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

24 Pages Posted: 19 Jan 2011 Last revised: 26 Feb 2023

See all articles by Kenneth L. Judd

Kenneth L. Judd

Stanford University - The Hoover Institution on War, Revolution and Peace; Center for Robust Decisionmaking on Climate & Energy Policy (RDCEP); National Bureau of Economic Research (NBER)

Lilia Maliar

CUNY The Graduate Center - Department of Economics

Serguei Maliar

Universidad de Alicante - Departamento de Fundamentos del Analisis Economico; Stanford University - Department of Economics

Date Written: January 2011

Abstract

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.

Suggested Citation

Judd, Kenneth L. and Maliar, Lilia and Maliar, Serguei, One-Node Quadrature Beats Monte Carlo: A Generalized Stochastic Simulation Algorithm (January 2011). NBER Working Paper No. w16708, Available at SSRN: https://ssrn.com/abstract=1743325

Kenneth L. Judd (Contact Author)

Stanford University - The Hoover Institution on War, Revolution and Peace ( email )

Stanford, CA 94305-6010
United States

Center for Robust Decisionmaking on Climate & Energy Policy (RDCEP) ( email )

5735 S. Ellis Street
Chicago, IL 60637
United States

National Bureau of Economic Research (NBER) ( email )

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

Lilia Maliar

CUNY The Graduate Center - Department of Economics ( email )

365 Fifth Avenue, 5th Floor
New York, NY 10016
United States

Serguei Maliar

Universidad de Alicante - Departamento de Fundamentos del Analisis Economico ( email )

Campus de San Vicente
Ap. Correos 99
03080 Alicante
Spain

Stanford University - Department of Economics ( email )

Landau Economics Building
579 Serra Mall
Stanford, CA 94305-6072
United States

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