Lower Bounds on Approximation Errors to Numerical Solutions of Dynamic Economic Models
提出一种评估动态经济模型数值解精度的方法，通过构造近似误差的下界来判断近似是否准确，并用新古典增长模型和新凯恩斯模型验证。
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.