The drawback with this multistage approach is that the elasticity estimates are dependent on the assumed separable structure of the utility function, which is difficult to test empirically. Aggregate versions of the discrete choice (DC) demand model reduce the number of coefficients by projecting the number of products on to a lower dimensional space, namely the product characteristics. Variants of the DC model are attractive because they explicitly model consumers’ heterogeneity of preferences over product characteristics. The main drawbacks DC models are the independence of irrelevant alternatives (IIA) property in logit and nested logit models,the computational complexity of the random coefficients model, and the assumption that the consumer purchases a single unit of the differentiated product. This last assumption clearly does not fit consumer behavior in many differentiated product markets.
Pinkse et al. (2002) [henceforth PSB] developed the distance metric (DM) technique to overcome the dimensionality limitation of neoclassical demand models by specifying the crossprice terms as a function of a brand’s location in product characteristic space relative to other brands. Various distance measures between brands may be constructed and used as weights to create cross-price indices for each distance measure. The cross-price coefficients and elasticities can then be computed using the estimated coefficients for the cross-price indices and the distance measures between brands. The advantages of the DM method are that it is easier to estimate than the random coefficient DC model; it allows testing the existence and strength of different product groupings as potential sources of competition; and it accounts for the location of brands location in product space.
In this paper, we employ the DM method to estimate the price and advertising elasticities of demand for 64 brands of beer in the United States. This is one of the first studies that estimates a large number of brand-level advertising elasticities.2 In addition, controlling for brand advertising is important because it reduces the likelihood of common demand shocks across regions, which improves the validity of our identifying assumption for prices.
While our estimated price elasticities are consistent with previous work, the estimated advertising elasticities convey new results. Positive and negative cross-advertising elasticities imply the presence of both cooperative and predatory effects. However, the former effect dominates suggesting that advertising increases the overall demand for beer. This is an important result in the long debate about the effects of advertising on alcohol consumption.
2. Empirical model
Previous DM applications (Pinkse and Slade, 2004; Slade, 2004) employ a quadratic indirect utility function and use Roy’s Identity to derive the uncompensated demand functions. If the marginal utility of income is constant, which may be plausible when using cross-sectional or very short panel data, its value may be normalized to equal one, greatly simplifying the demand functions to be estimated. Because of the length of panel data we employ, 20 quarters, it is less plausible that the marginal utility of income is constant. Thus, the quadratic indirect utility function is less attractive because the uncompensated demand functions are non-linear in the parameters. Given the large number of brands, estimating a model that incorporates the DM method and is non-linear in the parameters is not practical. To solve this problem, we employ a linear approximation of the Almost Ideal Demand System (Deaton and Muellbauer, 1980):