Sufficient Statistics for Unobserved Heterogeneity in Structural Dynamic Logit Models

TL;DR

This paper develops a method to identify and estimate structural parameters in dynamic logit models with unobserved heterogeneity, applicable to various economic decision-making scenarios, using a minimal sufficient statistic and conditional likelihood.

Contribution

It introduces a minimal sufficient statistic for unobserved heterogeneity in dynamic panel logit models and demonstrates identification of parameters with a conditional likelihood approach.

Findings

Successfully derives the minimal sufficient statistic.

Proves identification of key structural parameters.

Applies method to a machine replacement model.

Abstract

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.