Sequential Estimation of Dynamic Discrete Choice Models with Unobserved Heterogeneity

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%.