Dynamic demand for differentiated products with fixed-effects unobserved heterogeneity

Abstract

Summary This paper studies identification and estimation of a dynamic discrete choice model of demand for differentiated product using consumer-level panel data with few purchase events per consumer (i.e., short panel). Consumers are forward-looking and their preferences incorporate two sources of dynamics: last choice dependence due to habits and switching costs, and duration dependence due to inventory, depreciation, or learning. A key distinguishing feature of the model is that consumer unobserved heterogeneity has a Fixed Effects structure; that is, its probability distribution conditional on the initial values of endogenous state variables is unrestricted. I apply and extend recent results to establish the identification of all the structural parameters as long as the dataset includes four or more purchase events per household. The parameters can be estimated using a sufficient statistic—conditional maximum likelihood (CML) method. An attractive feature of CML in this model is that the sufficient statistic controls for the forward-looking value of the consumer’s decision problem, such that the method does not require solving dynamic programming problems or calculating expected present values.