A Bayesian approach to estimation of dynamic models with small and large number of heterogeneous players and latent serially correlated state

Abstract

We propose a Bayesian approach to estimating dynamic models that can have state variables that are latent, serially correlated, and heterogeneous. Our approach employs sequential importance sampling and is based on deriving an unbiased estimate of the likelihood within a Metropolis chain. Under fairly weak regularity conditions unbiasedness guarantees that the stationary density of the chain is the exact posterior, not an approximation. Results are verified by Monte Carlo simulation using two examples. The first is a dynamic game of entry involving a small number of firms whose heterogeneity is based on their current costs due to feedback through capacity constraints arising from past entry. The second is an Ericson-Pakes (1995) style game with a large number of firms whose heterogeneity is based on the quality of their products with firms competing through investment in product quality that affects their market share and profitability. Our approach facilitates estimation of dynamic games with either small or large number of players whose heterogeneity is determined by latent state variables, discrete or continuous, that are subject to endogenous feedback from past actions.