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

We propose a novel methodology for evaluating the accuracy of numeri-cal solutions to dynamic economic models. Speci\u85cally, 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 il-lustration of our methodology, we assess approximation errors in the \u85rst-and second-order perturbation solutions for two stylized models: a neoclas-sical 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. JEL classification: C61, C63, C68, E31, E52 Key Words: approximation errors; best case scenario, error bounds, Euler equation residuals; accuracy; numerical solution; algorithm; new Key-nesian mode