Working Paper: NBER ID: w17890
Authors: Peter Arcidiacono; Patrick Bayer; Federico A. Bugni; Jonathan James
Abstract: Many dynamic problems in economics are characterized by large state spaces which make both computing and estimating the model infeasible. We introduce a method for approximating the value function of high-dimensional dynamic models based on sieves and establish results for the: (a) consistency, (b) rates of convergence, and (c) bounds on the error of approximation. We embed this method for approximating the solution to the dynamic problem within an estimation routine and prove that it provides consistent estimates of the model's parameters. We provide Monte Carlo evidence that our method can successfully be used to approximate models that would otherwise be infeasible to compute, suggesting that these techniques may substantially broaden the class of models that can be solved and estimated.
Keywords: dynamic programming; value function iteration; approximation methods; sieve methods
JEL Codes: C13; C14; C54; C61; C63; C73
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| Sieve Value Function Iteration (SVFI) method (C69) | consistent estimates of model parameters (C51) |
| Sieve Value Function Iteration (SVFI) method (C69) | effectively approximate the value function (C60) |
| richness of the sieve space increases (R12) | SVFI method converges to the true value function (C61) |
| iterating the Bellman operator (C61) | more accurate approximation (C60) |
| Sieve Value Function Iteration (SVFI) method (C69) | reduced computational time (C63) |