Working Paper: CEPR ID: DP16354
Authors: Victor Aguirregabiria; Jesus Carro
Abstract: In nonlinear panel data models, fixed effects methods are often criticized because they cannot identify average marginal effects (AMEs) in short panels. The common argument is that the identification of AMEs requires knowledge of the distribution of unobserved heterogeneity, but this distribution is not identified in a fixed effects model with a short panel. In this paper, we derive identification results that contradict this argument. In a panel data dynamic logic model, and for T as small as four, we prove the point identification of different AMEs, including causal effects of changes in the lagged dependent variable or in the duration in last choice. Our proofs are constructive and provide simple closed-form expressions for the AMEs in terms of probabilities of choice histories. We illustrate our results using Monte Carlo experiments and with an empirical application of a dynamic structural model of consumer brand choice with state dependence.
Keywords: Identification; Average Marginal Effects; Fixed Effects Models; Panel Data; Dynamic Discrete Choice; State Dependence; Dynamic Demand of Differentiated Products
JEL Codes: C23; C25; C51
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| Fixed effects models (C23) | Identification of AMEs (C30) |
| Identification of AMEs does not require knowledge of the distribution of unobserved heterogeneity (C20) | Identification of AMEs (C30) |
| Identification results extend to more general models, including those with strictly exogenous explanatory variables and duration dependence (C32) | Identification results (C29) |
| AME of a change in the duration variable is identifiable (C41) | AME of a change in the duration variable (C41) |