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Title:High performance quadrature rules: How numerical integration affects a popular model of product differentiation PDF Logo
Authors:L. Judd, Kenneth
Skrainka, Ben
Issue Date:2011
Series/Report no.:cemmap working paper CWP03/11
Abstract:Efficient, accurate, multi-dimensional, numerical integration has become an important tool for approximating the integrals which arise in modern economic models built on unobserved heterogeneity, incomplete information, and uncertainty. This paper demonstrates that polynomialbased rules out-perform number-theoretic quadrature (Monte Carlo) rules both in terms of efficiency and accuracy. To show the impact a quadrature method can have on results, we examine the performance of these rules in the context of Berry, Levinsohn, and Pakes (1995)'s model of product differentiation, where Monte Carlo methods introduce considerable numerical error and instability into the computations. These problems include inaccurate point estimates, excessively tight standard errors, instability of the inner loop 'contraction' mapping for inverting market shares, and poor convergence of several state of the art solvers when computing point estimates. Both monomial rules and sparse grid methods lack these problems and provide a more accurate, cheaper method for quadrature. Finally, we demonstrate how researchers can easily utilize high quality, high dimensional quadrature rules in their own work.
Subjects:Numerical Integration
Monomial Rules
Gauss-Hermite Quadrature
Sparse Grid Integration
Monte Carlo Integration
pseudo-Monte Carlo
Product Differentiation
Econometrics
Random Coefficients
Discrete Choice
Persistent Identifier of the first edition:doi:10.1920/wp.cem.2011.0311
Document Type:Working Paper
Appears in Collections:cemmap working papers, Centre for Microdata Methods and Practice, Institute for Fiscal Studies (IFS)

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