How to solve dynamic stochastic models computing expectations just once

Abstract

[eng] We introduce a computational technique -precomputation of integrals -which 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 a computational burden and increases the accuracy of solutions. It is of special value in computationally intense applications. MATLAB codes are provided.