Solving Dynamic Discrete Choice Models Using Smoothing and Sieve Methods

TL;DR

This paper introduces a novel approach combining smoothing, simulation, and sieve methods to efficiently solve dynamic discrete choice models, improving computational speed and accuracy with theoretical guarantees.

Contribution

It develops a smoothed Bellman operator and adapts sieve methods for solving DDC models, providing asymptotic theory and practical performance analysis.

Findings

Sieve method offers faster computation and high accuracy.

Both proposed methods converge at root-N rate to Gaussian processes.

Numerical experiments demonstrate strong practical performance.

Abstract

We propose to combine smoothing, simulations and sieve approximations to solve for either the integrated or expected value function in a general class of dynamic discrete choice (DDC) models. We use importance sampling to approximate the Bellman operators defining the two functions. The random Bellman operators, and therefore also the corresponding solutions, are generally non-smooth which is undesirable. To circumvent this issue, we introduce a smoothed version of the random Bellman operator and solve for the corresponding smoothed value function using sieve methods. We show that one can avoid using sieves by generalizing and adapting the `self-approximating' method of Rust (1997) to our setting. We provide an asymptotic theory for the approximate solutions and show that they converge with root-N-rate, where $N$ is number of Monte Carlo draws, towards Gaussian processes. We examine their performance in practice through a set of numerical experiments and find that both methods perform well with the sieve method being particularly attractive in terms of computational speed and accuracy.