Leasing, Lemons, and Moral Hazard...what is the role of leasing in the new-car market, and why has new-car leasing grown so dramatically? Recently, both Hendel and Lizzeri (2002) and

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[Journal of Law and Economics, vol. 53 (May 2010)]� 2010 by The University of Chicago. All rights reserved. 0022-2186/2010/5302-0012$10.00

Leasing, Lemons, and Moral Hazard

Justin P. Johnson Cornell University

Michael Waldman Cornell University

Abstract

A number of recent papers have analyzed leasing in the new-car market as aresponse to the adverse-selection problem in the used-car market originallyexplored in the seminal 1970 paper by George Akerlof. In this paper we considera model characterized by both adverse selection, as in these earlier papers, andmoral hazard concerning the maintenance choices of new-car drivers. We showthat this approach provides explanations for a number of empirical findingsconcerning real-world new- and used-car markets, including that leasing hasbecome more popular over time, very high income new-car drivers lease more,and used cars that were leased when new sell for more than used cars that werepurchased when new. We also compare and contrast our approach to new-carleasing with alternative approaches.

1. Introduction

In the last 30 years there has been a dramatic change in the way new cars aremarketed. In the early 1980s consumer leasing of new cars was almost unheardof, while by the end of the first decade of the 2000s roughly one-fourth of newcars marketed directly to consumers were leased. The obvious questions are,what is the role of leasing in the new-car market, and why has new-car leasinggrown so dramatically? Recently, both Hendel and Lizzeri (2002) and Johnsonand Waldman (2003) have argued that leasing in the new-car market is a responseto the adverse-selection, or lemons, problem in the used-car market originallyexplored in Akerlof (1970). This paper analyzes a model characterized by bothadverse selection, as in these earlier papers, and moral hazard concerning con-sumer maintenance, and the resulting analysis provides explanations for a num-ber of empirical regularities concerning real-world new- and used-car markets.

As discussed in earlier papers such as Henderson and Ioannides (1983), Smithand Wakeman (1985), and Mann (1992), there is an important cost associatedwith leasing, which is that leasing is likely to be associated with moral hazardconcerning consumer maintenance. In particular, these authors argue that a

We would like to thank an anonymous referee and the editor, Sam Peltzman, for helpful suggestions.We would also like to thank Ari Gerstle and Kameshwari Shankar for research assistance.

308 The Journal of LAW& ECONOMICS

leased unit will be inadequately maintained because there is high probability thatthe consumer will return the unit to the lessor at the end of the lease contract.As we will show, given asymmetric information, moral hazard also applies tounits that are purchased when new because maintenance expenditures are notreflected in the price for which used units sell on the secondhand market. Theother important point to note is that in the automobile market real-world leasecontracts typically contain a variety of provisions, such as those concerningmandatory maintenance, that are included to reduce the moral hazard problem.As a result, in the automobile market moral hazard can actually be more severefor cars that were purchased rather than leased when new.

This paper’s model, which combines adverse selection and moral hazard, leavesunchanged most of the major results of Johnson and Waldman (2003) such asthat used cars that were leased when new sell for more than similar cars thatwere purchased when new, while at the same time a number of interesting newfindings emerge. First, our model provides a possible explanation for the dramaticgrowth in new-car leasing over time. Specifically, we find that leasing can increasewhen there is a significant increase in the degree to which new cars are reliableor trouble free, and in fact new-car reliability has substantially increased overtime. Second, consistent with empirical findings in Aizcorbe and Starr-McCluer(1997), we find that under plausible conditions high-income new-car drivershave a higher frequency of leasing. Third, although this is not a direct implicationof the model, because in the model new cars do not vary in terms of theirreliability, our general approach predicts that the frequency of leasing should behigher for car models that are more reliable or trouble free. This result is con-sistent with evidence reported in Desai and Purohit (1999) and Mannering,Winston, and Starkey (2002), which both show in cross-sectional analyses thatleasing is positively related to new-car reliability.

One focus of this paper is investigating the extent to which a model of thenew- and used-car markets based on adverse selection and moral hazard canexplain evidence from the automobile market. Adverse selection and moral haz-ard are potentially important in other markets as well, but we have not yet doneany systematic study of the extent to which this paper’s results are consistentwith evidence from other markets. For example, Gilligan (2004) finds evidencein favor of adverse selection in the market for used business aircraft, and itwould be interesting to know whether evidence concerning leasing in that in-dustry is consistent with our theoretical results.1

1 There are a number of empirical studies that look for evidence of adverse selection in automobilemarkets. Bond (1982, 1984) investigates the market for used pickup trucks and finds evidence ofadverse selection in the market for older trucks only, while Genesove (1993) finds some evidencefor adverse selection in dealer-auction markets for used cars. More recently, Porter and Sattler (1999)and Schneider (2008) find evidence inconsistent with adverse selection in studies of the automobilemarket, while Pierce (2007) and Emons and Sheldon (2009) find evidence in favor of adverse selectionin studies of the automobile market.

Leasing and Moral Hazard 309

2. Model and Preliminary Analysis

In this section we construct a model of the new- and used-car markets char-acterized by adverse selection. We then analyze the model and show the role ofleasing in reducing the problem. In Section 3 we introduce moral hazard.

2.1. The Model

There are two main differences between this section’s model and the modelanalyzed in propositions 1–3 in Johnson and Waldman (2003). First, here weallow more than two consumer groups. When we extend the model in Section3, this assumption allows us to develop results concerning how leasing shouldvary with consumer income. Second, new cars now come in varying levels ofquality.

Consider an infinite-period model in which a perfectly competitive industryproduces cars. Cars last 2 periods, and a car 0 periods old is referred to as new,while a 1-period-old car is referred to as used. There are types of cars,M � 1where a car of type m (m p 1, . . . , M � 1) is of quality when new andNqm

costs to manufacture. We further assume that and if .N Nc q 1 q c 1 c m ! km m k m k

Because of stochastic depreciation there is uncertainty concerning used-car qual-ity. In particular, the quality of a used car of type m is a random draw from adistribution described by a probability density function and cumulativeUh (q )m

distribution function , where for all andU U L U NH (q ) h (q ) 1 0 q ! q ! qm m m

for all outside of this interval. The expression denotes theU U Uh (q ) p 0 q E(q )m m

unconditional expected quality of a used car of type m.There are M groups of infinitely lived consumers, where consumer group m

consists of a continuum of nonatomic consumers of mass and m p 1,xm

. . . , M. In each period an individual in group m drives either no car or onecar, and is the valuation per unit of quality that a group-m individual placesvm

on driving a car in any period ( ). Also, firms and all con-v 1 v 1 . . . 1 v1 2 M

sumers are risk neutral and have a discount factor ( ).d 0 ! d ! 1New cars can be purchased or leased for a single period, and a lease contract

contains both lease and buyback prices. The buyback price is the price at whicha consumer who leases a new car can buy the car at the end of the lease period.If a consumer leases a new car in period t, then at the beginning of period

the consumer either returns the car or purchases the car at the buybackt � 1price. If the car is returned, then the firm sells the car on the secondhand marketin period .t � 1

The information assumptions follow. First, the quality of any specific usedcar is known only by the individual who drove the car when it was new.2 Second,as in Hendel and Lizzeri (2002) and Johnson and Waldman (2003), buyers on

2 However, we assume that the individual who drove the car when it was new cannot purchasethe car on the secondhand market (the consumer does have the option of purchasing a differentused car on the secondhand market). Without this assumption, leasing would not reduce adverseselection because it would not suppress the private information of new-car drivers.


the secondhand market can observe whether a used car was purchased or leasedwhen it was new, and they also know the car’s type.

The timing of moves in each period follows. First, each individual who drovea new car in the previous period learns the quality of his or her used car. Second,each consumer who leased a new car in the previous period decides whether toreturn it. Third, each firm chooses which type of car to produce and announcesa purchase price for a new car. Further, when leasing is an option, the firm alsoannounces lease and buyback prices. Fourth, consumers make their purchasingand leasing decisions. Fifth, a secondhand market opens up in which pricesequate supply and demand.3

Finally, to simplify the analysis we focus on equilibria in which contractingand trading options are stationary. When only buying and selling of new andused cars is allowed, we look for equilibria in which new- and used-car pricesare time invariant. When firms are also able to offer lease contracts, we focuson equilibria in which each firm offers the same contract in each period and inwhich market prices are invariant to time. Furthermore, to simplify the expo-sition, we do not consider equilibria in which firms offer terms that are notaccepted or equilibria characterized by trades among identical consumers.

2.2. Analysis

To simplify the analysis, we impose the following restrictions on the param-eters. First, we assume that equation (1) is satisfied for all pairs such that(m, k)

and :m ! M k ! M

N U N Uv q � dv E(q ) ! c ! v [q � E(q )]. (1)M m M m m m m k

This assumption ensures that group-M individuals never purchase or lease newcars of any type m, while individuals in groups 1 through never purchaseM � 1used cars. (At the end of the section we discuss how the analysis changes whenconsumers in more than one group are potential buyers on the secondhandmarket.) Second, we assume that . This assumption ensures that

M�1x 1 � xM mmp1

secondhand-market prices are positive. Third, for tractability reasons we imposea restriction that ensures that individuals in each group m (m p 1, . . . , M �1) purchase or lease type-m new cars rather than type-k new cars, where k (

(for details, see Johnson and Waldman 2008, app. A). Fourth, our earliermassumption—that for each car of type m, used-car quality is bounded between

and —ensures that there is necessarily an adverse-selection problem whenL Nq qm

there is asymmetric information and firms sell new cars (see Johnson and Wald-man 2008, app. A).

We begin with a second-best analysis in which firms only sell new cars. Suppose

3 In modeling the secondhand market we assume that trades are made anonymously. That is, aused-car buyer does not know the identity of the individual who drove the car in the previousperiod. This eliminates the possibility that a consumer who sells used cars will establish a reputationconcerning his or her behavior in the secondhand market.


there is a social-welfare-maximizing social planner who only controls the fre-quency with which a new-car driver sells the car on the secondhand market inthe following period (as is standard, we define social surplus as the summationof economic profits and consumer surplus). The equilibrium in this case is asfollows. First, for every , a group-m driver purchases a new car of typem ! Mm in any period in which he or she does not own a used car at the beginningof the period. Second, for every there exists a value such that consumer˜m ! M qm

i of type m who owns a used car at the beginning of period t keeps and drivesthe car if its quality exceeds . Third, in the same situation the consumer sellsqm

the car to a group-M consumer and purchases a new car of type m if the usedcar’s quality is less than . Fourth, group-M consumers never purchase newqm

cars, but in each period some purchase used cars on the secondhand market.In other words, new cars are driven by higher valuation consumers and, among

these consumers, there is a positive correlation between the new car an individualbuys and the valuation the individual places on quality. Further, owners of usedcars choose to keep higher quality used cars and sell lower quality used cars onthe secondhand market.

The next step is to consider what happens when firms only sell new cars andthere is no social planner determining the frequency of secondhand-market trade.In most respects this case does not look very different than the social plannercase just discussed. That is, consumers in groups 1 through buy new carsM � 1in any period in which they do not own used cars at the beginning of the period.Further, when such a consumer does own a used car at the beginning of a period,he or she keeps the car if its quality is high and sells the car and purchases anew car if its quality is low.

But there is an important difference. In the social planner case the frequencywith which used cars are traded on the secondhand market is socially efficient.That is no longer true in the present case. As first explored by Akerlof (1970),given asymmetric information concerning used-car quality, a car’s price on thesecondhand market reflects the average quality of similar used cars offered forsale rather than the car’s actual quality. The result is that too few used cars aretraded on the secondhand market.

Proposition 1 formalizes what happens in this case. Below, is the realizationUqit

for quality in period t of the used car that individual i purchased and drove inperiod when it was a new car, denotes the expected quality ofPUt � 1 E(q )m

secondhand-market used cars of type m, and is the secondhand-market pricePUpm

for those cars (for proofs, see Johnson and Waldman 2008, app. B). Note that,to simplify the statements of the propositions, we assume that a consumer whois indifferent between selling his or her used car and driving the car will sell it(similarly, a consumer who is indifferent between returning a leased car whenit becomes used and driving the car will return it).

Proposition 1. Suppose that firms sell new cars. Then there are one or more


equilibria each of which is characterized by a function ( ! for m p 1,˜q* q* qm m m

. . . , M � 1), such that propositions 1.i–1.iii describe the equilibrium.i) In every period t, all group-m consumers (m p 1, . . . , M � 1) who do

not own a used car at the beginning of the period purchase a new car of typem at price .cm

ii) In every period t, each consumer i in group m (m p 1, . . . , M � 1)who owns a used car at the beginning of the period characterized by 1 ( )Uq ≤it

keeps the used car and drives it (purchases a new car and sells the used car).q*miii) In every period t, some group-M consumers purchase a used car on the

secondhand market.

The main result in proposition 1 is that, as discussed above, because of adverseselection there is less trade on the secondhand market than in the social plannercase. Another interesting aspect of the proposition is that there are potentiallymultiple equilibria. The logic is that the return to selling a used car on thesecondhand market is positively related to the secondhand-market price, whichis itself positively related in equilibrium to the frequency with which a consumerwho owns a used car at the beginning of a period decides to sell the car. So,for example, for a fixed parameterization there can be both an equilibrium withlow secondhand-market prices and low values for and an equilibrium withq*mhigh secondhand-market prices and high values for . See Wilson (1980) andq*mKim (1985) for earlier analyses of secondhand-market models characterized byadverse selection with this type of multiplicity.

We now consider what happens when firms can sell or lease new cars. Notethat below, is the price for a new car leased to a group-m consumer, isL Bp pm m

the buyback price in the lease contract signed by group-m consumers, isLUE(q )m

the expected quality of type-m used cars leased when new and then sold on thesecondhand market, is the price for which these used cars sell, denotesLU �p pm

social surplus in this case, and denotes the highest equilibrium value for social′p

surplus when firms only sell new cars.

Proposition 2. Suppose that firms can both sell and lease new cars. Thenthere exists a unique equilibrium characterized by all new-car drivers leasingrather than purchasing new cars, where propositions 2.i–2.iv describe the equi-librium. Also, .� ′p 1 p

i) In every period t, all group-m consumers (m p 1, . . . , M � 1) who didnot lease a new car in the previous period lease a new car of type m at a price

and buyback price .L Bp pm m

ii) In every period t, each consumer i in group m who leased a new car inthe previous period characterized by purchases the car at the buybackU ˜q 1 (≤) qit m

price and drives it (returns the used car and leases a a new car).iii) In every period t, some group-M consumers purchase a used car on the

secondhand market.iv) Also, for all m (m p 1, . . . , M � 1).B LUp 1 pm m


Proposition 2 has a number of interesting results. First, when a car is leased,there is no adverse-selection problem in the following period when the carbecomes used. That is, the used car is sold on the secondhand market givenexactly the same set of realizations for used-car quality as in the earlier socialplanner analysis. The logic is that leasing and optimally setting the buyback pricesuppresses the private information of new-car drivers, with the result that adverseselection is avoided. Second, all new cars are leased rather than sold. This resultis a direct ramification of the first result. Since leasing avoids adverse selection,new-car drivers prefer to lease rather than purchase because it improves theirwelfare.

A third interesting result concerns buyback prices. As we found in Johnsonand Waldman (2003), a lease contract’s buyback price is higher than the car’ssecondhand-market price if it is returned. That is, for all m (m p 1,B LUp 1 pm m

. . . , M � 1). The logic is that it is only efficient for consumers in any groupm to keep used cars with quality close to , and in order to achieve this resultNqm

buyback prices are set higher than secondhand-market prices. As we discussedin detail in Johnson and Waldman (2003), this finding matches well with evidencewe collected from advertisements that appeared in the Sunday New York Timesduring 1998 (see also the recent empirical analysis in Pierce [2007]).

As a final point, without the parameter restriction for allN Uv [q � E (q )] 1 cm m k m

pairs such that and , there would be the possibility of multiple(m, k) m ! M k ! Mconsumer groups purchasing used cars on the secondhand market. We haveanalyzed this case and, given that an equilibrium exists, the results are quitesimilar.4 The only significant difference is that the matching of used cars to used-car buyers is potentially less efficient than in the analysis found above. In prop-ositions 1 and 2, since only one group purchases used cars in equilibrium, thematching of used cars sold and the purchasers of these cars is (trivially) efficient.In contrast, when multiple consumer groups purchase used cars, there is po-tentially inefficient matching of used cars sold with the purchasers of these carson the secondhand market.

3. Adverse Selection and Moral Hazard

In the previous section we showed that, given asymmetric information, new-car leasing improves social welfare because it avoids adverse selection. In thatanalysis, however, when firms had the option of leasing, the result was that allnew cars were leased, but the real-world automobile market clearly exhibits amix of selling and leasing. In this section we do two things. First, we derive anequilibrium that exhibits a mix of selling and leasing. Second, we discuss howthis model provides explanations for various empirical regularities concerningreal-world new- and used-car markets.

4 In our analysis of this case we were unable to show that an equilibrium necessarily exists. Thisis because of possible discontinuities in the secondhand-market prices of used cars that arise in thiscase.


3.1. The Model

In order to generate an equilibrium that exhibits a mix of selling and leasing,we introduce costs associated with leasing. The first cost we introduce is, as inJohnson and Waldman (2003), a cost to consumers of abiding by the standardrestrictions found in lease contracts such as those concerning maximum mileage.The second is a cost due to moral hazard concerning consumer maintenance.5

The idea is that if a consumer leases a new car, then the consumer underinvestsin maintenance because if the consumer returns the car, he or she does not bearthe consequences of inadequate maintenance. We also incorporate the idea thatin real-world lease contracts some aspects of this problem are avoided throughprovisions that stipulate mandatory maintenance activities.

We introduce the following changes. First, denotes the cost consumer izit

incurs in period t if he or she drives a leased car in period t. In particular, eachis a random draw from the probability density function and cumulativez f(z)it

distribution function , where if and for all zF(z) f(z) 1 0 0 ! z ! Z f(z) p 0outside of this interval. We also assume that each is privately observed byzit

individual i at the end of period . Note that for tractability reasons wet � 1assume that is a new draw from the probability density function eachz f(z)it

period rather than being constant from period to period.Second, consider consumer i, who purchases a new car in period t. During

period t the consumer privately observes the realization of a random variableand also the realization of . The variable captures both the inherentl z lit it�1 it

deterioration of the car as it ages and the car’s return to maintenance and is arandom draw from a distribution described by the probability density function

and cumulative distribution function , where for allg(l) G(l) g(l) 1 0 0 !

and for all outside of this interval. On the basis of thesel ! 1 g(l) p 0 l

realizations, the consumer then chooses a maintenance level , wheree e �it it

, for which he or she bears the cost , where is a strictly increasing¯[0, e] k(e ) k(e)it

and convex function with .′k(0) p k (0) p 0The quality of the used car owned by the consumer at the beginning of period

is then given by the continuously differentiable function , whereUt � 1 q (l , E )m it it

m is the car’s type, , and . We assume for all m (m p 1,E p e � y y � [0, Y ]it it

. . . , M � 1) that is strictly increasing in for any given E, strictlyUq (l, E) lm

increasing in E for any given , and strictly concave in E. We also assume forl

all m (m p 1, . . . , M � 1) that and for allU L U Nq (l, 0) p q q (l, E) ≤ qm m m

pairs. In words, independent of the realization of , used-car quality equals(l, E) l

the minimum value if both y and the maintenance expenditure equal zero, andused-car quality never exceeds new-car quality. Note that in this specification ycaptures the potential importance of moral hazard. That is, the smaller y is, the

5 See Mann (1992) for an earlier formal analysis of leasing and moral hazard concerning consumermaintenance. Other analyses that consider durable goods and consumer maintenance, but not interms of the leasing decision, include Schmalensee (1974), Kim (1985), Shapiro (1995), and Carltonand Waldman (2010).


larger the moral hazard problem, in the sense that not maintaining a used cartranslates into worse outcomes for used-car quality.

Third, consider consumer i, who leases a new car in equilibrium. With prob-ability the consumer is free to choose any maintenance level as above.1 � a

However, with probability a minimum maintenance level, , is specifiedCa e (l)m

in the lease contract, where m refers to the car’s type. In words, with probabilitya problem with the car is identified during routine maintenance and the leasea

contract specifies a minimum maintenance level, while with probability 1 � a

the consumer privately observes the problem, so the lease contract cannot specifya minimum maintenance level.

One interesting aspect of this moral hazard problem is that it applies to bothnewly leased and newly purchased cars. The logic is that because asymmetricinformation means that the secondhand-market price an individual receives fora used car is not directly a function of its quality, an individual who purchasesa new car and anticipates selling it in the subsequent period underinvests inmaintenance. A related point is that the moral hazard problem will sometimesbe more severe for new cars that are purchased than those that are leased. Thereason is that, as discussed above, when a new car is leased, part of the moralhazard problem is avoided by requiring minimum maintenance levels for prob-lems identified during routine maintenance, but this option is not available whena new car is purchased.

The timing of moves in each period is now as follows. First, each consumeri who drove a new car in the previous period finds out the realization of thatcar’s current quality. Second, each consumer who leased a new car in the previousperiod decides whether to return the car or purchase it at the buyback price.Third, each firm chooses which type of car to produce and announces a new-car purchase price. Further, when leasing is an option, each firm announces alease price, a buyback price, and a minimum maintenance level for each forl

new-car problems identified during routine maintenance. Fourth, consumersmake their purchasing and leasing decisions. Fifth, a secondhand market opensup in which prices equate supply and demand. Sixth, each consumer i whopurchased or leased a new car observes and and then, subject to con-l zit it�1

tractual provisions, chooses a new-car maintenance level.

3.2. Analysis

As in the previous section, we impose a number of parameter restrictions.First, as before, we restrict the analysis to parameterizations such that group-Mindividuals never purchase or lease new cars, while individuals in groups 1through never purchase used cars. To ensure this we assume that equationM � 1(1) is still satisfied for all pairs such that and , where(m, k) m ! M k ! M

now refers to the expected quality of a type-m used car given a maintenanceUE(q )m

expenditure equal to and is defined similarly. Second, we again imposeUe E(q )k

a restriction that ensures that individuals in each group m (m p 1, . . . , M �


1) purchase or lease type-m new cars rather than type-k new cars, where k (. Third, we restrict the analysis to parameterizations such that for each ofm

groups 1 through some individuals purchase new cars in equilibrium,M � 1which is ensured by assuming that Z is sufficiently large (an earlier assumptionensures that there is some leasing in equilibrium). Fourth, we continue to assumethat , which again ensures that secondhand-market prices are pos-

M�1x 1 � xM mmp1

itive (see Johnson and Waldman 2008, app. A).Similar to the analysis of the previous model, this analysis begins with a brief

discussion of what happens when firms only sell new cars and there is a socialplanner who only controls the frequency with which a new-car driver sells thecar on the secondhand market in the following period. In particular, as in theprevious model, the social planner chooses a frequency for each new-car driverto sell the car on the secondhand market in the following period, and then eachdriver keeps the used car if it is high quality or sells it if it is low quality. Inthis model this idea translates into a function such that an individual inlm

group m (m p 1, . . . , M � 1) who owns a used car at the beginning of periodkeeps the used car and drives it (purchases a new car and sells the usedt � 1

car to a group-M individual) if .˜l 1 (≤) lit m

We now consider what happens without a social planner when firms only sellnew cars. Given our parameter restrictions, in this case individuals in groups 1through do not purchase used cars, while individuals in group M do notM � 1purchase new cars. There are four additional conditions that characterize whathappens in this case. First, every individual in group m (m p 1, . . . , M � 1)purchases a new car of type m in every period in which he or she does not owna used car at the beginning of the period. Second, there is a function (m pKlm

1, . . . , M � 1) such that an individual in group m who owns a used car atthe beginning of period keeps the used car and drives it (purchases a newt � 1car and sells the used car to a group-M individual) if , whereKl 1 (≤) lit m

for all m (m p 1, . . . , M � 1). Third, in every period in which anK ˜l ! lm m

individual in group m (m p 1, . . . , M � 1) drives a new car and anticipatesselling the car in the following period, the maintenance expenditure equals zero.Fourth, for each group m (m p 1, . . . , M � 1) there is a single price thatapplies to all type-m used cars sold on the secondhand market, where this priceequals multiplied by the average quality of the type-m secondhand-marketvm

used cars (which itself depends on ).Klm

The intuition behind these results is as follows. Because of asymmetric in-formation, all used cars sold by a particular consumer group sell for the sameprice, and this price reflects the average quality of all the used cars this consumergroup offers on the secondhand market. In turn, because of adverse selection,just as in Akerlof’s (1970) analysis and the analysis of the previous section, fewercars are traded on the secondhand market than maximizes social welfare.

As discussed earlier, there is also moral hazard in this model even in theabsence of leasing. As just mentioned, with asymmetric information the second-hand-market price for a used car sold by a particular consumer in some group


m reflects the average quality of type-m secondhand-market used cars. Hence,moral hazard arises because when a consumer sells a used car, the price theconsumer receives is not a function of the previous maintenance expenditure.As a result, because new-car drivers correctly anticipate when they will sell theirused cars in the following period, the previous period’s maintenance expendituresfor cars offered on the secondhand market equal zero.

We now allow leasing. Below, , , , , , and have thePU LU PU LU � ′E(q ) E(q ) p p p pm m m m

same definitions as previously. Also, is the contractually specified mini-Ce (l )m it

mum maintenance level for a type-m new car leased when new, given that anew-car problem is identified during routine maintenance.

Proposition 3. Suppose that firms can both sell and lease new cars. Thenevery equilibrium is characterized by functions , , (z), , , and� K L Bz l (z) l* p pm m m m m

, such that propositions 3.i–3.v describe the equilibrium.Ce (l)m

i) In every period t, if , then each consumer i in group m (m p 1,�z ≥ zit m

. . . , M � 1) who drove a used car in the previous period purchases a newcar of type m at price and chooses a maintenance level ifc e p (1) 0 l ≤m it it

.K(1) l (z )m it

ii) In every period t, if , then each consumer i in group m (m p 1,�z ! zit m

. . . , M � 1) who drove a used car in the previous period leases a new car oftype m at price , where the contract is characterized by the buyback priceLpm

and maintenance function . For new-car problems identified duringB Cp e (l)m m

routine maintenance, the maintenance level chosen is at least , whereCe (l )m it

if is sufficiently small. For other problems ifCe (l) 1 0 l e p (1) 0 l ≤ (1)m it it

(z).l*miii) In every period t, each consumer i in group m (m p 1, . . . , M � 1)

who purchased a new car in the previous period keeps the car if l 1it�1

, sells the car and takes the actions described in proposition 3.i ifKl (z )m it

and , or sells the car and takes the actions described inK �l ≤ l (z ) z ≥ zit�1 m it it m

proposition 3.ii if and . Any used car sold is sold to aK �l ≤ l (z ) z ! zit�1 m it it m

group-M consumer for .PU PUp p v E(q )m M m

iv) Suppose that a new-car problem in period was not identified duringt � 1routine maintenance. In every period t, each consumer i in group m (m p 1,. . . , M � 1) who leased a new car in the previous period buys back the carif (zit), returns the car and takes the actions described in propositionl 1 l*it�1 m

3.i if (zit) and , or returns the car and takes the actions described�l ≤ l* z ≥ zit�1 m it m

in proposition 3.ii if (zit) and . Any returned used car is sold�l ≤ l* z ! zit�1 m it m

to a group-M consumer for .LU LUp p v E(q )m M m

v) Suppose that a new-car problem in period was identified duringt � 1routine maintenance. In every period t, each consumer i in group m (m p 1,. . . , M � 1) who leased a new car in the previous period either buys backthe car, returns the car and takes the actions described in proposition 3.i (thisrequires that ), or returns the car and takes the actions described in�z ≥ zit m


proposition 3.ii (this requires that ). Any returned used car is sold to a�z ! zit m

group-M consumer for .LU LUp p v E(q )m M m

Proposition 3 is characterized by a mix of selling and leasing. For each groupthat drives new cars in equilibrium, those with low leasing costs lease new carsand avoid adverse selection, while those with high leasing costs purchase newcars and avoid the leasing cost. The equilibrium is also characterized by moralhazard and specifically the idea that leasing allows a consumer to avoid moralhazard when a new-car problem is identified during routine maintenance. Thatis, propositions 3.i and 3.iii tell us that when a consumer purchases a new carand anticipates selling the used car in the following period, the consumer spendsnothing on maintenance. Similarly, propositions 3.ii and 3.iv tell us that whena consumer leases a new car, a new-car problem is not identified during routinemaintenance, and the consumer anticipates returning it to the manufacturer inthe following period, then nothing is spent on maintenance again. However, ifa consumer leases, a new-car problem is identified during routine maintenance,and is small so there is a large return to maintenance, then a positive amountl

is spent on maintenance whether or not the consumer anticipates returning thecar.

Finally, there can be multiple equilibria here for the same reason that multipleequilibria were possible in proposition 1, where each equilibrium has the prop-erties described in proposition 3. That is, there can be an equilibrium in whichthere are low secondhand-market prices for used cars that were purchased whennew and a small proportion of these cars are traded on the secondhand marketand an equilibrium in which these prices are high and a high proportion ofthese cars are traded. Further, there is now an additional reason why multipleequilibria can exist. That is, for each group m (m p 1, . . . , M � 1), there isa possibility of multiple lease contracts in equilibrium (each of which is consistentwith propositions 3.i–3.v), where each group-m consumer is indifferent acrossall these contracts.

3.3. Further Results

In this section we discuss five further results that follow from our approachto modeling the new- and used-car markets and that serve as explanations forvarious real-world empirical regularities.

Corollary 1 to Proposition 3. Holding all other parameters fixed, if y issufficiently small, then there exist values and ( ) such thata a 0 ! a ! a ! 1L H L H

an increase from a value to a value increases the percentage ofa ! a a 1 aL H

new cars leased.

The corollary states that, if y is sufficiently small—that is, the function thattranslates new-car maintenance into used-car quality is such that the moralhazard problem is potentially large—then increasing the proportion of new-carproblems identified during routine maintenance from a sufficiently low value to


a sufficiently high value increases leasing. The logic is as follows. Since, when anew-car problem is identified during routine maintenance, a minimum main-tenance level is specified in the lease contract, as the proportion of problemsidentified during routine maintenance rises, the advantage of using leasing toaddress these problems also rises. The end result is that increasing this proportionfrom a sufficiently low value to a sufficiently high value causes leasing to increase.6

This first result provides an explanation for the growth in leasing during thelast 30 years. The typical problem not identified during routine maintenanceoccurs when a part in the car becomes defective or worn out unpredictably.Hence, the above result suggests that if new cars become sufficiently more troublefree or reliable, the proportion of problems not caught by routine maintenancewill decrease, which in turn should increase leasing. This is an explanation forthe growth in leasing during the last 30 years because new cars have, on average,become substantially more trouble free or reliable during this time period. Forexample, Consumer Reports (2003, 2005), on the basis of survey evidence, reportsa significant increase in new-car reliability over this time period.7,8

Note that an alternative approach to modeling increased reliability is to assumethat increased reliability increases built-in durability, and thus a car’s qualitywhen used relies less on the maintenance decisions of new-car drivers. That is,increased reliability decreases the importance of the moral hazard problem. Al-though we do not show it formally, this alternative approach to modeling in-creased reliability provides a complementary avenue using our framework bywhich increased reliability can increase the proportion of new cars that are leased.

To see this, suppose that, as in corollary 1, the starting value for is low.a

With a sufficiently small the costs associated with moral hazard will be largera

for cars that are leased rather than purchased when new. This is because witha small , leasing’s advantage in addressing moral hazard through mandatorya

6 Given that the logic is straightforward, one might ask why the result holds only given a sufficientlysmall y and a large enough movement in . Basically, the model is such that the return to purchasingaa new car can increase (but does not have to) as increases, and this can stop the result fromaholding generally. Assuming a sufficiently small y limits how much the return to purchasing canincrease as increases, while the large change in places a lower bound on how much the returna ato leasing increases. Hence, these two conditions together are sufficient to ensure that the proportionof cars leased rises.

7 To make our argument more precise, we note that in reality there are two types of maintenance—one type is routine maintenance, such as oil changes, that can be made a function of vehicle ageand/or vehicle mileage, while the other is maintenance that is a response to vehicle problems thatarise over time. A lease contract can obligate the lessee to maintenance levels for all types of routinemaintenance and some proportion of problem-related maintenance. Given this, as the number ofproblems has decreased over time (see, for example, Consumer Reports 2003, 2005) the proportionof maintenance expenditures specified in lease contracts should have increased, which is basicallythe same as increasing in our model.a

8 Recently, there has been a decline in new-car leasing from roughly 30 percent of total new-cartransactions to roughly 25 percent. One possible reason for this recent decline is that lease terms inthe late 1990s and early 2000s were overly generous because manufacturers systematically overesti-mated residual values, and lease terms have become less generous recently as manufacturers realizedtheir mistake and started to more accurately estimate residual values This argument is consistentwith a discussion in ADESA Analytical Services (2003).


maintenance will be smaller than its disadvantage due to a higher probabilityof used cars being sold on the secondhand market when they were previouslyleased rather than purchased. This means that, ignoring any increase in duea

to increased reliability but assuming that the initial value for is low, leasinga

will be associated with higher moral hazard costs, but an increase in reliabilitythat reduces the moral hazard problem should reduce the magnitude of theseextra costs. In turn, since leasing rather than purchasing a new car reduces adverseselection, an increase in reliability that reduces the extra moral hazard costsassociated with leasing should increase the proportion of new cars that are leased.

A second result is that in a cross-sectional analysis more reliable new carsshould have a higher frequency of leasing. This result is not a direct implicationof our analysis, since in our analysis all new cars have the same . However, ita

clearly follows from our basic approach in that new cars that are more reliableshould have fewer problems not identified during routine maintenance, whichin turn means a smaller moral hazard problem if they are leased and thus leadsto more leasing. This result is consistent with evidence reported in Desai andPurohit (1999) and Mannering, Winston, and Starkey (2002). Desai and Purohitconduct an empirical analysis of how leasing varies by car model. They developa measure of reliability using information reported in Consumer Reports andshow that more reliable car models are leased more. Mannering, Winston, andStarkey report similar results in an empirical study of the probability that ahousehold leases rather than purchases a new car as a function of various con-sumer attributes.

The third result captured in proposition 3 is that individuals who have highercosts of abiding by the standard restrictions found in lease contracts shouldpurchase new cars, while those with lower costs should lease.9 The only studythat we know of that addresses this issue is the Mannering, Winston, and Starkeystudy just mentioned. One of their results is that the probability of leasing islower if the household has attributes that indicate that it expects to drive a highnumber of miles. In other words, leasing is less popular among households forwhom, on average, the cost of abiding by maximum mileage restrictions is likelyto be higher.

Our fourth result concerns how leasing varies with consumer valuation ofquality or, similarly, consumer income. Below, denotes the proportion ofLrm

group-m individuals who lease.

Corollary 2 to Proposition 3. Holding all other parameters fixed, if y issufficiently small and is sufficiently large, then (m p 2, . . . , M �L La r 1 r1 m

1), given a sufficiently large .v1

Corollary 2 to proposition 3 states that if y is sufficiently small and isa

sufficiently large, the highest valuation group leases more than lower valuation

9 Although we failed to point out this result in Johnson and Waldman (2003), it is also an im-plication of one of the analyses in that paper.


groups if the highest group’s valuation is sufficiently high. In other words, if weinterpret higher valuations for quality as higher incomes, then very high incomenew-car drivers lease more than lower income groups.

The logic behind this result follows. A sufficiently small y and a sufficientlylarge mean that the potential moral hazard problem is large, and leasing avoidsa

a significant proportion of the moral hazard problem through mandatory main-tenance. In turn, when the potential moral hazard problem is large and leasingavoids much of it, the frequency of leasing is primarily determined by moralhazard considerations. Given this, consider very high income new-car driverswhose valuation for quality is so high that they drive new cars almost everyperiod. For these consumers the moral hazard problem is severe, because theyalmost never keep their used cars and so their unconstrained incentive is toalmost always invest nothing in maintenance. The result is that, because leasingeliminates moral hazard for problems identified during routine maintenance,leasing is common among these consumers.

Corollary 2 is consistent with empirical findings in Aizcorbe and Starr-McCluer (1997). Aizcorbe and Starr-McCluer analyze data from the FederalReserve Board’s Survey of Consumer Finances and the Bureau of Labor Sta-tistics’s Consumer Expenditure Survey and find a positive relationship betweenleasing and consumer income.10 For example, using the Consumer ExpenditureSurvey, they find that in 1992 1.0 percent of households with incomes below$10,000 leased a car, 1.0 percent of households with incomes between $10,000and $25,000 leased, 1.6 percent of households with incomes between $25,000and $50,000 leased, 4.1 percent of households with incomes between $50,000and $100,000 leased, and 11.4 percent of households with incomes above$100,000 leased. One interesting aspect of their findings is that the proportionof new cars leased is not everywhere increasing with income (this follows giventhat for lower income groups the percentage of households acquiring new carsrose with income). Rather, similar to the result of our theoretical analysis, leasingis positively related to income in the sense that very high income householdslease more than lower income groups.11

10 Mannering, Winston, and Starkey (2002) also show that leasing is positively related to consumerincome, but they do not provide detailed evidence concerning how leasing varies with income class,as Aizcorbe and Starr-McCluer (1997) do.

11 Another possibility for why high-income households lease more often is that high-income house-holds are in possession of more new cars at any point in time (note that this would yield a positiverelationship between leasing and income because in 1992 used cars were almost never leased).However, other evidence reported by Aizcorbe and Starr-McCluer (1997) suggests that although thisis a contributing factor to their finding that high-income households lease more, it is not the solefactor, and thus high-income households also have a higher propensity to lease when they acquirenew cars. For example, using the Survey of Consumer Finances, Aizcorbe and Starr-McCluer findthat the top two income groups were in possession of the same average number of vehicles in 1992,while the percentage of these vehicles acquired as new was 52.9 percent for the second highest incomegroup and 66.0 percent for the highest income group. This factor by itself can explain why thehighest income group has a higher percentage of households in possession of a leased vehicle, butit does not easily explain why, as reported above, the highest income group’s percentage is more


Another interesting aspect of our fourth result is that the standard argumentconcerning moral hazard and leasing found, for example, in Smith and Wakeman(1985), makes exactly the opposite prediction. That is, the standard argumentsuggests that moral hazard is a larger problem for high-income individuals be-cause they drive new cars basically every period, but since in that argumentmoral hazard applies only to leased cars, the prediction is that leasing ratesshould be lower, not higher, among high-income individuals. In other words,the standard argument concerning moral hazard and leasing does not explainthe finding in the data that high-income consumers lease more, not less.

Our fifth result follows from the next corollary.

Corollary 3 to Proposition 3. For all m (m p 1, . . . , M � 1), .LU PUp 1 pm m

The fifth result is that for used cars of type m (m p 1, . . . , M � 1) thesecondhand-market price is higher for cars leased rather than purchased whennew. This result, which is also found in Johnson and Waldman (2003), followsfrom the idea that leasing reduces adverse selection. In other words, becauseleasing reduces adverse selection, type-m used cars offered on the secondhandmarket that were leased when new are of higher average quality and sell formore than type-m used cars offered on the secondhand market that were pur-chased when new. One might argue that in cases in which moral hazard is worsefor leased cars, the prediction should be ambiguous since leasing both increasesquality by reducing adverse selection but also decreases quality by increasingmoral hazard. But, in fact, this logic is wrong, and the price of used cars leasedwhen new must be higher.

To see why, suppose the opposite were true. That is, suppose that the used-car price for type-m cars that were purchased when new is higher than the used-car price for type-m cars that were leased when new. Then no type-m new carswould be leased, since a group-m consumer could do better by purchasing andinvesting in maintenance as if the consumer had leased. Hence, since given ourparameter restrictions some consumers in group m must lease, for every typem (m p 1, . . . , M � 1), the secondhand-market price for used cars that wereleased when new must be higher than the secondhand-market price for usedcars that were purchased when new.

Desai and Purohit (1998) provide evidence consistent with this result. Theyobtained used-car prices from a large automobile auction house and investigatedthe relationship between a used car’s price and whether the car was purchasedor leased when new. In their empirical analysis, Desai and Purohit look at theauction prices for a popular 1993-model car during the time period 1994–96.After controlling for the car’s age, mileage, and auction date, they find that used-

than double that of the second highest income group. It seems that the highest income group alsohas a higher propensity to lease when acquiring new vehicles.


car prices are indeed higher for used cars that were leased rather than purchasedwhen new.12,13

4. Alternative Explanations

There are a number of alternative explanations for why a durable-goods pro-ducer would lease, some of which specifically address leasing in the new-carmarket. One explanation for leasing is time inconsistency. Building on the seminalarticle of Coase (1972), an extensive literature explores the time-inconsistencyproblem faced by a durable-goods monopolist and the role of leasing (renting)in solving the problem (see, for example, Stokey 1981; Bulow 1982, 1986; Ausubeland Deneckere 1989; Butz 1990; Waldman 1993; Karp and Perloff 1996). Coase’sinsight was that a durable-goods monopolist that sells its output will not inter-nalize how its output decision in one period affects the value of units sold inprevious periods, with the result that output in later periods is so high that thefirm’s profitability is reduced. In turn, this leads to leasing, since with leasingthe firm retains ownership of units previously produced and, thus, eliminatesits incentive to sell too much in later periods.

There are a number of reasons why time inconsistency is not the correctexplanation for leasing in the new-car market. First, time inconsistency is sub-stantially reduced in a market characterized by replacement sales (see Bond andSamuelson 1984), and the automobile market has frequent replacement sales.Second, because time inconsistency is a monopoly explanation and there hasbeen increased foreign competition over time, the time-inconsistency argumentcounterfactually predicts that leasing rates should have shrunk rather than grownover time. Third, if leasing is used to reduce time inconsistency, then new-caroutput should have fallen as new-car leasing became a larger share of the market.But the evidence is not consistent with this prediction. For example, between1990 and 1999 the percentage of new cars leased grew from 7.3 percent of themarket to 30.2 percent of the market, while the size of the new-car market was13.86 million in 1990 and 16.88 million in 1999.14,15

12 To be precise, Desai and Purohit (1998) consider how quickly used-car prices decline with vehicleage. Given that they constrain the prices of 1-year-old cars to be independent of whether the carswere purchased or leased when new, if used cars that were leased when new sell for more, then, asthey find, price declines should be smaller for these cars.

13 There is one result in Johnson and Waldman (2003) and in Section 2 that is not found here.This is that buyback prices are above secondhand-market prices. In the current model the relationshipbetween these prices is ambiguous.

14 The source for these figures is U.S. Department of Transportation, Bureau of TransportationStatistics, Table 1-17: New and Used Passenger Car Sales and Leases (http://www.bts.gov/publications/national_transportation_statistics/html/table_01_17.html).

15 Another monopoly explanation for leasing is put forth in Waldman (1997) and Hendel andLizzeri (1999). In that argument, a durable-goods monopolist leases because leasing is an effectiveway of allowing the firm to reduce the availability of used units, where reducing used-unit availabilityallows the firm to charge a higher price for new units. There are two reasons why this argument isnot the correct one for the new-car market. First, as above, a monopoly explanation is inconsistentwith the substantial growth in new-car leasing over time. Second, a central component of this


Another explanation is that there are tax advantages associated with leasing(see, for example, Myers, Dill, and Bautista 1976; Franks and Hodges 1987).Since the Tax Reform Act of 1986 (Pub. L. No. 99-514, 100 Stat. 2085) includeda number of changes that increased the attractiveness of leasing an automobile(for discussions, see Crocetti 1988; Auster 1990), in contrast to the explanationsdiscussed above, this explanation is consistent with the growth in new-car leasingover the last 30 years. Specific changes include the phaseout of both sales taxand personal interest deductions. There is a problem with this explanation,however, in that it predicts growth in leasing after 1986 but a leveling off of thepercentage of new cars leased after the new-car market achieves a new equilib-rium. This is a problem because the growth in new-car leasing continued to besubstantial long after 1986.

Two other explanations follow. First, as argued, for example, by Wyman (1973)and Copeland and Weston (1982), leasing can be used as a way of transferringrisk. That is, if there is substantial uncertainty concerning the residual value ofassets, then leasing may be used to shift risk from risk-averse consumers to lessrisk averse manufacturers or distributors. Second, an explanation popular in thebusiness press is that leasing is used as a way of lowering monthly payments(see, for example, Woodruff 1994). The logic here is that, because of eitherconsumer myopia or imperfect capital markets, consumers perceive leasing as away of making new cars more affordable. Notice that both of these explanationspredict that new-car leasing rates should fall with consumer income. That is,(absolute) risk aversion is likely to be negatively correlated with income, andhigh-income consumers are likely both to be less myopic and to have betteraccess to captial markets. The problem with these explanations, therefore, is that,as discussed earlier, the evidence indicates that leasing is positively, not negatively,related to consumer income (see Aizcorbe and Starr-McCluer 1997; Mannering,Winston, and Starkey 2002).

In summary, there are a number of alternative explanations for why there issubstantial leasing in the new-car market, but none of the major alternatives fitthe evidence very well. The time-inconsistency explanation is inconsistent with theoverall growth in new-car leasing during the last 30 years, and the tax argumentis inconsistent with the details of the time-series evidence, while explanations basedon transferring risk and lowering monthly payments are inconsistent with thepositive relationship between leasing and consumer income. Our conclusion isthat our explanation for new-car leasing based on adverse selection and moralhazard matches the evidence better than any of the alternatives.

5. Conclusion

In this paper we have argued that two important factors determining theextent of new-car leasing are adverse selection and moral hazard. In particular,

argument is that the durable-goods producer scraps some or all of the used units returned to thefirm, but this is inconsistent with standard behavior in the automobile industry.


an important return to leasing is that it avoids the adverse-selection problem inthe used-car market by suppressing the private information of new-car drivers,while leasing as well as purchasing are associated with moral hazard concerningconsumer maintenance. We constructed and analyzed a model of the new- andused-car markets that incorporates both factors and also incorporates costs as-sociated with consumers abiding by the standard restrictions found in leasecontracts, and we showed that this approach provides explanations for a numberof empirical findings concerning real-world new- and used-car markets. Forexample, the model provides explanations for why leasing has become morepopular over time, why very high income consumers have a higher propensityto lease, and why used cars that were leased when new typically sell for morethan similar cars that were purchased when new. We also argued that this ap-proach is consistent with buyback provisions in new-car lease contracts and withthe cross-sectional variation in leasing across new-car models.

Much of the focus of durable-goods theory over the last 30 years has beenon the issue of time inconsistency first identified in Coase (1972).16 But webelieve that an equally important contribution to durable-goods theory is Ak-erlof’s (1970) seminal analysis of the market for lemons. That paper has, ofcourse, had an enormous impact in general since it was one of the papers thatstarted the asymmetric-information revolution in economic theory. But in termsof durable-goods theory, Akerlof’s paper was mostly ignored for almost 30 years.The main analysis in that paper, however, was an analysis of a secondhand market,and so clearly the paper has implications for understanding the operation ofdurable-goods markets. Our papers and Hendel and Lizzeri (2002) extend thetheoretical analysis of that paper in terms of its implications for durable-goodsmarkets and, most important, show that those implications match the empiricalevidence of the automobile market quite well. Hence, as we state above, ourfeeling is that Akerlof’s analysis should be thought of not only as a classiccontribution to the literature on asymmetric information but also as a classiccontribution to the literature on durable goods.

There are a number of ways in which the analysis in our paper could beextended. First, although we feel that useful insights follow from modeling theautomobile market as a perfectly competitive industry, it is clear that firms inthat industry possess some market power. Hence, one extension of the analysiswould be to explore the implications of adverse selection and moral hazard inan oligopoly or a monopolistically competitive framework. Second, we feel thatit might be useful to allow cars to potentially last more than 2 periods. We believethat such an extension would allow us to explain why leasing is common for

16 Although the issue of time inconsistency in durable-goods markets was first identified by Coase(1972), the focus of the theoretical literature on durable goods did not turn to the time-inconsistencyissue until the publication of Stokey (1981) and Bulow (1982). Prior to those papers, the focus ofthe literature was the analysis of optimal durability that appeared in Swan (1970, 1971) and Sieperand Swan (1973). See Waldman (2003) for a survey of durable-goods theory that discusses thishistory.


new cars but rare in the marketing of used cars. Third, we believe that a morerealistic model of the automobile market would also incorporate a transactioncost and/or switching cost associated with upgrading from a used car to a higherquality new car, where this cost could potentially vary with the manner in whichthis upgrading is achieved.

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Documents

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