Model-Adaptive Approach to Dynamic Discrete Choice Models with Large State Spaces

TL;DR

This paper introduces a model-adaptive sieve approach using conjugate gradient methods to efficiently solve large-scale dynamic discrete choice models, significantly improving computational speed and accuracy.

Contribution

It develops a novel, theoretically justified model-adaptive sieve method that enhances the efficiency of solving large state space dynamic models, outperforming traditional methods.

Findings

Superlinear decay of approximation error with sieve dimension

80% reduction in computational time compared to existing methods

Applicable to both conditional choice probability and full-solution estimators

Abstract

Estimation and counterfactual experiments in dynamic discrete choice models with large state spaces pose computational difficulties. This paper proposes a model-adaptive approach, based on the conjugate gradient (CG) method, to solve the linear system of fixed point equations of the policy valuation operator. We propose a model-adaptive sieve space, constructed by iteratively augmenting the space with the residual from the previous iteration. We show both theoretically and numerically that model-adaptive sieves dramatically improve performance. In particular, the approximation error decays at a superlinear rate in the sieve dimension, unlike a linear rate achieved using successive approximation. Our method works for both conditional choice probability estimators and full-solution estimators with policy iteration or Newton-Kantorovich iterations. We apply the method to analyze consumer demand for laundry detergent using Kantar's Worldpanel Take Home data. On average, our method is 80% faster than successive approximation and the exact equation solver in solving the dynamic programming problem, substantially reducing the computational cost of the Bayesian MCMC estimator.