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

We propose a novel methodology for evaluating the accuracy of numerical solutions to dynamic economic models. Speci…cally, 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 …rstand 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. JEL classification : C61, C63, C68, E31, E52 Key Words : approximation errors; best case scenario, error bounds, Euler equation residuals; accuracy; numerical solution; algorithm; new Keynesian model We bene…ted from comments of participants of the 2014 SITE workshop at Stanford University. Lilia Maliar and Serguei Maliar acknowledge support from the Hoover Institution and Department of Economics at Stanford University, University of Alicante, Ivie, Santa Clara University under the grant DPROV115, the Generalitat Valenciana under the grant Prometeo/2013/037 and the MECD under the grant ECO2012-36719. Corresponding author: Lilia Maliar, O¢ ce 249, Department of Economics, Stanford, CA 94305-6072, USA; email: [email protected].