The Discrete Choice Analytically Flexible (DCAF) Model of Demand for Differentiated Products

In this paper I develop the Discrete Choice Analytically Flexible (DCAF) model of demand for differentiated products. DCAF relaxes the constraints imposed on the matrix of own- and cross-price elasticities of demand by popular analytic discrete choice models such as the Multinomial Logit (MNL) and Nested MNL models. At the same time, in contrast to models such as Probit (Hausman and Wise (1978)) and Random Coefficient-MNL (RC-MNL) models (Berry, Levinsohn and Pakes (1995)), DCAF does not require estimation via simulation; it is fully analytic. I show DCAF is a flexible functional form in the sense of Diewert (1974), thus ensuring that its parameters can be chosen to match a well defined class of possible own- and cross-price elasticities of demand. Under well defined constraints on the parameters, which may or may not be imposed in estimation, DCAF is shown to be a previously unexplored member of Mcfadden's(1978) class of Multivariate Extreme Value (MEV) discrete choice models. Hence, under testable parameter restrictions, DCAF is fully consistent with an underlying structural model of heterogeneous, utility maximizing, consumers. I provide a small monte-carlo study to illustrate use of the model and establish its properties. A full application of the model using data from the UK confectionary market is provided in the companion paper, Davis (2006).