K-means Clustering of CCPs for Estimating Dynamic Discrete Choice Models with Unobserved Heterogeneity

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We propose to use k-means clustering of observed conditional choice probabilities (CCPs) to estimate latent variables that underlie unobserved heterogeneity in dynamic decision problems and dynamic games. Unobserved heterogeneity can have both time-invariant and time-varying components. We cluster (i) individual-specific (or, in the case of games, market-specific) CCPs to identify time-invariant types, and (ii) time-specific CCPs to identify time-varying types. Existing two-step estimators in the literature can then be computed using estimated latent states. We provide conditions for such estimators to be asymptotically equivalent to their infeasible counterparts that assume unobserved heterogeneity is known. Our proposal enables researchers to enjoy all the numerical advantages that a two-step approach has over full-solution or iterative estimation methods. We illustrate the approach with the closed-form OLS estimator of Sanches, Silva, and Srisuma (2016), which shows very good finite-sample performance in Monte Carlo simulations.