How to solve dynamic stochastic models computing expectations just once

• 成果类型: Article
• 署名作者: Judd, Kenneth L.; Maliar, Lilia; Maliar, Serguei; Tsener, Inna
• 署名单位: Stanford University; Stanford University; Santa Clara University; Universitat de les Illes Balears
• 刊物名称: QUANTITATIVE ECONOMICS
• ISSN/ISSBN: 1759-7323
• DOI: 10.3982/QE329
• 发表日期: 2017
• 页码: 851-893
• 关键词: Dynamic model; precomputation; numerical integration; dynamic programming; value function iteration; Bellman equation; Euler equation; envelope condition method; endogenous grid method; Aiyagari model

摘要

We introduce a computational techniqueprecomputation of integralsthat makes it possible to construct conditional expectation functions in dynamic stochastic models in the initial stage of a solution procedure. This technique is very general: it works for a broad class of approximating functions, including piecewise polynomials; it can be applied to both Bellman and Euler equations; and it is compatible with both continuous-state and discrete-state shocks. In the case of normally distributed shocks, the integrals can be constructed in a closed form. After the integrals are precomputed, we can solve stochastic models as if they were deterministic. We illustrate this technique using one- and multi-agent growth models with continuous-state shocks (and up to 60 state variables), as well as Aiyagari's (1994) model with discrete-state shocks. Precomputation of integrals saves programming efforts, reduces computational burden, and increases the accuracy of solutions. It is of special value in computationally intense applications. MATLAB codes are provided.