Competitive Pricing Behavior in the Auto Market: A ... · Competitive Pricing Behavior in the Auto...

MARKETING SCIENCE � 2001 INFORMSVol. 20, No. 1, Winter 2001, pp. 42–60

0732-2399/01/2001/0042/$05.001526-548X electronic ISSN

Competitive Pricing Behavior in the AutoMarket: A Structural Analysis

K. SudhirNew York University, 44 West Fourth St. MEC 8-80, New York, New York 10012,

[email protected]

AbstractIn a competitive marketplace, the effectiveness of any ele-ment of the marketing mix is determined not only by itsabsolute value, but also by its relative value with respect tothe competition. For example, the effectiveness of a price cutin increasing demand is critically related to competitors’ re-action to the price change. Managers therefore need to knowthe nature of competitive interactions among firms.

In this paper, we take a theory-driven empirical approachto gain a deeper understanding of the competitive pricingbehavior in the U.S. auto market. The ability-motivation par-adigm posits that a firm needs both the ability and the mo-tivation to succeed in implementing a strategy (Bouldingand Staelin 1995). We use arguments from the game-theo-retic literature to understand firm motivation and abilitiesin different segments of the auto market. We then combinethese insights from the game-theoretic literature and theability-motivation paradigm to develop hypotheses aboutcompetition in different segments of the U.S. auto market.To test our hypotheses of competitive behavior, we estimatea structural model that disentangles the competition effectfrom the demand and cost effects on prices.

The theory of repeated games predicts that firms with along-run profitability objective will try to sustain coopera-tive pricing behavior as a stable equilibrium when condi-tions permit. For example, markets with high concentrationand stable market environments are favorable for sustainingcooperative behavior and therefore provide firms with theability to cooperate. The theory of switching costs suggeststhat in markets in which a firm’s current customers tend tobe loyal, firms have a motivation to compete very aggres-sively for new customers, recognizing the positive benefitsof loyalty from the customer base in the long run. As con-sumer loyalty in the market increases, the gains from in-creasing market share by means of aggressive competitivebehavior are more than offset by losses in profit margins.Firms therefore have the motivation to price cooperatively.

Empirically, we find aggressive behavior in the minicom-pact and subcompact segments, cooperative behavior in the

compact and midsize segments, and Bertrand behavior inthe full-size segment. These findings are consistent with ourtheory-based hypotheses about competition in different seg-ments.

In estimating a structural model of the auto market, weaddress several methodological issues. A particular diffi-culty is the large number of car models in the U.S. automarket. Existing studies have inferred competitive behavioronly in markets with two to four products. They also userelatively simple functional forms of demand to facilitateeasy estimation. Functional forms of demand, however, im-pose structure on cross-elasticities between products. Suchstructure, when inappropriate, can bias the estimates ofcompetitive interaction. We therefore use the random coef-ficients logit demand model to allow flexibility in cross-elas-ticities. We also use recent advances in New Empirical In-dustrial Organization (NEIO) to extend structuralestimation of competitive behavior to markets with a largenumber of products. We use the simulation-based estima-tion approach developed by Berry et al. (1995) to estimateour model.

A frequent criticism of the NEIO approach is that its focuson industry-specific studies limits the generalizability of itsfindings. In this study, we retain the advantages of NEIOmethods but partially address the issue of generalizabilityby analyzing competitive behavior in multiple segmentswithin the auto industry to see whether there is a consistentpattern that can be explained by theory. Theoretical mod-elers can use our results to judge the appropriateness oftheir models in predicting competitive outcomes for themarkets that they analyze.

A by-product of our analysis is that we also get estimatesof demand and cost apart from competitive interactions forthe market. Managers can use these estimates to perform‘‘what-if’’ analysis. They can answer questions about whatprices to charge when a new product is introduced or whenan existing product’s characteristics are changed.(Auto Market; Competition; Structural Models; New EmpiricalIndustrial Organization; Game Theory; Ability-Motivation Para-digm)

COMPETITIVE PRICING BEHAVIOR IN THE AUTO MARKET: A STRUCTURAL ANALYSIS

MARKETING SCIENCE/Vol. 20, No. 1, Winter 2001 43

1. IntroductionIn a competitive marketplace, the effectiveness of anyelement of the marketing mix is determined not onlyby its absolute value, but also by its relative valuewith respect to the competition. For example, the ef-fectiveness of a price cut in increasing demand is crit-ically related to competitors’ reaction to the pricechange. Managers therefore need to know the natureand extent of competitive reactions. Recognizing this,there is substantial literature on the estimation ofcompetitor reaction functions. For example, see Hans-sens (1980) and Leeflang and Wittink (1992, 1996).Because the reaction function methodology is a re-duced-form technique, the reaction coefficients do notseparate out demand, cost, and competitive effects.Therefore the reaction coefficients are useful to man-agers only when the demand and cost structure ofthe market is the same as for the period of estimation.In the case of the auto market, which is the focus ofthis paper, new models of cars are routinely intro-duced, and model changes are an annual feature.Hence, the reaction coefficients are of limited value inpredicting competitive response.

In this paper, we therefore take a theory-driven em-pirical approach to gain a deeper understanding ofcompetitive behavior of firms in the U.S. auto marketthat is not a function of either demand or cost char-acteristics at any point of time. The firm-level ability-motivation paradigm posits that a firm needs boththe ability and the motivation to succeed in imple-menting a strategy (Boulding and Staelin 1993). Wecombine predictions from the game theoretic litera-ture and the firm-level ability-motivation paradigm(Boulding and Staelin 1993) to generate our hypoth-eses about competitive behavior in different segmentsof the auto market.1 To test these hypotheses aboutcompetitive behavior, we need an empirical approachthat can disentangle the effects of competitive behav-ior from the demand and cost characteristics thatdrive the observed prices in the market. The struc-

1The firm level paradigm is itself based on the individual-level abil-ity-motivation framework attributable to Heider (1958). The firm-level paradigm was presented as an empirical generalization inBoulding and Staelin (1995). We thank the Area Editor for sug-gesting the use of this paradigm in generating the hypotheses.

tural modeling approach in the New Empirical In-dustrial Organization (NEIO) framework is an idealmethodology for our purposes. We therefore estimatea structural model of the U.S. auto market with spe-cific focus on the differences in competitive behaviorin different segments of the market.

1.1 Expectations About Competitive BehaviorBesanko et al. (1996) and Carlton and Perloff (1994)offer an exhaustive list of conditions in which firmstaking a long-term perspective can sustain coopera-tion and generate higher long-term profits. Two of theconditions that they mention are (i) high concentrationand (ii) stable market environments. When a market ishighly concentrated, firms find it easier to achieve co-operation because coordination is needed only amongfewer firms. In a stable market environment, devia-tion by any firm from the cooperative equilibrium canbe more easily detected. This permits the other firmsin the market to punish the firm deviating from thecooperative level of prices or quantities. Such credi-bility of punishment threats in stable environmentsenable firms to sustain cooperation. Therefore, firmsare able to coordinate and price cooperatively in con-centrated markets with stable environments. Con-versely, firms are unable to sustain cooperation in un-stable markets and markets with low shareconcentration.

Table 1 contains the characteristics of different seg-ments of the auto market. Because concentration isgreater in the larger-car segment, firms should beable to sustain cooperation in the larger-car segments.They would be unable to sustain cooperation insmaller-car segments. In terms of share volatility,2 thesmallest-car segments tend to have the highest vola-tility. Hence, they will be unable to sustain coopera-tion in these segments.

The theory of switching costs (for example, seeKlemperer 1987) suggests that when a firm’s existingcustomers tend to be loyal, firms should price lower

2We follow Caves and Porter (1978) in defining share volatility in asegment, by averaging over the changes in firms’ shares within asegment. Volatility � 1/TF � � [(Shareft � Shareft�1)/Share ft]2,F t

f�1 t�1

where f indicates firm, t indicates time period, F is the number offirms in the market, and T is the number of time periods in thedata.

SUDHIRCompetitive Pricing Behavior in the Auto Market

MARKETING SCIENCE/Vol. 20, No. 1, Winter 200144

Table 1 Average Segment Characteristics (1981—1990) with Potential Impact on Competitive Behavior

Minicompact Subcompact Compact Mid-size Full-size

Share volatility3-Firm concentrationDomestic concentrationShare of Japanese firmsMean buyer age

0.2360.660.440.51*

0.1490.570.530.41

35.2

0.0490.710.700.26

41.1

0.0710.920.920.03

49.2

0.1061.001.000.00

59.3Buyer age �25 years (%)First new car (%)Segment share

**0.04

22.740.2

0.21

1020.1

0.29

5.410.2

0.25

0.42.30.10

The Newsweek data combined the minicompact and subcompact segments into one segment. Hence, the information on Mean buyer age, Percentage ofbuyers below 25 years, and Percentage of first time new car buyers are averages across both segments. The total Segment share of all segments is lessthan 100%, because we do not report the share of the luxury segment.

than their short-term optimal prices and competevery aggressively for first-time buyers, so that theycan reap the rewards of their later loyalty throughhigher prices in future purchases. In the auto market,consumers have significant loyalty to ‘‘country of or-igin’’ (Goldberg 1995). They also have significant‘‘firm loyalty.’’ A recent study by R. L. Polk and Com-pany (Los Angeles Times 1996) indicates that the per-centage of households owning a GM, Ford, or Chrys-ler car that bought the same company’s car again was67%, 63%, and 49%, respectively. Firms thereforehave the motivation to be aggressive in segments tar-geting young or first-time buyers who will rewardthem with a lifetime of loyalty. However, in segmentstargeted to older or repeat buyers, customers aremore loyal and less price-sensitive. Hence, the gainsin new customers from aggressive competition willbe more than offset by the losses in profit marginsfrom their existing customer base. Firms thereforehave the motivation to be cooperative.

As seen in Table 1, we find that the average age ofcar buyers is increasing in the size of cars.3 Also thepercentage of buyers under the age of 25 in the mini-compact and subcompact segments is more than dou-

3This data is from a Newsweek survey of New Car Buyers in 1988.Newsweek did not separate subcompact and minicompact segmentsin their report. We caution however that this general pattern hasmildly changed during the last decade. A 1997 study by MediamarkResearch, New York finds that there is hardly any age differencebetween subcompact and compact buyers. It should be interestingto study the impact of these changes in demographics of car buyersin these segments on competitive behavior in future research.

ble the percentage in the other segments. Also theproportion of first-time buyers in the minicompactand subcompact segments is double that of the com-pact segment and much larger than that of the mid-size and full-size segments. This indicates that firmshave a motivation to be aggressive in the minicom-pact and subcompact segments but to be cooperativein the larger-car segments. This effect is magnified bythe country-of-origin loyalty. Because the Japanesehave much smaller market shares in the larger-carsegments, compared to those in the smaller-car seg-ments, domestic firms would find it optimal to beaggressive in the smaller-car segments so that theydo not lose further market share to Japanese firms,which can be detrimental to their long-term marketshare. Japanese firms should also find it optimal tocompete aggressively in the smaller-car segment formarket share, because the resulting ‘‘country-of-ori-gin’’ effect could be beneficial in the long run throughspillover effects in the sales of their larger cars.

A recent Wall Street Journal article (White 1999) ex-plaining GM’s logic for aggressive pricing of theChevy Cavalier provides face validity to the motiva-tion argument.

GM loses about $1000 on every Cavalier it now sells. . . . Afterall Chevrolet needed an entry-level car to compete with thedomestic rivals and imports like the Toyota Corolla and theHonda Civic. The Cavalier, the logic went, brought young buy-ers into the GM family. . . . Its role within GM is a very, verystrategic one.

In contrast, firms have the motivation to be cooper-



ative regarding the mid-size and full-size car seg-ments toward which older customers tend to be moreloyal, because aggressive pricing reduces marginswithout increasing demand. Therefore the motivationis to be cooperative regarding the larger car segmentsand aggressive with the smaller car segments.

In summary, firms with long-term perspective aretherefore ‘‘able’’ and ‘‘motivated’’ to cooperate in thelarger-car segments. In contrast, in the small-car seg-ments firms have the ‘‘motivation’’ to be aggressiveand limited ‘‘ability’’ to cooperate. Overall, we there-fore expect cooperative behavior in the larger-car seg-ments and aggressive behavior in the smaller car seg-ments.

1.2 Methodological Issues in Estimating aStructural Model of the Auto Market

To estimate a structural model of the auto market, weneed to address several methodological issues thathave not yet been tackled in the current NEIO-basedliterature in marketing. Existing studies limit them-selves to interactions between two–four products andtwo–three firms. This makes sense when there are afew dominant products and dominant firms in theindustry (Coke-Pepsi rivalry studied by Gasmi et al.1992 and the Fuji-Kodak rivalry studied by Kadiyali1996 are examples). In other cases, the analysis ag-gregates demand for differentiated products with asingle brand name as demand for that one brand.There is questionable justification for this when thedifferentiated products are part of a product line forwhich firms choose separate prices for each of thedifferentiated products with the goal of maximizingoverall profits. This is precisely the case of the automarket, in which there are more than 150 models tar-geted to different segments. A structural model of theauto market therefore needs to be able to handle highproduct variety.

Existing NEIO studies typically specify an aggre-gate demand equation for each product, such that de-mand is a function of the firm’s own and competitors’marketing mix. If there are n products and price isthe only marketing mix variable, then there would ben demand equations in the following form4:

4Some researchers may use a log-linear or log-log specification, butthe problems are the same.

n

q � a � b p , j � 1, . . . , n.�i i i j jj�1

Such a demand system, with no structure of itsown and cross-price effects, has n(n � 1) parameters.As n becomes large (as in the case of the auto market),the number of parameters explodes, and the modelcannot be estimated. Clearly, some structure needs tobe imposed in the demand model to facilitate esti-mation.

A standard approach to impart structure is to fol-low Lancaster (1971) in treating the product as a bun-dle of characteristics and assume that consumers de-rive utility from these observed characteristics of aproduct. The demand system can now be describedby a much smaller set of parameters—one for eachcharacteristic describing the products. This ensuresthat the number of products have no impact on thenumber of parameters to be estimated.

In specifying the utility model, researchers have achoice of deterministic and random utility models. Intheir analysis of the auto market, Bresnahan (1987)and Feenstra and Levinsohn (1995) use a deterministicutility model; Berry et al. (1995) use a random utilitymodel. Deterministic utility models do not allow forunobserved taste differences among consumers forproducts that are identical on observed characteris-tics. Hence, two products with identical observedcharacteristics have zero profit margins in a deter-ministic utility model.5 The random utility modelhowever recognizes that consumers have unobserv-able taste differences, and this allows for nonzeroprofit margins, even among products that are iden-tical for observed characteristics. We therefore preferthe random utility approach.

In a structural model of competitive behavior, thefunctional form of the demand equation can have im-portant implications for pricing behavior. Studies inmarketing in the NEIO framework have previouslyused relatively simple functional forms for demandto facilitate easy estimation. Such functional forms ofdemand impose severe structure on the nature of

5Feenstra and Levinsohn (1995) computed that the Honda Accordhas zero profit margins, because it had identical observed charac-teristics with some other brand in their analysis.



Table 2 Relationship with Existing Literature on Structural Models of Competitive Interactions

Limited Firms/Limited Variety Several Firms/High Variety

Bertrand Competition assumed Bresnahan (1981) Deterministic Utility ApproachFeenstra and Levinsohn (1995)Random Utility ApproachBerry et al. (1995)Verboven (1996)Besanko et al. (1998)

Pick nature of competition based on fit withdata

Gasmi et al. (1992)Roy et al. (1994)Kadiyali (1996)Vilcassim et al. (1999)Putsis and Dhar (1997)

Deterministic Utility ApproachBresnahan (1987)Random Utility ApproachThis paper

cross-elasticities between products, which in turn af-fect the supply equations and can bias the estimationof competitive behavior. For a recent study that hasexplored the importance of the functional form of de-mand—in the estimation of competitive behavior—refer to Putsis and Dhar (1998). Berry (1994) and Ber-ry et al. (1995) have developed methods to estimatea random coefficients logit demand model that canmodel heterogeneity in consumer preferences usingaggregate data. Because the flexibility of this demandmodel minimizes the potential for bias, we use therandom coefficient logit model in this paper.

Berry et al. focus on estimating unbiased demandand cost parameters of the auto market, so they as-sume the Bertrand equilibrium in their paper. In con-trast, our focus in this paper is to estimate not onlythe demand and cost parameters but also to identifythe differences in competitive behavior in differentsegments of the auto market.

Table 2 positions this paper with respect to previ-ous work on structural estimation of oligopolisticmarkets. We classify previous research along twomain dimensions: (1) Are competitive interactions as-sumed or inferred from the data? (2) Do they deal withmarkets with limited variety or high product variety?Among papers that deal with high product variety,we classify papers on the basis of whether the de-mand model uses a deterministic utility or random util-ity framework.

In terms of its methodological contribution, this pa-per is thus the first to estimate competitive interac-

tions among firms in markets with many competingproducts using a random utility approach, especiallythe f lexible random coefficients logit demand model.From a substantive point of view, this paper is thefirst to focus on differences in the competitive interac-tion in each segment of the auto market. In contrast,studies such as that of Bresnahan (1987) estimated anaverage competitive interaction across all segments ofthe auto market. Also Nevo (forthcoming Ref. a) hascompared the reasonableness of inferred costs underassumptions of Bertrand and cooperative behavior topick the appropriate form of competition.

The rest of this paper is organized as follows. Sec-tion 2 describes the model. We derive the demandand supply estimation equations under various mod-els of competition. Section 3 describes the estimationprocedure. Section 4 describes the empirical analysis.Section 5 concludes with a discussion of some of theapplications and limitations of the paper.

2. ModelAn empirical model of a competitive market follow-ing the NEIO framework has three basic components:(1) demand specification, (2) cost specification, and (3)assumption on the nature of competitive interactionsin equilibrium.

2.1 Demand SpecificationAs discussed earlier, we use a flexible random coef-ficients logit model of demand. A utility maximizing



consumer who has a choice of J car models (denotedby j � 1, . . . , J) in period t (T � 1, . . . , T) and anoutside good (the option of not purchasing, denotedby j � 0) is assumed to solve the optimization prob-lem:

max u � � ln(y � p ) � x � � ��i jt it jt jkt k jtj∈{0, . . . ,J} k

� x � � , (1)� k jkt ik ijtk

where uijt is the utility of model j to consumer i inperiod t. For model j in period t, xjkt is the k th ob-served characteristic, pjt is the price, �jt is the level ofunobserved model quality, and yit is the income ofconsumer i. �ijt is the random utility across modelsand consumers and is assumed to be distributed i.i.d.Type I extreme value across models and consumers.

A characteristic xjkt contributes xjkt(�k � kik to theutility of the consumer i. �kxjkt represents the averageutility to all consumers from characteristic k, whereaskikxjkt represents the individual i’s deviation fromthat average. We assume that is drawn from a stan-dard normal distribution and k is the standard de-viation in the utility that consumers get from char-acteristic k. Unlike the unknown preferencedistribution for model characteristics (which we esti-mate in the model), we know the distribution for theincome variable (yit) from the Current Population Sur-vey (CPS). So we draw yit from a log-normal distri-bution, whose parameters are estimated from theCPS data. The advantage of using distributional in-formation from external sources is that we reduce thenumber of parameters that need to be estimated fromthe data.

The utility for the outside good (p0t � 0, x0kt � 0)is

ui0t � � ln(yit) � �0t � 0i0 � �i0t. (2)

The outside good captures utility from productsother than new models of cars (which are the insidegoods). We capture the heterogeneity in valuation ofthe outside good by the 0i0 term. Because marketshares in a logit model are only a function of differ-ences in utility with respect to a base good, we useUijt � uijt � ui0t in computing market shares for theinside goods. Given this differencing, the random co-

efficient on the constant term of the inside goods cap-tures the heterogeneity for the outside good.

Note that price enters the utility equation as ln(yit

� pjt), rather than as just yit � pjt. If we had just usedyit � pjt, an individual’s probability of buying a modelwould be independent of income, because the differ-ence between a model’s utility and the utility of theoutside good determines the purchase probability fora model (yit would have just cancelled out). Using alog-specification not only overcomes that problem,but also it is very intuitive because a higher price hasmuch lower impact on a high-income consumer’s util-ity than on a low income consumer’s utility.6 Thisimplies that a higher income consumer is more likelyto buy a more expensive car model than a low incomeconsumer.

Berry et al. (1995) interpret the unobservable com-ponent (�jt) to be ‘‘the difficult to quantify aspects ofstyle, prestige, reputation and past experience that af-fect the demand for different products, as well as theeffects of quantifiable characteristics of the car that wesimply do not have in our data.’’ For example, adver-tising can affect a model’s perceptions in the market.We do not have advertising data in our analysis, soadvertising effects and other unobserved character-istics are captured in our model by �jt. This unob-servable component is, however, perceived by boththe consumers and the price setting firm, and it there-fore influences prices.

The utility equation may be decomposed as fol-lows:

U � �(x , p , � , ) � �(x , p , , ) � �i jt jt jt jt 1 jt jt i 2 i jt

� � � � � � , (3)jt i jt i jt

where 1 � (�1, . . . , �k) is the set of parameters thatis associated with consumer independent character-istics, 2 � (�1, 1, . . . , k) is the set of parametersassociated with consumer characteristics, and 1 � (yi,i1, . . . , iK). �(xjt, pjt, �jt, 1) is independent of the in-

6We also tried a Box-Cox transformation [(yit � pjt)/�]� in the utilityspecification. The log transformation is a special case of the BoxCox transformation (� � 0). However, the actual value of � did nothave a serious impact on the results here. So we report results onlyfor the case of ln(yit � pjt).



dividual consumer characteristics, and �(xjt, pjt, i, 2)is a function of individual consumer characteristics.

Given the above utility we get the well-known logitformula for the probability of an individual buyingmodel j in period t:

exp(� � � )jt i jts � . (4)i jt J

1 � exp(� � � )� k iktk�1

Hence, the market share of model j in period t is

exp(�(x , p , � , ) � �(x , p , , ))jt jt jt 1 jt jt i 2s �jt � J 1 � exp(�(x , p , � , ) � �(x , p , , ))� kt kt kt 1 kt kt i 2

k�1

� P() d, (5)

where P() is the joint distribution over all of the el-ements of i � (yi, i1, . . . , iK). The above equationinvolves a multidimensional integral that has noclosed form. Hence, we need to use simulation tocompute the above integral. Drawing n vectors of i

from P(), we have an approximation to the integral

n1 exp(� � �(x , p , , ))jt jt jt i 2s � . (6)�jt Jn i�1 1 � exp(� � �(x , p , , ))� kt kt kt i 2k�1

Because, as noted earlier, the error �jt is correlatedwith a regression variable (price), we have an endo-geneity problem.7 We therefore need to use instru-mental variable estimation techniques. However, er-rors � jt enter equation (6) nonlinearly. Becauseinstrumental variable estimation techniques are notwell developed for nonlinear equations, Berry (1994)suggests an approach that enables the use of well-developed linear instrumental variables estimation.We outline this procedure below:

Berry et al. (1995) use Berry’s idea and suggest thefollowing contraction mapping to solve for �jt:

� � � � ln(Sjt) � ln(s(pjt, xjt, � , Pn; 2)),h�1 h hjt jt jt (7)

where Pn represents the actual n vectors drawn fromthe P() distribution, Sjt is the observed market share,

7This endogeneity problem affects even studies with individualdata, as shown by Villas-Boas and Winer (1999).

and s(pjt, xjt, � , Pn; 2) is the computed market sharehjt

from Equation (6).In practice, to reduce computing logarithms, we

follow Nevo (2000) by solving for wjt � exp(�jt) withthe following contraction mapping:

Sjth�1 hw � w . (8)jt jt hs( p , x , � , P ; )jt jt jt n 2

We iterate on this equation until we get conver-gence. To get quick convergence, we need good start-ing values, i.e., � . We use � � ln(Sjt) � ln(S0t), the0 0

t jt

solution to the homogeneous logit model, as our start-ing values.

We then compute the demand side errors condi-tional on 2 as

�jt � �jt( 2) � xjt 1. (9)

Because �jt enters linearly in �jt, we can use linearinstrumental variables estimation methods.

2.2 Cost SpecificationWe assume a log-linear marginal cost function. For afirm that produces model j in period t with a vectorof characteristics wjt, the marginal cost is given by:

ln(cjt) � �wjt � �jt, (10)

where �jt is the unobserved idiosyncratic cost asso-ciated with model j. wjt may include the same char-acteristics that affect demand xjt or different charac-teristics. For example, scale economies inmanufacturing affect costs but not demand.

2.3 Competitive InteractionsWe measure cooperative or aggressive behavior bythe degree of deviation from Bertrand prices. By mea-suring competitive behavior in terms of the deviationfrom Bertrand pricing, we separate out demand andcost effects from the competitive effects, because theBertrand price takes into account the effects of de-mand and cost. We use an ‘‘as-if’’ technique to inferdeviations from Bertrand behavior. When firms usean objective that places a positive weight on theircompetitor’s profits, the equilibrium outcomes will bemore cooperative relative to the Bertrand equilibri-um. This is intuitive, because perfect cooperation



(monopoly behavior) is obtained by putting equalpositive weights on all competing firms’ profits. Sim-ilarly, if a firm uses an objective in which it places anegative weight on its competitor’s profits, the equi-librium outcome will be more competitive relative tothe Bertrand equilibrium.

We implement this idea with the following objec-tive function for firm r:

� � ( p � c )s M � � ( p � c )s M ,� �rt jt jt jt t s( j) jt jt jt tj/∈J j/∈Jrt rt

(11)

where Jr is the set of models produced by firm r and�s( j) is the weight on a competitor’s profit from modelj that belongs to segment s. �s � 0 implies cooperativebehavior relative to Bertrand in segment s, whereas�s � 0 implies aggressively competitive behavior rel-ative to Bertrand in segment s. The first-order con-ditions for firms setting prices for each of its modelsunder the assumption of a cooperative pricing equi-librium is given below:

�s�� jtrt � M ( p � c )�t jt jt[�p �pj∈Jkt ktrt

�sjt� � ( p � c ) � s � 0. (12)� s( j) jt jt kt]�pj/∈J ktrt

The first-order conditions may be summarized bythe following equation in matrix form for all modelssold in period t. It therefore contains as many rowsas the number of models in the market.

�1�st Own Compp � c � � ·* � � � s , (13)�t t s t� � � �[ ]�p� � st��

� �Cost ��

Margin

where

1, if i, j are produced by same firm,Own� �i, j �0, otherwise,

and

� , if i, j belong to segment s andsComp � � are not produced by same firm,s i, j

0, otherwise.

Rewriting the pricing equation with the functionalform of the cost equation, we have

p � exp(�W � � )t t t� ��

Cost

�1�st Own Comp� � ·* � � � s . (14)� s t� � � �[ ]�p st

� ��

Margin

Hence, the supply side errors are given by

�1�st Own Comp� � ln p � � ·* � � � s�t t s t� � � �� [ ] ��p st

8� �W . (15)t

3. EstimationBecause price is correlated with the error term in thedemand equation (�), we need to use instruments forprice in the demand estimation.9 Price is also corre-lated with the error term in the cost equation (�).Because the demand and supply error terms are cor-related through the price term, there is a gain in ef-ficiency from using a simultaneous-equations esti-mation technique. We therefore need an instrumentalvariables-based simultaneous equations estimationprocedure.

Following Berry et al. (1995), we use the general-ized method of moments (GMM) estimation proce-dure. The GMM procedure for a system of nonlinearequations is outlined in Hamilton (1994). The basicprocedure is as follows: Let z be the set of instru-ments to be used. We assume z is exogenous and in-dependent of the error terms in the demand and pric-ing equations � and �. This implies that z is

8In an earlier version of this paper, we used a homogeneous logitmodel and estimated competitive interactions on a segment-by-seg-ment basis. This assumption enabled us to derive closed form es-timation equations for both the demand and the supply side equa-tions. This considerably simplified estimation, because we could useclosed form nonlinear estimation equations. Details of these deri-vations are available from the author. The derivations can also beextended to a nested logit model.9We discuss the instruments that we use in §4.2.



orthogonal to both � and �. Therefore, E(z�) � 0 andE(z�) � 0. These serve as the moment equations inour method of moments procedure. Let � � (��, ��).Let � { 1, 2 �, �s} be the set of parameters to beestimated.

The GMM estimator given our moment conditionsis defined as

�1min ��z(z��z) z��, (16)

where � is the standard weighting matrix given byE(��).

Note that in the minimization problem, conditionalon 2 and �s, the first order conditions on parameters 1 and � are linear and can be easily solved. Opti-mizing over 2 and �s is computationally cumber-some, because these first-order conditions are nonlin-ear. In the optimization, we therefore use a two-stepapproach. We first use a nonderivative simplex rou-tine (Nelder and Mead 1965) to optimize over 2 and�s and then, conditional on them, the linear param-eters 2 and � are estimated. This approach substan-tially reduces the estimation time.

The problem with this algorithm is that it is cir-cular. The optimal weighting matrix � is a functionof the estimated parameters, and the estimated pa-rameters are a function of �. We therefore start withinitial values of obtained by solving the homoge-neous logit model and compute � based on these val-ues. We then optimize the . There are two optionshere. We can either stop here or iterate further. Esti-mate a new � conditional on the new and iterateuntil converges. However, because the iterative pro-cedure is computationally cumbersome and has notbeen found to be dominant in finite samples over thenoniterative procedure (Hansen et al. 1996), we donot iterate over the � estimates.10

4. Empirical Analysis4.1 DataWe analyze pricing behavior in the auto market dur-ing the period from 1981 to 1990. By 1981, the effects

10We direct the reader who is interested in the nitty-gritty of thissimulation-based estimation procedure to the excellent implemen-tation-oriented paper by Nevo (2000).

of the oil price shock of the 1970s had boosted thedemand for smaller cars. This period can thus betreated as a time when customer preferences for char-acteristics like miles per gallon, size, etc. were stable.Because we pool data across time in our estimation,it is necessary that parameters be reasonably homo-geneous across time.

The data on model characteristics, prices and quan-tities are obtained from Ward’s Automotive Handbookfor the period from 1981 to 1990.11 Data on ConsumerPrice Indices published in the Statistical Abstracts areused to normalize the prices in constant 1983 dollars.

Ward’s Automotive Yearbook (1981–1990) segments thecar market into several segments based on the mar-keting intent of manufacturers: minicompact, sub-compact, compact, mid-size, large, and luxury.12 Seg-mentation along these lines is common in analyzingthe auto market (Train 1986, Goldberg 1995, Verboven1996). To provide the reader with a sense of whichcars belong to which segment in Ward’s classificationscheme, we provide some examples of car models inthe different segments (see below).

Minicompact: Ford Festiva, Geo Metro, Dodge Colt,Toyota Tercel

Subcompact: Geo Prizm, Ford Escort, Honda Civic,Toyota Corolla, Nissan Sentra

Compact: Buick Skylark, Ford Tempo, Dodge Shad-ow, Honda Accord, Toyota Camry, Nissan Stanza

Mid-size: Buick Century, Chevy Celebrity, Ford Tau-rus, Nissan Maxima

Full-Size: Buick LeSabre, Mercury Grand Marquis,Chevy Caprice, Dodge Diplomat

Luxury: The Cadillac line, Lincoln line, BMW, Mer-cedes Benz, Porsche, Lexus

Note that even though in terms of size, some carsin the luxury lines may be comparable to subcom-pact, compact, or large cars, Ward’s classifies them as

11We thank James Levinsohn for providing the bulk of the data usedin this analysis.12Further segmentation is into regular, specialty, and sporty sub-groups. We restrict our analysis to the group level in this paper.Nevertheless we model this segmentation by allowing for preferenceheterogeneity in variables such as Horsepower and Miles per Gal-lon. We discuss later how we use this additional segmentation ingenerating instruments.



luxury cars, because they take into account the mar-keting intent. We use Ward’s segmentation scheme forour analysis. We do not analyze the luxury market,because these markets tend to be thin markets withidiosyncratic demand, and an equilibrium analysismay be inappropriate for such thin markets.13

We use the following characteristic variables in thedemand equation: Horsepower (HP) gives us a mea-sure of the degree of power and acceleration of a car.14

Although the fuel efficiency of a car could be relevant,the importance of fuel efficiency could vary, depend-ing on the cost of fuel itself. We therefore use thevariable Miles per Dollar (MP$) by dividing Miles perGallon by Price per Gallon (price normalized by theConsumer Price Index). We also use size of the car asan explanatory variable. These variables are also usedin Berry et al. (1995). In addition, we use reliabilityof the car as an explanatory variable.15 Additionally,we use four dummy variables: GM, Ford, European,and Japanese.16

We did not include certain variables to reduceproblems of multicollinearity. For example, the num-ber of cylinders and miles per gallon (MPG) are high-ly correlated. We use MPG but ignore the number of

13Because Ward’s classification is based on marketing intent, it clas-sifies all cars from luxury car makers, such as BMW, Mercedes,Lexus, Infiniti, etc. as luxury cars, even though in terms of sizealone the cars may have been fitted into the sub-compact, compact,or large categories. We also do not analyze the minivan, SUV, andtruck segments.14We also used Horsepower/Weight as a variable following Berry etal. (1995) to account for the fact that for the same horsepower, aheavier car can have lower acceleration. The results were similar.15Reliability data is from Consumer Reports. Consumer Reports pro-vides data on surveys of previous year’s models. Because ratings inperiod t affect consumer demand, we used the ratings of period tfor the demand model in period t. However, for the cost equationwe used reliability data from period t � 1. I thank a reviewer fordrawing our attention to this subtle but important issue.16Hence, the utilities are relative to Chrysler, for which we do notuse a dummy. To reduce the number of dummy variables, we donot use manufacturer-specific dummies for Japanese and Europeanmanufacturers but only country-of-origin variable. One may wonderwhy we did not estimate segment-level dummies. Because size ishighly correlated with the segment classification, it enabled us toefficiently capture the segment effects with just one coefficient, in-stead of using multiple-segment dummy coefficients. This alsohelped us to improve the precision of our other estimates.

cylinders, because there is more variation in the MPGvariable compared to the cylinder variable.

We use all of the above variables, except MP$, asexplanatory variables for costs in the pricing equa-tion. We drop MP$ and use Miles per Gallon (MPG),as this is the more relevant variable for productioncosts. Note that as a cost variable, Captive imports(cars manufactured by Japanese firms and sold byAmerican firms) are treated as Japanese. Transplants(cars manufactured in the United States by Japanesefirms) are treated as domestic. In addition to the de-mand variables—to measure economies of scale—weuse the log of total production of that model (weproxy it with worldwide sales) as a variable in thecost equation. Note that for domestic cars, most mod-els were sold only in the United States and, therefore,total worldwide sales were equal to domestic sales.

We also need information on potential market size(Mt). Berry et al. (1995) use the number of householdsin the United States as a measure of the size of themarket. However, it is unlikely that a household thatpurchased a car this year will be in the market thenext year. According to the Motor Vehicles Manufac-turers Association (1990), the average age of a car inthe United States during the 1980s was stable ataround 7.6 years. The average number of cars for aU.S. household was 1.8. So we estimate the potentialmarket size in year t for cars as17:

Potential Market Size(t)

� [No. of Households(t)

� Average No. of Cars Per Household]

� Average Age of Cars.

Note that we use the income variable in our de-mand model. We use information about the mean andvariance of income in the United States from the Cur-rent Population Survey during the period from 1981to 1990. Because the CPI-adjusted mean and varianc-es from 1981 to 1990 did not differ much across yearswe used an average mean and variance for the peri-od. We assumed that income was drawn from a log-

17Potential market size here means the total market for new andused cars.



Table 3 Average of Segment Characteristics for 1981–1990

Minicompact Subcompact Compact Mid-size Full-size

Number of modelsNumber of domestic modelsNumber of Japanese modelsReliability (1–5 scale)Horsepower (hp)Size (Length � Width) in sq. inMPGMP$Price/CPI

6.101.702.203.57

67.629673.33

32.3929.47

5200

23.6011.2010.703.26

81.1410,823.59

28.5326.06

6802

32.4017.4010.902.99

105.0411,974.83

23.7221.48

8428

27.7020.901.202.62

109.8613,423.72

21.5119.38

10,251

7.207.200.002.25

129.7615.525.75

17.9316.47

10,613

normal distribution to ensure positive draws fromthe distribution.

The averages of the characteristics for different seg-ments during the period from 1981 to 1990 are listedin Table 3.

As one would expect, characteristics such as sizeand HP increase for larger segment sizes. MP$ andMPG fall for larger-segment sizes. The greater shareof Japanese cars in the smaller-car segment explainsthe greater reliability of cars in the smaller-car seg-ments. The average number of models in the mini-compact segment was 6.7, and in the full size seg-ment it was 7.1. These numbers are relatively small,compared to the number of models in other seg-ments. In all we had 932 observations over the fivesegments for 10 years, i.e., an average of 93 modelsin each of the 10 years of analysis.

4.2 IdentificationWe assume that the model characteristics xj and wj

(except for the economies of scale variable in wj,which is endogenous) are exogenous and that, con-sequently, they are orthogonal to the error terms (�j

and �j). This identification assumption is reasonable,considering that in the short run (within a year),firms cannot quickly change the characteristics of thecars that they sell.18

Prices and market shares are endogenous and are

18The endogeneity of product characteristics might be an issue ofinterest when studying issues related to choice of characteristics ina product line. Modeling that endogeneity would be of particularinterest in doing a what-if analysis. We discuss this issue in theconclusion.

correlated with the error terms �j and �j, even in theshort run. This is because they are simultaneously de-termined in equilibrium. For homogeneous goodsmodels of supply and demand, we have ready instru-ments to deal with the endogeneity problem: Thereare enough exogenous variables that affect demandalone and not costs, and vice versa. In differentiatedmarkets, however, most of the exogenous variablesare model characteristics, and these affect both de-mand and costs. Hence, we cannot use traditional in-struments based on exclusion restrictions.

Because prices are determined by means of anequilibrium, the physical characteristics of each car’scompetitors will be correlated with the car’s ownprice and demand. Berry et al. (1995) analyze gener-ation of efficient instruments when competitor char-acteristics are candidates. They suggest using: (1) theexogenous variable elements in the vectors xj and w,(2) the average or sum of all of the exogenous ele-ments of xj and wj across all cars produced by thesame firm (within firm sum or average), and (3) theaverage or sum of all the exogenous elements of xj

and wj across all cars not produced by the same firm(without firm sum or average).19

We find that the quality of instruments is some-

19These instruments are useful because of the form of the demandequation that we use. In our demand equation, ln(sj/s0) is indepen-dent of the characteristics of competitor models. A wide range oflogit specifications that are widely used in empirical work satisfiesthis property. However if in the demand equation for each model,competitor model characteristics also enter the right-hand side ofthe equation, then these instruments will not be useful. We thanka reviewer for drawing our attention to this issue.



what poor (i.e., the correlation of instruments basedon this approach is low). We therefore refine the in-struments using arguments similar to those of Bres-nahan et al. (1997), who compute the characteristicaverages only within a subset of similar models andnot for all the models in the entire market. Alongwith the segment information, we use country of or-igin and the regular/specialty/sporty classificationthat Ward’s provides in creating these subsets. Thusthe two similar subsets we create for each car are (i)all cars belonging to the same segment with the samecountry of origin as the car and (ii) all cars belongingto the same segment with the same regular/special-ty/sporty classification as the car. For example, theFord Taurus is a domestic, regular mid-size car.Hence, the similarity subset for the Ford Taurus willbe (i) all domestic mid-size cars and (ii) all regularmid-size cars. Note that these subsets may vary fromyear to year, depending on what cars are present ineach subset in any given year. Furthermore, evenwhen the same cars are there in the subsets, the char-acteristics of the cars can change from year to yearand, therefore, the instruments vary from year toyear. We thus compute the within-firm model averageand the without-firm model average for the two sim-ilarity sets to generate instruments. Thus we generatefour instruments for each variable.

We estimate 15 parameters on the demand side (themean coefficients on the four dummy variables andprice, the mean and standard deviation coefficients onintercept, Reliability, HP, Size, MP$). On the cost side,we estimate 10 parameters (the intercept, the coeffi-cients on the four dummy variables, Reliability, HP,Size, MPG, and ln(total production). We also estimatefive competition parameters, one for each segment. Inall, there are 30 parameters to estimate.20

We have nine exogenous variables (a constant, fourdummies, and four characteristics of cars) in xj andnine exogenous variables (a constant, four dummyvariables, and four characteristics of cars) in wj. Be-cause production is endogenous, we cannot use thisvariable for exogeneity restrictions, so we have only

20We estimate other models, one in which we constrain the com-petition parameters to be the same for minicompacts and subcom-pacts. In that model, we estimate only four competition parameters.

18 instruments based on the exogeneity restrictions,and we need more instruments to identify the model.We get overidentifying restrictions by generating in-struments that we discussed earlier. For each of thefour physical characteristics used in xj, we compute awithin-firm average (excluding the car for which wegenerate the instruments) and without-firm averagefor the two similarity subsets. For the constant term,we compute a within-firm and without-firm sum, re-flecting the number of competitors for the model.This produces 5 � 4 � 20 instruments. With the 18other instruments, we have in all 38 instruments.Now the model is overidentified.

4.3 ResultsTable 4 contains the estimation results. The identify-ing restrictions cannot be rejected at the 95% level,implying that the model fits the data well.21 We dis-cuss the demand, cost, and competition estimates inturn.

Demand. The � coefficients measure the averagepreference, and the coefficients measure the hetero-geneity in preferences for the characteristics. As ex-pected, consumers value reliable cars. It is interesting,however, that there is no significant heterogeneity inthe value they place on the reliability of cars (as in-dicated by the insignificance of the coefficient). Incontrast, consumers are heterogeneous in their valu-ation of horsepower. However, everyone has a posi-tive utility from higher horsepower, as indicated inthe much smaller standard deviation (1.06) relative tothe mean (24.87). The size variable is similar. People,on average, prefer larger cars, but there is also sig-nificant heterogeneity in the preference for size. Asper the coefficients on miles per dollar, consumers onaverage prefer more fuel-efficient cars. However,there is no significant heterogeneity in the valuationfor fuel efficiency. Note, however, that larger cars usu-ally have lower fuel efficiency, and so the heteroge-neity in fuel efficiency can also be captured in theheterogeneity in valuation of car size. What we find

21With 38 instruments (identifying restrictions) and 30 parameters,there are 8 degrees of freedom. The minimized value of the objec-tive function (1.42) is less than �2, therefore the identifying restric-tions cannot be rejected.



Table 4 Model Estimates with Competitive Interaction for 5 Segments

EstimateStandard

Deviation* t-stat EstimateStandard

Deviation* t-stat

� Demand

GMFordJapanEuropeConstant

0.86700.73480.23970.4072

�9.0852

0.11050.13460.13590.17750.6347

7.84315.45931.76392.2945

�14.3139 0.0274 0.0377 0.7257ReliabilityHorsepower (hp)SizeMP$In(Income-Price)

0.221324.87460.3190

17.10786.3560

0.04192.95060.0459

12.61800.5830

5.27718.43026.94631.3558

10.9028

0.01021.05920.00761.5875

0.01430.43840.00371.3862

0.71192.41612.03691.1452

CostsGMFordJapanEuropeConstant

�0.0258�0.0600

0.14740.22037.5975

0.02240.02250.03170.03600.2470

�1.1509�2.6679

4.64926.1173

30.7574ReliabilityHorsepower (hp)SizeMPGIn(Production)

0.03565.31370.0611

�0.0138�1.589E-07

0.00800.48970.01170.0040

5.195E-08

4.450410.85125.2198

�3.4815�3.0602

Competitive interactionMinicompactSubcompactCompactMid-sizeFullObjective Function

�1.1239�2.8660

1.06782.22120.1768

1.42

10.34891.41710.56390.65493.4287

�0.1086�2.0224

1.89353.39160.0516

�2(0.95,8) � 2.73

* SD.

is that the residual heterogeneity of fuel efficiency af-ter adjusting for size is not significant. As expectedln(Income � Price) has a positive coefficient, indicat-ing price sensitivity of consumers. The log specifica-tion ensures that higher-income customers are lessprice-sensitive than lower-income customers.

In terms of the dummy variables, we find that GMand Ford have larger coefficients than for Japanese,European, and Chrysler cars (whose utility is nor-malized to zero). However, because Japanese and Eu-ropean cars have a greater reputation for quality, oneshould expect that Japanese and European cars

should have larger intrinsic utility. This apparentanomaly is easily explained when we recognize thatthe Japanese and European dummies are capturingthe residual utility after the effect of reliability hasbeen accounted for. Because Japanese and Europeancars score higher on reliability, the results are stillconsistent with intuition.

Costs. Our cost equation estimates are also in linewith expectations. It costs more to produce reliablecars, larger cars and cars with higher horsepower. Itis cheaper to produce fuel-efficient cars. Althoughthis result is not obvious, it can be easily explained



Table 5 Margins

Price Margin

MinicompactSubcompactCompactMid-sizeFull

5,2006,2028,428

10,25110,613

1,4391,7862,3673,0082,719

when we recognize that miles per gallon is highlycorrelated with the number of cylinders of and theweight of a car. Essentially, this result implies that itis costlier to make heavier cars with a greater numberof cylinders.

One surprising result is the positive coefficient onJapan in the cost equation, given the reputation ofJapanese car manufacturers for their low costs of pro-duction. Petrin (1999) also finds a similar result in hisstudy of the minivan market. There are two reasonsfor this. First, the strength of the yen relative to thedollar in the 1980s put Japan at a competitive costdisadvantage, even though its manufacturing wasmore efficient than that of domestic manufacturers.22

Second, the voluntary export restraint (VER) wasbinding on Japanese firms in many years during the1980s (Goldberg 1995). Goldberg interprets the posi-tive coefficient for Japanese cars as a Langrangeanmultiplier associated with the quota constraint forJapanese cars. With such a binding constraint on thetotal quantity of sales in the United States, Japanesefirms may have had to price higher than if they wereinvolved in pure Bertrand competition without suchbinding constraints.

Competition. Of greater interest to us in this paperare the estimates of competitive interaction in eachsegment. Based on insights from game theory and theability-motivation paradigm that we discussed in theIntroduction, we expected aggressive behavior in thesmaller-car segments and cooperative behavior in thelarger-car segments. Consistent with this, we find ag-gressive competitive behavior in the minicompactsegment, although the estimate is not significant. Inthe subcompact segment we find aggressive compet-itive behavior. For the compact and mid-size seg-ments, we find cooperative behavior consistent withour expectations.

The full-size segment appears to be a puzzle ini-tially, because our estimates indicate that firms priceat the Bertrand level, although we expected cooper-ative behavior. On closer examination (refer to Table

22Trade magazines at that time considered this to be the primarycompetitive advantage for domestic cars, considering the qualitydisadvantage of domestic cars. For example, see Risen (1988) andEdid et al. (1986).

1), we find that the volatility in this segment is rela-tively high, compared to that of the mid-size andcompact segments. The high volatility inhibits theability to cooperate. Why is there a high degree ofvolatility in this segment? Unlike other market seg-ments that have been either gaining or maintainingtheir segment shares, the market share of the full-sizesegment is systematically declining. Segment sharehas fallen from a high of about 12.9% in 1981 to aslow as 9% by 1990. In such a declining segment, firmshave been attempting to maintain sales by aggressivepricing. Such aggressive pricing leads to changes inmarket shares from period to period and is reflectedin the higher share volatility in this segment. Hence,even though there is motivation to cooperate, theoverall declining segment share leads to higher sharevolatility and limits the ability of firms to cooperate.Without the ability to cooperate, it is not surprisingthat competitive behavior in this segment is close tothe Bertrand short-run equilibrium. Thus, the resultis consistent with predictions made using the ability-motivation paradigm. Overall, our estimates of com-petitive behavior are consistent with the game-theo-retic and ability-motivation arguments discussedearlier.

We tabulate the average margins for different seg-ments in Table 5, based on our estimates in Table 4.Indeed, the margins are lower for smaller cars thanfor larger cars, as would be expected from the esti-mates of competitive behavior.

Robustness Issues. We now consider a variety ofissues to see whether our inference about competitivebehavior is robust. From Table 3, we can see that thenumber of models in the minicompact and full seg-ments (therefore, observations) are fewer than in thesubcompact, compact, and mid-size segments. Couldit be that competition estimates for the minicompact



and full segments are not significantly different fromzero because of the small number of observations?

To test this, we check whether we could combinethese segments that have few models with theirneighboring segments that have a large number ofmodels and see what the impact on the estimatesmight be. This may be appropriate if the expectedcompetitive interactions in these neighboring seg-ments are similar. Note also that concentration inthese neighboring segments is similar, making thehypothesis of similar competitive interaction plausi-ble. We therefore estimate a model with one commoncompetition parameter for the minicompact and sub-compact segments. The results are tabulated in Table6. We find that the estimates of competition are neg-ative and significant in the minicompact and subcom-pact segments. Comparing the demand and cost es-timates in Tables 4 and 6 indicates that theseestimates have not changed substantially, lendingface validity to this constraint. We could not reject thehypotheses that competition parameters for minicom-pacts are the same as that of the adjoining sub-com-pacts by performing the D-Test of Newey and West(1987) at the 5% significance level.23

We also estimated a model in which we constrainthe parameter estimates of the full and mid-size carsegments to be equal to see whether the insignifi-cance in the full-size segment was attributable to thesmall number of models in this segment. We foundthat this significantly changed the parameter esti-mates from the unconstrained version (especially thecoefficients for Japan and Europe in the cost equa-tion), indicating that this constraint was inappropri-ate. This also lends face validity to our original ar-gument that the full-size segment should have adifferent competitive interaction than the mid-sizesegment because of the differences in the share vol-atility of these segments. The D-test rejected this con-straint at the 5% significance level.

23Essentially this test says the difference in minimized sum ofsquared errors of the moment restrictions between the restrictedand unrestricted models (using the same weighting matrix for bothmodels) follows a �2(J) distribution, where J is the number of re-strictions (in our case, 1). We used the weighting matrix of the un-restricted model for our test.

We tested the robustness of the estimates of com-petitive interaction to other issues relating to (i) mar-ket size definitions, (ii) segment definitions, and (iii)the use of list prices rather than transaction prices.For market size, we estimated different models byvarying the average size of the household from 1.5 to2 (actual value was 1.8). The estimates were not sen-sitive to these definitions. We also estimated a modelwith only regular cars in each segment by excludingthe specialty cares and sporty cars from the analysis.The competition estimates continued to be substan-tively similar.

Another important issue that could potentially im-pact our estimates is that we inferred competitive be-havior using list prices, rather than transaction prices.It would have been ideal to estimate the model withtransaction prices, but we could get rebate data onlyfor 1989 and 1990. We checked when the parameterestimates for these 2 years changed from the average.The differences were not significant. We caution,however, that this insignificance could be attributableto the sparseness of the rebate data. With the avail-ability of detailed rebate data and transaction pricesthrough such websites as Edmunds.com, future re-search in this area should evaluate more carefully theimplications of using transaction data, as opposed tothose of list prices, in inferring competition. Withsales and transactional data at the monthly level, itshould be possible to gain a deeper understanding ofthe impact of supply-side dynamics, such as the im-pact of inventory fluctuations and forecast errors oncompetitive behavior.

5. ConclusionWe estimated a structural model of the auto market,specifically focussing on inferring competitive behav-ior in different market segments. We now summarizethe main contributions of this paper.

Substantively, we find contrasting types of com-petitive behavior in different segments of the U.S.auto market. The behavior was consistent with pre-dictions using game-theoretic literature and the abil-ity-motivation framework. The estimates indicate thatthe pricing behavior of U.S. auto firms is consistent



Table 6 Model Estimates with Competitive Interaction Estimates Restricted for Minicompact and Subcompact Segments

EstimateStandard

Deviation* t-stat EstimateStandard

Deviation* t-stat

� Demand

GMFordJapanEuropeConstant

0.860.7370.2440.437

�9.299

0.1120.1310.1360.1660.878

7.6745.641.792.64

�10.597 0.0035 0.0071 0.4898ReliabilityHorsepower (hp)SizeMP$In(Income-Price)

0.22226.9010.329

20.7426.633

0.0353.9540.073

12.3280.364

6.3386.8044.4851.683

18.231

0.00970.84940.01211.4681

0.01250.42790.00450.6191

0.77751.98482.67062.3715

CostsGMFordJapanEuropeConstant

0.009�0.012

0.220.2737.474

0.0250.0260.0390.0350.215

0.36�0.459

5.6267.921

34.804ReliabilityHorsepower (hp)SizeMPGIn(Production)

0.0455.4880.071

�0.012�7.48E-07

0.0070.5150.01

0.0034.14E-06

5.97910.667.126

�3.733�5.535

Competitive InteractionMinicompact & Subcom-

pactCompactMid-sizeFullObjective Function

�2.21981.232

2.39860.1908

1.83

1.03010.52310.45230.5687

�2.15502.35515.30300.3354

�2(0.95,9) � 3.33

* SD.

with a long-term perspective. Managerially, this im-plies that we can look at certain structural character-istics of the market and use theoretical reasoning topredict competitive behavior in markets.

Methodologically, it illustrates how to estimatecompetitive interactions among firms in markets witha large number of products using a random utilityapproach. We use a flexible random coefficients logitspecification of demand to minimize bias in the esti-mation of competitive interactions. Estimating such ademand model that accounts for consumer hetero-geneity using aggregate data necessitates the use of

a simulation-based estimation procedure. The meth-odology is applicable in estimating competitive inter-actions in other types of markets in which there is alarge amount of variety (cereal markets, personalcomputers, airlines, etc). The methods used shouldalso be useful when we want to analyze demand forfrequently purchased consumer goods at the UPClevel, rather than using aggregation to the brand level.

A criticism of NEIO studies is that its findings arenot generalizable, because it typically confines anal-ysis to a single market or industry. In this study weretain the advantages of NEIO methods but address



the issue of generalizability by analyzing competitivebehavior in multiple segments within the auto indus-try to see whether there is a consistent pattern thatcan be explained by theory.24 Nevertheless, morestudies are required in other markets and using otherstructural characteristics of market before we cangain confidence in our ability to predict competitivebehavior.

Our estimates of demand, cost, and competitive be-havior can be helpful for ‘‘what-if’’ analysis. In oneof the early papers in marketing in the NEIO tradi-tion, Horsky and Nelson (1992) assume Bertrandcompetition among firms and choose optimal pricesand product positions for new products, based ontheir demand and cost estimates. Given our findingthat there are differences in competition across seg-ments, the optimal prices as well as product positionswill change. Optimal prices based on our estimateswill be lower for minicompact and subcompact seg-ments but higher for compact and mid-size segments,compared to those of Horsky and Nelson.

Our results are also consistent with research doneusing the Structure-Conduct-Performance paradigm.There is an established literature using this paradigmon the positive correlation between market share andprofitability (Prescott et al. 1986). Similarly, there is apositive correlation between high share stability andhigher prices (Caves and Porter 1978). By carefullyseparating demand, cost, and competitive effects, weare able to show that one of the reasons for the rela-tionship between concentration, volatility, and prof-itability is attributable to the cooperative conductachieved in concentrated and stable markets.

We now discuss some of the limitations and pos-sible extensions of our paper. Our model is static anddoes not have a dynamic component, either on thedemand or the supply side. For example, we do notexplicitly model how firms choose product character-istics. This implies that we cannot do ‘‘what-if’’ anal-ysis, when dynamic effects are important. For ex-ample, in response to the increase in gas prices in

24The interested reader is directed to Kadiyali et al. (forthcoming)for a detailed discussion of the conceptual and methodological ad-vantages of the use of NEIO methods for analyzing competitivebehavior.

1973, by about 1976 manufacturers had started pro-ducing smaller, more fuel-efficient cars. In the ab-sence of a dynamic model explaining how character-istics would change over time in response toexogenous events, our predictions would be poor.

Pakes and Ericson (1997) have developed a theo-retical model of dynamic industry equilibrium, andPakes and McGuire (1994) have developed a compu-tational algorithm to estimate such a model. Thesemodels need to be extended substantially to accom-modate the multifirm, multiproduct nature of theauto market. Doing this would be crucial in general-izing the ‘‘what-if’’ analysis that account for changesin product characteristics.

Our model of demand also has no dynamic com-ponent. A dynamic model incorporating transactioncosts of buying and selling a car, uncertainty aboutthe future, and a used car market for durable goodsneeds to be modeled carefully to perform a completepolicy analysis. Erdem (1997) has developed a struc-tural model of dynamic choice for frequently pur-chased consumer goods, but such a structural modelfor durable goods is yet to be developed.

We have modeled heterogeneity using widely avail-able aggregate level data for our analysis. Howeverwith disaggregate data, we can model heterogeneityand dynamics in a much richer framework. Goldberg(1995) and Horsky and Nelson (1992) illustrate howto estimate a model using disaggregate data. Berry etal. (1998) explore how to combine disaggregate in-dividual data with aggregate market level data in es-timating an equilibrium model of the market.

Our focus in this paper has been on price compe-tition, treating other marketing mix instruments asunobserved variables that exogenously affect demandand, thus, prices. However, investigating how firmscoordinate the use of multiple marketing instrumentsis an important issue for future research. Slade (1995)addresses the issue of multiple strategic weapons (inthe context of markets with limited products) bystudying price and advertising competition simulta-neously.

In this paper, we find that domestic firms price ag-gressively in entry-level segments, in which the Jap-anese have gained greater market share but are more



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This paper was received January 20, 1998, and was with the author 20 months for 5 revisions; processed by William Boulding.

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