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Essays on the competition between new and used durable products

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Content Essays on the Competition between New and Used
Durable Products
Dinakar Jayarajan
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(BUSINESS ADMINISTRATION)
Acknowledgements
My advisor Dr. S. Siddarth has been very instrumental for the successful completion of
my dissertation. I am greatly indebted to him not only for guiding me through the program
but also for helping me out in times of need in my personal life. It was also pleasure to work
with Dr. Jorge Silva-Risso, members of my dissertation committee and other marketing
faculty.
My heartfelt thanks go out to many people - Jack Trump, Prof. Wayne Ferson, Dr. Lee
Cerling, Elizabeth Poloskov, Maria Flores, Carol Schmitz, Seshadri Tirunillai and Suresh
Nallareddy, who significantly supported and helped me. I will always be indebted to you. I
would also like to thank Elizabeth Mathew, Ruth Joya, Elizabeth Chang and Michelle Lee
who managed all my administrative matters over the years.
My tenure at USC has rewarded me with many new friends - Andrea and Luis Perez,
Shibi and Saji George, Gurpreet and Mehidi Mohammadi, Junho and Junyoung Lee, Lak-
shmi and Mahesh Nair, Pooja and Deepak Hemachandran, Ardra and Prem Dhanendran. I
have your friendship to cherish for our lifetime.
The old proverb Behind every successful man is a smart woman is true in my case as
well. The smart woman is of course my lovely wife Ashy. She gracefully put up with all
the hardships of graduate life and more importantly managed the household very well. Our
son Pranav who was born in the first year of my program brought a lot of joy to our lives.
His birth has been the best thing that has happened to us in the last six years and if not for
him, our lives would have been quite dull.
Finally, I would also like to thank both our families, who although clueless about what
I was doing in school in my thirties, strongly supported us over the years. Well, now that
I have finished the program, I can assure them that I won’t be going back to school as a
student anymore!
i
Contents
1 Overview 1
2 WhyNewCarDealersSellUsedCars 4
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.3 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.3.1 Demand Side . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.3.2 Supply Side . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.3.3 Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.3.4 Endogeneity Correction . . . . . . . . . . . . . . . . . . . . . . . 20
2.4 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.4.1 Covariates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.4.2 Heterogeneity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.5.1 Counterfactual . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3 How Long Should a Durable Product Last? The Impact of Durability on Au-
tomobileDemand 32
ii
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.2 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.3 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.3.1 Durability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.3.2 Covariates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.3.3 Heterogeneity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4 ReplaceorWait: ADynamicModelofTemporalSubstitutionEffectsinDurable
ProductMarkets 52
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.2 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.3 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.3.1 Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
4.4 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.6 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
References 66
iii
ListofTables
2.1 Models included in the analysis . . . . . . . . . . . . . . . . . . . . . . . . 22
2.2 Number of dealers for each brand . . . . . . . . . . . . . . . . . . . . . . 22
2.3 Summary statistics averaged over 53 weeks . . . . . . . . . . . . . . . . . 22
2.4 Demand Estimates: Model with homogeneous coefficients . . . . . . . . . 27
2.5 Demand Estimates: Model with heterogeneous coefficients and endogene-
ity correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.6 Price elasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.7 Computed Price Cost Margin . . . . . . . . . . . . . . . . . . . . . . . . 29
2.8 Profit Estimates in Dollars . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.9 Computed Price Cost Margins . . . . . . . . . . . . . . . . . . . . . . . . 30
3.1 Transaction by Product . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.2 Estimates from regression of price histories . . . . . . . . . . . . . . . . . 41
3.3 Summary Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.4 Estimation Results for Homogenous Model . . . . . . . . . . . . . . . . . 46
3.5 Estimation Results for Heterogenous Model . . . . . . . . . . . . . . . . . 47
3.6 Price Elasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.7 Durability Elasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.8 Sales decomposition due to a 1% increase in durability . . . . . . . . . . . 50
iv
4.1 Top selling models in the midsize sedans segment . . . . . . . . . . . . . . 62
4.2 Top Trade-in models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.3 Summary statistics of includes models . . . . . . . . . . . . . . . . . . . . 63
4.4 Estimates from Full Model . . . . . . . . . . . . . . . . . . . . . . . . . . 64
4.5 Estimates from New alone Model . . . . . . . . . . . . . . . . . . . . . . 64
4.6 Estimates from Used alone Model . . . . . . . . . . . . . . . . . . . . . . 65
4.7 Price Elasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
v
ListofFigures
2.1 Used car vintages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 Used car odometer miles . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3.1 Predictedtradeacv with standardized age and mileage . . . . . . . . . . . 42
3.2 Durability for each model included in our dataset. Higher is better . . . . . 43
vi
Chapter1
Overview
The question of whether and how used versions of a durable product impact the sales of the
new version has interested marketers and economists for a long time. Previous research,
mainly analytical in approach, has identified several potential linkages between the new and
used product markets and their implications for manufacturers. For example, one stream
of literature suggests that because used products can cannibalize the sales of new goods,
a manufacturer should build in a lower level of durability into its new products (planned
obsolescence) or, alternatively, lease its product to consumers, instead of selling it to them
outright. Other research suggests that a benefit of the used good market is that it enhances
the ability of the manufacturer to price discriminate and charge a higher price for its new
product.
There has been relatively little empirical research into the substitutability of new and
used versions of a product and its implications for manufacturers. For starters, there is the
open question of how the durability of a product should be measured. Second, while the
mostly monopoly analysis common in the theoretical literature focuses on the competition
between new and used versions of the same product, it ignores the consequences of dura-
bility on the competition with new and used products made by other manufacturers. For
1
example, while higher durability levels might heighten the competition between the new
and used versions of a certain manufacturer’s product, it may also help to gain share from
its rivals in the new and used markets. Quantifying the relative costs and benefits of this
competition is crucial for manufacturers to make better pricing and durability choices.
The overall goal of my dissertation is to conduct empirical research to provide insights
into how the used durable product impacts different aspects of consumer demand in real
world markets and to uncover its implications for durable goods manufacturers and deal-
ers. In achieving this objective, I seek to make three major contributions to the existing
literature.
First, while Hendel and Lizzeri (1999) highlight the critical role of the marginal con-
sumer, who switches between the new and used version of the product, there have been
no previous attempts to analyze the new/used choices of this marginal consumer and their
substitution patterns. Because understanding these patterns is critical to both the manufac-
turer’s and dealer’s pricing decisions and profits, in Chapter 2, I propose a full equilibrium
model with heterogeneous consumers choosing between new and used cars and profit max-
imizing manufacturers and dealers choosing optimal prices. I estimate the demand- and
supply-side parameters of this model using transaction data from the mid-sized sedan cat-
egory, quantify the substitutability between new and used versions of different products,
and explore alternative models of retailer pricing. Specifically, I test whether dealer pric-
ing of new and used goods accounts for their demand linkages and, in turn, impacts the
distribution of profits between manufacturers and dealers.
The durability of cars and the existence of the secondary markets imply these products
have many lives - initially as a new product and subsequently as used products. The theoret-
ical economics literature has long been concerned with the optimal level of durability that a
manufacturer should build into a new product(e.g, Swan (1970)). However, these theoreti-
cal predictions have not been tested empirically and little is known about how the durability
2
impacts the competition between new and used products in the marketplace. This topic is
investigated in Chapter 3. Since a single accepted durability measure is absent from the
current literature, my first contribution is to explore an alternative way of measuring dura-
bility using transaction data of new and used car values. I then estimate a demand model
that incorporates these durability measures and explicitly accounts for the heterogeneity in
consumer preferences between new and used cars. I use counter-factuals to quantify the lat-
eral substituability between new and used version of the same product (Sankaranarayanan,
2007).
Given that most durable products in developed economies have market penetration rates
as high as 65% to 88% (Bayus, 1988; Fern´ andez, 2000), most new product purchase deci-
sions involve an implicit decision to replace their current product. Therefore, in Chapter 4,
I investigate a related phenomenon, under-emphasized or ignored by the theory, which
is the temporal substitution between the new and used version of the product currently
owned by the consumer. I propose and estimate a dynamic structural model in which
forward-looking, consumers periodically trade off the utility received from the currently
owned product with those available from the replacement marketplace in order to decide
on whether to replace their existing product. Using this model, I demonstrate the impor-
tance of trading off the utility from the current product when modeling the new product
purchase decisions of the consumer.
3
Chapter2
WhyNewCarDealersSellUsedCars: A
StructuralAnalysisoftheImpactof
UsedCarMarketsontheAutomobile
DistributionChannel
4
2.1 Introduction
Automobile manufacturers in the US (e.g., Toyota) are represented by a set of dealers in a
local market, each of whom exclusively sells the models offered by that manufacturer (e.g.,
Camry, Corolla). However, in addition to selling the new versions of different models,
most of these new car dealers also sell used cars from the same physical location, with
their inventory often including makes and models of competing manufacturers. Because
durable products have a usable life of many years and used versions have the potential
to cannibalize new car sales, it is interesting to understand the demand and supply side
consequences of the competition between new and used cars.
Aggravating the cannibalization issue is the fact that used cars sold by dealers are very
good substitutes for new cars. This is evident from Figures 2.1 and 2.2 which shows a
histogram of vintages and odometer miles respectively, of trade-in cars received and used
cars sold by a sample of dealers in the Los Angeles market in 2005. While only 36% of
the traded-in cars are four years old or younger, they account for about 71% of the used
cars sold by dealers. Similarly, while cars with less than 50,000 miles on them account
for only 39% of trade-in cars, they accounts for about 73% of used cars sold by dealers.
In other words, the dealers retain the best used cars that they receive for sale through their
dealerships. These cars tend to be relatively new with fewer miles on them with prices that
are much lower than those on new cars
1
.
The broader question of how used versions of durable goods impact the demand for its
new counterparts and the consequences for manufacturer’s product strategy has interested
economists and marketers for a long time. Previous research has put forth ambiguous sug-
gestions about the impact of the used market. For example, one stream of literature argues
that the used goods market positively benefits new products by allowing manufacturer to
1
How fast does my new car lose value?, at http://www.edmunds.com/car-buying/how-fast-does-my-new-
car-lose-value-infographic.html
5
price discriminate (Hendel & Lizzeri, 1999). In contrast, another stream highlights the
negative consequences because it can cannibalize new product sales (Liebowitz, 1982).
6
(a) Cars traded-in at dealers
(b) Cars sold by dealers
Figure 2.1: Used car vintages
7
(a) Cars traded-in at dealers
(b) Cars sold by dealers
Figure 2.2: Used car odometer miles
8
Most of the existing literature is theoretical and there has been relatively little empirical
research to test the conclusions from this literature. The purpose of the current research is to
conduct an empirical analysis of the competition between new and used cars and examine
its impact on manufacturers and dealers, thus making the following three contributions to
the literature.
First, we develop and estimate a model of consumer demand for both new and used
vehicles that accounts for product characteristics, consumer heterogeneity and price endo-
geneity. While the theoretical literature on this topic envisages different levels of substi-
tutability between new and used products, there has been relatively little empirical research
on this topic. The proposed research enables us to quantify substitutability between new
and used cars and provide insights into the nature of competition between these versions.
Second, we develop and estimate alternative full equilibrium supply models to identify
how these demand linkages impact the pricing decisions of the dealer and the manufacturer.
Specifically, we examine two alternative dealer pricing scenarios. In the first scenario, the
dealer sets new and used car prices, ignoring the substitutability between the two, in effect
treating his new and used car businesses as separate entities. In the alternative scenario, the
dealer takes into account the substitutability between new and used cars pricing them in
order to maximize the total profits across both categories. We compare the implied margins
and profits under these two scenarios to under how the dealer pricing strategy affects the
profits and margins of both the manufacturer and dealer.
Finally, recognizing that manufacturers have a lot more control over the pricing and
promotion strategies of new cars sold on dealer lots than those for used cars, we also exam-
ine the consequences of the used car market on the relative power of the dealer vis-a-vis the
manufacturer. Specifically, we calculate the implied change in profits accruing to manu-
facturers and dealers from new cars under the two scenarios to identify the shift in channel
power brought about by the used car market.
9
2.2 LiteratureReview
Automobiles comprise the single largest durable product category by sales in the US and
therefore, have been studied extensively.
The theoretical literature is ambiguous about the impact of the used product market
on new product sales. Akerlof (1970) suggests that a used product market benefits the
manufacturer as long as the consumers are heterogeneous in their preference for new-
ness/quality. A manufacturer can exploit this heterogeneity to price discriminate among
consumers (Hendel & Lizzeri, 1999). Anderson and Ginsburgh (1994) showed that the
presence of the secondary market endogenously segments the consumers into three groups,
those who buy only new (high type), those who buy only used (low type) and those who are
indifferent between the two. The manufacturer can then charge a higher price for the new
product and extract a higher surplus from the high type consumer. In an empirical analysis
of the video game market, Ishihara (2010) showed that the market for used games allowed
the manufacturer to extract a higher surplus from consumers who have a high preference
for the new product.
The used market also allows consumers to recover the residual value of their current
product. Consequently, consumers will be willing to include the residual value in the
price of the new car and therefore allowing firms to charge a high price and increase prof-
its (Shulman & Coughlan, 2007; Benjamin & Kormendi, 1974). The literature also points
out that the existence of an efficient used goods market may have a differential impact on
retailers and manufacturers (Shulman & Coughlan, 2007). Thus, while the used market
would allow the retailer to sell more products and make more profits, it could lower the
pricing power of the new product manufacturer by cannibalizing the future sales of new
products (Swan, 1980; Esteban & Shum, 2007).
Other negative consequences of the used product market have been identified. Gilbert
10
(1992) showed that products in the used markets are imperfect substitutes for new ones and
therefore, the manufacturer may be better off without the secondary market (Liebowitz,
1982). This is especially true in the case of an oligopolistic market structure. In an
oligopoly, if new and used goods are close substitutes, then it would be in the best interests
of firms to shut down the secondary market (Rust, 1986). Shutting down the secondary
market may reduce the prices of the new product but would increase profitability of the
new product manufacturer in the long run (Miller, 1974).
The analytical literature has also attributed many potential linkages due to the used car
market on the new car market. Zhao and Jagpal (2006) suggests that the prices of new
durable products should be chosen taking into consideration both the supply and demand
in the used market as well as on the future sales of new products. Smith (2012) showed
that in a market where both new and used goods are sold, a decrease in price of the new
product can lead to a corresponding decrease in demand for used products. Purohit (1992)
showed that the prices in the secondary market adjust to changes in the primary market.
Specifically, changes in the styling and product characteristics of the new product tends to
revise the used car prices upwards in some cases and downwards in others. The price of
the new good would be inversely proportional to the quantity of used goods available in the
secondary market (Porter & Sattler, 1999). Betts and Taran (2004) showed that used car
prices are affected both by the reliability of the model and its brand image.
Thus, while the theoretical literature puts forth many possible linkages between the new
and used markets, the empirical literature has not studied the lateral substitution between
new and used products and its implications. This work seeks to fill this gap in the literature
by studying how the presence of the used markets affects the demand for new products. We
seek to identify the existence of lateral substitution between brands and quantify the size
of this substitution. We also test the prediction that used markets leads to higher prices for
new products.
11
Our work also builds upon the empirical work on optimal pricing of automobiles. Berry,
Levinsohn, and Pakes (1995) propose a full equilibrium framework to study the optimal
prices of automobiles. The same framework was employed by Sudhir (2001) to infer the
competition between different segments of the new car market, such as compact, mid-size,
etc. However, neither of these studies consider the existence and impact of the used car
market in their analysis.
This research also ignores the dealer network, implicitly assuming that the manufac-
turers directly sell their products to the consumers. In reality, manufacturers cannot sell
directly to the consumer and instead have to rely on a dealer network to distribute their
products. Moreover, while the manufacturer has greater control the new car prices, the
dealer has substantial pricing power over both new and used cars that they sell. These
aspects are reflected in our model of optimal pricing of automobiles.
Previous work on automobile channels (Lusch, 1976) has concluded that traditionally
the manufacturer holds more power in the automobile channel,which the dealers have been
attempting to reduce. Because dealers have much more control over used car prices than
manufacturers, who tend to have much more control over new car prices, we study whether
the used car market permits dealers to increase channel power at the expense of the man-
ufacturer. We take a model based approach (Draganska, Klapper, & Villas-Boas, 2010;
Villas-Boas, 2007), to examine the split of profits between the dealers and manufactur-
ers (Iyer & Villas-Boas, 2003; Dukes, Gal-Or, & Srinivasan, 2006) to study how the chan-
nel power is altered by the used car markets. We investigate whether the used cars plays
the role of private labels in durable product markets. Finding that used cars can promote a
shift in channel power, would be analogous to previous findings that private labels increase
retailer power in the grocery channel (Meza & Sudhir, 2010)
Our empirical study extends the current literature by showing how the used car market
impacts the margins and profits of dealers and manufacturers. One piece of work which
12
comes close our objective is Chen, Esteban, and Shum (2011) who consider whether the
secondary market helps or hurts the new product manufacturer. They build a dynamic
equilibrium model of a durable market which accounts with secondary markets, deprecia-
tion, transaction costs and heterogeneity. But, they do not use real data and rather rely on
simulated data to arrive at their conclusions. Nevertheless, their results indicate that the
secondary market reduces profits in the channel by about 35%.
2.3 Model
We model a full equilibrium differentiated product market with both new and used products.
The demand side is specified as a mixed logit model (McFadden & Train, 2000) in which
heterogeneous consumers choose the utility maximizing alternative from either category,
or choose the no-buy option. The supply model is derived from the profit maximizing
behavior of multiple manufacturers and their affiliated dealers. We use a two-step approach
to estimate the model (Villas-Boas, 2007). In the first step we consistently estimate the
demand side by accounting for the endogeneity of price using instruments and use the
demand estimates to compute the price responses on the supply side.
2.3.1 DemandSide
Consumeri chooses between a new car, a used car or an outside option fromJ +1 products
with the outside option designated as j = 0. Each product j is specified as a unique
combination of the dealer, category and model, i.e., a used Toyota Camry sold by a Toyota
dealer is different from one that is sold by a Honda dealer.
The utility from consumer i buying product j at time t is given by Eqn 2.1 in which

ij
is an alternative specific intercept which varies over consumers, X
jt
is a vector of
observed product characteristics and
x
i
is a vector of individual level preferences for the
13
observed product characteristics. The price of the product isp
jt
and
p
i
is the associated
price sensitivity parameter for consumer i. In the subsequent discussion, we refer to the
vector of consumer specific parameters as
i
= [
i1

iJ

x
i

p
i
]
|
.
jt
represents the
unobserved product characteristic (unobserved to the econometrician but observed by the
consumer) and"
ijt
is a consumer, product and time-specific random demand shock. The
deterministic component of the utility for the outside option,V
i0t
, is normalized to zero and
thus its utility is defined asU
i0t
="
i0t
. The variables included in the product characteristics
vectorX include the promotions and mileage of the product.
U
ijt
=
ij
+X
jt

x
i
+p
d
jt

p
i
+
jt
+"
ijt
= V
ijt
+"
ijt
(2.1)
Assuming that the demand shock" has Type I extreme value distribution, the probability
that consumeri choosesj at timet is given by,
P
ijt
=
exp(V
ijt
)
1 +
P
J
k=1
exp(V
ikt
)
(2.2)
The share of productj at timet is given bys
jt
=
Z
P
ijt
@F (
i
).
2.3.2 SupplySide
Previous research employing a full equilibrium framework to analyze competition in the
automobile market (Berry et al., 1995; Sudhir, 2001) did not distinguish between dealers
and manufacturers in deriving their firm side results. In reality, the dealer network is an
important component of the automobile distribution channel holding significant power in
the channel. We remedy this shortcoming by explicitly modeling multiple dealers, who
have pricing control over both new and used cars, and multiple manufacturers who control
only the new car price.
14
Every manufacturer in the market is represented by a unique set of dealers and we
consider two different pricing scenarios for each dealer. In the first scenario, the dealer
ignores the across category substitution between new and used cars and only considers
within category substitution in making pricing decisions. In the second scenario the dealer
takes into account the cross-substitutability between new and used cars and prices the new
and used cars accordingly.
Scenario1: SeparatePricing
We now derive the supply side model for the first scenario in which the dealer ignores the
cross category substitution by pricing new and used cars separately. The profit for dealerd
is given by Eqn 2.3 where N and U are the set of new and used cars respectively andJ
dt
is
the set of products sold by dealerd.

dn
t
=
X
j2(J
dt
\N)
[p
d
jt
p
w
jt
c
d
jt
]s
jt
(p),8j2N

du
t
=
X
j2(J
dt
\U)
[p
d
jt
p
w
jt
c
d
jt
]s
jt
(p),8j2U

d
t
=
dn
t
+
du
t
(2.3)
The first equation represents the profits,
dn
, from new cars and the second equation
the profits,
du
, from used cars. The total dealer profits,
d
, is the sum of the two category
level profits. In order to obtain the optimal price, we differentiate the profit functions for
new and used cars in Eqn 2.3 with respect to the price and obtain the following first order
conditions.
@
dn
t
@p
d
jt
=s
jt
+
X
m2(J
dt
\N)
[p
d
mt
p
w
mt
c
d
mt
]
@s
mt
@p
jt
= 0 ifj2N
@
du
t
@p
d
jt
=s
jt
+
X
m2(J
dt
\U)
[p
d
mt
p
w
mt
c
d
mt
]
@s
mt
@p
jt
= 0 ifj2U
(2.4)
15
Eqn. 2.5 gives the expression for the margins in vector notation obtained by stacking
the first order conditions for all productsj2J.
P
d
t
P
w
t
C
d
t
=[T
d

d
t
]
1
S
t
(P ) =M
d
t
(2.5)
P
d
is the vector of prices charged by the dealers for theJ products, P
w
is the corre-
sponding wholesale price andC
d
is the cost to the dealer. T
d
is the ownership matrix with
element (i;j) = 1 if both productsi andj belong to the same category (i.e., new or used)
and are sold by the same dealer. The dealer response matrix,
d
t
contains the first derivative
of shares of each productj with respect to all the prices, i.e.,
d
t
(i;j) =
@s
jt
@p
it
and the op-
erator
denotes the element by element multiplication operator. S
t
(p) is aJ dimensional
vector of market shares for the products in timet.
Scenario2: JointPricing
We now derive the equations for the second scenario where the dealer accounts for the cross
category substitution by jointly pricing both the new and used cars on his lot. Therefore,
his profit function is given by

d
t
=
X
j2(J
dt
\fN;Ug)
[p
d
jt
p
w
jt
c
d
jt
]s
jt
(p
d
) (2.6)
and the corresponding first order condition is
@
d
t
@p
d
jt
=s
jt
+
X
m2(J
dt
\fN;Ug)
[p
d
mt
p
w
mt
c
d
mt
]
@s
mt
@p
jt
= 0 (2.7)
Stacking the first order conditions for all theJ products and rearranging the terms we
can write Eqn 2.7 in vector notation as
16
P
d
t
P
w
t
C
d
t
=[T
d

d
t
]
1
S
t
(P
d
) =M
d
t
(2.8)
The terms in the above equation are as defined in the previous scenario with the differ-
ence that the ownership matrix,T
d
, accounts both the categories.
ManufacturerDecision
The manufacturer takes the dealer pricing behavior as given and sets wholesale prices,P
w
,
to maximize its profits, i.e.,

w
t
=
X
j2Jwt
[p
w
jt
c
w
jt
]s
jt
(p(p
w
)) (2.9)
HereJ
wt
is the set of new cars sold by manufacturerw in timet. Assuming a Bertrand-
Nash competition between manufacturers, we differentiate Eqn. 2.9 with respect to whole-
sale price of product,p
w
jt
, to obtain the following first order condition
@
w
t
@p
w
jt
=s
jt
+
X
m2Jwt
[p
w
mt
c
w
mt
]
@s
mt
@p
w
jt
= 0 (2.10)
wherec
w
is the cost to the manufacturer. Stacking the first order conditions for all the
J products and rearranging the terms, we can write out the first order conditions in vector
notation as
P
w
t
C
w
t
=[T
w

w
t
]
1
S
t
(P
d
(P
w
)) =M
w
t
(2.11)
The term P
w
is the J dimensional vector of wholesale prices for the J products in
periodt,C
w
is aJ vector of wholesale costs in periodt. T
w
is aJJ ownership matrix
where element (i;j) = 1 if both productsi andj are made by the same manufacturer and
zero otherwise.
17

w
is the manufacturer response matrix containing the first derivative of market shares
of each product, s
jt
, with respect to the wholesale prices of each product, p
w
jt
, that is,

w
(i;j) =
@s
jt
@p
w
it
. The manufacturer response matrix is not straightforward to compute
since the wholesale price does not directly enter the demand equation. Therefore, we use
a method put forward by Villas-Boas (2007) and applied in Albuquerque and Bronnenberg
(2012). This method utilizes the fact that
w
t
=
p
0
t

d
t
where
p
t
(i;j) =
@p
jt
@p
w
it
is matrix
containing the first derivatives of all retail prices with respect to all wholesale prices and
d
t
is the dealer response matrix which can easily be computed given the demand estimates. In
order to compute
p
, we first compute a matrix G of sizeJJ with element
G
t
(j;k) =
@s
jt
@p
kt
+
J
X
l=1

T
d
t
(l;j)
@
2
s
lt
@p
jt
@p
kt
(p
lt
p
w
lt
c
d
it
)

+T
d
t
(k;j)
@s
kt
@p
jt
(2.12)
and aJ dimensional vectorH for each productf2J with element
H
t
(j;f) =T
d
t
(f;j)
@s
ft
@p
jt
(2.13)
Then,GdpH
f
dp
w
f
= 0, solving which we get an expression for a column of
p
t
as
dp
dp
w
ft
=G
1
t
H
ft
(2.14)
Computing Eqn. 2.14 for eachf2J and stacking the columns will give us
p
t
matrix
from which we can derive the required manufacturer response matrix as
w
t
=
p
0
t

d
t
.
In order to derive the estimation equations, we substitute the wholesale prices given in
Eqn 2.11 in the dealer pricing equations 2.5 and 2.8 for each of the two scenarios. Rear-
ranging the terms, we get
18
P
d
t
=C
w
t
+C
d
t
+M
w
t
+M
d
t
(2.15)
whereM
w
t
=[T
w

w
t
]
1
S
t
(P (P
w
)) is the manufacturer margin andM
d
t
=[T
d

d
t
]
1
S
t
(P ) are the dealer margins.
2.3.3 Estimation
We use simulated maximum likelihood (Train, 2009) to estimate the model. Letd
ijt
= 1 if
consumeri choose productj at timet and zero otherwise. Given a vector of parameters
i
,
the conditional probability that consumeri makes a sequence of decisions in each period
t = 1T
i
is given by
L
i
(
i
) =
Ti
Y
t=1
J
Y
j=0
P
ijt
(
i
)
d
ijt
(2.16)
The unconditional probability is the integral over the distribution of
i
f() given by
P
i
() =
Z
L
i
(
i
)f(
i
j)d
i
(2.17)
In order to evaluate Eqn 2.17, we takeR random draws
r
i
N(; ) and compute the
average of choice probabilities evaluated at each of these draws,
P
i
() =
1
R
R
X
r=1
L
i
(
r
i
) =
1
R
R
X
r=1
Ti
Y
t=1
J
Y
j=0
P
ijt
(
r
i
)
d
ijt
(2.18)
The likelihood of the sample is a function of = [;] and is given by
L() =
N
Y
i=1
(P
i
()) (2.19)
In practice, we use the log likelihood of the sample given by Eqn. 2.20. Maximizing
19
the log likelihood with respect to and gives us the required parameters.
LL() =
N
X
i=1
lnP
i
() (2.20)
We use the demand estimates to compute the margins as a closed form solution on the
supply side.
2.3.4 EndogeneityCorrection
The unobserved product characteristics term, , in Eqn 2.1 could influence the price thus
creating a potential endogeneity problem. We use the control function approach (Petrin &
Train, 2010) to correct for the endogeneity of price. We first regress the prices against a set
of instruments,z
jt
, and obtain the residual from the regression
0
jt
. The instruments used
include prices of Aluminum, Steel and Rubber, the hourly wage rate and the inventory
at dealers. Our instruments are analogous to that used in Villas-Boas (2007). We then
replace the term in the utility function (Eqn 2.1) with
0
jt
where is a parameter which
is estimated along with the other demand parameters and
0
is treated as a known variable.
2.4 Data
The data for the analysis is obtained from the Power Information Network (PIN). Each
transaction in the dataset corresponds to a vehicle sale by one of the participating deal-
ers. Both used and new cars sold by participating dealers are recorded in the dataset. The
dataset records 163 variables and includes pricing and cost information, profit informa-
tion, financing and leasing information, details about trade-in’s if any and a few customer
demographics such as age and gender.
We analyze data pertaining to transactions from the premium mid-sized sedans cate-
20
gory during January-December, 2004 in the Los Angeles market. We include the top three
models from Premium midsize sedans, listed in Table 2.1, which account for about 74% of
the transactions in this segment.
These three models belong to three nameplates - Honda, Toyota and Nissan and are
sold by 80 dealers located in the Los Angeles DMA. Upon close examination of the data,
we observed two dealers who appeared to sell multiple new car nameplates, which is not
possible in practice. Since it appeared that these were a result of a coding error in the
dataset, we removed the transactions due to these two dealers, which accounted for fewer
than 100 transactions.
The resulting dataset contains 78 dealers, whose breakup by make is shown in Table 2.2.
We further group the dealers by make and treat all dealers of a make as a composite dealer.
Grouping dealers into composite dealers focuses our analysis on inter-channel while ignor-
ing the intra-make competition within a nameplate.
There are a total of 30755 transactions after cleaning up the data which are used to
compute the covariates described below, and estimate the model.
2.4.1 Covariates
The covariates are computed using the inventory of available cars in each period. The
inventory is not directly available from the dataset, but is imputed using two variables -
DaysToTurn andCloseDate, which are recorded for each transaction. TheDaysToTurn
variable gives the number of days the car was on the lot before it was sold. TheCloseDate
is the date on which the car was sold. The difference between these two variables gives the
date from which the car was available on the lot. Using these two variables, we identify all
cars which were available at the dealer lot in each period. The covariates are computed as
follows:
21
MODEL Transactions Percent Cum. Percent
Altima 12070 27.89 27.89
Accord 10018 23.15 51.05
Camry 9790 22.65 73.67
Table 2.1: Models included in the analysis
Brand # Dealers
Honda 25
Nissan 29
Toyota 24
Table 2.2: Number of dealers for each brand
Mean
Category Model Trans. Price($) Promotion($) Age (Wks) Mileage
New
Accord 8283 21694 1079 0 0
Altima 10354 21109 1352 0 0
Camry 8069 20042 907 0 0
Used
Accord 1229 16162 0 147 37834
Altima 1450 17221 0 96 26981
Camry 1370 15080 0 139 35236
Table 2.3: Summary statistics averaged over 53 weeks
22
Price
We use the vehprice variable, which is the price paid by the consumer for the car, to
compute the price of an alternative in the choice set. In order to get a better representation
of the market price of an alternative, we use the inventory of cars available in a week to
compute the price. The median selling prices of all cars of a model available in a week is
taken as the price of that model in that week.
Mileage
This covariate is zero for the new alternatives and is relevant only for the used cars. The
mileage is defined as the number of miles on the odometer as recorded in the dataset. As
in the case of price, we use the inventory of the used cars available across all dealers in a
week to compute the median mileage.
Promotion
Auto manufacturers directly offer the consumer, three types of price promotions. These
are cash rebate, finance promotions and lease promotions. The dollar value of the cash
rebates are directly available from the data. The other two promotions take the form of
lower interest rates on the contract and the dollar value has to be imputed from the data.
Manufacturers differ in their choice of promotional instruments. For example, Honda
does not offer cash rebates but does offer promotional interest rates on their lease and
finance contracts. In order to account for such variations across manufacturers and to make
the magnitude of the three promotional instruments comparable, we use the data to compute
the dollar value of lease and finance promotions.
In the case of finance transactions, the PIN dataset records three variables - APR,
monthlypayment,term andamountfinanced which can be used to calculate the dollar
23
value of the finance promotion. The APR is the interest rate actually paid by the consumer,
theamountfinanced is the portion of the total cost of the vehicle that has been financed
and themonthlypayment is the equated payments made by the consumer to the financing
company calculated as a function of the APR and amount financed.
Since the dataset does not report the market interest rate, we use a heuristic to infer
the market rate from the data. In each period, we identify all finance transactions which
have an APR rate above 5%. This cutoff was chosen based on our discussion with the
data provider. The median APR (MAPR) of these transactions in a week is taken to be the
market rate for that period.
Once the median market rate,MAPR is identified, the net present value of themonthlypayment,
denoted asMAPRamt is computed using Eqn 2.21 with the market rate as the discount
rate. The dollar value of the finance promotion is computed as the difference between the
amountfinanced andMAPRamt as given in Eqn 2.22.
MAPRamt =monthlypayment
1
1
(1+
mapr
1200
)
term
1
1
(1+
mapr
1200
)
(2.21)
financepromo =amountfinancedMAPRamt (2.22)
The procedure to calculate the dollar value for lease promotions is similar. We obtain
the median APR for each period using the same heuristic as the finance promotion. The
key change is in the way the monthly payment amount is calculated. The monthly payment
for lease transactions includes two components - the finance charge which is dependent on
the APR and the monthly depreciation which is not dependent on the interest rate. Includ-
ing the monthly depreciation component when calculating the NPV of total payments will
inflate the dollar value of the promotion. Therefore, only actual finance charges paid by the
consumer which is the difference betweenmonthlypayment andmonthlydepreciation is
24
used to compute the net present value of total payments. The monthly finance charges un-
der the market APR is calculated using Eqn 2.23 where the first term is the average value of
the car and the second term is the interest rate. We then compute the NPV of total payments
using the actual finance charge and the MAPR finance charges as in Eqns 2.24 and 2.25
and take the difference as the lease promotion as in Eqn 2.26.
MAPRfincharge =
amountfinanced +leaseresidual
2

MAPR
12 100
(2.23)
ActualNPV =ActualFinCharge
1
1
(1+
apr
12100
)
term
1
1
(1+
apr
12100
)
(2.24)
MAPRNPV =MAPRFinCharge
1
1
(1+
mapr
12100
)
term
1
1
(1+
mapr
12100
)
(2.25)
leasepromo =MAPRnpvActualNPV (2.26)
After the dollar value of the lease and finance promotion is calculated, we compute the
max of all the three types of promotions available in a week as the promotion for a product
in a week.
The summary statistics of the computed covariates are shown in Table 2.3.
2.4.2 Heterogeneity
We observe only a single transaction per consumer in the dataset, so we incorporate zip
code level heterogeneity in our analysis (Silva-Risso & Ionova, 2008). Each zip code is
treated as a household and each transaction from within a zip code is considered to be a
25
repeat purchase by the household. Thus, the decision making is modeled at the zip code
level rather than at the individual level. This is analogous to the setting in work using
scanner panel data for grocery products (e.g., (Guadagni & Little, 1983)). We include only
those zipcodes which have at least 50 transaction in the span of our data. This results in
365 zipcodes/consumers across the Los Angeles DMA.
2.5 Results
We estimated two logit demand models - a baseline logit model with homogeneous coeffi-
cients and a heterogenous logit model with endogeneity correction using control functions.
The estimates obtained from the homogenous model are shown in Table 2.4. All parameters
have the expected sign and are significant. As would be expected, the estimates indicate
that the consumers are price sensitive and have a preference for cars with fewer miles on
them. Promotion is significant and positive as well. The estimates from the heterogeneous
model are shown in Table 2.5. This model fits the data better than the homogeneous model
indicating the presence of consumer heterogeneity. Again, all signs are as expected and sig-
nificant. The price coefficient is much higher in magnitude than in the homogenous case. It
is interesting to note that the standard deviations for the price, promotion and mileage co-
efficients are not statistically significant. We believe that this due to the fact that the dataset
consists of just three models which are quite similar in their characteristics. Judging by the
magnitude of the standard deviation of the product specific intercepts, it appears that much
of the heterogeneity among consumers is captured by these parameters.
We infer our first set of results on the substitution pattern between new and used cars
from the price elasticity of demand computed from the best fitting demand model as shown
in Table 2.6. We compute the elasticity by simulating a 1% change in prices and computing
the implied purchase probabilities. The percentage change in purchase probability gives
26
Parameter Mean,b SE

1
0:2337 0:0127

2
0:4382 0:0117

3
0:1824 0:0127

4
0:3926 0:0300

5
0:5283 0:0274

6
0:3358 0:0282
Price 0:1907 0:0060
Promotion 0:0614 0:0099
Mileage 0:3289 0:0052
LogLikelihood 63345
Table 2.4: Demand Estimates: Model with homogeneous coefficients
Parameter Mean,b SE SD,W SE

1
0:7633 0:0348 0:7898 0:0283

2
1:0950 0:0268 0:5271 0:0250

3
0:7222 0:0281 0:5866 0:0274

4
0:0969 0:0451 0:6028 0:0374

5
0:0178 0:0387 0:5052 0:0382

6
0:1194 0:0368 0:3837 0:0432
Price 0:5053 0:0096 0:0035 0:0573
Promotion 0:0522 0:0175 4:3 10
6
0:0237
Mileage 0:3464 0:0073 9:7 10
5
0:0203
0:0378 0:0151
LogLikelihood 60939
Table 2.5: Demand Estimates: Model with heterogeneous coefficients and endogeneity
correction
the price elasticity of demand. Comparing the cross elasticities, we find that new car prices
have a bigger effect on the demand for used cars while the used car prices exerts a smaller
effect on the demand for new cars. In other words, we find that the higher quality product
(new cars) draw market share from the lower quality product (the used cars) while the
reverse effect is not as prominent. This asymmetry in substitution pattern is consistent
with the quality tier competition observed in the case of grocery products (Blattberg &
Wisniewski, 1989). It also emphasizes the importance of explicitly including the used car
market when building an optimal pricing model for automobiles.
27
Elasticity
Own Cross
J Model NU New Used
1 Accord N 0:87 0:2195 0:1804
2 Altima N 0:74 0:2788 0:2281
3 Camry N 0:78 0:1975 0:1621
4 Accord U 0:62 0:0239 0:0202
5 Altima U 0:67 0:0298 0:0249
6 Camry U 0:59 0:0234 0:0194
Mean New Cars 0:80 0:2319 0:1902
Mean Used Cars 0:63 0:0257 0:0215
Table 2.6: Price elasticity
We now use the demand estimates from heterogeneous model and the supply models
previously specified to compute the implied price cost margins which are shown in Ta-
ble 2.7. The imputed margins for the dealer is comparable to that reported in Albuquerque
and Bronnenberg (2012) which does not account for the used car market. But our im-
puted manufacturer margins are much lower than the margins they report perhaps due to
the different model specification they use and the different set of vehicles they analyze.
The results in Table 2.7 indicate that in absolute dollar value, the dealer margins in-
crease when the dealers account for the substitutability between new and used cars in their
pricing decisions while manufacturer margins decrease slightly. Overall, the total channel
profits increases and the dealer is able to extract a slightly higher share of the profits.
Recall that in the separate scenario the dealer is treating the two category of products
as separate business without accounting for the cross substitution between them, while the
demand model accounts for this substitution. Thus, dealers can obtain higher margins by
pricing the two categories jointly taking into account the substitution between the cate-
gories. We highlight two conclusions from this result - one, the used car market has a
positive effect on the new car business, especially when the pricing accounts for the fact
that two categories are substitutable. Secondly, these results also highlights the importance
28
Model NU Dealer Manufacturer Total
Separate Joint Separate Joint Separate Joint
Accord N 2749.5 2851.6 3695.9 3657.2 6445.4 6508.9
Altima N 2907.4 3053.9 4262.7 4225.8 7170.1 7279.7
Camry N 2650.6 2761.3 3411.8 3366.3 6062.3 6127.6
Accord U 2093.3 2653.5 0.0 0.0 2093.3 2653.5
Altima U 2098.3 2944.5 0.0 0.0 2098.3 2944.5
Camry U 2075.2 2647.4 0.0 0.0 2075.2 2647.4
Mean New Car PCM
2769.2
(42.2%)
2888.9
(43.5%)
3790.1
(57.8%)
3749.8
(56.5%)
6559.3 6638.7
Table 2.7: Computed Price Cost Margin
Model NU Separate Joint
Dealer Manuf. Total Dealer Manuf. Total
Accord N 0.40M 0.54M 0.95M 0.42M 0.54M 0.96M
Altima N 0.54M 0.80M 1.34M 0.57M 0.79M 1.36M
Camry N 0.39M 0.50M 0.88M 0.40M 0.49M 0.89M
Accord U 0.05M 0.00M 0.05M 0.06M 0.00M 0.06M
Altima U 0.06M 0.00M 0.06M 0.08M 0.00M 0.08M
Camry U 0.05M 0.00M 0.05M 0.07M 0.00M 0.07M
Total New Car Profits
1.33M
(41.5%)
1.84M
(58.5%)
3.17M
1.39M
(43%)
1.82M
(57%)
3.21M
Total Car Profits 1.49M 1.84M 3.33M 1.60M 1.82M 3.42M
Table 2.8: Profit Estimates in Dollars
of including the dealer in an optimal pricing model for automobiles.
Finally, Table 2.8 shows the total profits computed using the implied price cost margins.
We observe that dealers can make a higher profit when they jointly price their products,
while manufacturer profits decrease slightly. The total profits in the channel go up as well.
More importantly, the dealer gets a higher share of the profits in the channel increasing the
dealers bargaining power in the channel.
29
Model Dealer Manuf. Total
Accord 2510 3145 5656
Altima 2576 3419 5995
Camry 2424 2868 5292
Mean New Car PCM 2503 3144 5647
Table 2.9: Computed Price Cost Margins
2.5.1 Counterfactual
We now study, through a counter factual, what the impact would be if manufacturers shut-
down the used market in order to lower the competition from used products as suggested in
the literature (Rust, 1986). Assume that dealers are no longer allowed to sell used cars. We
compute the impact that this situation will have on the margins. When the used car market
is shutdown, both the dealer and manufacturer margins go down (as seen in Table 2.9) as
compared to base line case where dealers sell both categories of products (Refer Table 2.7).
Thus, we conclude that shutting down the used car market at new car dealers is suboptimal
for both the dealers and manufacturers.
2.6 Discussion
We proposed and estimated a model of new and used car competition, and studied the
impact from the used cars on the new car dealer and manufacturer margins and profits. We
find that dealer margins go up when dealers fully account for the substitution between new
and used cars in their pricing decision, and the manufacturer margins decline slightly. Over
all, this shifts the channels power in favor of the dealer.
From our results, we conclude that the used car market is beneficial to both the dealer
and manufacturer. As suggested in the literature (Shulman & Coughlan, 2007), the used
car market allows dealers and manufacturers to extract a higher surplus from the new car
consumers. We also provide an additional explanation that the used car market increase the
30
channel power of the dealer and thus provides the dealer with an additional incentive to sell
used cars.
Due to the dealer agglomeration, the approach proposed in this work does not consider
the implications due to intra-make competition. We do realize that a good portion of the
competition in the auto market is due to competition among dealer of the same nameplate.
We propose expanding on the current results by relaxing the dealer agglomeration assump-
tion and studying products at the individual dealer level. We expect that doing so will
accentuate the current results.
31
Chapter3
HowLongShouldaDurableProduct
Last? TheImpactofDurabilityon
AutomobileDemand
32
3.1 Introduction
The automobile market is a highly differentiated oligopoly with strong competition be-
tween manufacturers on the prices, characteristics and durability of their products. The
durability of auto products and the existence of the secondary markets imply that these
products have many lives - initially as a new product and subsequently as used products.
If a used car is highly durable then consumers can substitute it instead of a new car. Thus
the durability decisions made by manufacturers can have consequences for the competition
between new and used products.
The theoretical economics literature has been concerned with how product durability
affects competition between new and used versions of durable products, mainly focused on
the question of the optimal level of durability that a manufacturer should build into a new
product. Some of the earliest literature suggested that a durable product monopolist will
have an incentive to lower the durability of its new products (Levhari & Srinivasan, 1969;
Schmalensee, 1970) in order to reduce competition from the used version of its products.
This intuition was overturned by the independence result of Swan (1970), who showed that
under certain conditions namely constant returns to scale a durable product monopolist will
have an incentive to provide the socially optimal level of durability in its products. In other
words, the choice of durability is independent of market structure.
In what is possibly one of the few studies that explicitly study durability choice in an
oligopoly setting, Bulow (1986) showed that firms have an incentive to collude to reduce
the durability of their products. On the other hand if firms compete on quantity, then
increasing durability will result in increased profits since it forces competitors to lower their
output. If firms in an oligopoly choose to increase the durability of their products, then used
versions of these products will be good (but imperfect) substitutes for new ones (Porter &
Sattler, 1999; Purohit, 1992). These highly durable used products can compete for market
33
share with the new products (Sankaranarayanan, 2007) and lower the pricing power of new
product manufacturers (Swan, 1980; Esteban & Shum, 2007).
Several papers have studied how manufacturers of new products could reduce competi-
tion with used versions of their products. One suggestion is for manufacturers to incorpo-
rate planned obsolescence into their products. This involves deliberately lowering the new
product durability in order to reduce its useful life (Bulow, 1986), decreasing the interpur-
chase cycle time and effectively reducing the availability of used products in the secondary
market. However, it is important to note that this strategy may only be feasible in the case
where the manufacturer is a monopoly. In an oligopoly setting firms that choose to lower
the durability of new products in order to stave off competition from its used version run
the risk of consumers simply switching to another brand that offers a higher quality, leading
to decreased market share or pricing power or both. Thus, the relative size of the cannibal-
ization and draw effects are a critical determinant of the success of planned obsolescence
strategies.
Even though, the theoretical literature provides numerous contrasting predictions about
the impact of durability, there has been a relative paucity of empirical work which analyzes
the effects of product durability on demand (Iizuka, 2007). The more recent empirical lit-
erature on the automobile market has considered various aspects of the demand such as
price (Berry et al., 1995; Sudhir, 2001), promotions (Silva-Risso & Ionova, 2008), dealer
network (Bucklin, Siddarth, & Silva-Risso, 2008; Albuquerque & Bronnenberg, 2012) but
not durability. Moreover, this literature only considers the competition between new cars
across brands and segments and does not consider the impact due to the used car cate-
gory. The existence of a well developed and organized secondary markets implies that
consumers can easily substitute highly durable used products for new products. In a simu-
lation study, Chen, Esteban, and Shum (2008) showed that increased durability of new cars
will result in a higher stock of used products which will compete with new cars.
34
Thus, while there is a large body of theoretical work which discusses durability, the
empirical literature falls short on that front. One consequence of the paucity of empirical
work in the area is that there is very little guidance on how to measure and operationalize
durability construct. One contribution of this work is to propose a durability metric that is
derived from the trajectory of used car prices over time. Further, we propose a structural
model of disaggregate demand for new and used cars that incorporates the impact of dura-
bility on consumer choice decisions. Our analysis quantifies the impact of durability on
demand and provides insights into the relative magnitude of the draw and cannibalization
effects of changes in durability on demand.
3.2 Model
We model a differentiated product market with both new and used products in which het-
erogeneous consumers choose the utility maximizing alternative from either category. Con-
sumeri chooses between a new or used car or the outside option from a total ofJ +1 prod-
ucts. Each productj2 1:::J is characterized by its price, durability and other observed
characteristics,x
j
. The outside option is designated asj = 0. The utility that consumeri
receives from choosing productj consists of two parts, the deterministic componentV and
an unobserved demand shock". Thus,
U
ijt
=V
ijt
(x
jt
;
i
) +"
ij
(3.1)
The deterministic component of utility V , given in Eqn. 3.2, is a linear function of
the observed product characteristics x and a set of consumer specific parameters
i
=
f
ij=1:::J
;
p
i
;
pp
i
;
m
i
;
d
i
g which are to be estimated.
35
V
ijt
(x
jt
;
i
) =
ij
+
pp
i
promo
jt
+
m
i
mileage
jt
+
d
i
durability
jt
+
p
i
price
jt
(3.2)
The deterministic utility of the outside option is normalized asV
i0t
= 0. We assume
that the unobserved demand shock,"
ij
, follows a Type I Extreme Value distribution. Given

i
, the probability that consumeri choosesj in periodt is given by
P
ijt
(
i
) =
exp(V
ijt
(x
jt
;
i
))
1 +
P
J
k=1
exp(V
ikt
(x
kt
;
i
))
(3.3)
Conditional on
i
, the probability of the sequences of choices made by a consumer is
given by Eqn 3.4 whered
ijt
= 1 indicates that consumeri chose productj in periodt.
P
i
(
i
) =
Ti
Y
t=1
J
Y
j=0
P
ijt
(
i
)
d
ijt
(3.4)
Since
i
is not known, there is no closed form solution for Eqn 3.4 and the probabil-
ities have to be simulated. Thus, assuming that
i
is drawn from a distribution f(), the
unconditional probability is the integral over the distribution of
i
~
P
i
() =
Z
P
i
(
i
)f(
i
j)d
i
(3.5)
In order to evaluate Eqn 3.5, we assume that
i
has a normal distributionN(; ) and
take R random draws,
r
i
from N(; ). The average of conditional choice probabilities
evaluated at each of these draws gives the unconditional choice probabilities as in Eqn 3.6.
~
P
i
() =
1
R
R
X
r=1
P
i
(
r
i
) =
1
R
R
X
r=1
Ti
Y
t=1
J
Y
j=0
P
ijt
(
r
i
)
d
ijt
(3.6)
The likelihood of the sample is the product of choice probabilities over all consumers
36
and is given by
L() =
N
Y
i=1
P
i
() (3.7)
In practice, we use the log likelihood of the sample given by Eqn 3.8 and maximiz-
ing the log likelihood with respect to and using the simulated maximum likelihood
method (Train, 2009).
LL() =
N
X
i=1
lnP
i
() (3.8)
3.3 Data
The JD Power PIN dataset is a transaction level dataset collected from a large number of
branded auto dealers in the US. We estimate the model on weekly sales of Premium Mid-
size sedans in the Los Angeles DMA in 2004. The best selling models in this segment are
the Honda Accord, Toyota Camry and Nissan Altima which account for 61% of new trans-
actions and 13% of used transactions. We specify the product at a distinct category-model-
model year tuple (e.g., New Accord 2004, Used Camry 2001) resulting in 14 products. The
number of new and used transactions for each product is shown in Table 3.1. We treat the
other models transacted in 2004 in this segment as the outside good and accounts for 26%
of the total transactions.
3.3.1 Durability
Many agencies such as Consumer Reports and J.D. Power attempt to estimate the durability
of products through lab testing and consumer surveys. Both these approaches are expensive
and do not factor in the effective life of the product. In this dissertation, we propose a new
37
Category Model Model Year Transactions
N Accord 2005 7454
N Accord 2004 6488
N Altima 2005 15134
N Altima 2004 2555
N Camry 2005 8986
N Camry 2004 5093
U Accord 2003 682
U Accord 2002 1402
U Accord 2001 1044
U Altima 2003 1663
U Altima 2002 1283
U Camry 2003 938
U Camry 2002 1087
U Camry 2001 1138
Table 3.1: Transaction by Product
approach to measure the durability of the product based on the depreciation of prices over
the lifetime of the car.
Durability represents the inherent quality of a car. A highly durable car should hold its
value longer and therefore have lower depreciation rate. The durability of a product can
be considered to be the change in quality of the product overtime (Anderson & Ginsburgh,
1994). If we consider the price of the product to be indicative of the quality, then the
change in prices between new and used versions of the same product can be considered
as an indicator of the durability of the product. Therefore, a car which loses only a small
amount of its monetary value should be more durable than a car which loses a higher
portion of its value over the same amount of time.
We define the durability of a car as the reciprocal of the depreciation rate (r) of the car.
A standard measure for the depreciation rate reported in the literature (Adda & Cooper,
2000; Pratt & Hoffer, 1990; Parks, 1974; Ackerman, 1973; Hulten & Wykoff, 1981b,
1981a) is the exponential rate of decrease in prices over time. The depreciation rate can
be computed by fitting an exponential decay function to the price trajectory of the car over
38
time. The durability of a car is computed as the inverse of the estimated decay rate for a
particular model and model year of a car, based on standard usage condition.
We obtain the price history of a car by using the trade-in value of a particular model
and model year each time it is traded in between the period starting from its model year of
the car to the year 2009. The odometer reading at the time of the trade-in is given by the
mileage variable in the dataset. The age of the car at the time of trade-in,age, is computed
as the number of weeks elapsed from the Jan 1st of themodelyear of the car. For example,
the age of a 2002 Camry that was traded-in during the first week of Jan 2003 would be
53 weeks. In addition, the dataset provides the market value of the trade-in cartradeacv,
which the dealers estimate of the value of the car in the wholesale auction market. We use
thetradeacv instead of the resale price of the used car since the resale price will include
any updates and repairs performed by the dealer on the car and may not accurately reflect
value given the condition of the car.
In order to obtain the price trajectory, we first regress the observedtradeacv for each
car in our dataset as a function of theage (in weeks) andmileage of the car as given in
Eqn 3.9. We estimate this regression separately for each model included in our analysis
and report the estimates in Table 3.2 TheR
2
for the individual regressions ranging between
0.60 and 0.85 indicating good model fit and the signs of the coefficients are as expected
and significant.
tradeacv = +
1
age +
2
mileage +
3
agemileage +" (3.9)
Using these regression estimates we now compute the price trajectories for each car
based on a set of standard conditions. We assume that each car is driven 12000 miles in a
year and then compute the predictedtradeacv for each week for a 5 year period using the
estimated regression coefficients for each car. This gives us the predicted depreciation in
39
value over a 5 year period for each car. Figure 3.1 shows the predicted price trajectories
over a 5 year period for the included products.
We fit a exponential decay model as given in Eqn 3.10 to the predicted price trajectories
to estimate the depreciation rate, R. The durability is calculated as the inverse of the
absolute depreciation rate (abs(R)
1
) for a particular model-model year. The measured
durability for a set of cars is shown in Fig 3.2.
^
tradeacv
t
=
^
tradeacv
0
exp(Rt) (3.10)
3.3.2 Covariates
Each alternative in the choice set has four covariates listed in Eqn 3.2. We compute the
durability as described in Section 3.3.1. The other covariates are computed as follows and
the summary statistics for these variables is reported in Table 3.3
Price
We use the vehicle price variable, which is the price paid by the consumer for the car, to
compute the price of an alternative in the choiceset. For new cars, we use the median of
the prices of all cars of a model sold in a week as the price of that model in that week. The
price for the used car is computed similarly, but instead of using the just the cars sold in a
week, we use the inventory of cars available in week to compute the median price.
Mileage
This covariates is zero for the new alternatives. Transaction data for used cars record the
odometer reading. We calculate the median odometer reading across the inventory of used
40
Model Model year
1

2

3
R
2
Accord 2001 18.69 0.03 0.07 1.2e-4 0.77
2002 18.29 0.02 0.05 6.4e-5 0.82
2003 19.98 0.03 0.07 1.1e-4 0.81
2004 19.86 0.03 0.06 7.4e-5 0.74
2005 20.02 0.03 0.06 1.2e-4 0.60
Altima 2002 17.59 0.02 0.07 9.6e-5 0.84
2003 17.41 0.02 0.06 7.6e-5 0.80
2004 18.37 0.03 0.07 1.2e-4 0.85
2005 18.99 0.03 0.08 2.02e-4 0.72
Camry 2001 15.91 0.02 0.07 1.4e-4 0.82
2002 16.42 0.02 0.05 6.7e-5 0.79
2003 16.89 0.02 0.05 6.8e-5 0.78
2004 17.87 0.02 0.05 7.2e-5 0.75
2005 17.86 0.02 0.06 8.6e-5 0.74
Table 3.2: Estimates from regression of price histories
Mean
J Category Model Model Year Price Promotion Mileage Durability
1 N Accord 2004 21693 846 0 22362
2 N Accord 2005 22007 329 0 20780
3 N Altima 2004 20517 674 0 17970
4 N Altima 2005 20803 1031 0 15165
5 N Camry 2004 20581 990 0 21686
6 N Camry 2005 20300 344 0 21940
7 U Accord 2001 14338 0 46288 20918
8 U Accord 2002 16159 0 32412 22595
9 U Accord 2003 18944 0 18699 22098
10 U Altima 2002 15570 0 35315 20385
11 U Altima 2003 17287 0 23000 20514
12 U Camry 2001 12468 0 45921 18989
13 U Camry 2002 15179 0 34037 24298
14 U Camry 2003 16956 0 23522 23437
Table 3.3: Summary Statistics
41
Figure 3.1: Predictedtradeacv with standardized age and mileage
42
Figure 3.2: Durability for each model included in our dataset. Higher is better
cars available in particular week and use this value to represent the mileage for used cars
in a particular week.
Promotion
Auto manufacturers directly offer three types of price promotions to the consumer. These
are cash rebate, finance promotions and lease promotions. Cash rebates are dollar pro-
motion and the value is directly available from the data. The latter two are in the form
of discounts on the interest rates. In order to make the three promotions comparable in
magnitude, we compute the dollar value of lease and finance promotions using the data.
In the case of finance transactions, the PIN dataset records three variables - APR,
monthlypayment,term andamountfinanced which can be used to calculate the dollar
value of the finance promotion. The APR is the interest rate actually paid by the consumer,
43
the amountfinanced is the portion of the total cost of the vehicle that has been financed
and the monthlypayment is the equated payments made by the consumer to the financing
company calculated as a function of the APR and amount financed.
Since the dataset does not report the market interest rate, we use a heuristic to infer
the market rate from the data. In each period, we identify all finance transactions which
have an APR rate above 5%. This cutoff was chosen based on our discussion with the
data provider. The median APR (MAPR) of these transactions in a week is taken to be the
market rate for that period.
Once the annual market rate,MAPR is identified, the net present value of themonthlypayment,
denoted asMAPRamt is computed using Eqn 3.11 with the market rate as the discount
rate. The dollar value of the finance promotion is computed as the difference between the
amountfinanced andMAPRamt as given in Eqn 3.12.
MAPRamt =monthlypayment
1
1
(1+
mapr
1200
)
term
1
1
(1+
mapr
1200
)
(3.11)
financepromo =amountfinancedMAPRamt (3.12)
The procedure to calculate the dollar value for lease promotions is similar. We obtain
the median APR for each period using the same heuristic as the finance promotion. The
key change is in the way the monthly payment amount is calculated. The monthly payment
for lease transactions includes two components - the finance charge which is dependent on
the APR and the monthly depreciation which is not dependent on the interest rate. Includ-
ing the monthly depreciation component when calculating the NPV of total payments will
inflate the dollar value of the promotion. Therefore, only actual finance charges paid by the
consumer which is the difference betweenmonthlypayment andmonthlydepreciation is
used to compute the net present value of total payments. The monthly finance charges un-
44
der the market APR is calculated using Eqn 3.13 where the first term is the average value of
the car and the second term is the interest rate. We then compute the NPV of total payments
using the actual finance charge and the MAPR finance charges as in Eqns 3.14 and 3.15
and take the difference as the lease promotion as in Eqn 3.16.
MAPRfincharge =
amountfinanced +leaseresidual
2

MAPR
12 100
(3.13)
ActualNPV =ActualFinCharge
1
1
(1+
apr
12100
)
term
1
1
(1+
apr
12100
)
(3.14)
MAPRNPV =MAPRFinCharge
1
1
(1+
mapr
12100
)
term
1
1
(1+
mapr
12100
)
(3.15)
leasepromo =MAPRnpvActualNPV (3.16)
3.3.3 Heterogeneity
We observe only a single transaction per consumer in the dataset. In order to estimate
the mode, we require multiple observations per consumer. Therefore we use zipcode level
heterogeneity in our analysis (Silva-Risso & Ionova, 2008). Each zipcode is treated as a
household and all consumers within a zipcode form a household. Each transaction from
within a zipcode is considered to be a repeat purchase by the household. We include only
those zipcodes which have at least 40 transactions in the span of our data. This results in
392 zipcodes across the Los Angeles DMA.
45
Parameter Mean,b SE,b

1
1:5091 0:0145

2
4:1744 0:0266

3
5:7477 0:0227

4
13:5107 0:0138

5
0:9347 0:0161

6
1:4387 0:0206

7
0:0524 0:0377

8
2:0889 0:0423

9
0:0049 0:0585

10
1:7030 0:0379

11
2:8600 0:0334

12
2:1197 0:0377

13
6:0475 0:0455

14
3:3676 0:0486
Price,
p
0:7028 0:0027
Promotion,
p
p 0:0322 0:0001
Mileage,
m
0:0067 0:0004
Durability,
d
1:7976 0:0020
LogLikelihood 57423
Table 3.4: Estimation Results for Homogenous Model
3.4 Results
We estimated two models - a baseline homogeneous model and the focal heterogeneous
model as specified in Section 3.2. The results are shown in Tables 3.4 and 3.5. The pa-
rameters in both models have the expected sign and are statistically significant. Price has a
negative coefficient indicating that consumers have a preference for lower prices products.
Durability has a positive coefficient indicating the consumer prefers highly durable prod-
ucts. The heterogeneous model fits the data better as evident from the log likelihood values
and therefore, subsequent results and discussion uses the estimates from the heterogeneous
model.
In order to understand how the change in price affects the demand, we computed the
price elasticities for the 14 products included in our analysis. The cross elasticities are av-
46
Parameter Mean,b SE,b Mean,w SE,w

1
0:0663 0:0548 1:0806 0:0658

2
0:6731 0:0419 0:7504 0:0420

3
1:3578 0:0260 0:1384 0:0440

4
2:4659 0:0228 0:2497 0:0302

5
0:8510 0:0347 0:8296 0:0413

6
0:2059 0:0401 0:8793 0:0428

7
0:0439 0:0403 0:0205 0:0000

8
0:3758 0:0429 0:0401 0:0000

9
0:0900 0:0616 0:0395 0:1788

10
0:7409 0:0372 0:0426 0:0629

11
1:5797 0:0322 0:2220 0:0590

12
0:1603 0:0413 0:0589 0:0000

13
1:7485 0:0476 0:0251 0:0944

14
0:7987 0:0471 0:0130 0:1000
Price,
p
0:3696 0:0032 0:0267 0:0041
Promotion,
p
p 0:0393 0:0002 0:0002 0:0004
Mileage,
m
0:0161 0:0006 0:0000 0:0013
Durability,
d
0:4567 0:0033 0:0564 0:0035
LogLikelihood 56157
Table 3.5: Estimation Results for Heterogenous Model
47
J Product
Own
Elasticity
Cross Elasticity
New Used
Mean SD Mean SD
1 2004 Accord N 4:77 1.232 0.5021 1.678 0.0369
2 2005 Accord N 4:97 0.453 0.4475 0.293 0.0316
3 2004 Altima N 5:58 0.318 0.2817 0.758 0.0545
4 2005 Altima N 4:91 1.400 0.6791 1.374 0.0833
5 2004 Camry N 4:98 0.930 0.4693 1.384 0.0408
6 2005 Camry N 5:26 0.489 0.3702 0.454 0.0332
7 2001 Accord U 5:10 0.099 0.0329 0.139 0.0032
8 2002 Accord U 5:73 0.100 0.0347 0.141 0.0038
9 2003 Accord U 6:74 0.053 0.0141 0.072 0.0011
10 2002 Altima U 5:50 0.126 0.0423 0.175 0.0041
11 2003 Altima U 5:94 0.223 0.0696 0.307 0.0056
12 2001 Camry U 4:47 0.083 0.0328 0.114 0.0032
13 2002 Camry U 5:37 0.077 0.0331 0.111 0.0030
14 2002 Camry U 6:02 0.087 0.0316 0.122 0.0039
Table 3.6: Price Elasticity
eraged across categories to obtain summary cross-elasticities as shown in Table 3.6. Thus,
for each category, we compute the average cross elasticities across new cars and used cars.
The own price elasticities indicate that the used car demand is more sensitive to price
than new car prices. The cross elasticities for new cars indicate that changes in new car
prices has a slightly higher effect on the demand for used cars. On the other hand, the used
car cross elasticities indicate that the used prices affect the demand for other used cars than
more new cars. The quality tier competition (Blattberg & Wisniewski, 1989) between the
categories observed in Chapter 2 (refer Section 2.5) are seen here are well.
We now study how the durability affects the demand by computing the elasticity of
durability for the 14 products as shown in Table 3.7. The summary cross elasticities are
computed as in the case of the price elasticities. The own elasticities indicate that higher
durability has a bigger effect on the demand for used cars more than for new cars. It is also
important to note that the own elasticity due to durability is about two percentage points
48
J Product
Own
Elasticity
Cross Elasticity
New Used
Mean SD Mean SD
1 2004 Accord N 6.36 1:642 0.6378 2:246 0.0676
2 2005 Accord N 6.03 0:551 0.5395 0:361 0.0382
3 2004 Altima N 6.51 0:372 0.3333 0:884 0.0630
4 2005 Altima N 4.49 1:268 0.5873 1:257 0.0698
5 2004 Camry N 6.99 1:301 0.6645 1:957 0.0718
6 2005 Camry N 7.83 0:731 0.5599 0:678 0.0502
7 2001 Accord U 9.80 0:190 0.0575 0:267 0.0064
8 2002 Accord U 10.78 0:188 0.0612 0:265 0.0087
9 2003 Accord U 10.66 0:084 0.0197 0:113 0.0032
10 2002 Altima U 9.46 0:218 0.0662 0:302 0.0068
11 2003 Altima U 9.32 0:349 0.1005 0:482 0.0097
12 2001 Camry U 8.75 0:162 0.0612 0:225 0.0066
13 2002 Camry U 11.80 0:169 0.0718 0:245 0.0079
14 2003 Camry U 11.32 0:164 0.0563 0:230 0.0090
Table 3.7: Durability Elasticity
higher than the price elasticity. The cross elasticities show that increased durability for
news cars will results in lower demand for used cars, while increased durability of used
cars has a relatively smaller effect on the demand for new cars.
We now look at the impact on sales due changes in the durability of a product. Table 3.8
shows how many additional units are sold for a 1% increase in durability and the category
from which the sales are drawn. As would be expected, an increase in durability has a
higher effect on the sales of used cars than on new cars. At the same time, an increase
in durability of new cars results in them drawing an average share of 1.3% from used
cars sales, while a corresponding increase in the durability of the used car only draws an
average of 0.2% from new cars sales. Thus, higher durability on used cars do not appear
to adverse effect on the sales of new cars. But, a 1% increase in durability of a new cars
draws about 1% share from its competing new cars, indicating that higher durability allows
a product to gain share from its competitors and therefore, durable product manufacturers
49
J Product
Drawn From
Sales
Increase
New Used
Own Other Own Other
1 2004 Accord N 438 (7.0%) -18 (1.0%) -308 (1.7%) -32 (2.0%) -78 (2.4%)
2 2005 Accord N 141 (7.7%) -17 (0.3%) -106 (0.6%) -5 (0.3%) -12 (0.4%)
3 2004 Altima N 152 (6.1%) -17 (0.2%) -92 (0.6%) -16 (1.0%) -27 (0.8%)
4 2005 Altima N 292 (3.8%) -13 (0.5%) -216 (1.4%) -25 (1.5%) -37 (1.1%)
5 2004 Camry N 377 (7.6%) -25 (0.9%) -255 (1.4%) -31 (1.9%) -65 (2.0%)
6 2005 Camry N 200 (6.8%) -25 (0.5%) -141 (0.8%) -10 (0.6%) -24 (0.7%)
7 2001 Accord U 62 (8.5%) -16 (0.2%) -34 (0.2%) -2 (0.3%) -9 (0.3%)
8 2002 Accord U 61 (10.7%) -16 (0.2%) -34 (0.2%) -2 (0.2%) -9 (0.3%)
9 2003 Accord U 28 (9.4%) -7 (0.1%) -15 (0.1%) -1 (0.1%) -4 (0.1%)
10 2002 Altima U 70 (9.8%) -21 (0.2%) -36 (0.2%) -4 (0.4%) -9 (0.3%)
11 2003 Altima U 111 (11.9%) -33 (0.3%) -59 (0.4%) -4 (0.5%) -14 (0.4%)
12 2001 Camry U 52 (7.2%) -14 (0.2%) -29 (0.2%) -2 (0.2%) -8 (0.2%)
13 2002 Camry U 56 (11.3%) -15 (0.2%) -30 (0.2%) -3 (0.2%) -8 (0.3%)
14 2003 Camry U 53 (12.4%) -14 (0.2%) -29 (0.2%) -3 (0.2%) -8 (0.2%)
Table 3.8: Sales decomposition due to a 1% increase in durability
in an oligopoly should aim to increase the durability of their products. Even at the brand
level, we find that higher durability for used products does not affect the new product of the
own brand much, rather the increase in sales appears to be from new cars of other brands.
3.5 Discussion
The durability of products such as automobiles, is perhaps the most important character-
istic of the product. Extant empirical literature has not studied how durability impacts the
demand for durable products. We propose and estimate a data driven metric for the dura-
bility of the product. We then incorporated this metric in demand model for new and used
automobiles.
Our results indicate that consumers have a positive preference for durable cars. We
also conclude that increased durability is beneficial for new car manufacturers. Increased
50
durability will allow the product to grab more market share from both new and used com-
petitors. Moreover, increased durability of used cars do not pose as much of a competition
to new cars as feared in the analytical literature (Sankaranarayanan, 2007).
51
Chapter4
ReplaceorWait: ADynamicModelof
TemporalSubstitutionEffectsin
DurableProductMarkets
52
4.1 Introduction
Automobile manufacturers typically produce cars based inflexible production schedule that
is fixed many months in advance and is hard to modify in response to short term market
demand shocks or inventory levels (Silva-Risso & Ionova, 2008). During the economic
downturn in 2008, the market for new automobiles shrunk from around 18 million units to
12 million units
1
. Since they could not reduce production immediately, manufacturers were
using price promotions to clear their inventory. But, in spite of their best efforts, consumers
were just not buying.
Subsequently, in 2009 the Obama administration introduced the Cash for Clunkers pro-
gram where consumers could trade-in older cars with higher mileage and buy a new car for
a significant rebate. This program turned out to be an instant hit with the same consumers
who were otherwise delaying replacing their existing cars
2
. This program was different
from the regular promotions offered by the manufacturers in two respects. One, the promo-
tion on the new car was quite high at about $4000 and two, it targeted a specific segment
of consumers who owned older vehicles. Thus, the promotional program shifted the focus
from the new product to both the new and used product.
The literature on durable product choice (e.g., Berry et al. (1995); Sudhir (2001); Train
and Winston (2007); Silva-Risso and Ionova (2008), etc) has typically treated the used
product as an outside good, from which consumers derive no utility. This ignores the con-
sumption utility and the replacement value that consumers can derive from their existing
product which could potentially overstate the effect of the marketing mix of the new prod-
ucts. The decision to buy a new durable product effectively involves two sub-decisions: a)
whether or not to replace the existing product, and b) if yes, which new model of car to buy?
It is important to model both these decisions in order to be able to correctly understand the
1
JD Power & Associate, Monthly Sales Report, April 2009
2
http://www.nhtsa.gov/CARS-archive/official-information/CARS-Report-to-Congress.pdf
53
sales response.
The current literature on product replacement has examined either how the new product
marketing mix or the depreciation of the used product impacts the replacement decision.
For example, Gordon (2009) studied the impact of quality and price of new computer pro-
cessors on the replacement cycles of consumers and showed that consumers with higher
preference for quality tend to replace earlier than price sensitive consumer who tend to
wait for the price to drop before buying. His analysis does not consider the depreciation of
the currently owned product.
On the other hand (Rust, 1987) studied how the number of miles on bus engines lead
to the decision to replace them, but does not include the effects of the new product mar-
keting mix on the replacement. The joint impact due to the evolution of both the new
product marketing mix and the current product depreciation has not been considered in the
literature.
Modeling the replacement decision in an integrated demand model for new cars is im-
portant for many reasons. Consumers may accelerate or decelerate their replacement tim-
ing decisions to take advantage of promotions on new products. The characteristics of the
currently owned product may also strongly influence the replacement decision. For exam-
ple, consumers who own cars of a very recent vintage, or those with very durable vehicles
whose performance has not deteriorated much, may be less likely to replace these products
relative to those whose cars are older or whose vehicles have lost much of their original
value.
In this study, I develop and estimate a disaggregate dynamic structural model of con-
sumers who replace their currently owned durable product with a new one. On each re-
placement opportunity, the consumer compares the expected discounted utility from the
current product to that from the new products available in the market and makes a utility
maximizing decision. The estimated demand parameters permit us to quantify the relative
54
impact of price, promotion and the depreciation of current product on the replacement de-
cision. We then compare the estimates from the full dynamic model to a model that only
includes the marketing mix of the new product but ignores the used product, i.e., treats
the no-buy alternative as an outside good. This enables us to quantify the extent to which
price elasticities are affected by ignoring the currently owned product. In order to show
the interplay between new and used product utilities, we also compare the full model to a
model which ignores the new product marketing mix and models the replacement decision
as a function of the used product characteristics alone.
4.2 LiteratureReview
Some of the early studies on durable product replacement sought to identify the demo-
graphic characteristics of consumers with different replacement rates. For example, in a
study on consumers with different replacement times, consumers who replaced faster had
higher income (Gilbert, 1992) and styling preferences (Bayus, 1991). These consumers
were also found to buy higher priced cars which were advertised more frequently.
Apart from consumer demographics, several new product characteristics have been
shown to impact the replacement. Bayus (1988) showed that the price and advertising can
accelerate the replacement decisions by about a year. Brand loyalty has also been shown
to affect both the new product choice as well as the replacement hazard (Che & Seethara-
man, 2009). New product upgrades, especially if they are very different from the current
generation of products in use tend to increase the desirability of the new product leading to
higher purchase intentions (Holak & Lehmann, 1990).
Very few studies have considered the impact of the condition of the used product on
the replacement decision. An exception is Rust (1987) who showed that depreciation of
the product coupled with an increase in the maintenance cost as a result of aging is a key
55
reason for replacement of durable products. In other studies, consumers who have a higher
valuation for the used product (Purohit, 1995) or face a negative equity on their currently
owned products due to rapid depreciation (Bruce, Desai, & Staelin, 2006), tend to postpone
their replacement decision. Adda and Cooper (2000) argued that the replacement hazard
for a car increases exponentially with its age which in turn was shown to be bimodal - the
resale patterns for used automobiles peaks at around 3 to 4 years and then again at around
10 years Stolyarov (2002).
While some of the work discussed above considers the presence of the secondary mar-
ket, they treat it as a ’sink’ for used products. Thus, when a consumer replaces an existing
product with a new one, he receives no utility for the replaced product. In reality, many
secondary markets act as an outlet for consumers to sell off their current product before
buying a new product. Thus, the current product commands a residual value which can
affect the replacement decision (Adda & Cooper, 2000). The residual value provides the
consumer with a non-zero utility which will impact the replacement decisions. Ignoring
this utility would affect the replacement elasticity. Most of the existing literature on au-
tomobile demand (Berry et al., 1995) ignores the utility derived from a currently owned
vehicle. We fill this gap in the literature by explicitly accounting for the utility of both the
new car as well as the currently owned car in the model.
The dynamic nature of the replacement decision has implications for how the problem
is modeled. Melnikov (2001) argues that a static discrete choice setting is unrealistic since
it cannot model the demand substitution over time where a consumer chooses to forgo a
purchase in the current period in order to buy a better product in the future. Product char-
acteristics change over time and it be should be explicitly modeled or else, will misstate
the effects. Consumers in the durable goods market are indeed forward-looking in their
behavior and ignoring this forward looking aspect leads to inaccurate results (Melnikov,
2001) and tend to delay their purchase to get a better price in the future Nair (2007). Sim-
56
ilarly, Chen et al. (2008) estimate a full equilibrium dynamic model of both primary and
secondary markets and shows that ignoring the dynamic nature of the decision problem
biases the demand estimates.
In light of this evidence we formulate the replacement decision using a dynamic dis-
crete choice model where forward looking consumers have expectations about how the
new product marketing mix will evolve as well on how their current product will depre-
ciate. They then trade off the utilities from these two alternatives and make the utility
maximizing choice. By modeling both the new and used product utilities we correct for
potential biases that models which ignore one or both of these utilities might produce.
4.3 Model
We build a dynamic structural model of replacement choice, where in each period, con-
sumers choose between buying a new product or retaining their current product. In making
these decisions, consumers factor in the utility from immediate consumption as well as that
which will accrue in the future.
Most previous models of durable product choice treat the currently owned product as
an outside option which is not included in choice set. The utility from the outside option is
normalized to zero implying that consumers do not derive any utility from it. In practice,
consumers do receive a non-zero utility from the current product and not considering this
will over state the replacement elasticity.
Consideri = 1N consumers choosing from amongj = 0; 1:::J products in each
decision epoch. The currently owned product is denoted asj = 0, with the available re-
placements products denoted asj = 1J. Each consumer makes a decisiony
it
= j in
each periodt = 1T on whether to replace his current product with a replacement prod-
uct. Herej = 0 indicates the decision not to replace, whilej > 0 indicates the replacement
57
decision. In each decision epoch, the consumer maximizes his expected discounted utility
from a sequence of decisions
i
=y
i1
y
i1
made over an infinite time horizon. Thus, the
consumer’s problem can be stated as in Eqn 4.1 where2 (0; 1) is the discount factor of
future utility.
max

i
E[
1
X
=t

U
ijt
(s
it
;"
it
;)] (4.1)
Lets
it
be the set of variables observed by consumeri at timet. We refer tos
it
as the
state of consumer i at time t. Let be a consumer specific random demand shock and
denote as the set of parameters which are to be estimated, then the utility functions can
be parameterized in terms of the statess and the parameter asU
ijt
(s
it
;
it
;).
We define the utility from the currently owned product j = 0 to consumer i in time
t as a function of the product characteristics s
0t
and an unobserved shock ". The utility
specification is given in Eqn 4.2.
U
i0t
(s
it
;"
it
;) =
a
age
t
+
m
mileage
t
+"
i0t
(4.2)
Given the utility from the currently used product, we assume that in each decision
epoch, the consumer observes a set of replacement products, and chooses the utility max-
imizing option from among this set. The utility from this option is compared against the
utility from the current product and a decision is made on whether to replace the current
product with the utility maximizing new product. We specify the utility from the replace-
ment productj as a function of its price and promotion. The utility specification is given
in Eqn 4.2.
U
ijt
(s
it
;"
it
;) =
j
+
p
price
jt
+"
ijt
(4.3)
58
The value to the consumer of being in a states is given by the value functionV (s;;)
and is given by the Bellman equation derived from Eqn 4.1 as
V (s
i
;"
it
;) = max
y
it
[U
ijt
(s
i
;"
it
;) +EV (s
0
i
;"
0
i
js
i
;"
i
;y
it
;)] (4.4)
wheres
0
indicates the states that the consumers are expected to be in the future. The
value function consists of two parts - the current period utility U and the expected dis-
counted utility EV that the consumer can derive from being in the current state s and
taking actionj. We assume that the consumer decision process is stationary. This implies
that the value of being in states is independent of the time and therefore being in the same
state at different decision epochs provides the consumer the same value. Due to the recur-
sive nature of the Bellman equation, it has no closed form solution and we have to estimate
it using a contraction mapping algorithm known as value function iteration (Rust, 1987),
which is described in the next section.
Computationally, it is better to estimate Eqn 4.4 using the choice specific value func-
tions which is the value of being in state s and taking action j as in Eqn 4.5. Doing so
transforms the value function to a form common in discrete choice model which consists
of a deterministic component and stochastic unobserved component. Note that the value
function in Eqn 4.4 is just the maximum over the choice specific value function.
V
ijt
(s
it
;"
it
;
i
) =U
ijt
(s
it
;
it
;) +EV (s
0
;"
0
js;";y
it
=j;
i
) (4.5)
If we assume that the unobserved component of utility in Eqns 4.2 and 4.3 is distributed
Type I Extreme Value, the probability of replacement (Rust, 1987) at timet is given by
P (y
it
=j) =
exp(V
ijt
)
P
J
k=0
exp(V
ikt
)
(4.6)
59
4.3.1 Estimation
In order to be able to calculate the likelihood, we need the to compute the value function
given in Eqn 4.4. In practice it is easier to calculate the choice specific value function
in Eqn 4.5. As pointed out previously, there is no closed form solution to compute this
function, so we use a contraction mapping algorithm known as value iteration to compute
a numerical solution to the value function (Rust, 1987).
The value iteration algorithm proceeds as follows. Given we can compute the current
period utility from Eqns 4.3 and 4.2. We assume a random starting value for the value
function forV and denote it asV
n
(s). We useV
n
on the right hand side of Eqn 4.5 to get
a new estimate of the value functionV
n+1
(s). We then assignV
n
= V
n+1
and repeat the
iterations untiljV
n+1
V
n
j< where is a tolerance value.
A key problem with the above method is that since the state variables are continuous,
it is not feasible to compute it at all possible values ofs. One solution to this problem is
to discretize the state space into a finite set of grid points and compute the value function
at those points (Rust, 1987). But, in order to obtain a good approximation to the contin-
uous value function, we have to calculate the value function using a very fine grid which
increases the computational burden.
One solution to this problem was proposed by Keane and Wolpin (1994) which aug-
ments the above technique with a suitable approximation method. We discretize the state
space into as many grid points as is computationally feasible and compute the value func-
tion at those grid points. We then use a suitable approximation technique (e.g., regression,
Chebyshev polynomials, splines, etc) to map the values to the grid points which constitute
the state space. We then use this approximation function to predict the value function at
any state.
We estimate the model using Rust’s Nested Fixed Point (NFXP) algorithm. In order to
60
compute the likelihood, assume that
ijt
are Type 1 extreme value distributed. Then, the
probability of replacementy
it
=j is given by Eqn 4.6. The likelihood for single consumer
is given by Eqn 4.7 and the overall sample loglikelihood is given in Eqn 4.8.
L
i
(s
i
;y
i
j) =
T
Y
t=1
P (y
it
js
i
;
i
) (4.7)
LL(s
i
;y
i
j) =
N
X
i=1
log
T
Y
t=1
P (y
it
js
i
;) (4.8)
4.4 Data
We use the JD Power PIN dataset for our analysis with the midsize sedans as our focal
product category. Previous results have shown that the change in replacement decision
ranges from about a year to 14 months (Bayus, 1988). Thus, we use two years worth of
transactions to estimate the model. Since we are interested in modeling the replacement
decision and need information on the currently owned product, we limit the data to those
transactions which include a trade-in transaction. The model is estimated using transactions
from the Los Angeles market for the period from 2005 to 2006.
The top 3 models, listed in Table 4.1, which were sold during this period are the Honda
Accord, Toyota Camry and Nissan Altima which together account for about 68% of trans-
actions with trade-ins. These three models along with the Honda Civic and Toyota Corolla,
listed in Table 4.2, are the most commonly traded in models and account for nearly 34%
of all overall trade-in transactions. So we limit for our analysis to those transactions where
one of Accord, Camry or Altima was bought while one of Accord, Camry, Altima, Civic
or Corolla was traded in.
Since we are using a dynamic model, it is not computationally feasible to estimate the
61
Model Trans. Percent
Nissan Altima 4957 26
Honda Accord 4006 21
Toyota Camry 3993 21
Table 4.1: Top selling models in the midsize sedans segment
Model Trans. Percent
Honda Accord 1716 9
Toyota Camry 1599 8
Nissan Altima 1558 8
Honda Civic 1004 5
Toyota Corolla 680 4
Table 4.2: Top Trade-in models
model separately on each new model included. We therefore, create a composite car by
aggregating the cars in stock across dealer in each period. Thus, a consumer who is making
a replacement decision is choosing between buying a composite new car or retaining their
current car.
We also have to impute the monthly marketing environment for the new cars as well
as create the evolution in age and mileages for the currently used car. We use transaction
data to go back in time to recreate the monthly market environment. For each month, we
compute the median price of all available new cars included in our sample in that period
and use it as the representative price for the new product. We observe the odometer mileage
at trade-in and we know the model year of the trade-in vehicle. Using this, we prorate the
monthly mileage for each month either to start of the model year (e.g, Jan 2002 for a 2002
model year car) or 2000 Jan, whichever comes first. The summary statistics of the data are
shown in Table 4.3
62
Model Price Miles
Accord 21566 82655
Altima 21251 61093
Camry 21191 80924
Civic - 69438
Corolla - 62823
Table 4.3: Summary statistics of includes models
4.5 Results
We setup and estimated three models - a full model as specified in Section 3.2, a new
product purchase model where the current product utility is set to zero and a used prod-
uct replacement model where the new product utility is set to zero. All three models are
dynamic models where consumers are forward looking in their utility.
The estimates from the three models are shown in Tables 4.4, 4.5 and 4.6. The fit of the
three models are measured using the loglikelihood values at the estimated parameters. The
full model fits the data better than the other two models indicating that consumers factor
in both the new product utility as well as used product utility when making replacement
decisions. It also emphasizes the importance of modeling both the new product marketing
mix and current product depreciation in a durable product demand model.
Compared to the full model, the restricted models tend to under state the price sensitiv-
ity parameter as well as the consumer response to mileage and age. The reduced sensitivity
to price is also evident from the price elasticity of demand shown in Table 4.7. We see that
the new alone model understates the price elasticity as compared to the full model.
These results also emphasize the importance of modeling both the new product market-
ing mix as well as the current product depreciation in durable product demand model. We
can thus conclude that ideally a new durable product demand model should factor in the
replacement decision by explicitly including the current product utility as well.
63
Parameter Est. SE

1
24:1365 0:0080
Promotion 0:0383 0:0008
Price 1:0240 0:0004
Mileage 0:0466 0:0012
Age 0:0293 0:0099
LogLikelihood 20912
Table 4.4: Estimates from Full Model
Parameter Est. SE

1
17:0692 0:0029
Promotion 0:0249 0:0003
Price 0:8288 0:0001
LogLikelihood 21103
Table 4.5: Estimates from New alone Model
4.6 FutureWork
Our analysis in the previous section demonstrates the importance of accounting for both
the new product marketing mix and used product characteristics in durable product de-
mand model. The models employed are homogeneous models which treat all consumers as
having the same preference. Ideally, a fully heterogeneous model with individual specific
parameters should be employed in order to tease our differences among different segments
of consumers.
The computational complexity of including level heterogeneity in the model is huge.
The value function is conditional on each consumer’s parameters
i
and therefore will have
to be computed for each of the R draws of
i
required to integrate out the probabilities
when using a simulated maximum likelihood to estimate the model. Thus, to evaluate the
likelihood at one candidate parameter, we will have to performNSR contraction
mapping iterations, where N is the number of consumers and S is the number of states,
which can take an enormous amount of time.
64
Parameter Est. SE

1
2:5871 0:0060
Mileage 0:0510 0:0009
Age 0:0602 0:0074
LogLikelihood 23358
Table 4.6: Estimates from Used alone Model
Elasticity
Specification Own Cross
Full Model -0.0019 0.1542
New Alone -0.0018 0.1534
Table 4.7: Price Elasticity
Rather than take a brute force approach to incorporating heterogeneity, one can reduce
the computational burden by using an algorithmic approach. Ackerberg (2009) suggests
using an importance sampling approach along with a change of variable. The idea behind
this approach is that instead of having to compute the value function at each of the S draws
of
i
for each candidate, we change the variable of integration tou, compute the likelihood
at eachu and use importance sampling to generate a weighted likelihood for each candidate
. Our attempts at implementing this approach to reduce the computational burden has been
unsuccessful. In simulated analysis, the method appears to be very sensitive to the starting
value and thus the estimated parameters. The convergence of the method is very unreliable.
As such, we do not have confidence in implementing this method to obtain stable estimates.
We plan to explore other alternatives to incorporate heterogeneity, such as the two step
method proposed in Arcidiacono and Miller (2011). We feel that the two-step approaches
to estimating dynamic models will be more scalable than methods derived from the Nested
Fixed Point approach used in this chapter.
65
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Abstract (if available)

Abstract The question of whether and how used versions of a durable product impact the sales of the new version has interested marketers and economists for a long time. There has been relatively little empirical research into the substitutability of new and used versions of a product and its implications for manufacturers and retailers. The decision to buy a new durable product involves two sub‐decisions: a) whether to replace the existing product, and b) if yes, which new product to buy? This dissertation conducts empirical research on both these decisions to provide insights into how the used durable product impacts different aspects of consumer demand in real world markets and to uncover its implications for durable goods manufacturers and dealers.

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University of Southern California Dissertations and Theses

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Asset Metadata

Creator Jayarajan, Dinakar (author)

Core Title Essays on the competition between new and used durable products

School Marshall School of Business

Degree Doctor of Philosophy

Degree Program Business Administration

Publication Date 07/14/2014

Defense Date 05/05/2014

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag durability,durable products,OAI-PMH Harvest,replacement,structural models,Used Cars

Format application/pdf (imt)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Siddarth, Sivaramakrishnan (committee chair), Dukes, Anthony (committee member), Luo, Lan (committee member), Ridder, Geert (committee member), Yang, Botao (committee member)

Creator Email dinakar.jayarajan@gmail.com,jayaraja@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c3-438310

Unique identifier UC11286886

Identifier etd-JayarajanD-2675.pdf (filename),usctheses-c3-438310 (legacy record id)

Legacy Identifier etd-JayarajanD-2675.pdf

Dmrecord 438310

Document Type Dissertation

Format application/pdf (imt)

Rights Jayarajan, Dinakar

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA