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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.

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

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Date of creation: 2012
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Handle: RePEc:fip:fedlwp:2012-062
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  1. Jes�s 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, 01.
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  3. Zhigang Feng & Jianjun Miao & Adrian Peralta-Alva & Manual Santos, 2009. "Numerical Simulation of Nonoptimal Dynamic Equilibrium Models," Working Papers 0912, University of Miami, Department of Economics.
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  7. Manuel S. Santos & Adrian Peralta-Alva, 2005. "Accuracy of Simulations for Stochastic Dynamic Models," Econometrica, Econometric Society, vol. 73(6), pages 1939-1976, November.
  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.
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