Piecewise-Linear Approximations and Filtering for DSGE Models with Occasionally Binding Constraints

63 Pages Posted: 15 Jun 2020

See all articles by S. Boragan Aruoba

S. Boragan Aruoba

University of Maryland

Pablo Cuba-Borda

Board of Governors of the Federal Reserve System

Kenji Higa-Flores

University of Maryland - Department of Economics

Frank Schorfheide

University of Pennsylvania - Department of Economics; Centre for Economic Policy Research (CEPR); National Bureau of Economic Research (NBER); University of Pennsylvania - The Penn Institute for Economic Research (PIER)

Sergio Villalvazo

Federal Reserve Board of Governors

Multiple version iconThere are 2 versions of this paper

Date Written: February, 2020

Abstract

We develop an algorithm to construct approximate decision rules that are piecewise-linear and continuous for DSGE models with an occasionally binding constraint. The functional form of the decision rules allows us to derive a conditionally optimal particle filter (COPF) for the evaluation of the likelihood function that exploits the structure of the solution. We document the accuracy of the likelihood approximation and embed it into a particle Markov chain Monte Carlo algorithm to conduct Bayesian estimation. Compared with a standard bootstrap particle filter, the COPF significantly reduces the persistence of the Markov chain, improves the accuracy of Monte Carlo approximations of posterior moments, and drastically speeds up computations. We use the techniques to estimate a small-scale DSGE model to assess the effects of the government spending portion of the American Recovery and Reinvestment Act in 2009 when interest rates reached the zero lower bound.

Keywords: Bayesian estimation, Nonlinear filtering, Nonlinear solution methods, Particle MCMC, zero lower bound (ZLB)

JEL Classification: C50, E40, E50

Suggested Citation

Aruoba, S. Boragan and Cuba-Borda, Pablo and Higa-Flores, Kenji and Schorfheide, Frank and Villalvazo, Sergio, Piecewise-Linear Approximations and Filtering for DSGE Models with Occasionally Binding Constraints (February, 2020). International Finance Discussion Paper No. 1272, Available at SSRN: https://ssrn.com/abstract=3625091 or http://dx.doi.org/10.17016/IFDP.2020.1272

S. Boragan Aruoba (Contact Author)

University of Maryland ( email )

College Park
College Park, MD 20742
United States

Pablo Cuba-Borda

Board of Governors of the Federal Reserve System ( email )

20th Street and Constitution Avenue NW
Washington, DC 20551
United States

Kenji Higa-Flores

University of Maryland - Department of Economics ( email )

United States

Frank Schorfheide

University of Pennsylvania - Department of Economics ( email )

Ronald O. Perelman Center for Political Science
133 South 36th Street
Philadelphia, PA 19104-6297
United States

HOME PAGE: http://www.econ.upenn.edu/~schorf

Centre for Economic Policy Research (CEPR)

London
United Kingdom

National Bureau of Economic Research (NBER) ( email )

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

University of Pennsylvania - The Penn Institute for Economic Research (PIER) ( email )

Philadelphia, PA
United States

Sergio Villalvazo

Federal Reserve Board of Governors ( email )

Washington, D.C., DC

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