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.”
1
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
2
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
3
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.
4
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).
5
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
5
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. 6
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,
6
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. 7
[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.
8
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
9
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
10
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
7
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.
11
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.
12
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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21
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.
22
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.
23
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.
24
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.
25
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.
26
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
27
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
28
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.
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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. 32