Methods for Applied Macroeconomic Research Book

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