The Interaction of Observed and Unobserved Factors in Discrete Choice Demand Models

Although universally maintained there is no compelling economic motivation to treat the demand unobservable as separable in preferences in the discrete choice demand setting. We develop an estimator for a utility function that allows for interactions between observed and unobserved product attributes. We show that the Berry (1994) inversion can still be used to recover the “mean” utility term. However, Berry’s instrumental variable (IV) solution is no longer consistent because the error in the non-separable setup is correlated with the instrumented price. We show that the standard conditional moment restrictions (CMRs) do not generally suffice for identification. We supplement the standard CMRs with new moments that we call “generalized” control function moments and we show together they are sufficient for identification of all of the demand parameters. A major advantage of our setup is it does not require anything more than the instruments used in this standard IV setting. We run several monte carlos that show our approach works when the standard IV approaches fail because of non-separability. We also test and reject additive separability in the original Berry, Levinsohn, and Pakes (1995) automobile data, and we show that demand becomes significantly more elastic when the correction is applied.