Training Neural Networks Embedded in Dynamic Discrete Choice Models

TL;DR

This paper introduces a novel estimator for infinite-horizon dynamic discrete choice models that leverages neural networks and dual Bellman representations, simplifying computation and enabling flexible utility modeling.

Contribution

It presents the first general-purpose, unnested fixed point estimators that separate utility parameters from dynamic programming, allowing non-parametric neural network utility functions.

Findings

Establishes consistency and asymptotic normality of the proposed estimators.

Demonstrates efficiency of the OUFXP estimator.

Enables flexible neural network utility modeling in dynamic choice models.

Abstract

We develop the first general-purpose estimator for infinite-horizon dynamic discrete choice models whose estimation problem, after pre-computation, is unencumbered by large systems of linear equations -- either imposed as constraints, or embedded in the objective function. Our unnested fixed point (UFXP) and optimal unnested fixed point (OUFXP) estimators exploit a dual representation of Bellman's equation to separate the utility parameters from the dynamic programming fixed point. We establish the consistency and asymptotic normality of UFXP and OUFXP, as well as the efficiency of the latter. Our estimators enable researchers to model utility functions non-parametrically via flexible neural-network approximations.