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

We develop numerically stable and accurate stochastic simulation approaches for solving dynamic economic models. First, instead of standard least-squares approximation 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 simu- lation algorithm (GSSA) in three applications: the standard representative - agent neoclassical growth model, a model with rare disasters, and a multicountry model with hundreds of state variables. GSSA is simple to program, and MATLAB codes are provided.