Sufficient Statistics for Unobserved Heterogeneity in Structural Dynamic Logit Models
57 Pages Posted: 23 May 2018
Date Written: May 10, 2018
We study the identification and estimation of structural parameters in dynamic panel data logit models where decisions are forward-looking and the joint distribution of unobserved heterogeneity and observable state variables is nonparametric, i.e., fixed-effects model. We consider models with two endogenous state variables: the lagged decision variable, and the time duration in the last choice. This class of models includes as particular cases important economic applications such as models of market entry-exit, occupational choice, machine replacement, inventory and investment decisions, or dynamic demand of differentiated products. The identification of structural parameters requires a sufficient statistic that controls for unobserved heterogeneity not only in current utility but also in the continuation value of the forward-looking decision problem. We obtain the minimal sufficient statistic and prove identification of some structural parameters using a conditional likelihood approach. We apply this estimator to a machine replacement model.
Keywords: Panel data discrete choice models; Dynamic structural models; Fixed effects; Unobserved heterogeneity; Structural state dependence; Identification; Sufficient statistic
JEL Classification: C23; C25; C41; C51; C61
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