Nonlinear and stable perturbation-based approximations

Users of regular higher-order perturbation approximations can face two problems: policy functions with odd oscillations and simulated data that explode. We propose a perturbation-based approximation that (i) does not have odd shapes, (ii) generates stable time paths, and (iii) avoids the drawbacks that hamper the pruned perturbation approach of Kim et al. (2008). For models with nontrivial nonlinearities, we find that our alternative and the pruned perturbation approximations give a good qualitative insight in the nonlinear aspects of the true solution, but can differ from the true solution in some quantitative aspects, especially during severe peaks and troughs.