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.