Advanced Numerical Methods in Macroeconomics



Jesús Fernández Villaverde (University of Pennsylvania) and Galo Nuño (Banco de España)



29 August - 2 September 2022



15:30 to 18:30 CEST




Intended for

Practitioners, researchers, and academics interested in state-of-the-art computational methods in Macroeconomics.


Participants are assumed to be comfortable following master or PhD level courses in economics. In particular they should have basic knowledge of dynamic programming and to be familiar with a programming language (Matlab, Julia, Python).


Since the financial crisis one decade ago, macroeconomics has made tremendous advances in incorporating nonlinear phenomena (such as sovereign or banking crises) and non-trivial heterogeneity in households and firms into dynamic general equilibrium models. These advances have, in turn, pushed the boundaries in numerical methods able to solve efficiently nonlinear models. The switch from discrete to continuous time methods in the formulation of macro models, the introduction of machine learning techniques -particularly deep learning- in the solution of these models, and the adoption of parallelization techniques to speed up computations are three of the more relevant developments, with far reaching consequences in the type of problems that macroeconomist can study. In this course we discuss these recent advances, providing students with the necessary tools to apply them to their research agendas, as well as including relevant examples in topics such as monetary policy or financial stability.


Dynamic programming in continuous time: finite difference method. Application to sovereign default models
Deep learning, reinforcement learning and its application so solving high dimensional dynamic programming problems
Heterogeneous-agent models in continuous time. Application of machine learning to solve models with aggregate shocks. Application to macro finance


Jesús Fernández-Villaverde is currently Professor of Economics at the University of Pennsylvania, where he serves as Director of Graduate Studies in the Economics Department, Visiting Professor at University of Oxford, Visiting Scholar at the Federal Reserve Banks of Chicago, Clevenland, and Philadelphia and the Bank of Spain, Advisor to the Hoover Institution at Stanford University’s Regulation and Rule of Law Initiative, and a member of the National Bureau of Economic Research and the Center for Economic Policy Research. In the past, he has hold academic appointments, among others, at Harvard University, Princeton University, Yale University, Columbia University, Duke University, and New York University, he has been Visiting Scholar at the Federal Reserve Banks of St. Louis, Minneapolis, Cleveland, and Atlanta, Research Professor at FEDEA (Spain), National Fellow of the Hoover Institution at Stanford University, Visiting Scholar at the Becker-Friedman Institute of the University of Chicago, Visiting Scholar at INET at University of Cambridge, Distinguished Visiting Professor at University of Melbourne (Australia), and he was the director of the Penn Institute for Economic Research. He is editor of the International Economic Review. In the past, he has served in the editorial board of several other learned journals. He has published many peer-reviewed papers, including American Economic Review, Econometrica, and Review of Economic Studies and edited and co-authored several books. His research focuses on macroeconomics, econometrics, and economic history. Among other topics, he is interested in the role of monetary and fiscal policy, the sources of economic growth, the importance of the rule of law, and the foundations of market economies.

Galo Nuño is Head of the Monetary Policy and Macroeconomic Analysis Division at the Bank of Spain. His research focuses on monetary economics, macrofinance and computational methods. In particular, he has developed, with different coauthors, some new theoretical and numerical techniques for the study of continuous-time heterogeneous-agent models, including the analysis of optimal policies and the solution and estimation of nonlinear models with aggregate shocks. His research has been published in journals such as the American Economic Journal: Macroeconomics, Journal of Monetary Economics, Journal of Economic Growth, Review of Economic Dynamics, or Economic Journal.