A Large Scale Study of the Small Sample Performance of Random Coefficient Models of Demand

Abstract

Despite the importance of Berry et al.(1995)'s model of demand for differentiated products (BLP hereafter), there are few results about its finite sample behavior. In theory, simulation experiments provide a tool to answer such questions but computational and numerical difficulties have prevented researchers from performing any realistic studies. Those Monte Carlo studies which exist focus on only one market and often take computational short-cuts.For example, Armstrong (2011) uses only 10 pseudo-Monte Carlo quadrature nodes and fixes the scale of the random coefficients. Nevertheless, by utilizing recent advances in optimization (Su and Judd, 2010; Dubé et al., 2011) and multi-dimensional numerical integration (Skrainka and Judd, 2011), I develop a fast, robust implementation of BLP and show that a large-scale simulation approach is now feasible.This study estimated BLP over 320,000 times and used 94,325 CPU-hours (See [sub:Computational.Cost] for further discussion.). I compute the finite sample behavior under both the traditional BLP instruments (characteristics of rival goods) and exogenous cost shifters using synthetic data generated from a structural model for realistic numbers of markets and products. This paper, then, has two objectives: to demonstrate the power of modern computational technology for solving previously intractable problems in Economics via massive parallelization and to characterize the finite sample behavior of the BLP estimator.

Keywords: Differentiated products, random coefficients, BLP, finite sample bias, GMM, simulation, quadrature, optimization, MPEC

JEL Classification: C1, C5, C6, L00, M3