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 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 simulation 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.

Technological Heterogeneity and Corporate Investment

“…An interesting avenue for future research would be to evaluate empirically models that incorporate both types of frictions (e.g., Gomes, 2001;DeAngelo, DeAngelo, and Whited, 2011), to derive their joint distribution in the cross section of firms. Although such models are characterized by a higher number of state variables, recent developments in numerical integration methods (Judd, Maliar, and Maliar, 2011) and the use of parallel computing (Aldrich, Fernandez-Villaverde, Gallant, and Rubio-Ramirez, 2011) alleviate the computational burden required for estimation. Table 1: Summary statistics of firm-specific empirical moments.…”

Approximate dynamic programming with post-decision states as a solution method for dynamic economic models

“…Both fall into category of stochastic simulation algorithms according to the taxonomy in Judd, Maliar, and Maliar (2011).…”

“…The only algorithm that outperforms MADP-POST in some of this paper's tests is PEA. However, unlike MADP-POST, PEA is difficult to parameterize in sophisticated applications; and is prone to instability in complex models (Judd, Maliar, and Maliar, 2011). Additionally, as is shown in a heterogeneous agents model application, the case for MADP-POST improves further when it is combined with the information sharing algorithm discussed above and GPU-computing.…”

“…For an overview of the Tikhonov regularization, as well as other numerically stable methods for updating parameter values, see Judd, Maliar, and Maliar (2011).…”

A Recursive Method for Solving a Climate–Economy Model: Value Function Iterations with Logarithmic Approximations

“…In addition, the solution method of this paper differs from the literature in that it searches for solutions on an ergodic set, whereas the other papers generally search for solutions on a carefully designed grid. A grid based method is generally prone to the 'curse of dimensionality' (for more discussion, see Judd et al, 2011). For instance, DICE has 2 control variables, 6 endogenous state variables, and 9 (time-dependent) exogenous variables.…”