Sufficient statistics for unobserved heterogeneity in structural dynamic logit models

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. We prove the identification of the structural parameters using a conditional likelihood approach. The structure of the model implies that there is a sufficient statistic such that the likelihood function conditional on this statistic no longer depends on the unobserved heterogeneity - neither through the current utility nor through the continuation value of the forward-looking decision problem - but still depends on the structural parameters. We apply this estimator to a machine replacement model. (C) 2020 Published by Elsevier B.V.