Identification

In an ideal and controlled setting, we would like brands to sell the same set of high- end and low-end car models in two similar geographic markets, where in one market brands use the same design while in the other market brands use different designs. This setting would allow us to clearly assess the effect of design differentiation on consumer prefer- ences and choices. However, brands do not vary design across geographic markets, which can confuse consumers and obscure brand image. With data of 207 car models sold in 120 months, we observe variations in car design across car models and changes in car de- sign over time. We rely on cross-sectional variations across car models and time-series variations within car models to identify the parameters of design variables as well as other structural parameters in Equation (4.2). Particularly, the effect of design differentiation on consumer preferences is identified by variations in the inverted market share across car models and across months that change with the variations in the design differentiation vari- able across car models and across months, after controlling for other factors that impact market share.

prices and advertising activities. Prices are likely endogenous for two reasons: omitted variables and simultaneity. First, there may be product quality attributes that are unob- served to researchers but considered by car makers to set prices and considered by con- sumers to choose cars. Such unobserved quality is included in the error term,ηjt, which induces correlation between the error term and prices, making prices endogenous. Sec- ond, prices are simultaneously determined by the demand side and car makers’ profit- maximizing behavior on the supply side. Without explicitly modeling the supply side, prices are endogenous due to simultaneity. Similarly, advertising activities may also be endogenous, as car makers may purposely advertise car models with certain unobserved characteristics in a period.

We take three steps to address these endogeneity problems. First, we use brand fixed effects to control for any brand level unobserved factors that impact prices, advertising, and market shares.‡ Second, we use month fixed effects to control for seasonality and unob- served month-specific factors that impact prices, advertising, and market shares. However, there could still be correlations between the error termηjt and prices or advertising on di- mensions that these fixed effects have not controlled for. We use instrument variables to control for potential sources of endogeneity on these dimensions.

Cost shifters from the supply side would be ideal instruments for prices and advertis-

‡_{Alternatively, one could use car model specific fixed effects to control for unobserved factors at the car} model level. However, the drawback of this approach is that car model fixed effects would absorb cross- sectional variations and only rely on time-series variations within car models for identification. However, car design does not change frequently. On average, the life cycle of a car design is seven years with a mid- life refresh (Weber 2009). Certain car models in our dataset have not changed design in the sample period. Hence, variations in the design variable are largely from the cross-sectional dimension. We use brand fixed effects to preserve variations in design variable while controlling for unobserved time-invariant factors at the brand level.

ing as they are not correlated with unobserved demand factors but correlated with prices and advertising levels. Positive shifters of production costs are expected to be positively correlated with prices and positive shifters of advertising costs are expected to be nega- tively correlated with advertising levels. We use the unit cost of advertising across media (cable TV, network TV, daily magazines, and national newspapers) that Ad$pender reports as instruments for advertising expenditure.

However, data on production cost shifters are not available. To address endogeneity problems of prices, the most popular identifying assumption used in prior research is that the locations of products in the characteristics space is exogenous, or at least determined prior to the revelation of consumers’ valuation of the unobserved product characteristics (Nevo 2000). We adopt this identifying assumption. We assume that car attributes, includ- ing design characteristics, are determined prior to the revelation of consumers’ valuation of the unobserved product characteristics. Based on this assumption, we follow prior re- search and use observed car characteristics to derive proper instruments for prices (Berry et al. 1995, Sudhir 2001). For example, to create a set of instruments for prices of car model

jof brandiusing horsepower, we compute the average horsepower of brandi’s car models other than j to be the own-brand horsepower instrument variable. We also compute the average horsepower of all car models of all other brands to be the other-brand horsepower instrument variable. We derive two sets of own-brand and other-brand horsepower instru- ments using two ways to group brands, the first based on country of origin and (regular or non-regular) car type, the second based on country of origin and (luxury or econoour)

classification. As a result, we derive four instruments based on each functional attribute variable. With the instruments, we estimate the model using GMM methods (see Nevo 2000 for details). Model estimates are shown in Table 4.2.