Tacit Collusion in the 1950s Automobile Industry? Revisiting
Bresnahan (1987).
David Rapson∗
Department of Economics, University of California, Davis
March, 2009
Abstract
This paper revisits the question of whether automobile manufacturers engaged in tacit collusion
in the 1950s. In his famous paper, Bresnahan (1987) develops a model of strategic interaction
between multi-product firms to explain a brief spike in quantity in 1955, and concludes that the
episode was caused by a temporary breakdown in tacit collusion. However, his model imposes
strong restrictions on the nature of consumer preferences and intra-firm, multi-product pricing
strategies. I reconstruct his original dataset and solve a random coefficients logit model that
allows for a broader range of substitution patterns and pricing strategies. I estimate the model
under multiple firm behavioral hypotheses: Bertrand competition between firms and between
brands, and perfect collusion. For no year in 1954-1956 can either form of bertrand competition
be rejected in favor of tacit collusion. Results also indicate that firms were not profit maximizing
during this period. Firm-level strategic pricing is rejected in favor of inter-brand competition
in 1955.
∗
I thank Marc Rysman, J. Bradford Rice, Jordi Jaumandreu, Randall Ellis, Laurence Kotlikoff, Ivan FernandezVal, Christopher Knittel, Scott Carrell, and Pontus Rendahl. Tom Blake provided excellent research assistance. All
errors are my own.
1
1
Introduction
This paper revisits one of the few empirical examples of tacit collusion that exists in the literature:
Bresnahan’s (1987) study of the 1950s automobile industry. Bresnahan developed a clever and
path-breaking framework to explain an unusual pattern of car sales. He concludes that the 1955
spike in quantity is due to a brief breakdown in collusion, which he finds characterized the market
in 1954 and 1956. I re-examine his study through the lens of a random coefficients logit (RCL)
model, which relaxes some of the most restrictive assumptions of his model. The main advantage of
the RCL model is that it allows for a broad range of substitution patterns among car buyers. This
makes it possible to account more accurately for intra-firm, multi-product strategic pricing, which
could lead firms to charge a premium over marginal costs. Failure to account for these markups,
which are consistent with competition in a product-differentiated market, may cause high margins
to be erroneously attributed to the presence of tacit collusion. By estimating the RCL model under
constrasting firm behavioral hypotheses (Bertrand competition between brands and between firms,
and tacit collusion) one can directly test which of these is most consistent with the data. For no
year does the RCL model reject any form of competition in favor of joint profit maximization.
The brief spike in quantity in 1955 has been a challenge for economists to explain. While
many demand-side economic indicators during that period followed a more or less steady trend,
the quantity of new cars sold spiked markedly in 1955 relative to adjacent years. These facts
lead Bresnahan to consider possible causes on the supply side, which ultimately motivated the
collusion hypothesis. His result, however, is surprising. Maintaining tacit collusion requires some
(unspoken) arrangement by which firms are compensated for acting on behalf of the coalition, even
when defection would yield higher short-run profits. Theoretical studies describe reasons why this
is difficult, and the paucity of empirical evidence is striking.
These considerations are reflected in the current interpretation of antitrust law. Any attempts
to overtly collude are illegal per se, regardless of whether collusion is achieved or sustained. Tacit
collusion, on the other hand, is de facto legal. This might change, however, if it were shown to
occur with any regularity. Then a case could be made to bring its legal treatment into line with its
heavily-prosecuted counterpart on the grounds that the efficiency implications are indistinguishable.
However, while economic theory does not easily distinguish between overt and tacit collusion,
the empirical literature does. When collusion is known to have occured, the effects can be seen in
2
price and quantity data, and models have successfully detected its presence. However, Bresnahan’s
study of the 1950s car industry stands as arguably the only compelling evidence of tacit collusion.
This paper proceeds with a brief discussion of how one might test for tacit collusion, including
examples from the literature. I then describe Bresnahan’s model and its RCL analog in some
detail, and contrast the important implications with respect to their ability to distinguish between
collusion and various competitive outcomes. I also discuss the dataset used in the paper, which is
a recreation of Bresnahan’s original dataset, which was lost in the devastating earthquake that hit
California in 1989.
2
Collusion in the Literature
Several studies present empirical evidence of collusion in industries where overt cooperation is well
documented–Porter (1983), Porter & Zona (1993 and 1999), Ellison (1994), Genesove & Mullin
(1998) to name a few. In these cases there is ex post evidence of overt communication between
company executives, so the econometrician need only confirm that collusion is transmitted to prices
and quantities. Many of these examples arise in an auction setting where abnormalities in bidding
patterns reveal bid-rigging. Other examples are set in a more traditional market context where
aggregate data on prices and quantities are combined with assumptions about the form of marginal
costs to demonstrate non-competitive markups. When testing for tacit collusion, the hope is that
these techniques will be effective in detecting collusion even without a smoking gun. However,
many attempts to do so have failed to produce compelling evidence. This could be for one of two
reasons: either available data and empirical techniques are insufficient for detecting collusion in
those cases, or collusion did not occur.
Green and Porter (1984) provide what is perhaps the best known framework for examining
tacit collusion as a repeated game. They claim that any reduction in profits, whether caused by
exogenous factors or by defection amongst colluding firms, must be punished as though defection
had occurred. It follows that one must observe at least four periods of data to evaluate this scenario:
a period of collusion, followed by a period of low profits, followed by a punishment period exhibiting
high quantities, followed by a resumption of collusion (assuming the punishment period is finite).
There is no reason to believe, ex ante, that the duration of these episodes ought to correspond to
the reporting frequency of data (which is prodominantly annual, quarterly, or, if the researcher is
3
particularly lucky, weekly). As such, even if effective diagnostic techniques exist, it may be difficult
to observe the data in time periods that are appropriate. Setting aside this concern about the
ability to identify episodes, there are compelling reasons to expect tacit collusion to be rare, if it
occurs at all.
A recent theoretical study by Athey and Bagwell (2001) explores the importance of communication in reaching and maintaining collusion. Their model predicts that, in the absence of communication, only the most elementary industry structures can support joint profit-maximizing behavior
between firms. In their model, a successful collusive agreement will favor allocating production
to low-cost firms to maximize industry profits. Side payments are one way to maintain such an
arrangement, with low cost firms paying high cost firms to restrict output. Regulation often makes
these arrangements illegal though. Firms seeking to collude may circumvent the rules by replacing
side payments with inter-temporal allocations of output. That is, if your firm has high costs this
period, cooperation can result in your being promised higher output in future periods as compensation for low output today. The coordination problem is non-trivial, though, since there is incentive
to defect.
Athey and Bagwell explore the conditions under which cooperation can be sustained. They
find that, even in the most basic industry structure (duopoly), only the simplest non-competitive
production allocations can occur in the absence of communication. In the Bertrand setting, all
quantity allocations require communication except for the basic cases of an equal split or one firm
producing all output. Due to the restrictive nature of this finding on the plausibility of a silent
coordination in duopoly setting, this indicates how difficult cooperation is when the number of
competitors is higher.
It should not be surprising that empirical evidence of tacit collusion is scarce. A handful of
studies examine industries that have traditionally been characterized by positive profits, and about
which there has been speculation that collusion may be the cause. Three famous studies in this area
reject the hypothesis of tacit collusion–Ashenfelter and Sullivan (1987), Nevo (2001), and VillasBoas (2007). Ashenfelter and Sullivan examine the market for cigarettes and interpret exogenous
changes in excise taxes as changes in costs to firms. Under an industry structure with market power,
they derive relationships between prices and quantities before and after the excise tax change. They
then use these relationships as a means to test the monopoly hypothesis non-parametrically. Based
4
on their results, they reject the hypothesis that the industry is characterized by monopoly pricing
or other market structures that do not exhibit at least moderate amounts of competition.
Nevo applies a RCL model to the ready-to-eat cereal market. He tests the hypothesis of
monopoly power against alternatives that allow for markups due to multi-product firm pricing
and product differentiation. That is, the model is able to distinguish between price-cost margins
arising from a non-collusive outcome (where multi-product firms have local pricing power in characteristic space and product differentiation earns a markup), and a collusive regime where the pattern
of markups implies tacit or overt cooperation between firms. Nevo’s model is closely based on the
Berry, Levinsohn, and Pakes (1995) model, and similar to the model that I use in this study. He
finds that most of the price-cost markups can be explained by non-cooperative firm behavior, where
product differentiation and advertising combine to influence perceptions of quality and willingness
to pay.
Finally, Villas-Boas uses supermarket scanner data to study margins on yogurt. She finds that
high price-cost markups by retailers are consistent with market power in the vertical chain, where
downstream firms have bargaining power or manufacturers pursue non-linear pricing strategies.
The alternative hypotheses of upstream, downstream, or full-industry collusion are rejected.
One study that does find evidence of tacit collusion is Knittel and Stango (2003), who examine
interest rates in the credit card industry, where regulation imposes a ceiling. They argue that
firms use the ceiling as a focal point for price-setting. Their model distinguishes whether clustering
around the ceiling is due to a binding constraint versus the alternative hypothesis of collusion,
using the ceiling as a focal point. The ceiling was nonbinding during the early 1980s, yet firms still
priced there, which is what one would expect when firms are cooperating. However, the presence
of a focal point is crucial to the empirical approach and results of the study, and in the period
preceding the imposition of the ceiling, there is no trace of collusion in the data.
Only one study exists that provides evidence of tacit collusion without the presence of a smoking
gun or other mechanism for cooperation. That study is, of course, Bresnahan’s examination of the
unusual episode in the 1950s U.S. car industry.
5
2.1
Bresnahan 1987
There are several facts about the automobile industry in the 1950s that, on the surface, are difficult
to reconcile. There was a marked spike in quantity produced and sold in 1955 relative to adjacent
years, and real car prices were correspondingly low. Aggregate economic indicators, such as per
capita disposible income and interest rates, followed a more consistent trend over those years,
making demand-side explanations for the quantity/price anomoly difficult. These facts form the
rationale for Bresnahan’s hypothesis that supply-side factors must have been responsible for the
unusual pattern.
Bresnahan’s empirical approach is to model firm pricing under two behavioral hypotheses
(bertrand competition and collusion) and test the goodness-of-fit against model-level price and
quantity data from 1954-1956. When 1954 and 1956 generate a superior model fit under the collusion hypothesis and 1955 does not, this serves as evidence in favor of Bresnahan’s hypothesis that
firms were jointly profit-maximizing before and after a breakdown in cooperation that occured in
1955. However, the result may hinge on restrictive assumptions about demand that are implicit in
his model.
In Bresnahan’s model, consumers are differentiated over a continuous (one-dimensional) spectrum of preferences for car quality. For households that purchase an automobile, their utility is
linear and additive in automobile quantity and consumption of an outside good.
U (x, Y, υ) = υx + Y − P
(1)
Here x is a scalar representing vehicle quality, Y is household income, and P is the car price.
Heterogeneity in consumer preferences is captured by υ, which is a uniformally-distributed taste
parameter with density δ ∼ [0, υmax ] that governs the marginal utility of car quality. Quality is in
turn assumed to be a function of automobile characteristics, where the quality of vehicle j is
xj =
p
βXj .
(2)
The vector Xj includes vehicle weight, length, horsepower, cylinders, and body type, and β are
parameters to be estimated.
Compressing vehicle characteristics onto a single dimension has serious implications for demand
and subsititution patterns. Demand for vehicle i, qi , is determined by the density of consumers on
6
the interval [υhi − υij ],
qi = δ[υij − υhi ],
(3)
where υij represents the selected quality level of the consumer who is just indifferent between
product i and j.1 Note that for this consumer
Pj − xj υij = Pi − xi υij
(4)
and
υij =
Pj − Pi
.
xj − xi
(5)
It follows that the own- and cross-price derivatives, respectively are
∂qi
δ
δ
= −(
−
)
∂Pi
xi − xh xj − xi
(6)
δ
∂qi
=
.
∂Ph
xi − xh
(7)
and
Notice that these are functions only of price and quality of adjacent models on the quality spectrum,
rendering any non-adjacent price changes irrelevant to predicted demand (this is commonly known
as the independence of irrelevant alternatives assumption, or IIA).
The implications of IIA are rather severe for a model built to test for collusion. It is highly likely
that car buyers have strong, idiosyncratic preferences for certain characteristics over others. This
observation is validated easily by casual observation, and serves as the motivation behind a vast
subsequent literature on auto demand that models cars in characteristic space. Further, cars that
are adjacent on the quality spectrum may have very different characteristics. In combination, these
observations imply that certain quality rankings could cause intra-firm pricing strategies (consistent
with, say, differentiated product Bertrand) that are mistakenly interpreted as collusion.
As an example, consider 3 cars ranked 1, 2, and 3 on the quality spectrum. Let cars 1 and 3
be close substitutes that are both produced by firm A, and car 2 be produced by competing firm
B and differentiated from cars 1 and 3 in characteristic space. This pattern could easily emerge
(consider, for example, a Jeep Cherokee SUV sandwiched between a Camry and a Lexus, which are
both Toyota-owned). Firms A and B will both charge high markups, either because they have local
1
For simplicity, I present equations only for the models on the interior of the quality spectrum. See Bresnahan
(1987) for treatment of products at the extrema.
7
market power in characteristic space (Firm A) or because they are selling a differentiated product
(Firm B). However, the demand system built on the quality spectrum sees cars 1 and 2 (and 2
and 3) as close substitutes (because they are adjacent), but will not capture Firm A’s incentive to
strategically set the prices 1 and 3 jointly. As a result, it attributes these high markups to collusion.
This limiting formulation of demand-side substitution patterns extends to supply-side considerations as well. In industries with imperfect competition, firms will compete by offering differentiated
products in the market. Often, as is the case with car manufacturers, firms sell multiple products
that not only compete with products from other firms, but are also viable substitutes for the other
products from that same firm. Knowing that consumers can be sorted based on their preferences
for various characteristics, a profit-maximizing firm will consider how the price of each of its models
will affect demand for its other models. In fact, this is one of Bresnahan’s key observations. To
the extent that a model has close subsitutes from other firms, that model’s markup is likely to be
low (in the absence of collusion). Conversely, if the only close substitutes are manufactured by the
same firm, it will be possible to exercise market power (earn higher markups) in that neighborhood
of characteristic space. Such considerations are likely to affect all aspects of firm strategy, including
price and quantity decisions. To fully capture the consequences of these strategies empirically, one
would prefer a model that allows for substitution at the characteristic level and places few (if any)
a priori restrictions on the set of available substitutes.
Enriching the model with the aid of random coefficients allows many of the restrictions outlined
above to be relaxed. These models did not exist (and were in any case computationally-infeasible)
when Bresnahan was working on his dissertation. His 1987 paper was instrumental in laying the
foundation for methodological developments that are still very much in progress over twenty years
later. In the following section I describe a standard random coefficients model, and show explicitly
why it offers a more flexible and realistic portrayal of the automobile market.
3
Random Coefficients Logit Model
The random coefficients logit (RCL) model was developed to allow for the prediction of realistic
subsitution patterns, without the need for micro data. In it, consumer heterogeneity is generated
through the use of simulation techniques, that make it feasible to estimate the distribution of
preferences over distinct product characteristics. Berry, Levinsohn, and Pakes (1995) (henceforth
8
BLP) extend the RCL model and apply it to the U.S. automobile industry in the 1970s and
1980s. Combining Berry’s (1994) inversion method for estimating demand-side parameters and a
then-novel approach to impute the value of unobserved product characteristics, BLP has become a
standard tool used to characterize demand for differentiated products. Because it allows researchers
to recover structural parameters, it is an attractive model for evaluating counterfactual hypotheses.
This is particularly appealing when, as is true in this study, multiple hypotheses about firm behavior
are potentially correct. In this section I describe the model that I use to re-examine the 1950s
automobile industry. It follows closely BLP.
3.1
Demand
Individuals decide between either purchasing a car or not purchasing, and gain utility from the
product characteristics of the car they select and from consumption of an outside good. I assume
the following specification for indirect utility:
uij = α
K+1
X
pj
+ Xj β + ξj +
σk xjk νik + εij
yi
(8)
k=1
Here, for individual i and model j, yi is income, pj is price, α is marginal utility of money, Xj is
a (K + 1) vector of product characteristics, β is a (K + 1) vector of preference parameters over
characteristics (average over population), ξj is unobserved characteristics, σk is weight placed on
utility from idiosyncratic component of characteristic k (note that this is the average weight and is
common to all consumers), νik is idiosyncratic weight placed on characteristic k by i, and εij is a
p
random shock. Note that ln(yi )+ yji is a linear approximation of ln (yi − pj ), and is the specification
used in Berry, Levinsohn, and Pakes (1999).2
The BLP methodology exploits the fact that this specification can be decomposed into average
utility, δj , and idiosyncratic utility, µij :
δj
µij
≡ Xj β + ξj
≡ α
pj
+
yi
K
X
(9)
σk xjk νik + εij
(10)
k=1
Three important characteristics of this utility form must be noted. First, consumers gain utility
2
Predicted purchase probabilities are not altered by the presence of ln(yi ) in utility, since it acts as a constant for
all models, j. Thus it can be dropped from the empirical specification of uij .
9
over product characteristics, and all consumers face the same characteristics (including price) for
each model. Second, ξj represents product characteristics that are observed by consumers but
not by the econometrician. Since characteristics used in the econometric specification must be
measurable, it is likely that some aspects of cars that enter into the consumers’ decisions are
excluded from the data. For example, one plausible interpretation of this unobservable is brand
image, where a high realization of ξ represents a particularly ”hip” model, and a low realization
represents a model with less brand cache. The fact that an unobservable might impact consumers’
demand for a product introduces an endogeneity problem and, as a result, the potential for bias in
our parameter estimates. Third, including yi nonlinearly as it appears in (8) incorporates wealth
effects into the consumers’ decision. Since car purchases comprise a large part of peoples’ budgets,
including wealth effects ought to improve the specification.
Estimation of the demand-side unobservables, ξ, requires assumptions about the distribution
of εij , a simulation approach to avoid calculating a high-order integral, implementation of a fixed
point algorithm, and an assumption that observable product characteristics are orthogonal to ξ.
Conditional on θ, taking Ixk draws (νik ) from N (0, 1) allows one to obtain a consistent estimate
of µij . Under the assumption that εij is distributed extreme value Type I, the predicted discrete
choice probabilities for each individual can be retrieved. The probability of individual i choosing
car j is
exp(δj + µij )
probij = PJ
.
h=1 exp(δh + µih )
(11)
Summing these expressions for model j across all individuals yields an estimate of j’s market share:
I
ŝj (δj ; θ) =
1X
probij
I
(12)
i=1
An estimate of the average utility of model j, δbj , can then be retrieved as the solution to a fixed
point algorithm that equates the vectors of observed and predicted market shares.3
δ h+1 = δ h + ln sobs − ln sb(δ h ; θ)
(13)
Finally, (9) yields consistent estimates of β which, in turn, yields estimates of the vector of unobb
servables, ξ.
3
I use successive approximations to solve for the fixed point, and iterate until the maximum absolute difference
between observed and predicted market shares falls below the 10−12 tolerance level.
10
3.2
Supply
The supply side of the industry is comprised of F firms, with each firm f controlling a set of brands,
Bf . These brands, in turn, produce a subset, Fbf , of the J total models available to consumers,
The set of all models produced by firm f is denoted Ff .
As in BLP, I assume that the log of marginal cost is linear in the vector of cost characteristics.
Again, characteristics are separated into those that are observed by the econometrician, Xj , and
those that are unobserved, ωj . Given these assumptions, the marginal cost of model j is specified
as
ln(mcj ) = Xj γ + ωj ,
(14)
where γ is a vector of parameters to be estimated.
The price-quantity relationship in supply is determined by the first order conditions that result
from the firms’ profit maximization problem. Let profit of firm f be
πf =
X
(pj − mcj )M sj (p, x, ξ; θ),
(15)
j∈Ff
where M is total market size and sj is the market share earned by product j. Each firm chooses
prices to maximize its profit conditional on pre-determined characteristics of its own and competing
models. The first order conditions that must be satisfied are
sj (p, x, ξ; θ) +
X
r∈Ff
The cross-price derivatives
∂sr
∂pj
(pr − mcr )
∂sr (p, x, ξ; θ)
= 0.
∂pj
(16)
must be viewed in light of strategic pricing that may occur within
and between firms. It is these interactions that comprise the behavioral hypotheses between which
I attempt to distinguish in this paper: inter-brand competition, inter-firm competition, and joint
profit maximization (tacit collusion). In inter-brand competition, each brand acts as its own profitmaximizing entity, and does not consider cross-price effects with models sold under another brand
(even if they are owned by the same firm). For example, Oldsmobile is a General Motors brand, but
under the inter-brand competition hypothesis Oldsmobile prices without regard to how its strategy
impacts the profitability of other GM brands. Inter-firm competition allows for strategic pricing
between brands within the same firm (say, Oldsmobile and Buick).
To capture these various hypotheses, define a new J by J matrix, ∆, of cross-price derivatives.
11
Under the assumption of inter-firm competition, the (j, r)th element of ∆ is given by

 −∂sr if r and j are produced by the same firm;
∂pj
∆jr =

0 otherwise
(17)
An analogous matrix can be formed for inter-brand competition and tacit collusion. Under collusion
firms set prices to strategically respond to the price-setting of others; hence each element ∆jr =
−∂sr
∂pj .
In this context it should be evident that the full range of substitution possibilities may be
considered by firms pursuing an optimal pricing strategy.
Now, given values for the non-linear parameters and an estimate of the demand-side unobservable, ξ, one can estimate the markup of price over marginal cost. That is, one can now rewrite (16)
in matrix notation as follows:
s(p, x, ξ; θ) + ∆(p, x, ξ; θ)[p − mc] = 0.
(18)
Solve for [p − mc] and define it as
b(p, x, ξ; θ) = ∆(p, x, ξ; θ)−1 s(p, x, ξ; θ).
(19)
Finally, replace for mcj in (14) to obtain an expression for cost in which the only unobservable is
ω:
ln(p − b(p, x, ξ; θ)) = wγ + ω.
(20)
An estimate of ω
b is obtained by calculating fitted residuals conditional on γ
b.
3.3
Estimation
The GMM objective function is formed using the sample analog of the orthogonality conditions on
the instruments and unobservables:
E[Zξ(θ)] = E[Zω(θ)] = 0.
(21)
I select instruments following the approach detailed in Bresnahan, Stern, and Trajtenberg (1997).
Recall that the endogeneity concern arises from the probably correlation between prices and unobserved product characteristics. Under the assumption that observed product characteristics are
exogenously determined, the characteristics themselves are valid instruments. Further, if cross-price
12
elasticities are non-zero, non-j model characteristics are valid instruments (whether produced by
j’s firm or not) for model j. In BLP, there are three sets of instruments for a model j produced by
firm f .
Z1 = Xj , Z2 =
X
k6=j∈Ff
Xk , Z3 =
X
Xk
(22)
k∈F
/ f
Howver, since I am examining the car market independently for each year, 1954-56, it is equivalent
to estimating the BLP model multiple times for single markets. This results in Z2 and Z3 being
near-colinear.4 For the results presented in this paper, I drop Z3 .
With the GMM function identified, the nonlinear parameters, θ, are estimated numerically. I
employ a two-stage numerical search to find the optimal parameters. First I use a compass search,
which is similar in spirit to the Nelder-Mead, but in practice is more robust and effective. One of
the advantages of the compass search over gradient-based methods is that it can be easily written
to deal with complex values of the objective (whereas gradient-based methods break down). This
is important since for, some parameter values, the predicted marginal cost used in (14) is negative.
Near the optimum, small changes in parameters allow the objective to remain in real space, so I the
switch to a more computationally-efficient quasi-Newton method (BFGS) to reach convergence.
3.4
Testing
The firm behavioral hypotheses that characterize the level of competition/collusion are non-nested,
so I use the Rivers and Vuong (2002) model selection test for selection between possibly misspecified, non-nested models. This test is appropriate for distinguishing between models that are
not fully specified, as is the case with the GMM approach outlined above. The test statistic,
√
T =
J
σ
b (Q1 (θ1 ) − Q2 (θ2 )),
is a function of the difference between the values of the GMM objective
functions at the optimal parameter values (Q(θ)) and an estimate of the sampling variance between
the objectives (σ 2 ). The statistic is compared to the critical values of a N (0, 1), thus forming a
two-sided test of the null hypothesis. Since the test requires that the weighting matrix be the same
between the various hypotheses, the objective values are taken from the first-stage of the GMM
4
It is easy to show that the colinearity
is exact for the constant terms. The number of non-j models produced
P
by the firm that makes model j is r∈Ff 1. The number of models not produced by the firm that makes model j is
P
P
P
equal to r∈F
/ f 1. In a single market, these have an exact linear relationship:
r ∈F
/ f 1 = J −1−
r∈Ff 1.
13
estimation and use W = (J −1 Z 0 Z)−1 as the weight matrix. The variance is
h 0
i
0
0
σ 2 = 4 G1 W E11 W G1 + G2 W E22 W G2 − 2G1 W E12 W G2
and is estimated using Ĝi = J −1
P
mi (θ̂) and Êij = J −1
P
(23)
0
mi (θ̂)mj (θ̂) .
As constructed, the test statistic uses as its null the hypothesis that the competitive and collusive
models are indistinguishable. This null is tested against the two alternatives that one of the models
is a superior fit than the other.
√
H0 :
H1 :
H2 :
4
lim
J→∞
√
lim
J→∞
lim
J→∞
√
J [Q1 (θ1 ) − Q2 (θ2 )] = 0
J [Q1 (θ1 ) − Q2 (θ2 )] = −∞
J [Q1 (θ1 ) − Q2 (θ2 )] = +∞
Data
When I decided to explore the possibility of this paper, I contacted Bresnahan to ask if he still had
his data. Unfortunately, it had been destroyed in the 1989 earthquake in California. The original
data sources were auto industry trade magazines from the 1950s, which I was able to locate at the
library at Harvard Business School. They generously granted me access to their facility, where I
recreated the original dataset.
The sample is comprised of 83-87 models (in characteristic space) for each of the three years.
Each model is associated with a brand that is, in turn, owned and controlled by a firm. Table (1)
shows the ownership structure of the industry in 1955.5 Bresnahan collected his data from four
primary sources: Ward’s Automotive, Automotive Industries, Automotive News, and Heasley’s
Production Figure Book for U.S. Cars. Each variable of interest (prices, model-year production,
weight, length, horsepower, cylinders, and body type) appears in at least two (and often three) of
these sources. In the appendix of his 1987 paper, Bresnahan describes his data collection methodology in detail, and I followed his description as closely as possible. Where a data point is available
from more than one source, Bresnahan seeks a pairwise match from two primary sources, and ap5
There are only small changes in the brand/ownership over the three years of the sample. In 1955 the Imperial
brand was introduced by Chrysler, and the Henry J brand was retired by Kaiser-Frazer. In 1956 Ford introduced
Continental, and Kaizer Frazer exited the industry.
14
peals to a third source to resolve any inconsistencies. See the appendix of his paper for a detailed
description.
In addition to the sources used by Bresnahan, I augment the data using the Standard Catalog
of American Cars (SCAC). This volume was created as a resource for vintage car enthusiasts,
and happens to include data that fill gaps in the original sources. In particular, there is more
granularity in the production figures in the SCAC than in the original sources, so the issue of
quantity aggregation is alleviated somewhat by the use of actual data. Also, certain models (e.g.
the Corvette) were missing some specification data (horsepower) in the 1950s trade magazines, but
the SCAC provides them. Including this source increases the number of data points (across all
three years) by 12, which is approximately 5 percent of the sample.
One of the main obstacles inherent in using these data is that some manufacturers reported
only aggregate production quantities, or sometimes model-level quantities that ignored withinmodel variation. For example, there were two types of Ford Fairlane models produced each year
in 1954-56: the Fairlane 6 and the Fairlane 8, where ”6” and ”8” correspond to the number of
cylinders in the engine. Since cylinders are a characteristic upon whose dimension we distinguish
”models” in characteristic space, the Fairlane 6 and the Fairlane 8 ought to enter the analysis as
two separate cars. However, only one quantity was reported by Ford, which was the sum of the
quantities of the 6 and 8-cylinder types. Bresnahan circumvented this problem by restricting the
sums of model quantities predicted by the model to equal the aggregate figures reported in the
data. He then corrects for heteroscedasticity.
Predicting model-level quantities using the RCL model, however, is not as straightforward as
with the Bresnahan model. This is due to the one-to-one mapping that is both assumed and
necessary between the model-level unobservables (ξj ’s) and the market shares in the data. Without
model-level quantities, the BLP contraction mapping cannot yield average unobserved quality at
the model level. I regain the one-to-one mapping by using coefficient estimates from a first-stage
hedonic regression of quantity on observable model characteristics to predict model-level shares,
the sum of which totals the aggregate figure reported in the data. This procedure risks introducing
measurement error in market shares that is correlated with observable model characteristic, which
in turn would yield bias coefficient estimates. However, the alternatives are to disaggregate quantity
by some more arbitrary method, or aggregate the characteristics (also in some arbitrary way) to
15
Table 1: Automobile Firms, Brands, and Models, 1955
treat the aggregate as a single model. Measurement error would also result in these cases, likely to
a larger extent (though one could argue that this measurement error, though larger, is uncorrelated
with observables). The analysis that follows uses the hedonic regression allocation approach, which
seems to be the least arbitrary/objectionable of the alternatives.
5
Results
I estimate the model under three behavioral hypotheses (inter-brand competition, inter-firm competition, and (perfect) tacit collusion) for each year of the data. Table (3) presents the test statistic
that compares the goodness-of-fit of each pair of non-nested hypotheses.6 The null hypothesis is
that the two alternatives are indistinguishable in the data. Table (3) can be interpreted as follows:
A negative test statistic implies that the model fits the data more closely under the hypothesis
listed in the row header; a positive statistic implies superior fit of the column-header alternative in
a pairwise comparison.
There are two primary results of economic interest. First, notice that the test statistics in the
column labelled Perfect Collusion are all negative. This implies that the model under the collusion
6
As proscribed in Rivers & Vuong (2002), the first stage weighting matrix is used to reach these estimates, since
the optimal (second stage) weight matrix is different for each of the behavioral hypotheses.
Table 2: Automobile Data Summary, 1954-56
16
17
Table 3: Test Statistics: Brand Competition vs. Firm Competition vs. Collusion
hypothesis has an inferior fit relative to both competitive alternatives. However, since none of the
statistics for these pairwise tests is significant, one is left to conclude that while competition cannot
be rejected in favor of collusion, neither can collusion be rejected in favor of either alternative in
any year. I interpret this as evidence that firms were likely not colluding, and that competitive
explanations appear to be (at least weakly) more consistent with the data.
The second result of interest is that firms do not appear to have been profit-maximizing in any
of the years in the sample. Test statistics in the column labeled Firm Competition compare model
fit between the inter-firm and inter-brand competition hypotheses. Negative values are evidence
that subsidiary brands within firms are engaged in competition with each other, despite common
ownership. In 1954 and 1956 these results are slightly stronger than the evidence against collusion,
but still not statistically significant. However, in 1955, firm competition can be rejected in favor of
inter-brand competition with 95 percent confidence.
Table (4) displays parameter estimates and chi-square statistics for each of the behavioral
models. Variables with the suffix d correspond to demand, whereas s corresponds to supply. The
nonlinear parameters (random coefficients) are have the nl suffix. In contrast to the statistics
in Table (3), parameter estimates in Table (4) are calculated using the efficient GMM estimator,
where second-stage estimates employ the optimal weighting matrix using the first stage residuals.7
This not only improves efficiency, but allows for a direct test of over-identifying restrictions. The
chi-square statistics fail to reject the over-identifying restrictions for each behavioral model and
The first-stage weighting matrix is (J −1
where û’s are the first-stage residuals.
7
P
j
Zj0 Zj )−1 and the optimal weighting matrix is (J −1
P
j
Zj0 ûj û0j Zj )−1 ,
18
year.
Parameter estimates for each hypothesis and year are quite similar. On the demand side, the
linear price coefficients are for the most part as desired: negative and significant. All else equal,
consumers appear to value heavy cars and assign a negative value to length. Average preferences for
horsepower, number of cylinders, and body type are not well identified, perhaps due to significant
correlation between these variables. The statistical insignificance of these parameters may also be
attributable to heterogeneity among consumers’ demand for these characteristics. Recall that, in
this specification, consumer heterogeneity is captured only by income (which is interacted with
price) and a random coefficient on the constant (which can be thought of as creating individual
differences in the level of utility achieved by car ownership). A full set of random coefficients is
feasible, but each additional one causes the objective to be less well-behaved.8 The supply-side
parameters are estimated with more precision than demand-side parameters. Horsepower, weight,
length, and the hard-top body type all contribute positively to costs. All else equal, additional
cylinders appears to reduce cost as well, though the magnitude of the coefficients is small.
The main feature of the RCL model that is appealing relative to the one-dimensional quality
spectrum approach is the possibility of obtaining realistic estimates of own- and cross-price elasticities. These, of course, are crucial to optimal pricing, and directly determine the level of markup
a firm can achieve for a given model. Table (5) presents average predicted price-cost markup
and own-price elasticities for each behavior/year combination. As expected, the predicted margins
under collusion are higher than in the competitive case.
Bresnahan does not publish the margins and elasticities implied by his model, so direct comparison would require replicating his results. However, in BLP’s (1995) study they predict elasticities
in the -5 to -40 range. These are roughly consistent with my estimates for 1954 and 1955, but the
1956 predicted elasticities are higher. Ex ante, it is not clear whether one would expect to see higher
or lower demand elasticities in the 1950s compared to the 1970s and 1980s (the period of BLP’s
data). 1956 was the final year before the U.S. auto industry was opened to foreign competition,
with Volkswagon entering the market in 1957. Increased competition from imports could cause
model-specific elasticities to be higher during the period examined by BLP. On the other hand, a
higher elasticity might be expected in the 1950s when cars were more of a luxury good than in the
8
See Knittel & Metaxoglou (2008).
Table 4: Parameter Values
19
20
Table 5: Average Predicted Price-Cost Markups and Own-Price Elasticities
1970s and 1980s. The results here do not provide clear evidence of a shift in demand elasticities,
so perhaps an off-setting combination of these stories is true.
It may be worth mentioning that the form of collusion that I test in this paper is extreme.
Firms’ intent to jointly profit-maximize could in practice result in imperfect collusion, especially
in the absence of communication. This could manifest itself in different ways. For example, it is
conceivable that a subset of firms collude while the rest of the industry engages in price competition.
The possibility of these coalitions is put forth in Jaumandreu and Moral (2006). They find evidence
of this sort of coalition in the Spanish car industry, where domestic and European producers are
likely to have acted in concert while Japanese and American firms competed on price. Another
weaker form of collusion could arise if firms are unable to perfectly account for the cross-price
effects of their rivals’ products. In concept, one could estimate a collusion intensity parameter (by
weighing the elements in the cross-price derivative matrix, ∆). These are potential avenues for
future work.
21
6
Conclusion
This paper re-examines the competitive landscape in the 1950s U.S. automobile industry, and
tests the robustness of the famous result from Bresnahan (1987) that firms were engaged in tacit
collusion. Using a re-creation of Bresnahan’s original dataset, I estimate a structural model of
supply and demand to test the fit of various firm behavioral hypotheses. The random coefficients
logit model allows for more realistic demand behavior than previous work, including a broad set of
possible subsitution patterns in characteristic space. In that context, firms are free to engage in a
more realistic set of potential actions, including intra-brand or intra-firm, multi-product strategic
pricing. Relative to Bresnahan’s framework, these improvements increase the likelihood that high
price-cost markups will be attributed properly to either strategic oligopoly behavior or collusion.
For no year can either of the forms of bertrand competition be rejected in favor of tacit collusion.
This stands in contrast to Bresnahan’s finding that firms were colluding in 1954 and 1956, with a
price war in 1955. Somewhat surprisingly, results indicate that firms were not profit-maximizing
during this period. The firm-competition model is rejected in favor of brand competition in 1955,
and is a better fit (though insignificantly) in 1954 and 1956.
These results accentuate the paucity of empirical evidence in favor of tacit collusion. Bresnahan’s (1987) famous paper is one of the only studies that claim evidence of its occurance. If, as
seems to be the case, his results are an artifact of certain key modelling choices, we are left once
again to question whether collusion is sustainable without the aid of communication. If it is not,
then the current antitrust laws, in which tacit collusion is de facto legal, seem sensible.
22
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