Quantitative Economics: Jul, 2011, Volume 2, Issue 2

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

Kenneth L. Judd, Lilia Maliar, Serguei Maliar

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 regulariza-
tion, least-absolute deviations methods, and principal component regression
method, all of which are numerically stable and can handle ill-conditioned prob-
lems. 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.
Keywords. Stochastic simulation, generalized stochastic simulation algorithm,
parameterized expectations algorithm, least absolute deviations, linear program-
ming, regularization.
JEL classification. C63, C68.

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