Methods for Applied Macroeconomic Research

"The last twenty years have witnessed a revolution in macroeconomic modeling. Yet an integrated and accessible treatment of the new methods has been notably lacking. Fabio Canova's book fills that gap magnificently. It is surely destined to be an indispensable reference for both students and researchers for years to come."--Charles Bean, Bank of England "This book will become an invaluable reference for applied macroeconomists as well as a much-needed teaching tool for graduate macroeconomic courses. Anybody who has an interest in quantitative macroeconomics, either as an academic or as a practitioner, should buy it."--Lucrezia Reichlin, European Central Bank "Dynamic general equilibrium models have become regular tools for policy analysis in central banks and other policy institutions. This book is a wonderful source for those who want to bring those models to the data. It is thorough and comprehensive, it has a great set of examples and exercises, and, above all, it provides many practical tips. A must-read for any applied macroeconomist."--Frank Smets, European Central Bank "To be able to describe and interpret business-cycle fluctuations using modern methods developed by researchers is crucial to economists who want to make and evaluate forecasts and policy advice. Fabio Canova has a long experience from research at the frontier, but also from teaching and from applied work at policy institutions such as central banks. His book provides an indispensable toolbox for any researcher that wants to have an influence on practical policy work."--Anders Vredin, Sveriges Riksbank "The material covered in this book is extensive, and the author always strives to provide an in-depth analysis and discussion for every topic, complete with the most up-to-date developments in the literature. The combination of DSGE macroeconomics and econometrics makes this book a unique product, likely to become an essential reference for empirical macroeconomists and policymakers."--Marco Del Negro, FRB Atlanta "This book is unprecedented among econometrics books for the way it incorporates careful and sophisticated macroeconomic theory. It is unprecedented among books on dynamic macroeconomics for its level of practical statistical advice and econometric sophistication. There is simply nothing close to this book available. Many of the best young researchers will want to study and teach from it."--Thomas J. Sargent, New York University "This book treats econometric, computational, and macroeconomic substantive issues jointly. Nearly all existing books in this area are either strictly econometric, strictly computational, or focus on substance without taking up econometric and computational issues. The need for a treatment like this on the part of applied researchers means there will be wide interest in it."--Christopher Sims, Princeton University

Fabio Canova

Preface xi Chapter 1: Preliminaries 1 1.1 Stochastic Processes 2 1.2 Convergence Concepts 3 1.3 Time Series Concepts 8 1.4 Laws of Large Numbers 14 1.5 Central Limit Theorems 16 1.6 Elements of Spectral Analysis 18 Chapter 2: DSGE Models, Solutions, and Approximations 26 2.1 A Few Useful Models 27 2.2 Approximation Methods 45 Chapter 3: Extracting and Measuring Cyclical Information 70 3.1 Statistical Decompositions 72 3.2 Hybrid Decompositions 83 3.3 Economic Decompositions 100 3.4 Time Aggregation and Cycles 104 3.5 Collecting Cyclical Information 105 Chapter 4: VAR Models 111 4.1 TheWold Theorem 112 4.2 Specification 118 4.3 Moments and Parameter Estimation of a VAR.q/ 126 4.4 Reporting VAR Results 130 4.5 Identification 141 4.6 Problems 151 4.7 Validating DSGE Models with VARs 159 Chapter 5: GMM and Simulation Estimators 165 5.1 Generalized Method of Moments and Other Standard Estimators 166 5.2 IV Estimation in a Linear Model 169 5.3 GMM Estimation: An Overview 176 5.4 GMM Estimation of DSGE Models 191 5.5 Simulation Estimators 197 Chapter 6: Likelihood Methods 212 6.1 The Kalman Filter 214 6.2 The Prediction Error Decomposition of Likelihood 221 6.3 Numerical Tips 228 6.4 ML Estimation of DSGE Models 230 6.5 Two Examples 240 Chapter 7: Calibration 248 7.1 A Definition 249 7.2 The Uncontroversial Parts 250 7.3 Choosing Parameters and Stochastic Processes 252 7.4 Model Evaluation 259 7.5 The Sensitivity of the Measurement 279 7.6 Savings, Investments, and Tax Cuts: An Example 282 Chapter 8: Dynamic Macro Panels 288 8.1 From Economic Theory to Dynamic Panels 289 8.2 Panels with Homogeneous Dynamics 291 8.3 Dynamic Heterogeneity 304 8.4 To Pool or Not to Pool? 315 8.5 Is Money Superneutral? 321 Chapter 9: Introduction to Bayesian Methods 325 9.1 Preliminaries 326 9.2 Decision Theory 335 9.3 Inference 336 9.4 Hierarchical and Empirical Bayes Models 345 9.5 Posterior Simulators 353 9.6 Robustness 370 9.7 Estimating Returns to Scale in Spain 370 Chapter 10: Bayesian VARs 373 10.1 The Likelihood Function of an m-Variable VAR(q) 374 10.2 Priors for VARs 376 10.3 Structural BVARs 390 10.4 Time-Varying-Coefficient BVARs 397 10.5 Panel VAR Models 404 Chapter 11: Bayesian Time Series and DSGE Models 418 11.1 Factor Models 419 11.2 Stochastic Volatility Models 427 11.3 Markov Switching Models 433 11.4 Bayesian DSGE Models 440 Appendix A Statistical Distributions 463 References 469 Index 487