Numerically stable and accurate stochastic simulation approaches for solving dynamic economic models

Abstract

We develop numerically stable and accurate stochastic simulation approaches for solving dynamic economic models. First, instead of standard least-squares methods, we examine a variety of alternatives, including least-squares methods using singular value decomposition and Tikhonov regularization, least-absolute deviations methods, and principal component regression method, all of which are numerically stable and can handle ill-conditioned problems. Second, instead of conventional Monte Carlo integration, we use accurate quadrature and monomial integration. We test our generalized stochastic simulation algorithm (GSSA) in three applications: the standard representative agent neoclassical growth model, a model with rare disasters and a multi-country models with hundreds of state variables. GSSA is simple to program, and MATLAB codes are provided.Stochastic simulation; generalized stochastic simulation algorithm (GSSA), parameterized expectations algorithm (PEA); least absolute deviations (LAD); linear programming; regularization.