Sincerest Form of Flattery?
Product Innovation and Imitation
in the Automobile Industry
Jeff Thurk∗
January 2017
Abstract
I study the impact of imitation on the returns to innovation in a differentiated product
industry. After Volkswagen’s introduction of the tdi diesel engine in 1989 and the
technology’s subsequent imitation by rival European firms, market penetration of diesel
cars in Europe increased from 10% to over 50% in ten years. I estimate an equilibrium
discrete choice, oligopoly model of horizontally differentiated products using a flexible
framework which nests several models of demand commonly used in the empirical
literature. Imitation benefited consumers by increasing product variety and reducing
prices 0.63% on average. Though imitation limited Volkswagen to attain only 14%
of the potential profits from the tdi, Volkswagen’s ability to differentiate its diesel
models made the tdi a worthwhile investment. Thus, differentiated product markets
may simultaneously promote dynamic (i.e., new products) and static (i.e., low prices)
efficiencies when imitation risk is high.
Keywords: Innovation, Imitation, General Technology, Diesel Cars.
JEL Codes: O31, O33, O34, L62.
∗
University of Notre Dame, Department of Economics, 919 Flanner Hall, Notre Dame, IN 46556. Phone:
574-631-3083. E–mail: [email protected]; http://www.nd.edu/ jthurk/
1 Introduction
Economic growth depends fundamentally on the willingness of firms to invest in developing
new technologies (Schumpeter, 1942; Lucas, 1988; Romer, 1990), while the ability of rivals
to easily imitate these innovations limits the incentive to innovate potentially leading to
sub-optimal investment (Aghion, Harris, Howitt, and Vickers, 2001). When goods are
differentiated, however, a firm may be able to minimize the effects of imitation by leveraging
other characteristics of its product (Petrin, 2002).
I study this trade-off in the context of the European automobile industry where
the introduction of the turbocharged direct injection (tdi) diesel engine by volkswagen
in 1989 took diesel passenger automobiles from a niche product category to the dominant
European engine choice in less than a decade – a dramatic transformation which has largely
failed to attract the interest of innovation economists.1,2 These new turbodiesel engines were
significantly quieter, cleaner (i.e., no black smoke), and more reliable than their predecessors
while maintaining superior fuel efficiency and torque relative to comparable gasoline models.
While volkswagen did patent technology associated with the tdi, the quick introduction
of turbodiesels by rival European firms such as psa and renault indicates the technology’s
generality was difficult to defend.3
Using automobile registration data from Spain – a
country which exhibited diesel adoption rates representative of Europe as a whole – I ask
two questions: What was the impact of imitation on equilibrium prices and profits? Did
imitation of the tdi make the innovation an ex post poor investment?
I answer these questions by estimating an equilibrium discrete choice oligopoly model
to study an industry which is far from competitive and where products are horizontally
differentiated. The structural demand-side model provides for flexible substitution patterns
across automobile characteristics and segments while accounting for product characteristics
known to consumers and firms but not to the researcher. It also nests a variety of models
commonly employed by researchers in the empirical industrial organization literature (logit,
nested logit, and random coefficients) so I place fewer restrictions on the substitution pat1
2
3
See Automobile Registration and Market Share of Diesel Vehicles in “ACEA European Union Economic
Report,” December 2009. This quick adoption process compares favorably to many others innovations
such as steam and diesel locomotives (Greenwood, 1997); the basic oxygen furnaces for steel mills (Oster,
1982); and the coal-fired, steam-electric high-pressure power generation (Rose and Joskow, 1990).
Perhaps a plausible explanation for this state of affairs is that well over two decades after the tdi
breakthrough the European automobile market remains an oddity in the global automobile industry as
diesel passenger vehicles failed to succeed anywhere else except, recently, in India. See Chug, Cropper,
and Narain (2011).
It is the generality of this technology what allows it to be imitated and reused easily by other manufacturers,
a good example of limited appropriability of profits of innovations of general purpose technologies that can
be recombined and reused in other applications. See Bresnahan (2010).
–1–
terns ex ante. The addition of a Bertrand-Nash pricing equilibrium not only increases the
identification of product elasticities (Reynaert and Verboven, 2013) but also allows for the
analysis of alternative counterfactual equilibria.
In this framework consumers consider a variety of product characteristics when making their purchase decisions leading to greater competition among firms with similar product
sets (in characteristic space). Consequently, the model allows for greater competition in the
diesel segment after the introduction of turbodiesels by rival European firms while the rich
substitution patterns extend competition to the gasoline segment as well. The estimated
model, therefore, disciplines the answers to the above questions by modulating the degree
to which product differentiation mitigates imitation risk.
I find that rival firms’ introduction of diesel engines based on the same technology as
the tdi limited volkswagen to capture only 14% of the potential innovative rents associated
with the tdi during the sample though the impact of imitation varied significantly across
firms. For instance, the introduction of turbodiesels by psa and renault generated substantial losses for volkswagen as these firms both introduced a large number of turbodiesels
and had product portfolios which competed heavily with volkswagen automobiles. During
the early part of the 1990s, however, Asian automakers like toyota and nissan were less
inclined to introduce their own turbodiesel models and relied instead on the their fuel-efficient
gasoline models to attract consumers. When they did introduce diesels later in the decade,
I find the impact on volkswagen profits was negligible.
It would be tempting to conclude that imitation made the tdi a poor investment.
Using a simple model of innovation and imitation, I show just the opposite as consumer
demand for the tdi increased overall market size while volkswagen’s ability to differentiate
its diesel models enabled the firm to generate substantial profits from its turbodiesels. I find
the vehicles accounted for nearly one-quarter of the firm’s profits at the beginning of the
sample when the tdi was new and 60.1% of its estimated profits by the year 2000 when
customer adoption had reached its steady-state. Overall, the firm generated e3.3 billion in
profit from its tdi diesel fleet during the sample. When we account for cannibalization of
gasoline models as well as the replacement of pre-existing diesel engines based on the legacy
technology, volkswagen’s benefit from the tdi ranges from e1.9 billion to e2.3 billion.
The story of the tdi, therefore, is one in which the innovator generated a lot of
profit from its innovation despite widespread imitation while consumers benefited from increased variety and low retail prices. Thus, the market equilibrium simultaneously delivered
both dynamic (i.e., a new product) and static (i.e., low prices) efficiencies leading to an
unambiguous increase in welfare as both firms and consumers benefited from the technology.
–2–
Moreover, it did so for a technology in which patents – the most common public policy tool
to encourage innovation – proved to be ineffective. This is significant since patent protection
itself creates a distortion by promoting dynamic over static efficiencies.
The remaining paper is organized as follows. I review this paper’s contribution to
relevant literature in Section 2 and discuss Volkswagen’s introduction of the tdi innovation,
its imitation by European auto makers, and summarize the main features of the Spanish
market for diesel automobiles in Section 3. In Section 4, I describe the equilibrium model of
discrete choice demand for horizontally differentiated products as well as the corresponding
supply-side pricing model. Section 5 describes the estimation approach, discusses identification, and reports the estimation results. In Section 6, I use a series of counterfactual
experiments to measure the effect of imitation on equilibrium prices and profits. Finally,
Section 7 summarizes the results and contribution as well as discusses avenues for future
research. Details of the estimation, additional results, data sources, and institutional details
of the Spanish automobile market are documented in the Appendix.
2 Related Literature
In this paper, I study the impact of imitation on dynamic and static efficiency. As such, it
contributes to a large literature on competition, innovation, and imitation which dates back
to Schumpeter (1942) who argued that temporary market power was needed to encourage
innovation. He theorized the long run benefits of new ideas (e.g., new products, better
processes) generate dynamic efficiencies which swamp any temporary static inefficiencies due
to market power.4 Imitation of a new technology by rival firms, however, extracts surplus
from the innovating firm. In a rational expectations equilibrium, the innovator internalizes
this risk leading to low levels of equilibrium innovation – a point addressed by Aghion
et al. (2001). Patent systems therefore provide a state-sanctioned monopoly to guarantee
temporary rents to the innovator (i.e., a static inefficiency) in hopes of increasing equilibrium
levels of research.
Whether imitation does actually impede innovation is fundamentally a quantitative
issue.
My finding that imitation and innovation can coexist even when the former is
significant adds to a growing concern that modern patent systems do more harm than
good.5 For instance, Boldrin and Levine (2008) argue the first-mover advantage inherent
in the innovative process is sufficient to drive research. In my data, however, there appears
4
5
See Gilbert (2006) and Cohen (2010) for a comprehensive literature review.
See Hall (2009) for a review
–3–
to be little if any first mover advantage as imitation is nearly contemporaneous with the
introduction of the tdi. Instead, I identify a new channel for innovation under imitation
risk as I show the introduction of a new product can grow the size of the pie while product
differentiation enables firms to each secure their piece.
There are also several related papers in the industrial organization literature. Petrin
(2002) uses the random coefficients model of Berry, Levinsohn, and Pakes (1995) – a workhorse
model in the empirical literature – to show chrysler’s introduction of the minivan generated
significant profits for the firm despite imitation by gm and ford. Moreover, he finds only
minor effects from imitation since these firms built their minivans on downsized versions of
full-sized van platforms. The consequence was a rear-wheel drive vehicle which was difficult
to maneuver whereas the front-wheel drive chrysler minivan handled similar to a passenger
car. In other words, chrysler was able to protect its minivans via product differentiation
– a similar conclusion to the one presented here. My contribution, therefore, is to show that
product differentiation can be an effective tool even when effects of imitation are large.
It is perhaps more appropriate to think of the automobile industry as a dynamic
game where manufacturers choose investment, imitation, and product characteristics in an
initial stage and then choose price conditional on their product portfolios. While appealing,
incorporating both dynamic and static effects in a tractable empirical framework is difficult
since doing so requires the researcher to address issues of endogenous firm beliefs and multiple
equilibria, both of which are exacerbated when goods are differentiated. Miravete, Moral,
and Thurk (2016) consider a two-stage game where firms simultaneously choose vehicle
characteristics (e.g., fuel efficiency) and then choose equilibrium prices.
Though firms
may have different beliefs regarding competitors’ attribute choices, they understand their
attribute choices influence equilibrium prices of automobile manufacturers through own and
cross-price effects. In contrast, I take observed product characteristics as given – a standard
assumption – but consider a richer model of consumer demand in order to generate better
substitution patterns. This places greater emphasis on the heterogenous firm-level effects of
imitation, particularly across different areas of product characteristic space.
Other authors evaluate the dynamics of innovation using models with little product
differentiation. A recent paper by Rust, Gillingham, Iskhakov, Munk-Nielsen, and Schjerning
(2016) studies dynamics within the Danish automobile industry but the authors simplify
static competition significantly to make the model tractable.6 Goettler and Gordon (2011)
use a quality-ladder model to show that competition by AMD led to lower innovation rates
by the industry leader Intel while Igami (2015) studies the dynamic effects of innovation in
6
Specifically, cars differ only in their type (i.e., diesel or gas engine) and age.
–4–
the hard drive industry – an industry with sufficient product homogeneity that he models
firm competition as Cournot. Interestingly, he also finds that patent protection decreases
firm innovation and overall welfare.
Answers to the research questions posed here, however, depend critically on the
impact of imitation on both dynamic and static efficiency, or equivalently on the prices
facing consumers both with and without imitation. I therefore focus my efforts on a feasible
extension of the Berry et al. (1995) framework to generate realistic substitution patterns
among differentiated goods taking volkswagen’s decision to introduce the tdi as well as
its imitation by other firms as given. This places greater emphasis on effectively measuring
the impact of imitation on retail prices and static profits. The issue of dynamic efficiency
then centers on addressing whether the tdi was a worthwhile investment for volkswagen
given the imitation risk posed by its rivals. My results, therefore, amount to an ex post
analysis of the incentive to innovate under imitation risk in differentiated goods markets.
3 The European Market for Diesel Automobiles in the 1990s
This section familiarizes the reader with the basic characteristics of the turbodiesel technology and the evolution of the Spanish automobile industry.
3.1 A Significant Innovation - Next Generation Diesel Engines
In the late 19th century, Rudolf Diesel designed an internal combustion engine in which heavy
fuel is injected into a cylinder and self-ignites due to levels of compression much greater than
a gasoline engine. However, it was only in 1927, many years after Diesel’s death, that the
German company Bosch built the injection pump that made the development of the engine
for trucks and automobiles possible. The first diesel vehicles sold commercially followed soon
after: the 1933 Citroën Rosalie and the 1936 Mercedes-Benz 260D. Large passenger and
commercial diesel vehicles became common in Europe in the late 1950s, while preferential
fuel taxation beginning in 1973 enabled diesel passenger cars to maintain a small but stable
market share.7
7
See Miravete et al. (2016) for a more thorough discussion of initial market conditions behind the diesel’s
success.
–5–
In 1989, Volkswagen introduced the turbocharged direct injection (tdi) diesel engine
in its Audi 100 model, a substantial improvement over the existing Perkins technology.8
A tdi engine uses a fuel injector that sprays fuel directly into the combustion chamber
of each cylinder. The turbocharger increases the amount of air going into the cylinders
and an intercooler lowers the temperature of the air in the turbo, thereby increasing the
amount of fuel that can be injected and burned. The result was an diesel-powered engine
which was significantly quieter, cleaner (i.e., no black smoke), and more reliable than their
predecessors while maintaining superior fuel efficiency and torque relative to comparable
gasoline models.9 For the average driver, greater torque makes the driving experience more
enjoyable by increasing the responsiveness of the car.
3.2 Evolution of Automobile Characteristics
The data include yearly car registrations by manufacturer, model, and fuel engine type in
Spain between 1992 and 2000. Retail prices and vehicle characteristics are from La guı́a del
comprador de coches (ed. Moredi, Madrid) where I aggregate trim types within a model by
selecting the price and characteristics of the mid-range trim version of each model, i.e., the
most popular and commonly sold. I further segment the cars into small, compact, sedan,
minivan, and luxury where the last includes sports cars.10
After removing observations with extremely small market shares (mostly luxury
vehicles) the sample is an unbalanced panel comprising 99.2% of all car registrations in Spain
during the 1990s.11 Spain was the fifth largest automobile manufacturer in the world during
the 1990s and also the fifth largest European automobile market by sales after Germany,
France, the United Kingdom, and Italy. In the sample automobile sales range from 968,334
to 1,364,687 units sold annually.
Figure 1 documents the evolution and composition of European automobile sales
during the 1990s. In particular we see that European diesel penetration (dashed line),
defined as the share of new vehicles sold with diesel engines, steadily increased over the
8
The 1987 Fiat Croma was actually the first diesel passenger car to be equipped with turbo direct-injection.
Whereas the Audi 100 controlled the direct injection electronically, the Fiat Croma was mechanical. The
difference proved crucial for commercial success as electronic controls improved both emissions and power.
9
See the 2004 report “Why Diesel?” from the European Association of Automobile Manufacturers (ACEA).
10
See “Euro Car Segment” definition described in Section IV of “Case No. COMP/M.1406 - Hyundai/Kia.”
Regulation (EEC) No. 4064/89: Merger Procedure Article 6(1)(b) Decision. Brussels, 17 March 1999.
CELEX Database Document No. 399M1406.
11
See Appendix A for further details.
–6–
Figure 1: Growth of Diesels (% New Vehicle Sales)
80
70
60
50
40
30
20
10
Spain
2010
2009
2008
2007
2006
2005
2004
2003
2002
2001
2000
1999
1998
1997
1996
1995
1994
1993
1992
1991
0
EU
Notes: Figure plots the growth in the percent of new car sales which have a diesel engine. Authors’
calculations. New passenger car registration data from Association Auxiliaire de l’Automobile
(AAA). In panel (a), European diesel penetration (dashed line) constructed gross domestic product
as weights (source: World Bank Development Indicators). Countries included: Austria, Belgium,
Denmark, France, Germany, Ireland, Italy, Luxembourg, Netherlands, Portugal, and the United
Kingdom.
1990s.12 Spain, the country of interest, exhibited growth representative of the continent as
a whole or even served as a leading indicator.13
It is common to see slow consumer adoption after the introduction of a new technology. Schumpeter (1950, p.98) theorized this was due to consumers waiting for incremental
improvements in the technology. This idea was later formalized by Balcer and Lippman
(1984) and was used by Manuelli and Seshadri (2014) to explain the half a century time
span needed for the diffusion of the much studied case of tractors. In contrast, the incredible
pace of adoption of diesel automobiles suggests that the tdi proved to be a significant
technological advance and consumers gained little from waiting for additional incremental
improvements.
The substantial growth in diesel sales was aided by an increase in supply. While
the tdi was only introduced to consumers in 1989, Table 1 shows that by 1992 a consumer
12
There is variance in the adoption of diesels across countries, however, as smaller countries such as Denmark
were slow adopters while France, led by Peugeot, adopted diesels earlier than Spain.
13
Initially in 1992, diesels represented only 16% of total sales but by the end of the decade diesels represented
54% of the market, growing from 161,667 to 732,334 units sold in years 1992 and 2000, respectively. Sales
of gasoline models were flat in 1993 and 1995, about 573,000, despite a scrappage program in 1994, when
they temporarily increased by 15%. While the sales of gasoline models has grown steadily since, it pales
in comparison to the growth of diesels.
–7–
Table 1: Diesel Imitation
1992
1994
1996
1998
2000
Gasoline Engines
97
109
124
135
134
Diesel Engines
- Volkswagen
- Fiat
- PSA
- Ford
- GM
- Mercedes
- Renault
- Nissan
- Rover
- BMW
- Mazda
- Mitsubishi
- Skoda
- Toyota
- Honda
- Hyundai
- Chrysler
- Kia
- Suzuki
- Daewoo
44
9
6
8
4
5
3
4
1
2
2
0
0
0
0
0
0
0
0
0
0
58
9
10
9
6
4
4
6
2
4
2
0
0
0
1
0
0
1
0
0
0
78
13
12
13
8
4
4
6
2
5
3
1
2
1
2
1
0
1
0
0
0
88
14
13
13
6
6
5
5
4
4
3
3
2
2
3
2
2
1
0
0
0
95
18
13
10
7
6
6
5
4
4
3
3
3
3
3
2
2
1
1
1
0
141
167
202
223
229
Total Offered
Notes: Automaker ownership groups sorted in descending order by number
of diesel models offered in 2000.
wishing to purchase a diesel had 44 models to choose from, or equivalently 31% of all new cars
models were equipped with diesel engines, most of which were turbodiesels. Of these, only
9 models were offered by volkswagen with the remainder being offered by rival European
firms. This indicates that not only was volkswagen unable to protect its tdi technology
from imitation by rivals, such imitation occurred quickly. For consumers, imitation increased
the number of diesel varieties by a factor of five across the sample and increased the consumer
product set 33% and 48% in 1992 and 2000, respectively.
Imitation was largely driven by rival European auto makers, particularly fiat and
psa. Asian automakers were slower to adopt the new technology and only began to enter
the space at the end of the decade.14
This suggests a low cost of imitation – a trait
which characterizes all “general technologies” (e.g., Bresnahan 2010) – due to the fact the
technology can be easily modified, reverse-engineered, or even licensed as in the case of
14
Asian imports include daewoo, honda, hyundai, kia, mazda, mitsubishi, nissan, suzuki, and
toyota.
–8–
many of the Asian car makers who chose not to develop the technology themselves but
rather purchased the diesel engines from European firms (e.g., toyota).15
When deciding what type of engine to purchase, drivers compare observable product
characteristics as well as likely related expected performance attributes of each engine.
Further, the difference between a diesel and gasoline version of a particular car model depends
on only what’s under the hood (i.e., they share the same chassis) so a consumer deciding
between aa Audi A4 gas or diesel car bases her decision on differences in performance not
car size. Diesel vehicles are about 10% heavier than similar gasoline versions; have 15% to
20% less horsepower; and are between one and two thousand euros more expensive. They
also consume 20% − 40% less fuel than a comparable gasoline model, enabling a diesel to
travel about 63% farther on a euro worth of fuel (Table 2).
Of course, engine type is not the only characteristic consumers consider when they
purchase a new car. Most purchases are in the compact, sedan, and small segments
though there is growth in the minivan segment across the decade largely driven by an
increase in vehicle choices in the segment.
Small vehicles are the least expensive and
most fuel-efficient options while luxury cars and minivans are just the opposite. Cars in
all segments are bigger and less powerful at the end of the decade and most are more
fuel-efficient. luxury cars, however, become less fuel-efficient (as do minivans) and more
powerful (i.e., hpw) over the sample. Overall, automakers at the end of the decade produced
cars which were 36.1% more expensive, are 4.4% larger, 11.6% less powerful (i.e., hpw),
2.3% more fuel-efficient in terms of mileage (i.e., c90), and 2.8% less expensive to drive
after accounting for higher fuel prices.
4 An Equilibrium Oligopoly Model of the Automobile Industry
In this section I present a structural equilibrium model of demand and supply where utilitymaximizing heterogenous consumers choose among a variety of car models each year and
vehicle prices are set among multi-product firms in a pure strategy Bertrand-Nash equilibrium. Since consumers consider a variety of product characteristics when making their
purchase decisions, there exists greater competition among firms with similar product sets
15
A natural question is why these Asian firms not offer their own turbodiesels. One possibility is that the
popularity of diesels was largely a European phenomenon so European auto makers chose to invest in the
technology since a significant portion of their profits came from European consumers whereas Europe was
a small market for Asian auto makers. The percent of revenue from the European market for bmw, psa,
renault, and volkswagen was 65%, 93%, 84%, and 74%, respectively, while for honda, mazda, and
toyota the shares are substantially smaller – 11%, 10%, and 8%, respectively (source: company 10-K
SEC filings).
–9–
Table 2: Vehicle Characteristics Available to Consumers
segment
models
share
price
c90
kpe
size
hpw
44
97
16.70
83.30
12.27
11.23
4.45
5.41
46.37
29.52
73.87
71.80
3.14
4.14
31
39
4
39
28
35.79
5.77
0.32
22.31
35.82
10.96
24.01
17.28
14.26
7.98
5.33
6.49
6.93
5.69
4.68
32.07
25.75
24.21
30.27
35.00
74.34
87.07
81.66
80.10
62.51
3.98
4.84
3.79
4.26
3.65
141
100.00
11.40
5.25
32.33
72.15
3.97
95
134
53.66
46.34
16.24
14.68
4.59
5.76
37.90
23.95
76.63
73.78
3.15
3.93
56
40
32
52
49
34.43
3.72
3.13
25.97
32.75
14.86
34.53
20.80
19.45
10.42
5.00
6.72
6.39
5.26
4.86
32.53
23.31
25.91
31.60
31.61
76.54
89.72
83.47
81.92
66.36
3.59
5.17
3.16
3.63
3.18
229
100.00
15.52
5.13
31.43
75.31
3.51
1992
By Fuel Type
Diesel
Gasoline
By Segment
Compact
Luxury
Minivan
Sedan
Small
Total
2000
By Fuel Type
Diesel
Gasoline
By Segment
Compact
Luxury
Minivan
Sedan
Small
Total
Notes: share is the market share as defined by automobiles sold. price is denominated in the equivalent of
thousands of 1994 euros and includes value added taxes and import tariffs. c90 is the fuel consumption (in liters)
required to cover 100 kilometers at a constant speed of 90 kilometers per hour. kpe is the distance, measured in
kilometers, traveled per euro of fuel. size is length×width measured in square feet. hpw is the performance ratio
of horsepower per hundred pounds of weight. Figure B.2 presents the distributions of these characteristics across
engine type.
(in characteristic space). The introduction of turbodiesels by rival European firms, therefore, leads to greater competition which erodes volkswagen’s market power and profits.
volkswagen’s ability to differentiate its vehicles from the competition mitigates this effect,
however.
4.1 Demand
Consumer demand is represented by a random coefficients nested logit (RCNL) discrete
choice framework introduced by Grigolon and Verboven (2014). The advantage of this model
is that it nests the logit, nested logit, and random coefficients models enabling the researcher
to fit a more flexible framework to the data.
– 10 –
Demand can be summarized as follows: consumer i derives an indirect utility from
buying vehicle j at time t that depends on price and characteristics of the car:
uijt = xjt βi∗ − αit∗ pjt + ξjt + ijt ,
where i = 1, . . . , It ;
j = 1, . . . , Jt ;
(1)
t = {1992, ..., 2000} .
where I define a product j as a model-engine type pair. This Lancasterian approach makes
the payoff of a consumer depend on the set of characteristics of the vehicle purchased, which
includes a vector of K observable vehicle characteristics xjt such as engine type, car size, or
fuel efficiency as well as others that remain unobservable for the econometrician, ξjt (e.g.,
reliability, leather interior) plus the effect of unobserved tastes of consumer i for vehicle j,
ijt .
An important component of (1) is that consumers have heterogenous responses to
changes in vehicle prices and characteristics:
αi∗
βi∗
!
=
α
β
!
+ ΠDit + Σηit ,
ηit ∼ F .
(2)
Consumer i in period t is characterized by a d vector of observed demographic attributes,
Dit , as well as a vector of random tastes, ηit distributed i.i.d. with cumulative distribution
function F commonly assumed to be standard normal. Π is a (n+1)×d matrix of coefficients
that measures the effect of a consumer’s demographics (e.g., income) on her valuation of
an automobile’s characteristics, including price. Similarly, Σ measures the covariance in
unobserved preferences across characteristics. A useful decomposition is to separate the
deterministic portion of the consumer’s indirect utility into a common part shared across
consumers, δjt , and an idiosyncratic component, µijt , given by:
δjt = xjt β + αpjt + ξjt ,
µijt = xjt pjt × ΠDit + Σηit .
(3a)
(3b)
I assume the idiosyncratic product j period t consumer valuations (ijt ) follow the
distributional assumptions of the nested logit literature, thereby increasing the valuations
of products within the same “group” or “nest.” Suppose there are g = 0, 1, ..., G groups
for which each car can be assigned to only one (i.e., segment) and define group zero as the
outside good. I can then write the idiosyncratic valuation as
ijt = ζigt + (1 − ρ)ijt
– 11 –
(4)
where ρ ∈ [0, 1], is assumed i.i.d. multivariate type I extreme value distributed, and ζigt
has the unique distribution for the group g to which product j belongs such that ijt is
extreme value – an assumption which is useful in constructing the purchase probabilities for
each agent. I call ρ the “nesting parameter” as its value modulates the importance of the
nests in explaining consumer purchases. As ρ goes to one consumers view products within
a group as perfect substitutes while ρ converging to zero drives within-group correlation to
zero. Plugging (4) into (1) yields:
uijt =
xjt βi∗
−
αi∗ pjt
+ ξjt +
G
X
1jgt ζigt + (1 − ρ)ijt
(5)
g=1
where 1jgt is an indicator variable equal to one when g is the group corresponding to product
j. From Equation (5) we can see the model’s flexibility. When Σ = 0 and ρ > 0 the model
collapses to nested logit. Alternatively, when ρ = 0 but Σ > 0 the model collapses to the
random coefficients model of Berry et al. (1995). When both Σ = 0 and ρ = 0 the model
returns the simple multinomial logit.
In each period t, a consumer i chooses the product j = 0, 1, ..., Jt which provides him/
her the most utility. Inclusion of the outside good (j = 0) in the consumer’s consideration
set allows him/ her to hold off a purchase decision for a future period. Define the set of
individual-specific characteristics leading to the optimal choice of car j as:
Aijt (x·t , p·t , ξ·t ; θ) = {(Dit , ηit , ijt ) |uijt ≥ uikt
∀k = 0, 1, . . . , Jt } ,
(6)
with θ summarizing all model parameters. The extreme value distribution of the random
shocks then allows us to integrate over the distribution of ijt to obtain the probability of
observing Ajit analytically where the probability (π) that consumer i purchases automobile
model j in period t is:
exp(Iigt )
,
exp(Iit )
" Jg
#
X
δmt + µimt
= (1 − ρ)ln
exp
1−ρ
m=1
!
G
X
exp(Iigt ) .
= ln 1 +
πijt =
where Iigt
Iit
δjt +µijt
)
1−ρ
Iigt
exp( 1−ρ
)
exp(
g=1
– 12 –
×
(7)
Finally, integrating over the distributions of observable and unobservable consumer
attributes Dit and ηit denoted by PD (Dt ) and Pη (ηt ), respectively, leads to the model
prediction of the aggregate market share for product j at time t:
Z Z
πijt dPDt (Dt )dPηt (ηt ) ,
sjt (xt , pt , ξt ; θ) =
ηt
(8)
Dt
with s0t denoting the market share of the outside option.
4.2 Pricing
In this section I append supply-side costs and pricing to the RCNL discrete choice demand
model. This serves two objectives. First, Reynaert and Verboven (2013) show the addition
of the supply-side pricing decision increases identification for the demand-side parameters,
particularly the price coefficient. Second, including a supply-side pricing decision enables
computation of equilibrium prices under alternative product sets – a component which will
be crucial for measuring both the static and dynamic implications of imitation.
Equilibrium prices are found as the solution to a non-cooperative pure strategy
Bertrand-Nash game among the competing auto makers. Specifically, static profit-maximization
by each firm f implies that equilibrium prices (pw ) can be written a nonlinear function of
the product characteristics (X), market shares s(x, p, ξ; θ), retail prices (p), and markups:
−1
pw
jt = mcjt + ∆t (p, x, ξ; θ)sjt (p, x, ξ; θ) ,
|
{z
}
bjt (p, x, ξ; θ)
(9)
where pjt = pw
jt × (1 + τjt ) and τjt is the import duty applicable to model j in period t, if any.
The vector of equilibrium markups bjt (·) depends on market shares sjt (·) and the matrix
∆t (·) with elements:
∆rj
t (x, p, ξ; θ) =

∂srt (x, p, ξt ; θ) ∂pjt


× w , if products {r, j} ∈ Jtf ,


∂pjt
∂pjt




0
(10)
otherwise .
where Jtf is the set of products offered by firm f in period t. Equilibrium prices are then a
function of consumer demand, import tariffs, and the portfolio of products offered by each
firm.
– 13 –
In estimating marginal costs I make a common assumption that firms have CobbDouglas cost functions of the following (log-linear) form:
log c = Zγ + ω .
(11)
where Z are logged observable characteristics and ω are cost components known to firms but
unobserved by the researcher.
5 Estimation
I define structural parameters of the model as θ = [β, Σ, Π, γ, ρ], the demand-side structural
error as ν D (θ) = ξ, and the supply-side structural error as ν S (θ) = ω. Under the common
assumption that the product set (and the corresponding characteristics) is exogenous so
that E[ξ|X] = 0 and E[ω|Z] = 0, demand and supply parameter estimates (β, Σ, Π, γ, ρ)
are recovered via a generalized method of moments (gmm) estimator (Hansen, 1982) using
observable product characteristics as basis functions to construct identifying moment conditions (H). The gmm estimator exploits the fact that at the true value of parameters (θ? ),
the instruments H are orthogonal to the structural errors ν D (θ? ), ν S (θ? ) so that the gmm
estimates solve:
θ̂ = argmin {g(θ)0 HW H 0 g(θ)} ,
(12)
θ
where g(θ) is a stacked vector of the demand and supply-side structural errors and W is the
0
weighting matrix, representing a consistent estimate of E[H gg 0 H].16
I construct the structural errors as follows. I solve for the mean utilities δ(θ) via
a contraction mapping which connects the predicted purchase probabilities in the model
to observed shares in the data for a given value of θ (see Grigolon and Verboven, 2014).
In constructing predicted aggregate shares, I follow Skrainka and Judd (2011) and use
a quadrature rule based on eight nodes. The demand-side structural error then follows
from (3a). Observed prices, ownership structure, and tariff rates plus equation (9) generate
marginal costs as a function of the parameter guess. The supply-side structural error then
follows from (11).
Knittel and Metaxoglou (2013) and Dubé, Fox, and Su (2012) point out that finding
a global solution to (12) is difficult since the objective function is highly non-linear so any
16
0
In constructing the optimal weighting matrix, I first assume homoscedastic errors and use W = [H H]−1
to derive initial parameter estimates. Given these estimates, I solve equation (12) and use the resulting
structural errors (ν D , ν S ) to update the weight matrix.
– 14 –
line, gradient, or simplex search will likely only result in a local solution. To increase the
likelihood of achieving a global minimum, I employ a state-of-the-art minimization algorithm
(Knitro Interior) starting from several different initial conditions – a strategy shown by Dubé
et al. (2012) to generate the global solution in monte carlo simulations.
5.0.1 Specification Bringing the model to the data requires the researcher to make explicit
assumptions about what characteristics consumers value when they purchase a new vehicle as
well as the set of potential supply-side shocks faced by firms. Consumer demand (both mean
and idiosyncratic) includes measures of automobile performance: horsepower divided by
weight (hpw), exterior dimensions (size), the cost of driving (kpe), and engine type (diesel)
where the inclusion of diesel as a random coefficient allows for different substitution patterns
within the diesel segment. I also include a constant random coefficient (constant) to
capture changes in substitution patterns due to the increasing product set and a linear diesel
trend (diesel × trend) in mean utility which I found helpful in explaining the increasing
popularity of diesel vehicles among consumers. I define the product nests as car segments
(i.e., small, compact, sedan, luxury, and minivan) thereby allowing for valuations of products
within a segment to be correlated. I limit the demographic interactions (Π) to be just the
interaction between price and income where I simulate individuals from yearly census data
to account for growth in income and the expansion of the Spanish economy.
The supply-side largely mirrors the demand-side with a couple modifications. First,
I include logged values of the continuous observed characteristics (hpw, size, and kpe).
Second, I replace kpe, which includes the effect of fluctuations in fuel price, with a measure
solely based on fuel-efficiency, c90. Consequently, audi’s choice of fuel-efficiency for a
gasoline model A4 impacts its cost directly as measured by c90, but demand for A4’s will
also be influenced by changes in the price of gasoline due to economic factors outside of
audi’s control. Hence, I include kpe in the demand rather than in the supply equation.
Similarly, I allow for increasing steel prices to impact the cost of producing larger, heavier
cars by multiplying car weight and size by an index for the price of steel. This leads to
shifts of hpw and size in supply but not demand. I also include brand (e.g., audi, bmw,
volkswagen) and segment (e.g., compact) dummies to account for differences in marginal
cost across these dimensions. Finally, changes in import tariff rates are accounted for in p
while changes in firm ownership due to mergers and acquisitions impact the ∆ matrix and
ultimately estimated marginal costs through Equation (9).17
17
See Appendix A for details on acquisitions and mergers in the European automobile industry during the
1990s.
– 15 –
5.0.2 Parameter Identification The parameter estimates are pinned down in the gmm
estimation via the instruments H. The intuition into how data variation (via H) identifies
different components of θ is as follows. Mean utility parameters β and cost parameters γ are
recovered using the linear projection outlined in Nevo (2000) using equations (3a) and (11).
Consequently, the mean utility vector β is identified by correlations between market shares
and observable product characteristics. The identification of γ follows from variations in
observable product characteristics and implied marginal costs where the latter depends on
variation in price and market shares (via the price coefficient, α) plus the shocks to fuel price
and steel prices. Hence, the components of X and Z are sufficient instruments.
I identify the remaining parameters (Σ, ρ, Π) using variation in the product set, the
distributions of distances in product characteristic space (e.g., size, hpw), prices, and
quantities. The price coefficient (α) is identified by changes in income, prices, and quantity
sold over the sample period. I construct instruments for the constant and diesel random
coefficients using the total number of products and diesel vehicles accounting for differences
in firm portfolios. Similarly, I construct an instrument for the nesting parameter ρ as the
number of other vehicles in a car’s segment after accounting for variation in firm product
portfolios.
I construct instruments for the hpw and kpe random coefficients by approximating
the “optimal instruments” of Chamberlain (1987) using “differentiation IVs” introduced by
Gandhi and Houde (2015).18 The idea is to use the distributions of product characteristics to
identify Σ by constructing cdf’s for each continuous characteristic based on the distances in
the corresponding product space. For example, we can construct a cdf for a 1995 Audi A4 in
kpe space by looking at the distance between between that model’s fuel efficiency and the fuel
efficiency of other models in that year. The addition or subtraction of fuel-efficient models
over time then impacts this distribution. When consumers value fuel efficiency, orthogonality
between ν d (θ) and this cdf is achieved by increasing the kpe random coefficient – a similar
intuition to the instruments used in Berry et al. (1995).
I operationalize this approach by replacing the large-dimensional cdfs with sample
statistics. Specifically, the period t instrument for product j and characteristic k is
k,λ
Hjt
(θ̂)
=
Jt
X
1(dkrj,t < cλ ) × dkrj,t
(13)
r6=j
18
See Reynaert and Verboven (2013) and Gandhi and Houde (2015) for a further discussion on instruments
and identification of discrete choice demand systems.
– 16 –
where cλ designates a cut-off in the cdf in which to construct the instrument and dkrj,t is the
distance in product characteristic space k defined as xkr,t − xkj,t . In practice, I chose cλ for
each characteristic such that the bins are evenly-distributed and set λ = 4, or equivalently
four identifying instruments for each of these continuous product characteristics.
5.1 Estimation Results
Estimation results are presented in Table 3. Overall, the estimates are reasonable, statistically significant, and congruent with the descriptive evidence of the industry from Section 3.
Significant parameter estimates for both the nesting parameter ρ and the random coefficients
(σ ∈ Σ) allows me to reject all three of the nested models common in the empirical literature:
logit, nested logit, and random coefficients, or equivalently the RCNL of demand fits the data
better than these alternative models.
Table 3: Demand and Supply Estimates for Different Specifications
Demog. Interactions (Π)
Random Coefficients (Σ)
Mean Utility (β)
Price/Income
HP/Weight
Size
KM/Euro
Diesel
Diesel-x-Trend
Constant
Trend
Non-Euro
Seat
Nest (ρ)
Coefficient
Rob. SE
2.3445
5.2133
0.8566
−12.9378
0.6322
−15.4655
0.0120
−1.1285
0.8421
0.2759
(1.5275)
(1.0631)
(1.1715)
(1.5114)
(0.0774)
(1.2234)
(0.0213)
(0.1735)
(0.2819)
(0.0880)
Coefficient
Rob. SE
−1.8236
2.4665
(0.2205)
(0.3060)
3.3593
3.8745
(0.0150)
(0.3594)
0.0547
(0.2663)
Cost (γ)
Coefficient
Rob. SE
0.7963
2.4352
0.2074
0.3537
−0.0034
0.0998
0.0028
(0.0667)
(0.1548)
(0.0709)
(0.0343)
(0.0039)
(0.1456)
(0.0036)
Statistics:
-
Avg. SW Elasticity
Avg. SW Margin
Number of observations
Simulated agents per year
J-Statistic
3.7
31.6
1,740
1,305
151.5
Notes: Robust standard errors in parentheses. Cost fixed effects for brand and segment not reported. “Margin” defined as
100 × p−c
where price excludes import tariffs, if applicable. Statistics for average “Elasticity” and “Margin” are weighted by
p
quantity sold (“SW”). Equilibrium prices account for year-specific ownership structure as reported in Appendix A.
The results indicate that diesels are more expensive to manufacture than gasoline
models. The marginal costs of production are also higher for larger, more powerful, and
fuel-efficient cars. The insignificant trend variables indicate there are no important efficiency
gains occurring during the decade in the production of either gasoline or diesel engines.
The estimation also accounts for differences in marginal costs by brand (e.g., Audi),
which I report in Figure 2 relative to the Spanish market leader, renault. Results are
– 17 –
very reasonable as German upscale brands audi, bmw, and mercedes, are among the most
expensive to produce while Chrysler and Asian imports such as daewoo, hyundai, kia,
and mitsubishi are relatively less expensive to produce. European manufacturers with lower
unit costs of production than renault, include the Czech brand skoda and the old Spanish
brand seat, both of them acquired by volkswagen to sell streamlined versions of their
vehicles targeting lower income customers. Another interesting case of relatively low cost of
production is ford, which produces most of its smaller European models in a large plant
located in Spain.
Figure 2: Production Cost Differences Across Brands
(Reference: Renault)
0.50
0.45
0.40
0.35
0.30
0.25
0.20
0.15
0.10
0.05
0.00
-0.05
-0.10
-0.15
-0.20
-0.25
-0.30
-0.35
-0.40
-0.45
-0.50
-0.55
-0.60
Volvo
Volkswagen
Toyota
Suzuki
Skoda
Seat
Saab
Rover
Peugeut
Opel
Nissan
Mitsubishi
Mercedes
Mazda
Lancia
Kia
Hyundai
Honda
Ford
Fiat
Daewoo
Citroen
Chrysler
BMW
Audi
Alfa Romeo
-0.65
The estimated demand curves are all downward slopping and elastic; amounting to an
average sales-weighted estimated price elasticity of 3.7 and an average 31.6% estimated pricecost margin. There is however substantial heterogeneity across products as the standard
deviation for the price elasticities and price-cost margins are 1.28 and 8.80, respectively.
This wide range of margins are due to heterogeneous valuation of cars’ characteristics at a
moment in time, the evolution of preferences over time, and the changing product offering
– 18 –
over the decade.19 Average estimated margins, both of gasoline and diesel vehicles, remain
quite stable, only decreasing very slightly during the middle 1990s. For both engine types,
the dispersion of margins grows during the last three years of the sample as a growing
economy increases dispersion of consumer incomes.
Estimates of Table 3 indicate that, all else equal, drivers favor gasoline over diesel
engines at the beginning of the sample (βDiesel < 0) but consumer attitudes towards diesels
improve across the decade (βDiesel
× T rend
> 0) due either to consumers learning about
these new turbodiesels or improvements in the technology. Consumers also prefer larger
cars (positive coefficient for size) after controlling for segment and other observable product
characteristics such as price. The average consumer is indifferent about performance and fuel
efficiency (insignificant coefficient for hpw and kpe in mean utility) though the significant
random coefficients for both characteristics indicate a great deal of heterogeneity. I also
find a large and statistically significant value for the diesel random coefficient indicating
that the substitution patterns between diesel cars are significantly different than between a
diesel and non-diesel car even after controlling for fuel efficiency. This suggests that other
product characteristics such as torque differentiate diesel cars from their gasoline-powered
competition.
The negative and significant estimate for non-eu combined with the positive and
significant estimate for the domestic brand, seat, indicates a “home bias” for domestic
brands – an empirical regularity in the international trade literature.20 Since the focus here
is on a specific industry rather than a set of bilateral trade flows across many sectors, I
can provide a more detailed interpretation. At this time, Asian imports were first sold in
the European market and were considered low quality, fuel-efficient alternatives to European
vehicles but they lacked both brand recognition as well as a widespread network of dealerships
for maintenance. Thus, the negative sign of non-eu is not surprising. Meanwhile, the
domestic brand seat was owned by the volkswagen group thus it could be that the
positive estimated coefficient is picking up demand characteristics brought to the company
via volkswagen but not observed to the econometrician.
19
Although ignoring the distinction between diesel and gasoline models, Moral and Jaumandreu (2007) show
that demand elasticities are smaller but also very heterogeneous across market segments and product life
cycle.
20
See Cosar, Grieco, Li, and Tintelnot (2015) for estimates of cross-country home bias in the automobile
industry.
– 19 –
Figure 3: Substitution Patterns
Distance in Product Space (0 = Near, 90 = Far)
Distance in Product Space (0 = Near, 90 = Far)
.015
Avg. Cross-Price Elasticity
Avg. Cross-Price Elasticity
.015
.01
.005
0
0
10
20
30
40
50
60
70
80
.01
.005
0
90
0
10
20
30
(a) hpw
Distance in Product Space (0 = Near, 90 = Far)
Dies-Dies
Avg. Cross-Price Elasticity
Avg. Cross-Price Elasticity
70
80
90
Gas-Gas
Diesel-Gas
.005
0
10
20
30
40
50
60
70
80
.03
.02
.01
0
90
1992
(c) kpe
1996
2000
(d) Fuel Type
.03
Avg. Cross-Price Elasticity
.03
Avg. Cross-Price Elasticity
60
.04
.01
.02
.01
0
50
(b) size
.015
0
40
1992
1996
Compact
Luxury
.01
0
2000
Sedan
Minivan
.02
Small
1992
1996
Compact
Luxury
(e) Segment (ref: Compact)
2000
Sedan
Minivan
Small
(f) Segment (ref: Sedan)
Notes: Panels (a)-(c) present average cross-price elasticity on product characteristic space where two products are “close” when
the observed product characteristic is similar (i.e., distance between is small). Panel (d) compares the average cross-price
elasticities across engine fuel types. Panels (e) and (f) compare average product elasticities within and across segments using
different reference segments.
– 20 –
The estimated model also generates reasonable substitution patterns (Figure 3).
Panels (a) - (c) document how the random coefficients Σ for continuous characteristics
such as hpw impact the cross-price elasticities. I do this by first solving for the distance
between each pair of products in a particular characteristic (e.g., hpw). I then divide the
product-pairs into deciles where the first decile correspond to pairs which are most alike. The
last step is to compute the average cross-price elasticity for each bin. From Figure 3, we see
that for all of the characteristics considered in the estimation, substitution between similar
products is much more likely than for products far apart in characteristic space. Since diesel
is a discrete variable, I show the average cross-price elasticity within and across fuel types
(panel d). Again, consumers are much more likely to substitute within fuel type.
Panels (e) and (f) document the impact of the nesting parameter ρ on cross-price
elasticities across segments. In panel (e) we see that the cross-price elasticity within compact
cars is roughly double than the cross-price elasticity between a compact car and the other
segments. In panel (f) we see the same is true for sedans though the magnitude is greater
and, of course, similar results hold for the remaining car segments as well.
6 Measuring the Impact of Imitation
With robust estimates of demand and supply in-hand, the objective in this section is to
measure the implications of imitation on static and dynamic efficiency. First, I show that
imitation led to significant price competition among European automakers though the effect
on volkswagen profits varied significantly across firms (Section 6.1). Second, I show that
while imitation enabled rivals to steal a substantial amount of potential business from the
tdi, volkswagen’s ability to differentiate its diesel models enabled the firm to generate
a lot of profit from its innovation. Hence, the tdi remained a worthwhile investment for
the firm (Section 6.2). This suggests that imitation, though significant, still provided for a
dynamically efficient outcome.
6.1 Imitation, Prices, and Profits
I begin with an evaluation of the static implications of imitation on volkswagen equilibrium
pricing and profits using an approach similar to Berry and Jia (2010) who address the effects
of low cost carriers in the airline industry. In Table 4, I compare the observed equilibrium
with two extreme counterfactual equilibria in order to quantify the effects of imitation on
equilibrium pricing behavior as well as volkswagen profits. In the first experiment I
consider the equilibrium where diesels are either not allowed by regulators or were simply
– 21 –
never developed by any automobile manufacturer.21 I call this experiment “No Diesel”
and use it to evaluate the value of diesels in general. Interestingly, in this experiment the
European auto market comes closest to replicating market shares in the North American
market where diesel vehicles maintained a negligible market share during this period.
In the second experiment, I consider the equilibrium in which volkswagen successfully defends its intellectual property and remains the sole producer of this next generation
technology. For simplicity I assume other automakers choose to remove their legacy diesel
passenger cars entirely from the product choice set since the advancements of the tdi in
terms of performance made these vehicles uncompetitive.22 volkswagen (including its
affiliate brands) is therefore the sole provider of diesel vehicles. These results are presented
in the column labeled “Monopoly.”
These two experiments therefore provide end-points of a spectrum. The task then is
to assess whether the observed equilibrium is closer to one in which volkswagen is able
to differentiate its innovation from the competition and thereby be largely unaffected by
imitation (as in Petrin, 2002) or whether imitation materially reduced the innovative rents
of the tdi.
Table 4: Value of TDI Technology to Volkswagen
1992
2000
No Diesel
Data
Monopoly
No Diesel
Data
Monopoly
Prices (eThousand)
- Diesel
- Gas
11.57
11.57
11.71
12.86
11.56
12.41
15.11
11.59
14.80
14.80
16.30
16.87
15.44
19.81
21.18
15.38
Market Share (%)
- Diesel
- Gas
18.98
18.98
17.79
11.90
18.97
23.20
100.00
18.81
19.08
19.08
22.31
25.11
19.05
50.33
100.00
19.32
Margin (%)
- Diesel
- Gas
38.35
38.35
37.57
31.57
38.32
38.93
40.12
38.57
34.85
34.85
30.76
29.03
33.41
41.16
43.10
34.91
616.54
0.00
616.54
656.67
69.81
586.86
867.21
262.83
604.39
667.89
0.00
667.89
1,385.68
833.39
552.29
4,438.82
3,793.59
645.23
Profit (eMillion)
- Diesel
- Gas
Notes: “Price” is in thousands of 1994 euros. “Market Share” is the percent share of cars sold in the respective
category. “Margin” is defined as p−c
where price includes tariffs. “Profit” is measured in millions of 1994 euros.
c
See Figure B.3 for the evolution of estimated price-cost margins across the decade.
From Table 4 we see that imitation created significant price competition among the
firms leading to lower prices for consumers. Had volkswagen been able to maintain
21
22
For example, due to strict standards regarding nitrogen oxide emissions. See Miravete et al. (2016).
While this assumption may be strong, I remind the reader that diesel passenger cars were a niche product
in the European marketplace before the introduction of the tdi.
– 22 –
monopoly power over the tdi, retail prices for diesel and gasoline powered automobiles
in 1992 would have been 17.5% and 0.3% greater, respectively, leading to a 6.0% increase
in the average price facing consumers. The fact that increased market power in the diesel
segment could also translate to changes in retail prices for gasoline vehicles is due to the rich
substitution patterns implied by the estimated demand model.
Changes in consumer demand (i.e., βDiesel−x−T rend > 0) plus growth in consumer
incomes over the decade exacerbate these effects. Retail prices for diesel and gasoline powered
automobiles in 2000 would have been 25.6% greater and 0.4% lower, respectively, leading
to a 21.5% increase in the average price facing consumers had volkswagen been able to
remain a monopolist – a significant difference.23 Furthermore, increased price competition
compressed volkswagen margins. Had volkswagen been able to maintain a monopoly
over diesel engines its overall margins would have increased from 37.8% to 38.9% in 1992 and
from 30.8% to 41.2% in 2000. We also see a significant increase in industry concentration as
23.2% of new cars are sold by a volkswagen brand in 1992 (up from 17.8% in the data)
and 50.3% of new cars are sold by a volkswagen brand in 2000 (up from 22.3% in the
data).
Imitation by rival firms not only applied downward pressure to volkswagen prices,
it also enabled these firms to use their turbodiesel versions to cull volkswagen consumers.
The net result was significantly lower profits for the innovator. I show this by defining the
share of potential tdi profits which volkswagen was able to capture as:
“Rent Capture” ≡ 100 ×
π benchmark − π nodiesels
.
π monopoly − π nodiesels
(14)
Overall, imitation limited volkswagen to capture only 14.5% of the potential profits
from its innovation, though there is significant variation across the decade (Figure 4).
Estimated volkswagen profits in 1992 would have been 1.3 times larger (e210 million) than
the estimated equilibrium had the company been able to maintain dominance of the diesel
segment. Increasing consumer interest in turbodiesels (i.e., βDiesel−x−T rend > 0) increased
this factor to 3.2x (e3.1 billion) by the end of the decade.
Periods of low rent capture coincide with an economic downturn in Spain following
its accession into the EU while the periods of relatively high rent capture correspond to
periods of economic growth. Recall from the estimated model that consumers become
23
In the Appendix I consider the role of imitation in growing the potential market by exposing customers to
these next generation diesel vehicles. Even if consumer learning constituted only a small part of demand
of the growing demand for diesels, it still likely grew the market for volkswagen and mitigated some of
the business stealing effects.
– 23 –
Figure
4: Volkswagen’s
(%)
Capture
of InnovativeRent
RentsCapture
Over Time
20
19.0
17.8
16.5
16.0
15.6
15.0
15
10.6
10.3
10
9.6
5
0
Notes:
1992
1993
1994
1995
1996
1997
1998
1999
2000
π benchmark −π nodiesels
is the percent of profits
π monopoly −π nodiesels
from the tdi where (π nodiesels , π benchmark , π monopoly )
“Rent capture” = 100 ×
volkswagen was able to capture
are the volkswagen profits when diesels do not exist, in the current equilibrium, and
when the company maintains a monopoly over diesels, respectively.
less price-sensitive as incomes grow enabling firms to charge higher margins. The fact
that volkswagen’s rent capture appears to be pro-cyclical indicates that that its product
portfolio was better able to capture this growth. Moreover, this result suggest that business
stealing in differentiated goods industries depends not only on product characteristics but
also on the demand elasticities which are themselves a function of consumer characteristics
such as income.
Figure 5: Imitation, Business Sealing, and Static Efficiency
Fitted Values
PSA
Renault
Others
Fitted Values
PSA
Renault
Others
Percent Change in VW Price
Percent Change in VW Profits
2
30
25
20
15
10
5
0
1
0
0
5
10
15
20
Percent of Diesels No Longer Offered
0
5
10
15
20
Percent of Diesels No Longer Offered
(a) VW Profits
(b) VW Prices
Notes: Panels (a) and (b) present the change in VW profits and average retail prices, respectively, as a function of the diesel
offerings of rival firms. For each observation I begin from the observed product portfolios and remove a rival firm’s line of diesel
automobiles. The x-axis is the percent reduction in diesel models available to consumers.
– 24 –
When goods are differentiated and firms are heterogenous the impact of imitation
likely varies significantly across firms. In panel (a) of Figure 5, I evaluate this hypothesis
by looking at the impact of firm-level imitation on volkswagen profits. As expected,
removing diesel models decreases options for consumers leading to greater volkswagen
profits (dashed blue line) and the impact varies widely across firms. In particular we see that
psa and renault both invested significantly in developing their turbodiesel fleet leading to
greater negative effects on volkswagen profits. Asian manufacturers, on the other hand,
either invested little in supplying diesel models or had negligible impacts on volkswagen.
In panel (b) I conduct a similar analysis but instead look at the impact of imitation on
equilibrium volkswagen retail prices in order to assess the role of imitation in promoting
static efficiency. Removing a rival firm’s diesel portfolio would have enabled volkswagen
to increase retail prices 0.63% on average though imitation by psa and renault had much
larger effects: 1.24% and 0.91%, respectively.
How much business was psa and renault able to steal from volkswagen? In
Figure 6 I present the average change in volkswagen profits for each diesel model removed
(panel a) or introduced (panel b) by the firms. In panel (a) we see the average increase in
volkswagen profits from removing a psa diesel in 1992 was e1.4 million which is roughly
1.5 times greater than the average impact of a renault diesel (e910 thousand). Increasing
consumer interest in these vehicles led to greater effects by the end of the decade as the
introduction of a psa diesel in 2000 amounted to e5.4 million decline in volkswagen
profits. The impact of renault follows a similar pattern though less pronounced.
Figure 6: Business Stealing by EU Firms
Foregone Profits per Competitor Model
Renault
Foregone Profits per Competitor Model
PSA
Renault
300
5.40
5
4
3
2.51
2
1.44
1
0.91
Millions of Euros per Diesel Model
Millions of Euros per Diesel Model
6
1992
250
225
206.70
200
175
150
125
100
75
50
0
2000
(a) Reference Equilibrium: Data
284.23
275
25
0
PSA
24.95
20.27
1992
2000
(b) Reference Equilibrium: VW Diesel Monopoly
Notes: Panels (a) and (b) present the value (in 1994 euros) per diesel model introduced by the renault and psa. In panel
(a), I begin from the observed product portfolios and remove each rival firm’s line of diesel automobiles. The reported statistic
is the increase in volkswagen profits divided by the total number of diesel vehicles removed. In panel (b), I begin from the
counterfactual world in which VW has a monopoly and each firm’s observed diesel models. The reported statistic is the decrease
in volkswagen profits divided by the total number of diesel vehicles introduced.
– 25 –
In panel (b) I look at the effect of imitation had each rival firm been the sole
imitator of the tdi. I do so by beginning from the “Monopoly” counterfactual equilibrium
in which volkswagen is the sole provider of diesel vehicles. For each rival firm, I compare
this equilibrium to the one in which that firm but no other firms introduce a turbodiesel
alternative. While see a similar pattern as the one presented in panel (a), the effects are
much larger. In 1992, the introduction of a diesel model by either firm would have decreased
volkswagen monopoly profits by approximately e20 million. By 2000 introduction of a
renault diesel model reduced volkswagen profits by e284 million on average; greater
than the e207 million impact of the average psa turbodiesel. Moreover, the large differences
between panels (a) and (b) indicate the marginal effects of imitation decrease significantly
as the impact to volkswagen profits is largest among the first firms to imitate.24
6.2 Imitation and Dynamic Efficiency
Thus far I have demonstrated that imitation had a significant negative effect on volkswagen
profits. An open question among innovation economists is the role of imitation in inhibiting
firm investment. In this section I build a simple model of innovation to show the tdi was
still a good investment for volkswagen despite this significant level of imitation.
6.2.1 A Simple Model of Innovation In this section I present a simple model of innovation
to fix ideas about the trade-off facing an innovating firm. Define π(x, s) as profits of a
firm which sells a product of quality x and faces competitors who sell products of quality
s = {s1 , ..., sF −1 } where F is the total number of firms. I assume π is increasing in x (i.e., the
product quality produced by the innovating firm) and “decreasing” in the product quality of
the competition.25 The innovating firm can choose to invest in a new technology x0 > x but
to do so requires a one-time development cost of κ > 0. Similarly, a rival firm f can invest
to imitate the innovating firm’s technological innovation so that s0f > sf . The pay-offs for
the innovating firm which decides whether to innovate (V I ) or not (V N ) are
I
0
Z
V (x, s) = π(x , s) + δ
V (x0 , s0 )dH(s0 |x0 , s)
V N (x, s) = π(x, s) + δV (x, s) ,
24
25
(15)
(16)
There is a similar effect for equilibrium prices. See Figure B.4 in the Appendix.
For example, under Dixit-Stiglitz preferences the product qualities of the competition collapses into a single
measure of competition, the price index, so when the competition increases the quality of their products,
the price index falls leading to less profits for the innovating firm.
– 26 –
where V (x, s) is the innovating firm’s continuation value discounted by δ > 0 and H is
the imitation risk which the innovating firm perceives. In (15) we see two important forces.
First, there is a first-mover advantage for the innovating firm, via π(x0 , s), which increases the
returns to the innovation. On the other hand, imitation risk (via H), the second force, drives
down the firm’s future profits. If the firm chooses to not undertake the project (Equation 16),
I assume product qualities do not change, so period profits are fixed. The innovating firm
chooses to undertake the project if and only if
V I (x, s) − κ ≥ V N (x, s)
(17)
so the innovating firm also accounts for the cannibalization of profits under its current
technology. The project is valued by society (under marginal cost pricing) when
CSI (s) − κ ≥ CSN (s)
(18)
where CS(s) corresponds to aggregate consumer surplus under industry state (s). I call
an equilibrium dynamically efficient when a project valued by society (Equation 18) is
undertaken (Equation 17). Consider the case when a project is valued by society, then
dynamic efficiency is attained whenever an innovator can extract sufficient surplus from its
innovation to make the project worthwhile. Conversely, a project may not be undertaken
but nonetheless be valued by society (i.e., a dynamically inefficient equilibrium) when the
firm cannot extract sufficient rents from its innovation due to significant imitation by rivals.
– 27 –
6.2.2 Was the TDI a Worthwhile Investment? Thus far, I have shown that imitation of
the tdi limited volkswagen to attain only a small fraction of the potential profits. The
objective of this section is to evaluate whether the tdi was indeed a worthwhile investment
ex post, thereby providing insight into whether the equilibrium was dynamically efficient.
In Figure 7, I document the growing importance of diesels to volkswagen and the
European rivals who imitated the technology. From panel (a) we see significant growth in
diesel profits for all firms across the decade, while in panel (b) we see diesels become the
dominant profit source for these firms by the end of the decade. The estimates indicate that
volkswagen generated e3.3 billion in profits from sales of its diesel engines in the Spanish
market alone and e7.7 billion overall (i.e., V I ).
Figure 7: Importance of Share
Diesels
of Total Profits From Diesels
Diesel Profits Over Time
VW
Other European Firms
VW
2,400
2191.1
2,200
Diesel Profits
2,000
1,800
1,600
1,400
1252.4
1,200
1,000
833.4
807.9
800
600
415.8
400
200
Other European Firms
70
146.8
1994
1997
2000
Diesel Share of Total Profits (%)
2,600
60.1
60
48.3
50
56.1
46.0
40
30
31.0
25.0
20
10
0
(a) Diesel Profit (Millions)
1994
1997
2000
(b) Diesel Share of Profits
Pinning down a value for V N is difficult since the profits the firm would have attained
had it not introduced the tdi requires the researcher to take a stand on what the product
set would have looked like in this alternative reality. As before I consider two potential
counterfactual equilibria in order to provide bounds for V N . Under the first I consider the
“No Diesels” equilibrium from the static analysis (Section 6.1). In the second, I simulate
an environment where firms offer diesels under the previous technology. I do so by taking
advantage of two facts: (a) that diesel penetration at the beginning of the sample was small
and close to the penetration rate prior to the tdi’s introduction (≈ 10%), and (b) demand
estimates indicate a positive trend for diesel models (βDiesel−x−T rend > 0). If we interpret
βDiesel−x−T rend > 0 as a reduced-form representation of consumers learning about these new
turbodiesels, setting βDiesel−x−T rend = 0 eliminates this mechanism and forces consumers to
make decisions based on their perceptions of the old diesel technology. I call this experiment
“No tdi”.
– 28 –
Table 5: Value of TDI Technology
VN
Year
VI
No Diesel
No tdi
1992
1993
1994
1995
1996
1997
1998
1999
2000
656.67
495.82
587.19
620.83
703.67
860.74
1,078.19
1,267.22
1,385.68
616.54
465.41
508.19
515.23
600.93
554.90
682.44
730.53
667.89
656.67
480.89
543.59
542.86
567.03
623.43
752.67
812.20
825.97
Total
7,656.01
5,342.06
5,805.31
Notes: V I , V N corresponds to the total estimated profits (diesel
plus gasoline models) to the volkswagen group measured in
millions of 1994 euros in the estimated equilibrium and counterfactual environment without the tdi, respectively.
From Table 5 we see that both experiments tell a similar story – the tdi was very
successful innovation for volkswagen despite the large scale imitation by its rivals. When
we eliminate diesels altogether, total volkswagen profits fall by e2.3 billion over the
decade. Similarly, constraining consumer demand for the engines but maintaining growth
in the number of diesels with the “old” technology implies that volkswagen profits would
have fallen e1.9 billion during the period. Put differently, I estimate the value of the tdi (i.e.,
V I − V N ) to be e1.9 to e2.3 billion in the Spanish market alone. Extending the analysis
to the rest of Europe would only increase this estimate. Thus, the tdi was a successful
innovation provided the fixed costs of development (κ) were not enormous.26
26
I am unaware of fixed cost estimates for volkswagen to develop the tdi. As a point of reference,
however, the estimated fixed cost to build CERN’s Large Hadron Collider, the largest and most complex
machine ever built, is e4.6 billion (source: Agence Science-Presse. “LHC: Un (très) petit Big Bang”. Lien
Multimédia. December 7, 2009).
– 29 –
Figure 8: Imitation
and Market Size
Quantity Sold Over Time
Benchmark
No Diesel
No TDI
1.36
1.4
Quantity Sold (in Millions)
1.2
1
0.97
0.97
0.85
0.91
0.85
.8
0.66
0.73
0.75
.6
.4
.2
0
1992
1996
2000
Notes: Statistics represent total new vehicle sales in the Spanish
auto industry (in millions). “Benchmark” corresponds to the
data. The “No Diesel” and “No TDI” counterfactual equilibria
correspond to the equilibria from Table 5.
How was volkswagen recover its investment in the tdi despite significant imitation?
In Figure 8, I present the total number of vehicles sold in Spain across the three equilibria
considered in Table 5. The figure clearly shows that total market size shrinks under both
counterfactual equilibria. Put differently, the tdi’s introduction increased the size of the
Spanish market as turbodiesels increased consumers’ willingness to buy new vehicles even
after controlling for changes in incomes.27 Thus, the market was able to support both
innovation and significant levels of imitation because the tdi increased the size of the pie
while product differentiation enabled firms to each secure a sufficient piece. More generally,
the results suggest that differentiated goods markets may still be dynamically efficient (i.e.,
promote investment in new goods) even with significant imitation risk as these markets
provide the innovator an opportunity to secure future profits by differentiating its products
horizontally.
27
One could also evaluate the value of the tdi to consumers as in Petrin (2002) for the minivan. Ackerberg
and Rysman (2005), however, point out that such calculations over-estimate the value of new goods in
models with unobserved product differentiation.
– 30 –
7 Concluding Remarks
The objective in this paper was to evaluate the impacts of imitation to dynamic and static
efficiency in a differentiated goods market. I do so via the study of a new diesel engine technology in the European auto industry – the tdi. The estimated model of consumer demand
for differentiated products allows for flexible substitution patterns while the oligopoly pricing
increases identification of price elasticities. As the estimated model generates reasonable
estimates and substitution patterns, I use it to evaluate the equilibrium effects of imitation
on firm pricing, profits, and consumer demand via a series of counterfactual experiments. I
find that widespread imitation of the tdi by European auto makers due to the technology’s
generality led to significant price competition. The amount of business stolen by these firms
was substantial and limited volkswagen to capture only 14% of the potential profits from
the tdi. That said, the firm’s ability to differentiate its diesel models horizontally enabled
it to generate a significant amount of profit, likely making the R&D investment required
to introduce the tdi worthwhile. Thus, imitation benefited consumers by simultaneously
increasing the number of products in the consideration set and decreasing retail prices
while product differentiation enabled the innovator to carve out a sufficient market niche
to maintain significant profits for its innovation. I conclude that, at least for the tdi, the
market delivered an equilibrium which was both dynamically and statically efficient without
government intervention (i.e., without the aid of patents). As this result amounts to an ex
post analysis of a particular industry, further research is required to identify the degree to
which this is generally true for differentiated goods markets.
– 31 –
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Appendix
A Spanish Data Sources
To control for household income distribution a thousand individuals are sampled each year
from the Encuesta Continua de Presupuestos Familiares (Base 1987 for years 1992-1997 and
Base 1997 for years 1998-2000) conducted by INE, the Spanish Statistical Agency.28 The
outside option varies significantly during the 1990s due to the important recession between
1992 and 1994 and the very fast growth of the economy and population (immigration) in the
second half of the decade. I also use these consumer surveys to set the size of the outside
option for each year in the sample. Starting with 1992, they are: 0.92, 0.94, 0.93, 0.93, 0.93,
0.92, 0.91, 0.89, and 0.89, respectively.
Fuel prices were also obtained from INE. In real 1994 euro-equivalent denominations
per liter, these are 0.445, 0.488, 0.490, 0.493, 0.543, 0.560. 0.530, 0.565, and 0.695 for
diesel and 0.580, 0.628, 0.655, 0.678, 0.706, 0.724, 0.702, 0.737, and 0.875 for gasoline, for
years 1992 to 2000, respectively. As for the Spanish steel prices used as instruments for the
cost equations, they are obtained from the 2001 edition of Iron and Steel Statistics – Data
1991-2000 published by the European Commission (Table 8.1).
For the analysis of demand I build a data set using prices and vehicle characteristics
as reported by La guı́a del comprador de coches, ed. Moredi, Madrid. I select the price and
characteristics of the mid-range version of each model, i.e., the most popular and commonly
sold. Demand estimation also makes use of segment dummies. Other than the luxury
segment, which also includes sporty cars, the car segments follow the “Euro Car Segment”
definition described in Section IV of “Case No. COMP/M.1406 - Hyundai/Kia.” Regulation
(EEC) No. 4064/89: Merger Procedure Article 6(1)(b) Decision. Brussels, 17 March 1999.
CELEX Database Document No. 399M1406.
28
See http://www.ine.es/jaxi/menu.do?L=1&type=pcaxis&path=/t25/p458&file=inebase for a description of these databases in English.
–i–
B Additional Results
Figure B.1 presents quantity sold of diesel and gasoline vehicles by different brands.
Figure B.1: Sales by Firm and Type of Engine
CITROEN
PEUGEOT
RENAULT
FORD
SEAT
OPEL
FIAT
VOLKSWAGEN
MERCEDES
AUDI
BMW
NISSAN
LANCIA
ROVER
ALFA ROM
VOLVO
HONDA
TOYOTA
MAZDA
MITSUBIS
HYUNDAI
SUZUKI
SAAB
CHRYSLER
SKODA
0
25000
50000
75000
Diesel
100000
125000
150000
Gasoline
(a) Year 1992
CITROEN
SEAT
RENAULT
PEUGEOT
OPEL
FORD
VOLKSWAGEN
AUDI
NISSAN
FIAT
BMW
MERCEDES
SKODA
ROVER
ALFA ROM
HYUNDAI
TOYOTA
VOLVO
SAAB
CHRYSLER
LANCIA
MAZDA
KIA
HONDA
MITSUBIS
SUZUKI
DAEWOO
0
25000
50000
75000
Diesel
Gasoline
(b) Year 2000
– ii –
100000
125000
150000
Until Spain ended its accession to the European Union transition period in 1992, it
was allowed to charge import duties on European products. Similarly, import duties for
non-European products converged to European levels. European imports paid tax duty of
4.4% in 1992, and nothing thereafter. Non-European manufacturers had to pay 14.4% and
10.3%, respectively. Thus, for the estimation of the equilibrium random coefficient discrete
choice model of Table 3 I distinguish between prices paid by consumers (p) and those chosen
by manufacturers (pw ) .
The other relevant factor that changes during the 1990s is the ownership structure
of automobile firms. During this decade fiat acquired alfa romeo and lancia; ford
acquired volvo; and gm acquired saab. bmw acquired rover in 1994 but sold it in
May 2000 (with the exception of the “Mini” brand) so these are treated as separate firms.
Table B.1 describes the ownership structure at the beginning and end of the decade.
– iii –
Table B.1: Automobile Groups: 1992 vs. 2000
Year 1992
Firm
alfa romeo
audi
bmw
chrysler
citroën
daewoo
fiat
ford
honda
hyundai
kia
lancia
mazda
mercedes
mitsubishi
nissan
opel
peugeot
renault
rover
saab
seat
skoda
suzuki
toyota
volkswagen
volvo
Gasoline Diesel
5,038
16,689
17,855
1,243
68,890
–
35,677
121,140
4,805
2,704
–
11,117
3,064
9,352
3,041
16,010
110,286
61,323
147,907
15,255
1,551
85,773
724
2,058
4,425
50,561
10,179
64
1,982
1,906
–
36,851
–
5,733
17,468
–
–
–
905
–
4,129
–
905
11,099
35,494
27,448
425
–
11,787
–
–
–
5,471
–
Year 2000
Owner
Gasoline
Diesel
Owner
alfa romeo
volkswagen
bmw
2,941
15,273
13,683
5,941
46,420
25,201
30,557
55,268
8,782
30,150
9,778
2,206
2,205
13,953
3,660
17,855
66,488
55,371
76,925
10,173
1,867
58,072
5,003
3,250
16,827
47,125
7,379
3,983
24,184
15,838
2,389
111,694
–
17,967
57,013
1,072
3,590
1,387
2,126
1,480
10,684
1,013
21,971
75,418
92,496
99,360
8,491
2,424
109,447
10,385
486
3,584
50,296
3,566
fiat
volkswagen
bmw
psa
fiat
ford
lancia
mercedes
gm
psa
renault
rover
saab
volkswagen
skoda
volkswagen
volvo
psa
fiat
ford
fiat
mercedes
gm
psa
renault
rover
gm
volkswagen
volkswagen
volkswagen
ford
Notes: Sales of vehicle by manufacturer and fuel type. “Owner” indicates the name of the automobile
group with direct control on production and pricing. Those without a group are all non-European
manufacturers and defined as non-eu in the analysis.
– iv –
Figure B.2: Change in the Distribution of Automobile Attributes
(a) Gasoline: Mileage (c90)
(b) Diesel: Mileage(c90)
(c) Gasoline: Cost of Driving (kpe)
(d) Diesel: Cost of Driving (kpe)
(e) Gasoline: size
(f) Diesel: size
(g) Gasoline: Performance (hpw)
(h) Diesel: Performance (hpw)
–v–
B.1 Estimated Demand Elasticities and Margins Figure B.3 presents the estimated volkswagen
demand elasticities and corresponding price-cost margins across the decade. We see that both
are fairly stable across the decade.
11
11
10
10
9
9
8
8
Price Elasticity
Price Elasticity
Figure B.3: Evolution of Estimated VW Price-Cost Margins
7
6
5
7
6
5
4
4
3
3
2
2
1
1
1992
1993
1994
1995
1996
1997
1998
1999
2000
1992
excludes outside values
1994
1995
1996
1997
1998
1999
2000
(b) Elasticity - Gasoline Vehicles
70
70
65
65
60
60
55
55
50
50
45
45
Margin (PCM)
Margin (PCM)
1993
excludes outside values
(a) Elasticity - Diesel Vehicles
40
35
30
25
40
35
30
25
20
20
15
15
10
10
5
5
0
0
1992
1993
1994
1995
1996
1997
1998
1999
2000
excludes outside values
1992
1993
1994
excludes outside values
(c) Margins - Diesel Vehicles
1995
1996
1997
1998
1999
(d) Margins - Gasoline Vehicles
– vi –
2000
B.2 Solving for Counterfactual Automobile Prices In this section I provide computational
details to find the profit-maximizing prices under each policy experiment. For the sake
of brevity, I suppress the period subscripts. Each firm f produces some subset J f of the
j = 1, . . . , J automobile brands and chooses a vector of pre-tariff prices {pw
j } to solve:
max
w
{pj }

X
p w
 × M sj ,
−
c
j
j
(B.1)
j∈J f
The firm’s first-order condition for price conditional on product characteristics is given by:
sj +
X
(pw
r − cr ) ×
r∈J f
∂sr
= 0.
∂pw
j
(B.2)
Optimality requires that Equation (B.2) hold for all products sold in period t. I express the
set of firm f first-order conditions in matrix notation as:
s + ∆ × (pw − c) = 0 ,
where an element of the matrix Ω is defined as:

∂sj


, if {j, r} ⊂ J f ,

 ∂pw
r
Ωjr =



 0
otherwise .
(B.3)
(B.4)
For a given vector of marginal costs c, I use (B.3) to find the fixed point to the
system of equations – a common practice in the literature dealing with this class of models.
To my knowledge there exists no proof of convergence or uniqueness for this contraction
operator and fixed point. My experience (as is common) is that convergence is monotonic
and proceeds quickly. Further, starting from different starting values yields an identical
result.
– vii –
B.3 Firm-Level Imitation In Figure B.4 I evaluate firm-level imitation using the counterfactual environment in which volkswagen is the sole provider of diesel vehicles as
benchmark. There exists a strong linear relationship (dashed blue line) and a large degree of
heterogeneity across firms, led by psa and renault. Firm-level imitation of the tdi leads
to a 1.84% average decline in volkswagen price with renault (4.33%) and psa (5.60%)
again playing the role of outlier. In comparison to Figure 5, we see that the impact on
volkswagen profits and retail prices are much larger. This indicates a decreasing marginal
impacts of imitation where the largest impact on equilibrium prices and profits occurs with
the initial imitators.
Figure B.4: Imitation, Business Sealing, and Static Efficiency
Fitted Values
PSA
Renault
Others
Fitted Values
PSA
Percent Change in VW Price
Percent Change in VW Profits
110
100
90
80
70
60
50
0
50
100
150
Percent Increase in Diesels Offered
Renault
Others
3
2
1
0
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
0
50
100
Percent Increase in Diesels Offered
(a) VW Profits
(b) VW Prices
Notes: Panels (a) and (b) present the change in VW profits and average retail prices, respectively, as a function of the
diesel offerings of rival firms. For each observation I begin from the counterfactual world in which VW has a monopoly
and add the corresponding rival firm’s observed diesel models. The x-axis is the percent increase in the total number of
diesel vehicles available to consumers.
– viii –
150
B.4 “Customer Learning” Thus far I have only considered the negative impact that imitation can have on the value of an innovation. The objective in this section is to estimate the
positive effects of imitation by looking at the ability of imitation to promote a product to new
consumers, thereby growing the market for all firms. In Figure B.5 I evaluate this effect by
comparing volkswagen’s equilibrium diesel profits conditional on the degree of consumer
learning which is captured in the model through the diesel time trend (βDiesel × T rend ). The
underlying assumption is that a positive estimate for the diesel trend in demand is due solely
to increased consumer awareness of this next generation diesel technology.
Figure B.5:VW
Volkswagen
Profits Conditional
on Customer
Learning
Profits TDI
Conditional
on Consumer
Learning
1994
1997
2000
Percent of Benchmark Profits
100
90
80
70
60
50
0
20
40
60
80
100
Consumer Learning (% of Estimated)
Figure B.5 illustrates the significant impact of diesels on volkswagen profits, particularly later in the decade when the estimated amount of customer learning is greatest.
Of course to attribute all of the growth in consumer perceptions to the imitation of rival
European firms is extreme as it is likely that volkswagen’s large diesel fleet itself would
have generated such a change, but nonetheless Figure B.5 suggests the consumer learning
can play a significant role in growing a market segment. Further the steep gradient of
volkswagen’s profits at points from 80 to 100% of the estimated level of consumer learning
suggests that imitation by rivals likely does convey large benefits to an innovator.
– ix –