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

Kenneth Judd, Lilia Maliar and Serguei Maliar

No 2014-06, BYU Macroeconomics and Computational Laboratory Working Paper Series from Brigham Young University, Department of Economics, BYU Macroeconomics and Computational Laboratory

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.

Keywords: approximation errors; best case scenario, error bounds, Euler equation residuals; accuracy; numerical solution; algorithm; new Keynesian model (search for similar items in EconPapers)
JEL-codes: C61 C63 C68 E31 E52 (search for similar items in EconPapers)
Pages: 50 pages
Date: 2014-08
New Economics Papers: this item is included in nep-cmp and nep-mac
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:byu:byumcl:201406

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