 763 Exhaust 216 169 219 222 Front end 221 76 126 161 Motor tune-up 561 316 166 190 Shocks 64 55 290 305 Steering 171 143 340 368 Tire purchases and mounting 928 644 231 210 Tire repairs 194 7 31 55 Repairs (all parts) 2986 2240 422 606 Repairs excluding body work 2930 2178 409 589 Discretionary (Audio, Accessories) 251 143 245 343 Other services, parts, equipment 860 274 126 274 Notes: The unit of observation is a car in a quarter. Except for the middle column, the statistics are calculated for the 9,538 car-quarters in the broadest estimation sample. “Number of car-quarters with repair over $100” is the number of car-quarters with at least $100 in repairs.
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Table 3: Effect of post-purchase repairs on log of used price (1) (2) (3) Repair 0.043** 0.040** 0.038** [0.018] [0.017] [0.018] Repair x purchased from dealer
(4) 0.028 [0.029] 0.019 [0.036]
(5) 0.053** [0.023]
Repair x income above 50%
-0.034 [0.034] Purchased from dealer 0.487*** 0.509*** 0.525*** 0.521*** 0.525*** [0.040] [0.039] [0.042] [0.044] [0.042] Purchased with trade-in 0.246*** 0.224*** 0.204*** 0.204*** 0.204*** [0.038] [0.037] [0.039] [0.039] [0.039] Car age at purchase (years) -0.120*** -0.119*** -0.120*** -0.120*** -0.119*** [0.008] [0.007] [0.008] [0.008] [0.008] Air conditioning 0.191*** 0.175** 0.175** 0.174** [0.066] [0.072] [0.072] [0.072] Sunroof 0.022 0.029 0.029 0.029 [0.056] [0.059] [0.059] [0.059] Automatic transmission 0.043 0.021 0.021 0.022 [0.056] [0.059] [0.059] [0.059] Number of cylinders 0.025 0.028 0.028 0.028 [0.018] [0.019] [0.019] [0.019] Four-wheel drive 0.164*** 0.164*** 0.164*** 0.164*** [0.054] [0.054] [0.054] [0.054] Female 0.015 0.015 0.015 [0.032] [0.032] [0.032] Black -0.049 -0.049 -0.049 [0.052] [0.052] [0.052] Region dummies X X X X Additional driver dummies X X X Observations 9,538 9,219 8,603 8,603 8,603 R-squared 0.850 0.865 0.870 0.870 0.870 Notes: The unit of observation is a car in a quarter. The dependent variable is the natural log of car price. The sample consists of cars purchased used within one year of the observation quarter that were over four years old at purchase. “Repair” is an indicator for at least $100 in repairs that quarter. All specifications include dummies for car group, defined as model, vintage in three-year intervals, and mileage in 30,000mile intervals; continuous forms of vintage and mileage to capture within-group vintage and mileage effects; and an intercept. “Region dummies” are the driver’s region (Northeast, Midwest, South, West). “Additional driver dummies” include driver age in ten-year intervals, education in one of four ranges, and household income percentile in deciles. “Repair x income above 50%” is the interaction of indicators for repair and being above the 50th income percentile. Heteroskedasticity-robust standard errors clustered at the car level are reported in brackets. Sample size varies across specifications due to missing values for some variables. ** and *** indicate significance at the 5 and 1 percent levels.
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Table 4: Effect of post-purchase repairs with breakout on log of used price (1) (2) Repair excluding body work 0.049*** 0.047*** [0.019] [0.017] Repair excluding body work x income above 50% Body work
(3) 0.046** [0.018]
-0.178** [0.083]
-0.157** [0.077]
-0.194** [0.080]
0.009 [0.045]
-0.038 [0.045]
-0.017 [0.047]
Body work x income above 50% Discretionary Discretionary x income above 50%
(4) 0.061** [0.024] -0.032 [0.035] -0.135* [0.076] -0.131 [0.170] -0.023 [0.071] 0.012 [0.094]
Repair excluding body work - body work 0.227** 0.204** 0.240*** F-test p-value 0.007 0.011 0.004 Repair excluding body work - discretionary 0.040 0.085* 0.064 F-test p-value 0.426 0.081 0.212 Observations 9,538 9,219 8,603 8,603 R-squared 0.850 0.865 0.870 0.870 Notes: The specifications in columns (1)-(3) are identical to those in columns (1)-(3) of Table 3 except that “Repair” is split between “Repair excluding body work” and “Body work,” and the “Discretionary” category, which is comprised of the “Audio Equipment and Installation” and “Vehicle Accessories and Customization” categories (described in Table A2). “Repair excluding body work” is an indicator for at least $100 of repairs excluding body work that quarter. The specification in column (4) is the same as in column (3) except it includes interactions of the repair indicators and the household being in the top half of the income distribution, indicated by the variables with “x income above 50%.” The rows “Repair excluding body work – body work” and “Repair excluding body work – discretionary” are the differences in the indicated coefficient estimates, with p-values from F-tests for the differences. Heteroskedasticityrobust standard errors clustered at the car level are reported in brackets. Sample size varies across specifications due to missing values for some variables. *, **, and *** indicate significance at the 10, 5, and 1 percent levels.
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Table 5: Effect of post-purchase repairs by part on log of used price Standard Coefficient error of Repair category estimate estimate Body work -0.201*** [0.077] Air conditioning -0.130* [0.066] Clutch/transmission -0.044 [0.065] Other -0.043 [0.037] Suspension -0.024 [0.042] Discretionary -0.011 [0.047] Tire -0.008 [0.028] Exhaust 0.009 [0.047] Engine repair 0.018 [0.033] Engine cooling 0.028 [0.049] Electrical 0.052 [0.052] Brakes 0.062 [0.044] Battery 0.065 [0.067] Motor tune-up 0.081** [0.039] Notes: The specification is the same as that in Table 3, column 3, except that “Repair” is split into individual repair categories. Coefficient estimates for the repair-rate effects are reported, and sorted by magnitude. The estimation sample has 8,603 observations and an R-squared value of 0.870. A description of the repair categories is in Table A2 of the Appendix, though several similar repair categories are combined when instances of repairs are small, as described in the text. Heteroskedasticity-robust standard errors clustered at the car level are reported in brackets. *, **, and *** indicate significance at the 10, 5, and 1 percent levels.
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APPENDIX Table A1: Kelley Blue Book car-quality categories EXCELLENT — 3% of all cars we value Looks new and is in excellent mechanical condition Has never had any paint touch-ups and/or bodywork Does not need reconditioning The engine compartment is clean and free of leaks Is free of rust The body and interior are free of wear or visible defects Wheels are flawless All tires match and are like new Has a clean title history and will pass a safety and smog inspection Has complete and verifiable service records VERY GOOD — 23% of all cars we value Has minor cosmetic defects and is in excellent mechanical condition Has had minor paint touch-up and/or bodywork Requires minimal reconditioning The engine compartment is clean and free of leaks Is free of rust The body and interior have minimal signs of wear or visible defects Wheels are flawless All tires match and have 75% or more of tread remaining Has a clean title history and will pass a safety and smog inspection Most service records are available GOOD — 54% of all cars we value Has some repairable cosmetic defects and is free of major mechanical problems May need some servicing The paint and bodywork may require minor touch-ups The engine compartment may have minor leaks Has only minor rust, if any The body may have minor scratches or dings The interior has minor blemishes characteristic of normal wear Wheels may have minor repairable scratches or scrapes All tires match and have at least 50% of tread remaining Though it may need some reconditioning, it has a clean title history and will pass a safety and smog inspection Some service records are available FAIR — 18% of all cars we value Has some cosmetic defects that require repairing and/or replacing Requires some mechanical repairs The paint and bodywork may require refinishing and body repair The engine compartment has leaks and may require repairs May have some repairable rust damage The body has dents, chips, and/or scratches The interior has substantial wear, and may have small tears Wheels may be warped or bent, have major scratches, scrapes, or pitting and require replacement
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The tires may not match and need replacing Needs servicing, but is still in reasonable running condition with a clean title history A few service records are available POOR Kelley Blue Book does not provide prices for cars in poor condition
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Table A2: CES repair category definitions AIR CONDITIONING WORK, including — compressor, condenser, motor/switch, recharging AUDIO EQUIPMENT AND INSTALLATION, including — antenna, CB antenna, CB radio, radio, speakers, stereo equipment, tape player BATTERY PURCHASES AND INSTALLATION BODY WORK AND PAINTING, including — convertible top, crash repairs, doors, glass replaced, rust proofing, sanding, T-roof, vinyl top BRAKE WORK, including — anti-lock brake, bleed brake system, brake adjustment, brake fluid, hydraulic system, master cylinder, machine drums/rotors, parking brake, shoes or pads, wheel calipers, wheel cylinder CLUTCH OR TRANSMISSION WORK, including — clutch cable, clutch fork, flywheel, hydraulic system, master cylinder, pilot bearing, rebuilt transmission, safety switch, shaft seal, transaxle, transmission filter, transmission fluid DRIVE SHAFT OR REAR-END WORK, including — axle fluid, axle mounts/bushings, coil or leaf springs, CV joints, differential, grommet, rear axle, rear wheel axle seal, rear wheel bearings, suspension, tie rods, universal joint ELECTRICAL SYSTEM WORK, including — alternator belt, alternator/generator, battery charging, car computer, coil, gauges/instruments, ignition system, starter motor, switches, voltage-regulator, wiring ENGINE COOLING SYSTEM WORK, including — coolant or filter, cooling fan/controls, cooling fan relay, fan or water pump belt, fan switch or motor, heater core, hoses, pressure cap, radiator, thermostat, water pump ENGINE REPAIR OR REPLACEMENT, including — carburetor, choke, crankshaft bearings, fuel injector, fuel pump/lines/filter, gaskets, motor mounts, oil pump/cooler/hoses/lines, pistons/rods, timing chain/gears or belt, turbo charge EXHAUST SYSTEM WORK, including — catalytic converter, exhaust pipe, hanger/clamps, manifold gasket, muffler, resonator FRONT END ALIGNMENT, WHEEL BALANCING, WHEEL ROTATION MOTOR TUNE-UP, including — adjust ignition timing or mixture, adjust valve, air/fuel filter, breather/vapor/air filter elements, computer sensor, distributor cap or rotor, emissions control, ignition wires, pcv valve, spark plugs OTHER VEHICLE SERVICES, PARTS, AND EQUIPMENT, including — battery cables, brake lights, car wash, charcoal canister filters, gas cable/pan/can, gasket set, headlights, heater repair, hub caps, jack, light bulbs, speedometer cable, tire pressure gauge, tire/wheel combination, vent filters, wheel lugs, wheels, windshield wipers SHOCK ABSORBER REPLACEMENT, including MacPherson struts
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STEERING OR FRONT-END WORK, including — axle bearing/seals, axle shafts, ball joints, bushings, CV joints/boots, idler arms, power steering fluid/filter, rack and pinion, steering box/linkage, studs, lug nuts, tie rods, wheel hubs TIRE PURCHASES AND MOUNTING TIRE REPAIRS VEHICLE ACCESSORIES AND CUSTOMIZING, including — alarm system, bike/ski rack, bumper guards, carpeting, fender skirts, luggage rack, running boards, seat covers, spoilers, steering wheel covers
30
0
.05
Fraction
.1
.15
Figure A1: Number of car-quarters per model-vintage-mileage group
0
10 20 Number of car-quarters per group
30
Notes: Groups are defined according to car model, three-year vintage intervals, and 30,000-mile intervals.
0
.1
Fraction .2
.3
.4
Figure A2: Number of unique cars per model-vintage-mileage group
0
5 10 Number of unique cars per group
15
Notes: Groups are defined according to car model, three-year vintage intervals, and 30,000-mile intervals.
31
0
.02
Fraction
.04
.06
Figure A3: Car purchase price variation within model-vintage-mileage group
0
.5 1 Coefficient of variation of price within group
1.5
Notes: Groups are defined according to car model, three-year vintage intervals, and 30,000-mile intervals. The coefficient of variation is calculated using unique cars (i.e., only one quarter per car is included for this calculation because there is no variation in car purchase price within a car). The coefficient of variation is the standard deviation divided by the mean.
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