A Comparison of Numerical Methods for the Solution of Continuous-Time Dsge Models

Abstract

This study evaluates the accuracy of a set of techniques that approximate the solution of continuous-time Dynamic Stochastic General Equilibrium models. Using the neoclassical growth model, I compare linear-quadratic, perturbation, and projection methods. All techniques are applied to the Hamilton–Jacobi–Bellman equation and the optimality conditions that define the general equilibrium of the economy. Two cases are studied depending on whether a closed-form solution is available. I also analyze how different degrees of non-linearities affect the approximated solution. The results encourage the use of perturbations for reasonable values of the structural parameters of the model and suggest the use of projection methods when a high degree of accuracy is required.

Risk Matters: Breaking Certainty Equivalence

“…For the stochastic growth model we pick the positive root, C K > 0, since it is the one that is consistent with a concave value function (see Parra-Alvarez, 2018). The remaining constant, C η , corresponds to the solution of the stochastic component of the approximation, and is given by…”

Risk Matters: Breaking Certainty Equivalence

“…This section investigates the economic implications of the approximated solutions by measuring the pricing errors made when using the First-Order CE approximation, the First-Order approximation, and the Second-Order approximation defined in Section 3.1. The pricing mismatch is computed relative to a benchmark that is obtained using a global non-linear projection method based on a Chebyshev polynomial approximation of the unknown value function (see Parra-Alvarez, 2018;Posch, 2018). This approach delivers highly accurate solutions but is costly in terms of computational efficiency.…”

“…While others focus on accuracy measures based on the computation of Euler equation errors (cf. Judd, 1998;Aruoba et al, 2006;Parra-Alvarez, 2018), we are more interested in the implications that each of the approximations have on the pricing mismatch incurred by an investor that does not have/use the 'true' solution of the model.…”

“…Hence, recent research is concerned with the ability of local approximations of non-linear stochastic macroeconomic models to account for risk, with a particular focus on perturbation methods originally introduced in economics by Judd and Guu (1993). Although perturbation-based methods only provide local precision around a particular point, usually the model's deterministic steady state, many authors suggest that they can generate high levels of accuracy, comparable to that delivered by global approximation techniques, as the order of the approximation is increased (see Judd, 1998;Aruoba et al, 2006;Caldara et al, 2012;Parra-Alvarez, 2018). In many applications, however, we are interested in the first-order perturbation and the resulting linear approximation of the equilibrium conditions.…”

Análisis bibliométrico de los modelos estocásticos de equilibrio general

“…Los modelos DSGE son en realidad modelos dinámicos y estocásticos, y des criben el equilibrio general de la economía (Parra-Alvarez, 2018). Su modelación se fundamenta básicamente en tres decisiones estratégicas.…”