IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this paper or follow this series

Analysis of numerical errors

  • Adrian Peralta-Alva
  • Manuel S. Santos

This paper provides a general framework for the quantitative analysis of stochastic dynamic models. We review convergence properties of some numerical algorithms and available methods to bound approximation errors. We then address convergence and accuracy properties of the simulated moments. Our purpose is to provide an asymptotic theory for the computation, simulation-based estimation, and testing of dynamic economies. The theoretical analysis is complemented with several illustrative examples. We study both optimal and non-optimal economies. Optimal economies generate smooth laws of motion defining Markov equilibria, and can be approximated by recursive methods with contractive properties. Non-optimal economies, however, lack existence of continuous Markov equilibria, and need to be computed by other algorithms with weaker approximation properties.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: http://research.stlouisfed.org/wp/2012/2012-062.pdf
Download Restriction: no

Paper provided by Federal Reserve Bank of St. Louis in its series Working Papers with number 2012-062.

as
in new window

Length:
Date of creation: 2012
Date of revision:
Handle: RePEc:fip:fedlwp:2012-062
Contact details of provider: Postal: P.O. Box 442, St. Louis, MO 63166
Fax: (314)444-8753
Web page: http://www.stlouisfed.org/

More information through EDIRC

Order Information: Email:


References listed on IDEAS
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.:

as in new window
  1. Klaus Reiner Schenk-Hoppé & Björn Schmalfuss, . "Random Fixed Points in a Stochastic Solow Growth Model," IEW - Working Papers 065, Institute for Empirical Research in Economics - University of Zurich.
  2. Futia, Carl A, 1982. "Invariant Distributions and the Limiting Behavior of Markovian Economic Models," Econometrica, Econometric Society, vol. 50(2), pages 377-408, March.
  3. Ellison, Glenn & Fudenberg, Drew, 1992. "Rules of Thumb for Social Learning," IDEI Working Papers 17, Institut d'Économie Industrielle (IDEI), Toulouse.
  4. Lawrence J. Christiano & Jonas D.M. Fisher, 1997. "Algorithms for solving dynamic models with occasionally binding constraints," Working Paper 9711, Federal Reserve Bank of Cleveland.
  5. Schmitt-Grohé, Stephanie & Uribe, Martín, 2001. "Solving Dynamic General Equilibrium Models Using a Second-Order Approximation to the Policy Function," CEPR Discussion Papers 2963, C.E.P.R. Discussion Papers.
  6. 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.
  7. Judd, Kenneth L., 1992. "Projection methods for solving aggregate growth models," Journal of Economic Theory, Elsevier, vol. 58(2), pages 410-452, December.
  8. Felix Kubler & Karl Schmedders, 2001. "Stationary Equilibria in Asset-Pricing Models with Incomplete Markets and Collateral," Discussion Papers 1319, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  9. Jeremy Greenwood & Gregory W. Huffman, 1993. "On the existence of nonoptimal equilibria in dynamic stochastic economies," Research Paper 9330, Federal Reserve Bank of Dallas.
  10. Hellwig, Martin F., 1983. "A note on the implementation of rational expectations equilibria," Economics Letters, Elsevier, vol. 11(1-2), pages 1-8.
  11. 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.
  12. Manuel S. Santos & Michael Woodford, 1993. "Rational Asset Pricing Bubbles," Working Papers 9304, Centro de Investigacion Economica, ITAM.
  13. Manuel S. Santos & Adrian Peralta-Alva, 2003. "Accuracy Of Simulations For Stochastic Dynamic Models," Economics Working Papers we034615, Universidad Carlos III, Departamento de Economía.
  14. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
  15. Grandmont Jean-michel, 1983. "On endogenous competitive business cycles," CEPREMAP Working Papers (Couverture Orange) 8316, CEPREMAP.
  16. Kubler, Felix & Schmedders, Karl, 2002. "Recursive Equilibria In Economies With Incomplete Markets," Macroeconomic Dynamics, Cambridge University Press, vol. 6(02), pages 284-306, April.
  17. Christopher Phelan & Ennio Stacchetti, 2001. "Sequential Equilibria in a Ramsey Tax Model," Econometrica, Econometric Society, vol. 69(6), pages 1491-1518, November.
  18. Datta, Manjira & Mirman, Leonard J. & Reffett, Kevin L., 2002. "Existence and Uniqueness of Equilibrium in Distorted Dynamic Economies with Capital and Labor," Journal of Economic Theory, Elsevier, vol. 103(2), pages 377-410, April.
  19. Wilbur John Coleman II, 1989. "Equilibrium in a production economy with an income tax," International Finance Discussion Papers 366, Board of Governors of the Federal Reserve System (U.S.).
  20. Den Haan, Wouter J & Marcet, Albert, 1994. "Accuracy in Simulations," Review of Economic Studies, Wiley Blackwell, vol. 61(1), pages 3-17, January.
  21. Ericson, Richard & Pakes, Ariel, 1995. "Markov-Perfect Industry Dynamics: A Framework for Empirical Work," Review of Economic Studies, Wiley Blackwell, vol. 62(1), pages 53-82, January.
  22. Benhabib, Jess & Day, Richard H., 1982. "A characterization of erratic dynamics in, the overlapping generations model," Journal of Economic Dynamics and Control, Elsevier, vol. 4(1), pages 37-55, November.
  23. Manuel S. Santos, 2000. "Accuracy of Numerical Solutions using the Euler Equation Residuals," Econometrica, Econometric Society, vol. 68(6), pages 1377-1402, November.
  24. Kydland, Finn E. & Prescott, Edward C., 1980. "Dynamic optimal taxation, rational expectations and optimal control," Journal of Economic Dynamics and Control, Elsevier, vol. 2(1), pages 79-91, May.
  25. Kehoe, Timothy J & Levine, David K, 2001. "Liquidity Constrained Markets versus Debt Constrained Markets," Econometrica, Econometric Society, vol. 69(3), pages 575-98, May.
  26. Manuel S. Santos & Jesus Vigo-Aguiar, 1998. "Analysis of a Numerical Dynamic Programming Algorithm Applied to Economic Models," Econometrica, Econometric Society, vol. 66(2), pages 409-426, March.
  27. Blume, Lawrence E., 1982. "New techniques for the study of stochastic equilibrium processes," Journal of Mathematical Economics, Elsevier, vol. 9(1-2), pages 61-70, January.
  28. Karl Schmedders, Felix Kubler, 2001. "Asset Pricing in Models with incomplete markets and default," Computing in Economics and Finance 2001 58, Society for Computational Economics.
  29. Lee, Bong-Soo & Ingram, Beth Fisher, 1991. "Simulation estimation of time-series models," Journal of Econometrics, Elsevier, vol. 47(2-3), pages 197-205, February.
  30. Hopenhayn, Hugo A & Prescott, Edward C, 1992. "Stochastic Monotonicity and Stationary Distributions for Dynamic Economies," Econometrica, Econometric Society, vol. 60(6), pages 1387-406, November.
  31. Per Krusell & Anthony A. Smith, Jr., . "Income and Wealth Heterogeneity in the Macroeconomy," GSIA Working Papers 1997-37, Carnegie Mellon University, Tepper School of Business.
  32. Zhigang Feng & Jianjun Miao & Adrian Peralta‐Alva & Manuel S. Santos, 2014. "Numerical Simulation Of Nonoptimal Dynamic Equilibrium Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 55, pages 83-110, 02.
  33. Darrell Duffie & Kenneth J. Singleton, 1990. "Simulated Moments Estimation of Markov Models of Asset Prices," NBER Technical Working Papers 0087, National Bureau of Economic Research, Inc.
  34. Carl Futia, 2010. "Invariant Distributions and the Limiting Behavior of Markovian Economic Models," Levine's Working Paper Archive 497, David K. Levine.
  35. Hansen, Lars Peter & Singleton, Kenneth J, 1982. "Generalized Instrumental Variables Estimation of Nonlinear Rational Expectations Models," Econometrica, Econometric Society, vol. 50(5), pages 1269-86, September.
  36. Manuel S. Santos, 2010. "Consistency properties of a simulation-based estimator for dynamic processes," Papers 1001.2173, arXiv.org.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:fip:fedlwp:2012-062. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Anna Xiao)

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 references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link 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 profile, as there may be some citations waiting for confirmation.

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

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.