  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 (FE)
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.
