Sequential Estimation of Dynamic Discrete Choice Models with Unobserved Heterogeneity

TL;DR

This paper introduces an efficient EM-NPL(q) framework for estimating dynamic discrete choice models with unobserved heterogeneity, reducing computational costs while maintaining statistical accuracy.

Contribution

It establishes a truncation-invariance property for linear-in-parameters models and proves the estimator's consistency, asymptotic normality, and convergence.

Findings

EM-NPL(q) reduces runtime by at least 20%.

It can be 3-5 times faster than traditional methods.

Ignoring unobserved heterogeneity significantly underestimates elasticities and welfare effects.

Abstract

Estimating dynamic discrete choice models with unobserved heterogeneity is computationally costly because it requires repeatedly solving fixed-point equations for all unobserved types. We develop the EM-NPL(q) framework that combines the Expectation-Maximization (EM) algorithm with an inner fixed-point solver truncated to q iterations. For the workhorse class of linear-in-parameters models, we establish a truncation-invariance result: for any q$\geq$1, EM-NPL(q) is numerically identical to the EM-NPL estimator that solves the inner fixed-point problem to convergence. Therefore, the choice of q affects computation but not statistical properties. We also establish consistency, asymptotic normality of our estimator, and local convergence of the EM-NPL(q) algorithm. In Monte Carlo simulations, EM-NPL(q) reduces runtime by at least 20% and can be 3--5 times faster. In an application to cola demand, we show that ignoring unobserved heterogeneity understates long-run own-price elasticities by up to 60%, short-run elasticities by up to 85%, and compensating variation from a soda tax by up to 90%.