Working Paper: NBER ID: w15296
Authors: Kenneth Judd; Lilia Maliar; Serguei Maliar
Abstract: We develop numerically stable stochastic simulation approaches for solving dynamic economic models. We rely on standard simulation procedures to simultaneously compute an ergodic distribution of state variables, its support and the associated decision rules. We differ from existing methods, however, in how we use simulation data to approximate decision rules. Instead of the usual least-squares approximation methods, we examine a variety of alternatives, including the least-squares method using SVD, Tikhonov regularization, least-absolute deviation methods, principal components regression method, all of which are numerically stable and can handle ill-conditioned problems. These new methods enable us to compute high-order polynomial approximations without encountering numerical problems. Our approaches are especially well suitable for high-dimensional applications in which other methods are infeasible.
Keywords: No keywords provided
JEL Codes: C63; C68
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| linear regression models and various regularization techniques (C51) | numerical stability of the stochastic simulation algorithm (C69) |
| singular value decomposition (SVD) in the least-squares approach (C29) | mitigate issues related to ill-conditioning (C62) |
| normalization of variables (C29) | improved accuracy in polynomial approximations (C60) |
| use of Hermite polynomials (C69) | reduce the multicollinearity problem (C20) |
| new numerical methods (C60) | more reliable solutions in high-dimensional applications (C52) |