Analysis of Numerical Errors

FRB of St. Louis Working Paper No. 2012-062A

50 Pages Posted: 5 Jan 2013

See all articles by Adrian Peralta-Alva

Adrian Peralta-Alva

Federal Reserve Bank of St. Louis

Manuel Santos

University of Miami - School of Business Administration - Department of Economics

Date Written: December 1, 2012

Abstract

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.

Keywords: Stochastic Dynamic Model, Markov Equilibrium, Numerical Solution, Approximation Error, Accuracy, Simulation-Based Estimation, Consistency

JEL Classification: C63, E60

Suggested Citation

Peralta-Alva, Adrian and Santos, Manuel, Analysis of Numerical Errors (December 1, 2012). FRB of St. Louis Working Paper No. 2012-062A, Available at SSRN: https://ssrn.com/abstract=2196587 or http://dx.doi.org/10.2139/ssrn.2196587

Adrian Peralta-Alva (Contact Author)

Federal Reserve Bank of St. Louis ( email )

411 Locust St
Saint Louis, MO 63011
United States

HOME PAGE: http://research.stlouisfed.org/econ/peralta-alva/index.html

Manuel Santos

University of Miami - School of Business Administration - Department of Economics ( email )

P.O. Box 248126
Coral Gables, FL 33124-6550
United States

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