Approximating high-dimensional dynamic models: sieve value function iteration

Arcidiacono, Peter; Bayer, Patrick; Bugni, Federico A.; James, Jonathan

doi:10.26509/frbc-wp-201210

Working Paper

Approximating high-dimensional dynamic models: sieve value function iteration

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: Estimation theory; Quantitative policy modeling; Simulation modeling;

https://doi.org/10.26509/frbc-wp-201210