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Analysis of numerical errors

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  • Adrian Peralta-Alva
  • Manuel S. Santos

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.

Suggested Citation

  • Adrian Peralta-Alva & Manuel S. Santos, 2012. "Analysis of numerical errors," Working Papers 2012-062, Federal Reserve Bank of St. Louis.
    • Handle: RePEc:fip:fedlwp:2012-062
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    2. Martin M Andreasen & Jesús Fernández-Villaverde & Juan F Rubio-Ramírez, 2018. "The Pruned State-Space System for Non-Linear DSGE Models: Theory and Empirical Applications," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 85(1), pages 1-49.
    3. Kenneth L. Judd & Lilia Maliar & Serguei Maliar, 2014. "Lower Bounds on Approximation Errors: Testing the Hypothesis That a Numerical Solution Is Accurate?," BYU Macroeconomics and Computational Laboratory Working Paper Series 2014-06, Brigham Young University, Department of Economics, BYU Macroeconomics and Computational Laboratory.

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    More about this item

    Keywords

    Error analysis (Mathematics); Markov processes;

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General

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