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Numerically approximating multi-dimensional integrals has become an increasingly important part of an economist's toolbox because heterogeneity, uncertainty, and incomplete information -often key factors in modern models -require integrating accurately over some probability density function. This paper demonstrates that polynomial-based rules out-perform number-theoretic quadratures rules, namely pseudo-Monte Carlo, for Berry, Levinsohn, and Pakes (1995)'s model of product differentiation. Indoi:10.2139/ssrn.1870703 fatcat:7h6qhu7shnf2hbmpksu7qviwji