Accounting for primary and secondary demand effects with aggregate data

Discrete choice models of aggregate demand, such as the random coefficients logit, can handle large differentiated products categories parsimoniously while still providing flexible substitution patterns. However, the discrete choice assumption may not be appropriate for many categories in which we expect consumers may purchase more than one unit of the selected item. We derive the aggregate demand system corresponding to a discrete/continuous household-level model of demand. We also propose a method-of-simulated-moments procedure that provides consistent estimates of the structural parameters when only aggregate data are available. The procedure also enables the researcher to control both for the potential endogeneity of marketing variables as well as potential heterogeneity in consumer tastes. Using or aggregate estimates, we can measure the decomposition of price elasticities into incidence, brand choice, and purchase quantity components. We also propose several empirical tests to assess the validity of the discrete/continuous demand system versus that of the logit model. In several simulation experiments, we demonstrate the robustness of this model across datasets in which quantity choices may or may not be important. Our empirical calibration to store-level data in the refrigerated orange juice category indicates a considerable improvement in fit of the observed aggregate sales using the discrete/continuous model.