A Quantitative Analysis of the Used-Car Market

TL;DR: The authors quantitatively investigate the allocative and welfare effects of secondary markets for cars and show that transaction costs have a large effect on volume of trade, allocations, and the primary market.

Abstract: We quantitatively investigate the allocative and welfare effects of secondary markets for cars. An important source of gains from trade in these markets is the heterogeneity in the willingness to pay for higher-quality (newer) goods, but transaction costs are an impediment to instantaneous trade. Calibration of the model successfully matches several aggregate features of the U.S. and French used-car markets. Counterfactual analyses show that transaction costs have a large effect on volume of trade, allocations, and the primary market. Aggregate effects on consumer surplus and welfare are relatively small, but the effect on lower-valuation households can be large.

Summary

1 Introduction

• Secondary markets play an important allocative role for some durable goods.
• The authors then use the model to perform several counterfactuals, with the purpose of understanding the functioning of secondary markets and their impact on the market for new goods.
• The authors further consider the allocative and welfare effects of a scrappage policy that forces households to scrap their cars earlier than they otherwise would.
• Another interesting consequence of lower heterogeneity is that car prices are flatter in France than in the U.S., starting with a lower new-car price and ending with higher used-car prices in France for the oldest vintages.

2 Related Literature

• This article contributes to two main strands of the literature.
• First, the theoretical literature on consumer durable goods has investigated the role of secondary markets in allocating new and used goods (Rust, 1985; Anderson and Ginsburgh, 1994; Waldman 1997, 2003; Hendel and Lizzeri, 1999a,b; Stolyarov, 2002).
• The authors contribute to this strand of the literature by providing a quantitative analysis of the allocative and welfare effects of secondary markets, and by evaluating policies that affect secondary markets.
• Many influential papers analyze product differentiation and consumers’ choices among new cars (Bresnahan, 1981; Berry, Levinsohn and Pakes, 1995; Goldberg, 1995; Petrin, 2002) or manufacturers’ pricing (Verboven, 1996; Goldberg and Verboven, 2001), but they do not consider used goods and secondary markets.

3.1 Assumptions

• The authors modify a model of vertical product differentiation, which has become a standard way to model secondary markets (see, for instance, Rust, 1985; Anderson and Ginsburgh, 1994; Hendel and Lizzeri, 1999a and 1999b).
• The authors then evaluate how this simple model can account for some aggregate features of the data, while abstracting from some important features of car markets, such as horizontal product differentiation.
• Specifically, the authors assume that each household has a preference parameter θ that determines the flow of utility that the household enjoys from its cars.
• 11Some of their counterfactuals require aggregation of heterogeneous scrappage decisions.
• In order for the model to generate interesting implications for trade in the secondary market, and to match relevant features of the data, the authors introduce some frictions.

3.2 Household problem

• A household chooses how many cars to own and, for each car, which vintage to buy and how long to keep it.
• 14The fact that transaction costs are paid by the sellers is immaterial: just like for taxation, equilibrium allocations are invariant to the “statutory incidence” of transaction costs.
• With probability (1− γ) γ, the household exogenously scraps its vintage-b car.
• It then chooses which vintage a′ to acquire to replace the scrapped car and chooses whether to replace the depreciated vintage-(b+ 1) car with a different vintage-b′ car.
• (2) Equation (2) says that a household with preferences θ and α and cars of vintages a and b faces the random exogenous scrappage of their cars.

4.1 Data

• The authors use data from the 2000 Consumer Expenditure Survey (CEX), a cross-sectional survey of 7,860 U.S. households.
• Table 1 reports some aggregate statistics on households’ car holdings, computed from the CEX.
• The quantitative analysis of their model will aim to match these moments.
• The second row reports that one in every 4.5 cars was purchased within the last 12 months.
• The fourth row reports that, on aggregate, households’ non-durable consumption predicts households’ car holdings, but heterogeneity in households’ preferences plays an important role in determining their car holdings.

4.2 Choice of Parameters

• The authors calibrate the model to investigate whether it can quantitatively replicate the aggregate statistics for the U.S. markets reported in Table 1.
• The authors report in Table 2 the numerical values of the parameters that they use in their calibration, and they describe below how they choose these numerical values, thereby providing intuitive arguments on the “identification” of these parameters.
• One important input into their quantitative analysis is the distribution F of the marginal valuation for quality θ, which is not directly observable.
• 18 17Most previous empirical papers (see Section 2) on the auto market show that several observable households’ characteristics (income, household size, age etc.) affect car choices.
• The authors set c = $1, 350 by computing the per-car annual average expenditure on car maintenance, insurance and gasoline in the CEX.20.

4.3 Computational Algorithm

• This is consistent with the persistent improvement in car durability and reliability over time that Cohen and Greenspan already observed in their sample period.
• 21Transaction costs are increasing in the age of the car in percentage terms.
• 22The authors estimates of transaction costs do not take into account that transaction costs may be heterogeneous across households.
• Specifically, for individuals who choose to transact with dealers, the bid-ask spread is a lower bound on their transaction costs.
• The authors choose the parameters that minimize the maximum absolute value of the percentage differences between the empirical and the theoretical moments reported in Table 1 (of course, the last line is redundant, so the objective function does not include it).

4.4 Results

• Table 3 reports the numerical results of the calibration of their model, along with the observed values in the data.
• The authors now discuss in more detail some key outcomes of the calibrated model.
• 23We stop searching for prices when this absolute value is less than 1 N .the authors.the authors.
• Table 3 shows that the model matches the fraction of households with no car, one car, and more than one car very well.
• The fast decline of equilibrium prices—approximately 20 percent per year— is the joint outcome of cars’ physical depreciation (captured by the parameters γ, δ and T ) and the equilibrium sorting of consumers across vintages.

5 Counterfactual Analyses

• Specifically, the authors analyze the effects of transaction costs by considering two extreme cases: frictionless secondary markets and complete shutdown of secondary markets.
• By changing the frictions in the secondary market relative to their calibrated baseline, these counterfactuals can help us gain some quantitative insights into the allocative and welfare effects of secondary markets.
• Second, the authors consider the case of perfectly inelastic supply—i.e., the quantity of new cars does not respond to changes in transaction costs, but the price does.
• The authors wish to emphasize that their counterfactuals do not include some additional long-run effects, such as the change in the durability of cars; see the Conclusions for additional discussions.
• Lower transaction costs have the partial-equilibrium indirect effect of allowing a finer matching between households’ preferences and the quality of their cars.

5.1 The Effects of Transaction Costs

• The authors consider the allocative and welfare effects of transaction costs.
• This is the natural starting point to study the importance of secondary markets.
• The authors now consider two extreme counterfactual scenarios: frictionless secondary markets and complete shutdown of secondary markets.

5.1.1 Frictionless Resale Markets

• Households hold the same car vintage/quality over time by trading in their depreciated units every period.
• Hence, while the elimination of transaction costs raises households’ willingness to pay, this effect is smaller for older goods than for newer goods.
• Hence, the scrappage age is determined by the equality of the utility flow for the last vintage (either θ′′qT or αθ ′′′qT ) and the holding cost c of the lowest-valuation used-car owner (either θ ′′ or αθ′′′).
• When supply is inelastic, producers’ profits increase relative to the baseline case since new-car prices are higher.

5.1.2 No Resale Markets

• When transaction costs are prohibitive (i.e., λa = 1 for all a), households purchase only new cars, and their key choice is how long to keep them before scrapping and replacing them.
• Note that this implies that output is non-monotonic in transaction costs since Table 4 shows that new-car output is also larger when there are no transaction costs relative to the baseline case.
• The reason is that, with inelastic supply, new-car output does not increase to partially compensate for earlier scrappage, leading to a higher new-car price and dampening the incentive to scrap early.
• The figure also shows that households at the bottom of the valuation distribution suffer the largest surplus loss relative to the baseline case because the lower stock of cars implies that these households do not own a car.
• When new-car supply is inelastic, producers’ profits increase substantially since new-car prices increase by 41 percent, as indicated in the first row of Table 5.

5.2 Scrappage Policies

• The authors investigate how scrappage policies affect equilibrium allocations and welfare.
• Thus, the decrease in the fraction of households with two cars is larger when the new-car supply is inelastic.
• This effect leads to higher welfare in the case of the scrappage policy relative to the case of prohibitive transaction costs.
• Second, households can choose when to scrap their cars when transaction costs are prohibitive, but not with the scrappage policy, thereby allowing households to keep cars older than T.
• The reason is that the first effect allows for a finer matching of relatively young vintages to high-valuation consumers, whereas the second effect allows for finer control of relatively low-quality cars for low-valuation consumers.

6 The Effect of Heterogeneity: A Comparison with France

• As the authors highlight throughout their analysis, gains from trade in secondary markets for many durable goods arise from heterogeneous valuations for quality.
• The authors calibrate their model using France’s distribution of non-durable consumption to investigate the quantitative performance of the model on data from a different country.
• The first row reports that, on average, only one out of every 4.5 households acquired a car in France within the last year (the ratio is equal to three in the U.S.; see Table 1).
• Overall, these aggregate statistics show that secondary markets for cars are substantially less active in France than in the U.S., indicating that their model linking the dispersion of preferences with the volume of trade is qualitatively consistent with these cross-market differences.
• Table 8 confirms that their model is a quantitative success despite the constraint on the calibration.

7 Conclusions

• Secondary markets play a potentially important role in determining the set of durable goods available to consumers and how different households with heterogeneous preferences benefit from such goods.
• These many margins of adjustments imply that any change in secondary markets— because of changes in transaction costs over time or because of policies that directly affect them, such as scrappage policies—has potentially large effects on the volume of trade and allocations, but smaller effects on consumers’ surplus and welfare.
• Calculating the welfare consequences of accounting for endogenous durability requires a measure of the cost savings that come from such a reduction in durability.
• The top rows of the table indicate that the output of the high-quality new good falls, whereas the cheaper, low-quality good captures approximately 45 percent of total new-car sales, as households with intermediate preferences substitute towards it.

Figures

Fig. 6: The figure displays counterfactual consumer surplus with prohibitive transaction costs relative to baseline consumer surplus by percentile of valuation θ, elastic supply of new cars of two qualities. Consumer surplus is calculated as the average value function before purchasing any car: ∫ 1 0 Vθ,α (T + 1, T + 1) dG (α).

Fig. 2: The figure displays counterfactual consumer surplus with prohibitive transaction costs relative to baseline consumer surplus by percentile of valuation θ, elastic new-car supply (dashed line) and inelastic new-car supply (solid line). Consumer surplus is calculated as the average value function before purchasing any car: ∫ 1 0 Vθ,α (T + 1, T + 1) dG (α).

Table 3: Secondary Markets: Model vs. Data

Fig. 3: The figure displays counterfactual car prices relative to baseline car prices when new-car supply is elastic (dashed line) and inelastic (solid line).

Table 6: Allocative and Welfare Effects of Scrappage Policies

Fig. 1: The figure displays counterfactual consumer surplus with no transaction costs relative to baseline consumer surplus by percentile of valuation θ, elastic new-car supply (dashed line) and inelastic new-car supply (solid line). Consumer surplus is calculated as the average value function before purchasing any car: ∫ 1 0 Vθ,α (T + 1, T + 1) dG (α).

Table 8: Secondary Markets: Model vs. Data, France

Table 7: Non-Durable Consumption, U.S. vs. France

Fig. 5: The figure displays car prices in the U.S. (dashed line) and in France (solid line). Prices are in U.S. dollars. French prices are converted into U.S. dollars using the average exchange rate during the year 2000: 1 U.S. Dollar = 1.085 Euro.

Table 2: Calibration Parameters

Table 4: Allocative and Welfare Effects of Secondary Markets, No Transaction Costs

Table 1: Secondary Market for Cars, U.S.

Table 10: The Role of Demographic Characteristics

Table 5: Allocative and Welfare Effects of Secondary Markets, Prohibitive Transaction Costs

Table 9: Allocative and Welfare Effects of Secondary Markets, Prohibitive Transaction Costs, Elastic Supply of New Cars of Two Qualities

Fig. 4: The figure displays counterfactual consumer surplus with the scrappage policy relative to baseline consumer surplus by percentile of valuation θ, elastic new-car supply (dashed line) and inelastic new-car supply (solid line). Consumer surplus is calculated as the average value function before purchasing any car: ∫ 1 0 Vθ,α (T + 1, T + 1) dG (α).

Full text

Alessandro Gavazza, Alessandro Lizzeri, Nikita Roketskiy
A quantitative analysis of the used-car
market
Article (Accepted version)
(Refereed)
Original citation:
Gavazza, Alessandro, Lizzeri, Alessandro and Roketskiy, Nikita (2014) A quantitative analysis of
the used-car market. American Economic Review. pp. 1-44. ISSN 0002-8282 (In Press)
© 2014 American Economic Association
This version available at: http://eprints.lse.ac.uk/55720/
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A Quantitative Analysis of the Used-Car Market
∗
Alessandro Gavazza
¶
Alessandro Lizzeri
§
Nikita Roketskiy
k
January 2014
Abstract
We qu antitatively investigate the allocative and welfare effects of secondary markets
for cars. An important source of gains from trade in these markets is the heterogeneity
in the willingness to pay for higher-qu ality (newer) goods, but tran saction costs are
an impediment to instantaneous trade. Calibration of the model su ccessfu lly matches
several aggregate features of the U.S. and French used-car markets. Counterfactual
analyses sh ow that transaction costs have a large effect on volume of trade, allocations,
and the primary market. Aggregate effects on consumer surplus and welfare are relatively
small, but the effect on lower-valuation hou seholds can be large.
∗
We are grateful to Chad Syverson, four anonymous referees and the editor, and many seminar audiences
for insightful comments, and to Alistair Wilson for excellent research assistance. NSF support is gratefully
acknowledged. The authors acknowledge the use of the UCL Legion High Performance Computing Facility
(Legion@UCL), and associated support services, in the completion of this work.
¶
Department of Economics, London School of Economics. Houghton Street, London WC2A 2AE, United
Kingdom. Email: a.gavazza@lse.ac.uk.
§
Department of Economics, New York University, 19 West 4th Street, New York, NY 10012-1119, United
States. Email: alessandro.lizzeri@nyu.edu.
k
Department of Economics, University College London, 30 Gordon Street, London, WC1H 0AX, United
Kingdom. Email: n.roketskiy@ucl.ac.uk.

1 Introduction
Secondary markets play an importa nt allocative role for some durable goods. For instance,
in the U.S., the number of used-car transactions is approximately three times as large as the
number of new-car transactions. Furthermore, the dispersion of used-car prices (measured by
the coefficient of variation) is approximately five times as large as the dispersion of new-car
prices, suggesting that secondary markets play an important role in broadening the spectrum
of goods available to consumers.
1
The amount of activity in secondary markets varies dramatically across goods, with some
markets extremely active (e.g., cars, aircraft) and others much less so (e.g., household a ppli-
ances, computers). More surprisingly, the amount of activity also varies substantially a cro ss
different countries for the same goods. For instance, the American used-car market is much
more active than the French market. What forces are responsible for these differences? What
are the consequences for prices and allocations, for producers’ pro fits and consumers’ welfare?
How do these differences in activity affect the extent of variety available to consumers? Can
some of the observed differences in the primary markets across goods and countries be due, in
part, to the underlying causes of the differences in activity in the secondary markets? These
are some of the questions that this paper addresses.
2
We present a simple model of durable-goods markets to tackle t hese issues. As in all
markets, activity in secondary markets a r ises because of some gains from trade between coun-
terparties. In the car market, an important source of such gains from trade is heterogeneity
in the willingness to pay for quality: high-willingness-to-pay consumers sell used units when
they upgrade to a new unit.
3
Transaction costs are an impediment to instantaneous (i.e., 100
percent) trade.
4
The extent of trade depends on the degree of heterogeneity in preferences.
We quantitatively investigate how the distribution of non-durable consumption contributes
to this heterogeneity by calibrating our model to match the aggregate volume of trade in the
used-car market. Despite its simplicity, the model fits the data very well.
1
The coefficient of variation is calculated from the National Automobile Dealers Association (NADA) Car
Price Guide.
2
Empirical studies of secondary markets include the following markets: car s (Porter and Sattler, 1999;
Adda and Cooper, 2000; Stolyarov, 2002; Esteban and Shum, 2007; Chen, Esteban and Shum, 2013; and
Schiraldi, 2011); tr uck tractors (Bond, 1983); commercial aircraft (Pulvino, 1998; Gavazza, 2011a and 2011b);
business aircraft (Gilligan, 2004; Gavazza, 2013); and capital equipment (Eisfeldt and Rampini, 20 09).
3
There are, of co urse, other reasons for trade. For ins tance, the ideal car depends on household size, so
changes in the number of children may lead some households to trade in their sedan to purchase a minivan.
We could, in principle, add such characteristics to our model.
4
Jovanovic (1998 and 2009) c onsiders fric tionless reassignment in a v intage model.
1

We then use the model to perform several counterfactuals, with the purpose of understand-
ing the functioning of secondary markets and their impact on the market for new goods. First,
we examine the effects of transaction costs by comparing two polar cases with the baseline
calibrated model: perfectly functioning secondary markets with zero transaction costs and
complete shutdown of secondary markets with prohibitive transaction costs. Naturally, we
exp ect any changes in secondary markets to affect primary markets. Thus, the supply re-
sponse of new-goods producers is an import ant element determining the welfare consequences
of secondary markets’ frictions. We consider two extreme supply scenarios that help highlight
how primary markets adjust: 1) a perfectly elastic supply—i.e., the price of new cars does not
respond to changes in transaction costs, but the quantity does; and 2) a perfectly inelastic
supply—i.e., t he quantity of new cars does not respond to changes in transaction costs, but
the price does. We believe that these counterfactuals are useful to understand the importance
of transaction costs for manufacturers, since they indicate that either output or prices change
when transaction costs change, even in an oligopolistic market for new cars.
5
Three key economic forces affect allocatio ns and welfare in our counterfactuals with differ-
ent transaction costs relative to the baseline case: 1) Higher (lower) transaction costs have the
partial-equilibrium direct effect of destroying (freeing) resources, thereby affecting households’
willingness to pay because they obt ain different net resale prices; 2) lower (higher) transaction
costs have the partial-equilibrium indirect effect of allowing a finer (coarser) matching between
households’ preferences and the quality of their cars; and 3) the two previous forces feed into
the general- equilibrium effects of changing new- and used-car prices and/or quant ities relative
to the baseline case.
Overall, we find that the impact of transaction costs on allocations in b oth the secondary
market and in the market for new goods is large. In contrast, the effects on aggregate welfare
are small, although the distribution of these effects is uneven, with low-valuation households
suffering large losses from increases in t r ansaction costs. For instance, if transaction costs
are large enough to shut down secondary mar kets, the aggregate consumer-surplus loss equals
two t o six percent of the ag gregate baseline consumer surplus (in which transaction costs
are calibrat ed to the data), depending on the elasticity of new-car supply. However, some
households with preferences below the median suffer surplus losses larger than 50 percent of
their baseline surplus. Aggregate welfare changes are smaller because, due to heterogeneity,
the highest-valuation households have disproportionate weights in the calculation of ag gre-
5
Most of our analys is focuses on a s ingle quality of new cars to simplify the way in which secondary markets
expand the array of goods available to consumers, but we also co nsider how the forces that we discuss oper ate
when ne w car s of different qualities are available (see Section 5.1.2).
2

gate surplus. These households have the smallest surplus loss when transaction costs increase
because several margins of adjustment allow them to reduce the effects of transaction costs—
for example, they can scrap their cars if resale is prohibitively expensive—and they do not
suffer much fr om the higher costs that accompany such adjustments. However, since transac-
tion costs lower the total quant ity of cars by increasing scrappage, low-preference households
disproportionately suffer from this reduced availability of cars.
These counterfactual analyses also reveal some additional intriguing findings. For example,
we find that either new-car output or new-car prices (depending on whether new-car supply is
elastic or inelastic) is non-monotonic in transaction costs, with either output or prices going
up relative to the baseline case. This non-monotonicity is due to the different quantitative
magnitudes of the key economic forces for different levels of transaction costs. When transac-
tion costs are zero, frictionless secondary markets lead to much finer matching of qualities to
households’ valuations, thereby raising high-valuatio n households’ willingness to pay for new
cars. When supply is perfectly elastic (inelastic), the quantity (price) of new cars produced
must increase. When transaction costs are prohibitive, however, used-car markets shut down
completely, so the only way for households to upgrade quality is to scrap their used units.
Indeed, scrappage increases substant ially, with car s lasting only two thirds as long as in the
baseline scenario. This increased scrappage feeds into a substantially higher demand for new
cars and, hence, higher output or price, depending on the elasticity of supply.
We f urther consider the allocative and welfare effects of a scrappage policy that for ces
households to scrap their car s earlier than they otherwise would. Scrappage policies have
been introduced in a number of count ries, and the p olicy that we consider is closest to the
Japanese shaken system of tough emission inspections that induces a particularly young fleet
of cars in Japan.
6
Specifically, we impose that households have to scrap their cars when they
reach the (approximate) scrappage age that keeps the to tal stock of cars equal to the stock in
the counterfactual with prohibitive transaction costs, so this choice facilitates the comparison
between these counterfactuals. However, two substantive differences arise between these two
counterfactuals. First, secondary markets are active when there is a scrappage policy, but
they are not when transaction costs are prohibitive. Second, households’ scrappage decisions
are heterogeneous when tra nsaction costs are prohibitive, with higher- valuat ion households
scrapping their cars substantially earlier than lower-valuation households. However, this het-
erogeneity does not arise under the scrappage policy since all cars have positive net resale
6
As we explain in Section 5.2, our steady-state model is less well suited to an analysis of temporary policies
such as cash for clunkers. See Adda and Cooper (2000) for such an analysis that does not, however, take into
account the effects of secondary markets.
3

Frequently asked questions

Q1. What are the contributions mentioned in the paper "A quantitative analysis of the used-car market" ?

The authors quantitatively investigate the allocative and welfare effects of secondary markets for cars. The authors acknowledge the use of the UCL Legion High Performance Computing Facility ( Legion @ UCL ), and associated support services, in the completion of this work. 

Q2. How does the exogenous scrappage effect affect the value of cars?

While cars are endogenously scrapped at T = 20, the exogenous scrappage γ implies that the ratio of the stock of cars to the flow of new cars equals 16.64, lower than T. 

Q3. What are the main economic forces that affect allocations and welfare?

5Three key economic forces affect allocations and welfare in their counterfactuals with different transaction costs relative to the baseline case: 1) Higher (lower) transaction costs have the partial-equilibrium direct effect of destroying (freeing) resources, thereby affecting households’ willingness to pay because they obtain different net resale prices; 2) lower (higher) transaction costs have the partial-equilibrium indirect effect of allowing a finer (coarser) matching between households’ preferences and the quality of their cars; and 3) the two previous forces feed into the general-equilibrium effects of changing new- and used-car prices and/or quantities relative to the baseline case. 

Q4. How much of the surplus is lost by households with preferences below the median?

some households with preferences below the median suffer surplus losses larger than 50 percent of their baseline surplus. 

Q5. What is the average and median percentage surplus gain from frictionless resale markets?

the average and median percentage surplus gains from having frictionless resale markets equal 0.8 to 2.4 and one to 2.6 percent of the baseline surplus, respectively, depending on the elasticity of the new-car supply. 

Q6. How many households acquired a car in the 12 months prior to the survey interview?

the first row reports that, on average, one in every three U.S. households acquired a car in the 12 months prior to the survey interview. 

Q7. Why do households at the bottom of the valuation distribution suffer the largest surplus decrease relative to the baseline?

The figure confirms that households at the bottom of the valuation distribution suffer the largest surplus decrease relative to the baseline case because the lower stock of cars implies that these households do not own a car. 

Q8. Why does the data show that the price of new cars increases when there is no transaction cost?

The reason is that, with inelastic supply, new-car output does not increase to partially compensate for earlier scrappage, leading to a higher new-car price and dampening the incentive to scrap early. 

Q9. How can the authors extend the model to allow for this possibility?

The authors can extend the model to allow for this possibility by assuming that there is a competitive (i.e., infinitely elastic) supply of lower-quality cars. 

Q10. Why does the fraction of people without cars increase relative to the baseline case?

Table 6 shows that the smaller stock of cars, due to the shorter lifespan of cars, increases the fraction of people without cars relative to the baseline case. 

Q11. How does the research show that the welfare of households is higher with a scrappage policy than?

the authors find that welfare is higher with this scrappage policy than with prohibitive transaction costs, further highlighting the welfare gains of resale markets. 

Q12. What is the effect of removing transaction costs on consumer surplus and welfare relative to the baseline case?

when there are no transaction costs, the first two effects increase consumer surplus and welfare relative to the baseline case. 

Q13. What is the parameter that allows the model to match these statistics?

The parameter that allows the model to match these statistics is α, the ratio between the preference for the second and for the first car. 

Q14. How do the authors calculate the average annual depreciation of car prices?

The authors further let qa = (1− δ) a q0, with a value of δ = 0.0236 to match the average annual depreciation of car prices of around 20 percent.