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Analysis of Numerical Errors

  • Manuel S. Santos

    (Department of Economics, University of Miami)

  • Adrian Peralta-Alva

    (Research Department, Federal Reserve Bank of Saint Louis)

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.

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File URL: http://bus.miami.edu/_assets/files/repec/WP2012-06.pdf
File Function: First version, 2012
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Paper provided by University of Miami, Department of Economics in its series Working Papers with number 2012-6.

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Length: 48 pages
Date of creation: 08 2012
Date of revision:
Publication status: Forthcoming: Under Review
Handle: RePEc:mia:wpaper:2012-6
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Web page: http://www.bus.miami.edu/faculty-and-research/academic-departments/economics/index.html

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  1. Stephanie Schmitt-Grohe & Martin Uribe, 2002. "Solving Dynamic General Equilibrium Models Using a Second-Order Approximation to the Policy Function," NBER Technical Working Papers 0282, National Bureau of Economic Research, Inc.
  2. Lawrence J. Christiano & Jonas D.M. Fisher, 1997. "Algorithms for Solving Dynamic Models with Occasionally Binding Constraints," NBER Technical Working Papers 0218, National Bureau of Economic Research, Inc.
  3. 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.
  4. 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.
  5. 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.
  6. 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.
  7. Carl Futia, 2010. "Invariant Distributions and the Limiting Behavior of Markovian Economic Models," Levine's Working Paper Archive 497, David K. Levine.
  8. Manuel S. Santos & Michael Woodford, 1993. "Rational Asset Pricing Bubbles," Working Papers 9304, Centro de Investigacion Economica, ITAM.
  9. Greenwood Jeremy & Huffman Gregory W., 1995. "On the Existence of Nonoptimal Equilibria in Dynamic Stochastic Economies," Journal of Economic Theory, Elsevier, vol. 65(2), pages 611-623, April.
  10. Peralta Alva, Adrián & Santos, Manuel S., 2003. "Accuracy of simulations for stochastic dynamic models," UC3M Working papers. Economics we034615, Universidad Carlos III de Madrid. Departamento de Economía.
  11. 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.
  12. Per Krusell & Anthony A. Smith & Jr., 1998. "Income and Wealth Heterogeneity in the Macroeconomy," Journal of Political Economy, University of Chicago Press, vol. 106(5), pages 867-896, October.
  13. Duffie, Darrell & Singleton, Kenneth J, 1993. "Simulated Moments Estimation of Markov Models of Asset Prices," Econometrica, Econometric Society, vol. 61(4), pages 929-52, July.
  14. Manjira Datta & Leonard Mirman & Kevin Reffett, . "Existence and Uniqueness of Equilibrium in Distorted Dynamic Economies with Capital and Labor," Working Papers 2132846, Department of Economics, W. P. Carey School of Business, Arizona State University.
  15. Grandmont Jean-michel, 1983. "On endogenous competitive business cycles," CEPREMAP Working Papers (Couverture Orange) 8316, CEPREMAP.
  16. 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.
  17. Judd, Kenneth L., 1992. "Projection methods for solving aggregate growth models," Journal of Economic Theory, Elsevier, vol. 58(2), pages 410-452, December.
  18. 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.
  19. Christopher Phelan & Ennio Stacchetti, 1999. "Sequential equilibria in a Ramsey tax model," Staff Report 258, Federal Reserve Bank of Minneapolis.
  20. Hellwig, Martin F., 1983. "A note on the implementation of rational expectations equilibria," Economics Letters, Elsevier, vol. 11(1-2), pages 1-8.
  21. Richard Ericson & Ariel Pakes, 1995. "Markov-Perfect Industry Dynamics: A Framework for Empirical Work," Review of Economic Studies, Oxford University Press, vol. 62(1), pages 53-82.
  22. Wilbur John Coleman, 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.).
  23. Futia, Carl A, 1982. "Invariant Distributions and the Limiting Behavior of Markovian Economic Models," Econometrica, Econometric Society, vol. 50(2), pages 377-408, March.
  24. 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.
  25. Allison, G. & Fudenberg, D., 1992. "Rules of Thumb for Social Learning," Working papers 92-12, Massachusetts Institute of Technology (MIT), Department of Economics.
  26. Wouter J. Den Haan & Albert Marcet, 1994. "Accuracy in Simulations," Review of Economic Studies, Oxford University Press, vol. 61(1), pages 3-17.
  27. 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.
  28. Kehoe, Timothy J & Levine, David K, 2001. "Liquidity Constrained Markets versus Debt Constrained Markets," Econometrica, Econometric Society, vol. 69(3), pages 575-98, May.
  29. Manuel S. Santos, 2000. "Accuracy of Numerical Solutions using the Euler Equation Residuals," Econometrica, Econometric Society, vol. 68(6), pages 1377-1402, November.
  30. Felix Kubler & Karl Schmedders, 2003. "Stationary Equilibria in Asset-Pricing Models with Incomplete Markets and Collateral," Econometrica, Econometric Society, vol. 71(6), pages 1767-1793, November.
  31. 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.
  32. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
  33. 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.
  34. 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.
  35. Kubler, Felix & Schmedders, Karl, 2002. "Recursive Equilibria In Economies With Incomplete Markets," Macroeconomic Dynamics, Cambridge University Press, vol. 6(02), pages 284-306, April.
  36. Manuel S. Santos, 2010. "Consistency properties of a simulation-based estimator for dynamic processes," Papers 1001.2173, arXiv.org.
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