Bayesian Estimation of DSGE Models

by Edward P. Herbst, Frank Schorfheide

Overview

Dynamic stochastic general equilibrium (DSGE) models have become one of the workhorses of modern macroeconomics and are extensively used for academic research as well as forecasting and policy analysis at central banks. This book introduces readers to state-of-the-art computational techniques used in the Bayesian analysis of DSGE models. The book covers Markov chain Monte Carlo techniques for linearized DSGE models, novel sequential Monte Carlo methods that can be used for parameter inference, and the estimation of nonlinear DSGE models based on particle filter approximations of the likelihood function. The theoretical foundations of the algorithms are discussed in depth, and detailed empirical applications and numerical illustrations are provided. The book also gives invaluable advice on how to tailor these algorithms to specific applications and assess the accuracy and reliability of the computations.

Bayesian Estimation of DSGE Models is essential reading for graduate students, academic researchers, and practitioners at policy institutions.

Product Details

ISBN-13:	9780691161082
Publisher:	Princeton University Press
Publication date:	12/29/2015
Series:	The Econometric and Tinbergen Institutes Lectures
Edition description:	New Edition
Pages:	296
Product dimensions:	5.80(w) x 8.50(h) x 1.00(d)

About the Author

Edward P. Herbst is an economist in the Division of Research and Statistics at the Federal Reserve Board. Frank Schorfheide is Professor of Economics at the University of Pennsylvania and research associate at the National Bureau of Economic Research. He also is a fellow of the Penn Institute for Economic Research, a visiting scholar at the Federal Reserve Banks of Philadelphia and New York, and a coeditor of Quantitative Economics. For more, see edherbst.net and sites.sas.upenn.edu/schorf.

Table of Contents

Figures xi

Tables xiii

Series Editors’ Introduction xv

Preface xvii

I Introduction to DSGE Modeling and Bayesian Inference 1

1 DSGE Modeling 3

1.1 A Small-Scale New Keynesian DSGE Model 4

1.2 Other DSGE Models Considered in This Book 11

2 Turning a DSGE Model into a Bayesian Model 14

2.1 Solving a (Linearized) DSGE Model 16

2.2 The Likelihood Function 19

2.3 Priors 22

3 A Crash Course in Bayesian Inference 29

3.1 The Posterior of a Linear Gaussian Model 31

3.2 Bayesian Inference and Decision Making 35

3.3 A NonGaussian Posterior 43

3.4 Importance Sampling 46

3.5 Metropolis-Hastings Algorithms 52

II Estimation of Linearized DSGE Models 63

4 Metropolis-Hastings Algorithms for DSGE Models 65

4.1 A Benchmark Algorithm 67

4.2 The RWMH-V Algorithm at Work 69

4.3 Challenges Due to Irregular Posteriors 77

4.4 Alternative MH Samplers 81

4.5 Comparing the Accuracy of MH Algorithms 87

4.6 Evaluation of the Marginal Data Density 93

5 Sequential Monte Carlo Methods 100

5.1 A Generic SMC Algorithm 101

5.2 Further Details of the SMC Algorithm 109

5.3 SMC for the Small Scale DSGE Model 125

6 Three Applications 130

6.1 A Model with Correlated Shocks 131

6.2 The Smets-Wouters Model with a Diffuse Prior 141

6.3 The Leeper-Plante-Traum Fiscal Policy Model 150

III Estimation of Nonlinear DSGE Models 161

7 From Linear to Nonlinear DSGE Models 163

7.1 Nonlinear DSGE Model Solutions 164

7.2 Adding Nonlinear Features to DSGE Models 167

8 Particle Filters 171

8.1 The Bootstrap Particle Filter 173

8.2 A Generic Particle Filter 182

8.3 Adapting the Generic Filter 185

8.4 Additional Implementation Issues 191

8.5 Adapting s_t-1 Draws 198

8.6 Application to the Small-Scale DSGE Model 204

8.7 Application to the SW Model 212

8.8 Computational Considerations 216

9 Combining Particle Filters with MH Samplers 218

9.1 The PFMH Algorithm 218

9.2 Application to the Small-Scale DSGE Model 222

9.3 Application to the SW Model 224

9.4 Computational Considerations 229

10 Combining Particle Filters with SMC Samplers 231

10.1 An SM C² Algorithm 231

10.2 Application to the Small-Scale DSGE Model 237

10.3 Computational Considerations 239

Appendix 241

A Model Descriptions 241

A.1 Smets-Wouters Model 241

A.2 Leeper-Plante-Traum-Fiscal Policy Model 247

B Data Sources 249

B.1 Small-Scale-New Keynesian DSGE Model 249

B.2 Smets-Wouters Model 249

B.3 Leeper-Plante-Traum Fiscal Policy Model 251

Bibliography 257

Index 271

What People are Saying About This

From the Publisher

"This book depicts valuable and revealing methods for solving, estimating, and analyzing a class of dynamic equilibrium models of the macroeconomy. It describes formally tractable techniques for the study of macroeconomic models that feature transition mechanisms for a large number of underlying shocks. Both authors have played important roles in developing and applying these techniques. This is a terrific resource for how to use these methods in practice."—Lars Peter Hansen, David Rockefeller Distinguished Service Professor of Economics, University of Chicago, and recipient of the Nobel Prize in economics

"This timely book collects in one place many of the key Markov chain Monte Carlo methods for numerical Bayesian inference along with many of their recent refinements. Written for applied users, it offers clear descriptions of each algorithm and illustrates how it can be used to estimate dynamic stochastic general equilibrium models in macroeconomics."—James D. Hamilton, Professor of Economics, University of California, San Diego

"This is perhaps the most thorough book available on how to estimate DSGE models using sophisticated Bayesian computation tools. It is an excellent resource for professionals and advanced students of the topic."—Serena Ng, Professor of Economics, Columbia University

Editorial Reviews

"Well written and well organized, and the topic analyzed is very interesting and current."—-Manuel Salvador, MathSciNet

"The book is well written and clearly arranged. It can be recommended to economists and researchers who are interested in applying state-of-the-art computational methods to estimate DSGE models as well as to econometricians who want to learn about the application of DSGE models in empirical macroeconomics."—-Peter Hackl, Statistical Papers

From the Publisher