Solution methods for models with rare disasters

Abstract

This paper compares different solution methods for computing the equilibrium of dynamic stochastic general equilibrium (DSGE) models with rare disasters along the lines of those proposed by Rietz (1988), Barro (2006), Gabaix (2012), and Gourio (2012). DSGE models with rare disasters require solution methods that can handle the large nonlinearities triggered by low‐probability, high‐impact events with accuracy and speed. We solve a standard New Keynesian model with Epstein–Zin preferences and time‐varying disaster risk with perturbation, Taylor projection, and Smolyak collocation. Our main finding is that Taylor projection delivers the best accuracy/speed tradeoff among the tested solutions. We also document that even third‐order perturbations may generate solutions that suffer from accuracy problems and that Smolyak collocation can be costly in terms of run time and memory requirements.

Solving the Diamond-Mortensen-Pissarides model accurately

“…Most prior studies compare different solution methods for the stochastic growth model and its extensions. Prominent examples include Aruoba, Fernández-Villaverde, and Rubio-Ramírez (2006), Caldara, Fernández-Villaverde, Rubio-Ramírez, andYao (2012), andLevintal (2016) for the baseline stochastic growth model, Algan, Allais, and Den Haan (2010), Den Haan and Rendahl (2010), and Maliar, Maliar, and Valli (2011) for the incomplete markets model with heterogenous agents and aggregate uncertainty, as well as Kollmann, Maliar, Malin, and Pichler (2011), Maliar, Maliar, and Judd (2011), Malin, Krueger, and Kubler (2011 for the multicountry real business cycle model. We are not aware of any prior studies that compare solution methods for the DMP model.…”

Where modern macroeconomics went wrong

“…Though some of the models incorporate some of the features that we argue here should be included in any good macro-model, they still leave out many crucial features, make many unreasonable parameterizations, and test their models using unsatisfactory methodologies, as described elsewhere in this paper. For a survey of the advances in non-linear methodologies, seeFernandez-Villaverde and Levintal (2017), and the references cited there.…”

Climate Disaster Risks – Empirics and a Multi-Phase Dynamic Model

“…Recent literature frames this issue in the context of DSGE models. Numerical solution methods for solving DSGE models with disasters -by measuring disasters as physical capital and output losses -have been developed by Fernandez-Villaverde and Levintal (2016). Disasters are then mainly modeled as highly persistent shocks with mean reversion after the event.…”