IDENTIFICATION OF DISCRETE CHOICE DYNAMIC PROGRAMMING MODELS WITH NONPARAMETRIC DISTRIBUTION OF UNOBSERVABLES

Abstract

This paper presents semiparametric identification results for the Rust (1994) class of discrete choice dynamic programming (DCDP) models. We develop sufficient conditions for identification of the deep structural parameters for the case where the per-period utility function ascribed to one choice in the model is parametric but the distribution of unobserved state variables is nonparametric. The proposed identification strategy does not rely on availability of the terminal period data and can therefore be applied to infinite horizon structural dynamic models. Identifying power comes from assuming that the agent’s per-period utilities admit continuous choice-specific state variables that are observed with sufficient variation and satisfy certain conditional independence assumptions on the joint time series of observables. These conditions allow us to formulate exclusion restrictions for identifying the primitive structural functions of the model.