Working Paper: NBER ID: w18540
Authors: Yongyang Cai; Kenneth L. Judd
Abstract: Numerical dynamic programming algorithms typically use Lagrange data to approximate value functions over continuous states. Hermite data is easily obtained from solving the Bellman equation and can be used to approximate value functions. We illustrate this method with one-, three-, and six-dimensional examples. We find that value function iteration with Hermite approximation improves accuracy by one to three digits using little extra computing time. Moreover, Hermite approximation is significantly faster than Lagrange for the same accuracy, and this advantage increases with dimension.
Keywords: Dynamic Programming; Hermite Approximation; Value Function Iteration
JEL Codes: C61; C63
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| Hermite approximation methods (C60) | improved accuracy of value function iterations (C61) |
| Hermite approximation methods (C60) | minimal extra computational time (C69) |
| HVFI (I19) | accuracy of LVFI (C52) |
| HVFI (I19) | computational efficiency (C63) |
| dimensionality (C39) | advantage of HVFI (L94) |
| gradient information (F12) | approximation process (C60) |