Sufficient Statistics for Markovian Feedback Processes and Unobserved Heterogeneity in Dynamic Panel Logit Models

TL;DR

This paper explores identification challenges in dynamic panel logit models with Markovian feedback and unobserved heterogeneity, proposing sufficient statistics and conditions for identification.

Contribution

It introduces sufficient statistics for feedback and heterogeneity, and establishes conditions under which identification via conditional likelihood is possible.

Findings

Identification via conditional likelihood is infeasible with a Markov covariate.

Point identification fails beyond the conditional likelihood framework without additional restrictions.

Two assumptions are proposed to achieve identification under certain conditions.

Abstract

In this paper, we examine identification in dynamic panel logit models with state dependence, a first-order Markov feedback process, and individual unobserved heterogeneity by introducing sufficient statistics for the feedback process and the unobserved heterogeneity. If a sequentially exogenous discrete covariate follows a first-order Markov process, identification via conditional likelihood is infeasible regardless of the time period. We also establish the failure of point identification beyond the conditional likelihood framework, which necessitates additional restrictions for identification. We present two assumptions for identification via conditional likelihood, imposed on the feedback process and the initial condition, respectively.