Econometrica: May 2017, Volume 85, Issue 3

Lower Bounds on Approximation Errors to Numerical Solutions of Dynamic Economic Models

https://doi.org/10.3982/ECTA12791
p. 991-1012

Kenneth L. Judd, Lilia Maliar, Serguei Maliar

We propose a novel methodology for evaluating the accuracy of numerical solutions to dynamic economic models. It consists in constructing 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, the approximation is inaccurate. Our lower‐bound error analysis is complementary to the conventional upper‐error (worst‐case) bound analysis, which provides a sufficient condition for accuracy. As an illustration of our methodology, we assess approximation 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.

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Supplemental Material

Supplement to "Lower Bounds on Approximation Errors to Numerical Solutions of Dynamic Economic Models"

In Appendices A and B, we describe additional details of the lower-bound error analysis in the neoclassical stochastic growth model and in the new Keynesian model studied in the main text.

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Supplement to "Lower Bounds on Approximation Errors to Numerical Solutions of Dynamic Economic Models"

This zip file contains the replication files for the manuscript.

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