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Computing the Distributions of Economic Models Via Simulation

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  • John Stachurski

Abstract

This paper studies the convergence properties of a Monte Carlo algorithm for computing distributions of state variables when the underlying model is a Markov chain with absolutely continuous transition probabilities. We show that the L1 error of the estimator always converges to zero with probability one. In addition, rates of convergence are established for L1 and integral mean squared errors. The algorithm is shown to have many applications in economics.

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Bibliographic Info

Paper provided by The University of Melbourne in its series Department of Economics - Working Papers Series with number 949.

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Length: 25 pages
Date of creation: 2005
Date of revision:
Handle: RePEc:mlb:wpaper:949

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References

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  1. Deaton, A. & Laroque, G., 1989. "On The Behavior Of Commodity Prices," Papers 145, Princeton, Woodrow Wilson School - Development Studies.
  2. Sarno, Lucio & Valente, Giorgio, 2002. "Comparing the Accuracy of Density Forecasts from Competing Models," Computing in Economics and Finance 2002 223, Society for Computational Economics.
  3. Nishimura, Kazuo & Stachurski, John, 2005. "Stability of stochastic optimal growth models: a new approach," Journal of Economic Theory, Elsevier, vol. 122(1), pages 100-118, May.
  4. Neil Shephard & Ola Elerian & Siddhartha Chib, 1998. "Likelihood inference for discretely observed non-linear diffusions," Economics Series Working Papers 1998-W10, University of Oxford, Department of Economics.
  5. Johnson, Paul A., 2005. "A continuous state space approach to "Convergence by Parts"," Economics Letters, Elsevier, vol. 86(3), pages 317-321, March.
  6. A. S. Hurn & K. A. Lindsay & V. L. Martin, 2003. "On the efficacy of simulated maximum likelihood for estimating the parameters of stochastic differential Equations," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(1), pages 45-63, 01.
  7. Brock, William A. & Mirman, Leonard J., 1972. "Optimal economic growth and uncertainty: The discounted case," Journal of Economic Theory, Elsevier, vol. 4(3), pages 479-513, June.
  8. Esteban Rossi-Hansberg & Mark L. J. Wright, 2007. "Establishment Size Dynamics in the Aggregate Economy," American Economic Review, American Economic Association, vol. 97(5), pages 1639-1666, December.
  9. Hansen, Bruce E., 2005. "Exact Mean Integrated Squared Error Of Higher Order Kernel Estimators," Econometric Theory, Cambridge University Press, vol. 21(06), pages 1031-1057, December.
  10. Nishimura, Kazuo & Rudnicki, Ryszard & Stachurski, John, 2006. "Stochastic optimal growth with nonconvexities," Journal of Mathematical Economics, Elsevier, vol. 42(1), pages 74-96, February.
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Cited by:
  1. António Antunes & Tiago Cavalcanti & Anne Villamil, 2006. "Computing General Equilibrium Models with Occupational Choice and Financial Frictions," SCAPE Policy Research Working Paper Series 0611, National University of Singapore, Department of Economics, SCAPE.
  2. Vance Martin & Yoshihiko Nishiyama & John Stachurski, 2011. "A Goodness of Fit Test for Ergodic Markov Processes," ANU Working Papers in Economics and Econometrics 2011-557, Australian National University, College of Business and Economics, School of Economics.
  3. R. Anton Braun & Huiyu Li & John Stachurski, 2011. "Generalized Look-Ahead Methods for Computing Stationary Densities," ANU Working Papers in Economics and Econometrics 2011-558, Australian National University, College of Business and Economics, School of Economics.
  4. Bildirici, Melike & Ersin, Özgür, 2012. "Nonlinear volatility models in economics: smooth transition and neural network augmented GARCH, APGARCH, FIGARCH and FIAPGARCH models," MPRA Paper 40330, University Library of Munich, Germany, revised May 2012.
  5. Richard Anton Braun & Huiyu Li & John Stachurski, 2009. "Computing Densities: A Conditional Monte Carlo Estimator," CIRJE F-Series CIRJE-F-678, CIRJE, Faculty of Economics, University of Tokyo.

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