A Computationally Efficient Fixed Point Approach to Dynamic Structural Demand Estimation

Abstract

This paper develops a computationally efficient approach to the estimation of random coefficients logit model of dynamic consumer demand using product panel data. The conventional GMM estimation relies on two computationally intensive fixed point algorithms, each developed by Rust (1987) and Berry, Levinsohn, and Pakes (1995), nested within an optimization routine. We transform the GMM estimation into a quasi-Bayesian (Laplace type) framework and develop a Markov Chain Monte Carlo (MCMC) method that solves the fixed point problems incrementally with Markov chain simulation. The proposed approach has two main advantages. First, it reduces the computational burden of the nested fixed point (NFP) algorithm employed by GMM without sacrificing the model flexibility. Our Monte Carlo experiments demonstrate that the new method outperforms both NFP and MPEC in computational speed by substantial margin, particularly in the most computationally intensive estimations. Second, the proposed method requires only moment restrictions as GMM, thereby avoiding the risk of misspecification bias in equilibrium frameworks.

Keywords: Nested fixed point, BLP, dynamic programming, MCMC, Laplace, random coefficients logit

JEL Classification: C11, C13, C51