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Monte Carlo simulation and numerical integration

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  • John Geweke

Abstract

This is a survey of simulation methods in economics, with a specific focus on integration problems. It describes acceptance methods, importance sampling procedures, and Markov chain Monte Carlo methods for simulation from univariate and multivariate distributions and their application to the approximation of integrals. The exposition gives emphasis to combinations of different approaches and assessment of the accuracy of numerical approximations to integrals and expectations. The survey illustrates these procedures with applications to simulation and integration problems in economics.

Suggested Citation

  • John Geweke, 1995. "Monte Carlo simulation and numerical integration," Staff Report 192, Federal Reserve Bank of Minneapolis.
    • Handle: RePEc:fip:fedmsr:192
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    References listed on IDEAS

    as
    1. Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, vol. 57(6), pages 1317-1339, November.
    2. Geweke, John, 1994. "Priors for Macroeconomic Time Series and Their Application," Econometric Theory, Cambridge University Press, vol. 10(3-4), pages 609-632, August.
    3. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 2002. "Bayesian Analysis of Stochastic Volatility Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 69-87, January.
    4. McGrattan, Ellen R., 1996. "Solving the stochastic growth model with a finite element method," Journal of Economic Dynamics and Control, Elsevier, vol. 20(1-3), pages 19-42.
    5. P. Wild & W. R. Gilks, 1993. "Adaptive Rejection Sampling from Log‐Concave Density Functions," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 42(4), pages 701-709, December.
    6. Anthony A. Smith, Jr., 1991. "Solving Stochastic Dynamic Programming Problems Using Rules Of Thumb," Working Paper 816, Economics Department, Queen's University.
    7. William A. Brock & Leonard J. Mirman, 2001. "Optimal Economic Growth And Uncertainty: The Discounted Case," Chapters, in: W. D. Dechert (ed.), Growth Theory, Nonlinear Dynamics and Economic Modelling, chapter 1, pages 3-37, Edward Elgar Publishing.
    8. Taylor, John B & Uhlig, Harald, 1990. "Solving Nonlinear Stochastic Growth Models: A Comparison of Alternative Solution Methods," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(1), pages 1-17, January.
    9. Geweke, John, 1986. "Exact Inference in the Inequality Constrained Normal Linear Regression Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 1(2), pages 127-141, April.
    10. Geweke, John, 1988. "Antithetic acceleration of Monte Carlo integration in Bayesian inference," Journal of Econometrics, Elsevier, vol. 38(1-2), pages 73-89.
    11. W. R. Gilks & P. Wild, 1992. "Adaptive Rejection Sampling for Gibbs Sampling," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 41(2), pages 337-348, June.
    12. H. Kahn & A. W. Marshall, 1953. "Methods of Reducing Sample Size in Monte Carlo Computations," Operations Research, INFORMS, vol. 1(5), pages 263-278, November.
    13. Kloek, Tuen & van Dijk, Herman K, 1978. "Bayesian Estimates of Equation System Parameters: An Application of Integration by Monte Carlo," Econometrica, Econometric Society, vol. 46(1), pages 1-19, January.
    14. Tauchen, George, 1985. "Diagnostic testing and evaluation of maximum likelihood models," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 415-443.
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    More about this item

    Keywords

    Econometrics;

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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