Continuous-time Methods in Macroeconomics
(with applications to heterogeneous agent models)
by Jesús Fernández-Villaverde (University of Pennsylvania) and Galo Nuño (Bank of Spain)
Date:
Wednesday, 30 September 2020 to Friday, 2 October 2020
Venue:
via Zoom
General Description
We are pleased to announce details of the latest EABCN Training School; a two-day course entitled „Continuous-time Methods in Macroeconomics (with applications to heterogeneous agent models)“. Professor Jesús Fernández-Villaverde and Galo Nuño will teach the course. It is primarily aimed at participants in the Euro Area Business Cycle Network,, but applications will also be considered from doctoral students, post-doctoral researchers,, and economists working in central banks and government institutions outside of the network, as well as commercial organisations (fees are applicable for non-network non-academic organisations).
Course outline
A recent literature has shown that heterogeneous agent (HA) models can be crucial for the understanding of the transmission mechanism of monetary and fiscal policies. So far, a significant barrier to the widespread use of HA models in academic and policy circles, including central banks, has been the complexity in the solution and estimation of this class of models. New analytical and numerical tools, however, have emerged in the last years that greatly simplify this task. Continuous-time methods, in particular, provide important advantages for the analysis of HA models.
This training course introduces the main tools, as well as some recent advances, in continuous-time methods in macroeconomics, with a focus on their application to HA models. This course will provide participants with the necessary background to apply these tools in practice as well as introduce some relevant applications in macro and monetary economics.
The course is divided into five sessions taught over three days.
Session 1. Dynamic programming: the deterministic case. The Hamilton-Jacobi-Bellman (HJB) equation and the Hamiltonian. Numerical methods and viscosity solutions. Finite difference method (FDM).
Session 2. Dynamic programming: the stochastic case. Wiener processes and Itô?s lemma. Stochastic calculus. Feynman-Kac formula and the Kolmogorov forward equation. The HJB equation. Boundary conditions. The case of Poisson processes. FDM with stochastic processes. Deep learning for high-dimensional HJB equations.
Session 3. Heterogeneous agent models. The Aiyagari-Bewley-Huggett model. Computation of the stationary equilibrium. Transitional dynamics. Heterogeneous agent new Keynesian (HANK) models.
Session 4. Heterogeneous agent models with aggregate shocks. The problem with aggregate shocks. Perturbation approaches. Bounded rationality: the Krusell-Smith methodology. Analysis of nonlinear aggregate dynamics using machine learning. Estimation of HA models. Application to HA models with a financial sector.
Session 5. Optimal policies with heterogeneous agents. Introduction to the calculus of variations. Constrained-efficient allocation in HA models. Ramsey policies. Optimal monetary policy with heterogeneous agents.