Nonlinear and stable perturbation-based approximations

Users of regular higher-order perturbation approximations can face two problems: policy functions with odd undesirable shapes and simulated data that explode. Kim, Kim, Schaumburg, and Sims (2008) propose an alternative, namely pruned perturbation, which avoids the instability problem. In this paper, we document that pruned perturbation approximations have some important drawbacks. We propose an alternative perturbation-based approximation that (i) does not have odd shapes, (ii) generates stable time paths, and (iii) avoids the drawbacks that hamper pruning. We consider models for which the highlighted problems of regular higher-order perturbation are relevant. We find that our alternative and pruned perturbation approximations give a good qualitative insight in the nonlinear aspects of the true solution, but— with a few exceptions— differ from the true solution in some quantitative aspects, especially during severe peaks and throughs.