Judd, K.L., L. Maliar and S. Maliar
Econometrica – 85.3 (2017). 991-1012.

Keywords: Approximation errors, error bound, forward error analysis, backwarderror analysis, Euler equation residuals, upper error bound, lower error bound, accu-racy, numerical solution, approximate solution, new Keynesian model

Abstract: 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.