Sequential Estimation of Dynamic Discrete Choice Models with Unobserved Heterogeneity

Abstract

Unobserved heterogeneity is empirically central in dynamic discrete choice models but computationally costly to incorporate: estimation requires repeatedly solving fixed-point equations for every latent type. We develop EM-NPL($q$), a unified framework combining the sequential pseudo-likelihood (NPL) and finite-mixture Expectation-Maximization (EM) algorithms, truncating the inner solver to $q$ iterations, and accommodating the Bellman, policy valuation, Euler, and Efficient Pseudo-Likelihood (EPL) equations, with step-by-step implementation guidance. For linear-in-parameters models estimated via the policy valuation or EPL equations, we establish truncation invariance: for any $q\geq 1$, EM-NPL($q$) is numerically identical to the fully converged EM-NPL estimator, so q affects computation but not statistical properties. We establish consistency, asymptotic normality, and local convergence. Truncation reduces runtime by up to 26\% for PV\_GMRES in single-agent simulations and 58\% for EPL in dynamic games. In a cola-demand application, ignoring unobserved heterogeneity understates own-price elasticities and soda-tax compensating variation by up to 85\% and 90\%.