DP12930 Sufficient Statistics for Unobserved Heterogeneity in Structural Dynamic Logit Models

Author(s): Victor Aguirregabiria, Jiaying Gu, Yao Luo
Publication Date: May 2018
Keyword(s): dynamic structural models, fixed effects, identification, Panel data discrete choice models, Structural state dependence, Sufficient statistic, Unobserved heterogeneity
JEL(s): C23, C25, C41, C51, C61
Programme Areas: Industrial Organization
Link to this Page: cepr.org/active/publications/discussion_papers/dp.php?dpno=12930

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.