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Lower Bounds on Approximation Errors: Testing the Hypothesis That a Numerical Solution Is Accurate?

Author

Listed:
  • Kenneth L. Judd

    (Hoover Institution, Stanford University)

  • Lilia Maliar

    (Department of Economics, Stanford University)

  • Serguei Maliar

    (Leavey School of Business, Santa Clara University)

Abstract

We propose a novel methodology for evaluating the accuracy of numerical solutions to dynamic economic models. Specifically, we construct a lower bound on the size of approximation errors. A small lower bound on errors is a necessary condition for accuracy: If a lower error bound is unacceptably large, then the actual approximation errors are even larger, and hence, we reject the hypothesis that a numerical solution is accurate. Our accuracy analysis is logically equivalent to hypothesis testing in statistics. As an illustration of our methodology, we assess approximation errors in the first- and second-order perturbation solutions for two stylized models: a neoclassical growth model and a new Keynesian model. The errors are small for the former model but unacceptably large for the latter model under some empirically relevant parameterizations.

Suggested Citation

  • 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.
  • Handle: RePEc:byu:byumcl:201406
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    File URL: https://docs.google.com/file/d/0B6KGaihAO5TJeDhERnROOFlDc2s/edit
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    References listed on IDEAS

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    Cited by:

    1. Fernández-Villaverde, J. & Rubio-Ramírez, J.F. & Schorfheide, F., 2016. "Solution and Estimation Methods for DSGE Models," Handbook of Macroeconomics, Elsevier.

    More about this item

    Keywords

    approximation errors; best case scenario; error bounds; Euler equation residuals; accuracy; numerical solution; algorithm; new Keynesian model;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C68 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computable General Equilibrium Models
    • E31 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Price Level; Inflation; Deflation
    • E52 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - Monetary Policy

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