One-node Quadrature Beats Monte Carlo: A Generalized Stochastic Simulation Algorithm

Kenneth Judd, Lilia Maliar, Serguei Maliar

NBER Working Paper No. 16708
Issued in January 2011
NBER Program(s):The Economic Fluctuations and Growth Program, Technical Working Papers

In conventional stochastic simulation algorithms, Monte Carlo integration and curve fitting are merged together and implemented by means of regression. We perform a decomposition of the solution error and show that regression does a good job in curve fitting but a poor job in integration, which leads to low accuracy of solutions. We propose a generalized notion of stochastic simulation approach in which integration and curve fitting are separated. We specifically allow for the use of deterministic (quadrature and monomial) integration methods which are more accurate than the conventional Monte Carlo method. We achieve accuracy of solutions that is orders of magnitude higher than that of the conventional stochastic simulation algorithms.

Acknowledgments

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Document Object Identifier (DOI): 10.3386/w16708

Published: Kenneth L. Judd, Lilia Maliar and Serguei Maliar, (2011). “Numerically Stable and Accurate Stochastic Simulation Methods for Solving Dynamic Models" and "Supplement", Quantitative Economics 2, 173-210.

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