IDEAS home Printed from https://ideas.repec.org/a/ecm/emetrp/v73y2005i6p1939-1976.html
   My bibliography  Save this article

Accuracy of Simulations for Stochastic Dynamic Models

Author

Listed:
  • Manuel S. Santos
  • Adrian Peralta-Alva

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.

Suggested Citation

  • Manuel S. Santos & Adrian Peralta-Alva, 2005. "Accuracy of Simulations for Stochastic Dynamic Models," Econometrica, Econometric Society, vol. 73(6), pages 1939-1976, November.
    • Handle: RePEc:ecm:emetrp:v:73:y:2005:i:6:p:1939-1976
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1111/j.1468-0262.2005.00642.x
    File Function: link to full text
    Download Restriction: Access to full text is restricted to subscribers.
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Duffie, Darrell & Singleton, Kenneth J, 1993. "Simulated Moments Estimation of Markov Models of Asset Prices," Econometrica, Econometric Society, vol. 61(4), pages 929-952, July.
    4. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, December.
    5. 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.
    6. Futia, Carl A, 1982. "Invariant Distributions and the Limiting Behavior of Markovian Economic Models," Econometrica, Econometric Society, vol. 50(2), pages 377-408, March.
    7. 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.
    8. Manuel Santos, "undated". "Estimation by Simulation of Monotone Dynamical Systems," Working Papers 2133542, Department of Economics, W. P. Carey School of Business, Arizona State University.
    9. Christiano, Lawrence J & Eichenbaum, Martin, 1992. "Current Real-Business-Cycle Theories and Aggregate Labor-Market Fluctuations," American Economic Review, American Economic Association, vol. 82(3), pages 430-450, June.
    10. 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.
    11. 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.
    12. Manuel Santos, "undated". "On Non-Existence of Markov Equilibria in Competitive-Market Economies," Working Papers 2133305, Department of Economics, W. P. Carey School of Business, Arizona State University.
    13. Ellison, Glenn & Fudenberg, Drew, 1993. "Rules of Thumb for Social Learning," Journal of Political Economy, University of Chicago Press, vol. 101(4), pages 612-643, August.
    14. 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.
    15. Wouter J. Den Haan & Albert Marcet, 1994. "Accuracy in Simulations," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 61(1), pages 3-17.
    16. Aruoba, S. Boragan & Fernandez-Villaverde, Jesus & Rubio-Ramirez, Juan F., 2006. "Comparing solution methods for dynamic equilibrium economies," Journal of Economic Dynamics and Control, Elsevier, vol. 30(12), pages 2477-2508, December.
    17. Duncan K. Foley & Martin F. Hellwig, 1975. "Asset Management with Trading Uncertainty," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 42(3), pages 327-346.
    18. Hopenhayn, Hugo A & Prescott, Edward C, 1992. "Stochastic Monotonicity and Stationary Distributions for Dynamic Economies," Econometrica, Econometric Society, vol. 60(6), pages 1387-1406, November.
    19. Rabi Bhattacharya & Mukul Majumdar, 2003. "Random dynamical systems: a review," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 23(1), pages 13-38, December.
    20. John Laitner, 1988. "Bequests, Gifts, and Social Security," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 55(2), pages 275-299.
    21. Krebs, Tom, 2004. "Non-existence of recursive equilibria on compact state spaces when markets are incomplete," Journal of Economic Theory, Elsevier, vol. 115(1), pages 134-150, March.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Santos, Manuel S., 2004. "Simulation-based estimation of dynamic models with continuous equilibrium solutions," Journal of Mathematical Economics, Elsevier, vol. 40(3-4), pages 465-491, June.
    2. Santos, Manuel S., 2003. "Simulation-based estimation of dynamic models with continuous equilibrium solutions," UC3M Working papers. Economics we034716, Universidad Carlos III de Madrid. Departamento de Economía.
    3. Manuel S. Santos & Adrian Peralta-Alva, 2012. "Analysis of Numerical Errors," Working Papers 2012-6, University of Miami, Department of Economics.
    4. John Stachurski, 2009. "Economic Dynamics: Theory and Computation," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262012774, December.
    5. Lilia Maliar & Serguei Maliar & John B. Taylor & Inna Tsener, 2020. "A tractable framework for analyzing a class of nonstationary Markov models," Quantitative Economics, Econometric Society, vol. 11(4), pages 1289-1323, November.
    6. Serguei Maliar & John Taylor & Lilia Maliar, 2016. "The Impact of Alternative Transitions to Normalized Monetary Policy," 2016 Meeting Papers 794, Society for Economic Dynamics.
    7. Jesús Fernández-Villaverde & Juan F. Rubio-Ramírez & Manuel S. Santos, 2006. "Convergence Properties of the Likelihood of Computed Dynamic Models," Econometrica, Econometric Society, vol. 74(1), pages 93-119, January.
    8. Fernández-Villaverde, J. & Rubio-Ramírez, J.F. & Schorfheide, F., 2016. "Solution and Estimation Methods for DSGE Models," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 527-724, Elsevier.
    9. Aruoba, S. Boragan & Fernandez-Villaverde, Jesus & Rubio-Ramirez, Juan F., 2006. "Comparing solution methods for dynamic equilibrium economies," Journal of Economic Dynamics and Control, Elsevier, vol. 30(12), pages 2477-2508, December.
    10. Posch, Olaf & Trimborn, Timo, 2013. "Numerical solution of dynamic equilibrium models under Poisson uncertainty," Journal of Economic Dynamics and Control, Elsevier, vol. 37(12), pages 2602-2622.
    11. Stephanie Becker & Lars Grüne & Willi Semmler, 2007. "Comparing accuracy of second-order approximation and dynamic programming," Computational Economics, Springer;Society for Computational Economics, vol. 30(1), pages 65-91, August.
    12. Kenneth L. Judd & Lilia Maliar & Serguei Maliar, 2014. "Lower Bounds on Approximation Errors: Testing the Hypothesis That a Numerical Solution Is Accurate?," BYU Macroeconomics and Computational Laboratory Working Paper Series 2014-06, Brigham Young University, Department of Economics, BYU Macroeconomics and Computational Laboratory.
    13. José Cao-Alvira, 2010. "Finite Elements in the Presence of Occasionally Binding Constraints," Computational Economics, Springer;Society for Computational Economics, vol. 35(4), pages 355-370, April.
    14. Lars J. Olson & Santanu Roy, 2006. "Theory of Stochastic Optimal Economic Growth," Springer Books, in: Rose-Anne Dana & Cuong Le Van & Tapan Mitra & Kazuo Nishimura (ed.), Handbook on Optimal Growth 1, chapter 11, pages 297-335, Springer.
    15. Datta, Manjira & Mirman, Leonard J. & Morand, Olivier F. & Reffett, Kevin L., 2005. "Markovian equilibrium in infinite horizon economies with incomplete markets and public policy," Journal of Mathematical Economics, Elsevier, vol. 41(4-5), pages 505-544, August.
    16. Ambler, Steve & Pelgrin, Florian, 2010. "Time-consistent control in nonlinear models," Journal of Economic Dynamics and Control, Elsevier, vol. 34(10), pages 2215-2228, October.
    17. Jaime McGovern & Olivier Morand & Kevin Reffett, 2013. "Computing minimal state space recursive equilibrium in OLG models with stochastic production," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(3), pages 623-674, November.
    18. S. Sirakaya & Stephen Turnovsky & M. Alemdar, 2006. "Feedback Approximation of the Stochastic Growth Model by Genetic Neural Networks," Computational Economics, Springer;Society for Computational Economics, vol. 27(2), pages 185-206, May.
    19. Heer Burkhard & Maußner Alfred, 2011. "Value Function Iteration as a Solution Method for the Ramsey Model," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 231(4), pages 494-515, August.
    20. Albert Marcet & David A. Marshall, 1994. "Solving nonlinear rational expectations models by parameterized expectations: convergence to stationary solutions," Working Paper Series, Macroeconomic Issues 94-20, Federal Reserve Bank of Chicago.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ecm:emetrp:v:73:y:2005:i:6:p:1939-1976. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/essssea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.