Heteroscedastic Exponomial Choice

Modeling Choices with Different Variabilities In “Heteroscedastic Exponomial Choice” (HEC), Aydın Alptekinoğlu and John Semple investigate a discrete choice model that can handle choices with utilities having different variances. This new model, the HEC model, nests the exponomial choice (EC) model as a special case. Like EC, HEC has excellent structure and permits the choice probabilities, demand elasticities, and consumer surplus to be expressed in an analytically convenient (closed) form. Determining optimal monopoly prices for products in an assortment as well as determining equilibrium prices for an oligopoly of single-product firms are both tractable problems. Moreover, fitting the choice model to real data is straightforward, given the shape (log-concavity) of the likelihood function for a given variance structure. The HEC model performed well against MNL (multinomial logit) and EC models in empirical tests on household panel data for 30 categories of grocery products. In particular, brand variance was statistically significant in virtually every product category tested. We investigate analytical and empirical properties of the Heteroscedastic Exponomial Choice (HEC) model to lay the groundwork for its use in theoretical and empirical studies that build demand models on a discrete choice foundation. The HEC model generalizes the Exponomial Choice (EC) model by including choice-specific variances for the random components of utility (the error terms). We show that the HEC model inherits some of the properties found in the EC model: closed-form choice probabilities, demand elasticities, and consumer surplus; optimal monopoly prices that are increasing with ideal utilities in a hockey-stick pattern; and unique equilibrium oligopoly prices that are easily computed using a series of single-variable equations. However, the HEC model has several key differences with the EC model, which show that variances matter: the choice probabilities (market shares) as well as equilibrium oligopoly prices are not necessarily increasing with ideal utilities; and the new model can include choices with deterministic utility or choices with zero probability. However, because the HEC model uses more parameters, it is harder to estimate. To justify its use, we apply HEC to grocery purchase data for 30 product categories and find that it significantly improves model fit and generally improves out-of-sample prediction compared with EC. We go on to investigate the more nuanced