Solution and Estimation Methods for DSGE Models

Abstract

provided excellent research assistance. We thank our discussant Serguei Maliar, the editors John Taylor and Harald Uhlig, John Cochrane, and the participants at the Handbook Conference hosted by the Hoover Institution for helpful comments and suggestions. The views expressed herein are those of the authors and do not necessarily reflect the views of the National Bureau of Economic Research. NBER working papers are circulated for discussion and comment purposes. They have not been peerreviewed or been subject to the review by the NBER Board of Directors that accompanies official NBER publications.

Bayesian estimation of agent-based models

“…A limited number of equations implies that even if linearisation is not imposed, and a more complicated filter is used, simulation of the model is relatively fast. Still, the computational time required to repeatedly solve the model is an issue in DSGE modelling, as recognised by Fernández-Villaverde et al (2016): "[C]losed-form solutions are the exception and typically not available for models used in serious empirical applications. [...] This ultimately leads to a trade-off: given a fixed amount of computational resources, the more time is spent on solving a model conditional on a particular θ, e.g., through the use of a sophisticated projection technique, the less often an estimation objective function can be evaluated.…”

Managing Climate Change Under Uncertainty: Recursive Integrated Assessment at an Inflection Point

“…The brunt of the computational challenge rests in approximating V t+1 (·) over the relevant state space, which is just T t in our stylized example but is of much higher dimension in any standard climate-economy model. Judd (1998) and Miranda and Fackler (2002) provide textbook descriptions of the relevant computational methods, and recent reviews include Cai and Judd (2014), Maliar (2014), andFernández-Villaverde et al (2016). We describe computational techniques in Section 6.…”

“…Other approximating functions used in the literature include neural networks Kolstad, 1999b, 2001), which can be universal approximators of continuous functions on compact sets, and splines (Fitzpatrick and Kelly, 2016), which have advantages if the value function is non-differentiable and which can target regions of the state space over which the value function is especially curved. 33,34 32 Boyd's Moral Principle (Boyd, 2000) essentially says to always use a Chebyshev basis, unless you are exceptionally sure that another basis is better for your problem (Fernández-Villaverde et al, 2016). 33 Traeger (2014) compares cubic spline and Chebyshev bases.…”

“…These do not have a direct mapping into errors in policy or welfare, but nonetheless can give us some insight into the accuracy of our approximation. Judd et al (2014a) and Fernández-Villaverde et al (2016) give some suggestions regarding residuals to test, such as Bellman errors, first-order condition errors, or a χ 2 accuracy test. 42 The model solves in 15-20 minutes on a 28 core machine.…”

The Fiscal Theory of the Price Level With Nominal Revenues and Expenditures

“…Using the software Dynare, and based on (26) and (27), first, we use the minimization routine csminwel.m (by Prof Christopher Sims) to search for a local minimum of the negative log posterior function. This value is used to initialize the estimation.…”