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Accuracy of Simulations for Stochastic Dynamic Models

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Manuel S. Santos
Adrian Peralta-Alva

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Abstract

This paper is concerned with accuracy properties of simulations of approximate solutions for stochastic dynamic models. Our analysis rests upon a continuity property of invariant distributions and a generalized law of large numbers. We then show that the statistics generated by any sufficiently good numerical approximation are arbitrarily close to the set of expected values of the model's invariant distributions. Also, under a contractivity condition on the dynamics, we establish error bounds. These results are of further interest for the comparative study of stationary solutions and the estimation of structural dynamic models. Copyright The Econometric Society 2005.

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File URL: http://hdl.handle.net/10.1111/j.1468-0262.2005.00642.x
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Publisher Info
Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 73 (2005)
Issue (Month): 6 (November)
Pages: 1939-1976
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Handle: RePEc:ecm:emetrp:v:73:y:2005:i:6:p:1939-1976

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. S. Boragan Aruoba & Jesus Fernandez-Villaverde & Juan Francisco Rubio-Ramirez, 2003. "Comparing solution methods for dynamic equilibrium economies," Working Paper 2003-27, Federal Reserve Bank of Atlanta. [Downloadable!]
    Other versions:
  2. Manuel S. Santos, 2003. "Estimation by Simulation of Monotone Dynamical Systems," Levine's Bibliography 506439000000000229, UCLA Department of Economics. [Downloadable!]
  3. Christiano, Lawrence J. & Fisher, Jonas D. M., 2000. "Algorithms for solving dynamic models with occasionally binding constraints," Journal of Economic Dynamics and Control, Elsevier, vol. 24(8), pages 1179-1232, July. [Downloadable!] (restricted)
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  4. Schenk-Hoppe, Klaus Reiner & Schmalfu[ss], Bjorn, 2001. "Random fixed points in a stochastic Solow growth model," Journal of Mathematical Economics, Elsevier, vol. 36(1), pages 19-30, September. [Downloadable!] (restricted)
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  5. Ellison, Glenn & Fudenberg, Drew, 1993. "Rules of Thumb for Social Learning," Journal of Political Economy, University of Chicago Press, vol. 101(4), pages 612-43, August. [Downloadable!] (restricted)
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  6. Lucas, Robert E, Jr, 1980. "Methods and Problems in Business Cycle Theory," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 12(4), pages 696-715, November. [Downloadable!] (restricted)
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  13. Futia, Carl A, 1982. "Invariant Distributions and the Limiting Behavior of Markovian Economic Models," Econometrica, Econometric Society, vol. 50(2), pages 377-408, March. [Downloadable!] (restricted)
  14. Santos, Manuel S., 2002. "On Non-existence of Markov Equilibria in Competitive-Market Economies," Journal of Economic Theory, Elsevier, vol. 105(1), pages 73-98, July. [Downloadable!] (restricted)
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  17. Tom Krebs, 2002. "Non-Existence of Recursive Equilibria on Compact State Spaces When Markets are Incomplete," Working Papers 2002-17, Brown University, Department of Economics. [Downloadable!]
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  18. Easley, David & Spulber, Daniel F, 1981. "Stochastic Equilibrium and Optimality with Rolling Plans," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 22(1), pages 79-103, February. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Adrian Peralta-Alva & Manuel S. Santos, 2009. "Problems in the numerical simulation of models with heterogeneous agents and economic distortions," Working Papers 2009-036, Federal Reserve Bank of St. Louis. [Downloadable!]
  2. Cuong Le Van & John Stachurski, 2004. "Parametric Continuity of Stationary Distributions," Department of Economics - Working Papers Series 899, The University of Melbourne. [Downloadable!]
    Other versions:
  3. John Stachurski, 2004. "Asymptotic Statistical Properties Of The Neoclassical Optimal Growth Model," Department of Economics - Working Papers Series 898, The University of Melbourne. [Downloadable!]
  4. Jesús Fernández-Villaverde & Juan F. Rubio-Ramirez & Manuel Santos, 2005. "Convergence Properties of the Likelihood of Computed Dynamic Models," Levine's Bibliography 122247000000000822, UCLA Department of Economics. [Downloadable!]
    Other versions:
  5. Manuel S. Santos, 2003. "Simulation-Based Estimation Of Dynamic Models With Continuous Equilibrium Solutions," Economics Working Papers we034716, Universidad Carlos III, Departamento de Economía. [Downloadable!]
  6. Matteo Richiardi, 2004. "The Promises and Perils of Agent-Based Computational Economics," Computational Economics 0401001, EconWPA. [Downloadable!]
    Other versions:
  7. Den Haan, Wouter, 2008. "Assessing the Accuracy of the Aggregate Law of Motion in Models with Heterogeneous Agents," CEPR Discussion Papers 6971, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
  8. Zhigang Feng & Jianjun Miao & Adrian Peralta-Alva & Manuel S. Santos, 2009. "Numerical simulation of nonoptimal dynamic equilibrium models," Working Papers 2009-018, Federal Reserve Bank of St. Louis. [Downloadable!]
    Other versions:
  9. Jesús Fernández-Villaverde & Juan F. Rubio-Ramirez, 2006. "Estimating Macroeconomic Models: A Likelihood Approach," Levine's Bibliography 122247000000000849, UCLA Department of Economics. [Downloadable!]
    Other versions:
  10. Manjira Datta & Leonard J. Mirman & Olivier F. Morand & Kevin L. Reffett, 2005. "Markovian Equilibrium in Infinite Horizon Economies with Incomplete Markets and Public Policy," Tinbergen Institute Discussion Papers 05-013/2, Tinbergen Institute. [Downloadable!]
    Other versions:
  11. Olson, Lars & Roy, Santanu, 2005. "Theory of Stochastic Optimal Economic Growth," Working Papers 28601, University of Maryland, Department of Agricultural and Resource Economics. [Downloadable!]
  12. Takashi Kamihigashi & John Stachurski, 2009. "Asymptotics Of Stochastic Recursive Economies Under Monotonicity," KIER Working Papers 666, Kyoto University, Institute of Economic Research. [Downloadable!]
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