Counterfactual Policy Predictions Using Dynamic Discrete Choice Models Without Normalization of Per Period Utilities

Abstract

This paper studies the nonparametric identification and estimation of the structural parameters, including the per period utility functions, discount factors, and state transition laws, of general dynamic programming discrete choice (DPDC) models. I show an equivalence between the identification of the DPDC model and the identification of a linear GMM system. Using such an equivalence, I simplify both the identification analysis and the estimation practice of DPDC model. First, I prove a series of identification results for the DPDC model by using rank conditions. Previous identification results in the literature are based on normalizing the per period utility functions of one alternative. Such normalization could severely bias the estimates of counterfactual policy effects. I show that the structural parameters can be nonparametrically identified without the normalization. Second, I propose a closed form nonparametric estimator for the per period utility functions, of which computation involves only least square. The existing estimation procedures rely on assuming the dynamic programming (DP) problem is stationary or on solving the DP problem numerically with the aid of terminal conditions. Neither my identification nor the estimation requires terminal conditions, the DPDC model to be stationary, or a sample that covers the entire decision horizon.