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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.

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

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    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. Ellen R. McGrattan, . "Solving the stochastic growth model with a finite element method," Staff Report, Federal Reserve Bank of Minneapolis.
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    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.
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    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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    Cited by:

    1. Adnan Haider Bukhari & Safdar Ullah Khan, 2008. "A Small Open Economy DSGE Model for Pakistan," The Pakistan Development Review, Pakistan Institute of Development Economics, vol. 47(4), pages 963-1008.
    2. Kilian, Lutz & Zha, Tao, 1999. "Quantifying the Half-Life of Deviations from PPP: The Role of Economic Priors," CEPR Discussion Papers 2334, C.E.P.R. Discussion Papers.
    3. Eduardo Fé & Richard Hofler, 2013. "Count data stochastic frontier models, with an application to the patents–R&D relationship," Journal of Productivity Analysis, Springer, vol. 39(3), pages 271-284, June.
    4. Christopher G. Lamoureux & H. Douglas Witte, 2002. "Empirical Analysis of the Yield Curve: The Information in the Data Viewed through the Window of Cox, Ingersoll, and Ross," Journal of Finance, American Finance Association, vol. 57(3), pages 1479-1520, June.
    5. Waggoner, Daniel F. & Zha, Tao, 2003. "A Gibbs sampler for structural vector autoregressions," Journal of Economic Dynamics and Control, Elsevier, vol. 28(2), pages 349-366, November.
    6. Daniel F. Waggoner & Tao Zha, 2000. "A Gibbs simulator for restricted VAR models," FRB Atlanta Working Paper 2000-3, Federal Reserve Bank of Atlanta.
    7. Torben G. Andersen & Tim Bollerslev, 1997. "Answering the Critics: Yes, ARCH Models Do Provide Good Volatility Forecasts," NBER Working Papers 6023, National Bureau of Economic Research, Inc.
    8. Gary Chamberlain & Guido W. Imbens, 1996. "Hierarchical Bayes Models with Many Instrumental Variables," Harvard Institute of Economic Research Working Papers 1781, Harvard - Institute of Economic Research.
    9. Christopher Otrok & Charles H. Whiteman, 1996. "Baynesian Leading Indicators: Measuring and Predicting Economic Conditions," Macroeconomics 9610002, University Library of Munich, Germany.
    10. William Greene, 2001. "Fixed and Random Effects in Nonlinear Models," Working Papers 01-01, New York University, Leonard N. Stern School of Business, Department of Economics.
    11. Chokri Dridi, 2002. "A Short Note on the Numerical Approximation of the Standard Normal Cumulative Distribution and Its Inverse," Computational Economics 0212001, University Library of Munich, Germany, revised 07 Mar 2003.
    12. Luca Spataro, 2002. "New Tools in Micromodeling Retirement Decisions: Overview and Applications to the Italian Case," CeRP Working Papers 28, Center for Research on Pensions and Welfare Policies, Turin (Italy).
    13. Andersen, Torben G. & Lund, Jesper, 1997. "Estimating continuous-time stochastic volatility models of the short-term interest rate," Journal of Econometrics, Elsevier, vol. 77(2), pages 343-377, April.
    14. Ghysels, E. & Harvey, A. & Renault, E., 1995. "Stochastic Volatility," Papers 95.400, Toulouse - GREMAQ.
    15. Xiao-Hui Sun & Toshiyuki Yamamoto & Kazuhiro Takahashi & Takayuki Morikawa, 2018. "Home charge timing choice behaviors of plug-in hybrid electric vehicle users under a dynamic electricity pricing scheme," Transportation, Springer, vol. 45(6), pages 1849-1869, November.
    16. William Greene, 2004. "Convenient estimators for the panel probit model: Further results," Empirical Economics, Springer, vol. 29(1), pages 21-47, January.
    17. Waggoner, Daniel F. & Zha, Tao, 2003. "Likelihood preserving normalization in multiple equation models," Journal of Econometrics, Elsevier, vol. 114(2), pages 329-347, June.
    18. Lutz Kilian & Tao Zha, 2002. "Quantifying the uncertainty about the half-life of deviations from PPP," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(2), pages 107-125.
    19. Michael Hazilla, 1997. "Separability and capital aggregation in sectoral models of US production," Applied Economics, Taylor & Francis Journals, vol. 29(7), pages 955-974.

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