Working Paper: NBER ID: w16894
Authors: Amit Gandhi; Kyoo Il Kim; Amil Petrin
Abstract: We develop an estimator for the parameters of a utility function that has interactions between the unobserved demand error and observed factors including price. We show that the Berry (1994)/Berry, Levinsohn, and Pakes (1995) inversion and contraction can still be used to recover the mean utility term that now contains both the demand error and the interactions with the error. However, the instrumental variable (IV) solution is no longer consistent because the price interaction term 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 that it requires little more than the existence of the same 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
Keywords: Discrete choice; Demand estimation; Endogeneity; Instrumental variables
JEL Codes: C25; L00
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| standard CMRs are insufficient for identification (L15) | generalized control function moments are required (C51) |
| generalized control function moments allow for consistent estimation of demand parameters (C51) | interactions between endogenous and exogenous variables and unobserved demand error (C51) |
| inclusion of interaction terms (C31) | demand elasticities become significantly more elastic (H30) |
| reject additive separability assumption (D10) | accurate demand estimation (C51) |
| endogenous variables interact with unobserved demand error (C51) | mean utility term recovery (D11) |