Structural Macroeconometrics

Preface xiiiPreface to the First Edition xvPart I IntroductionChapter 1: Background and Overview 31.1 Background 31.2 Overview 4Chapter 2: Casting Models in Canonical Form 92.1 Notation 92.1.1 Log-Linear Model Representations 112.1.2 Nonlinear Model Representations 112.2 Linearization 122.2.1 Taylor Series Approximation 122.2.2 Log-Linear Approximations 142.2.3 Example Equations 15Chapter 3: DSGE Models: Three Examples 183.1 Model I: A Real Business Cycle Model 203.1.1 Environment 203.1.2 The Nonlinear System 233.1.3 Log-Linearization 263.2 Model II: Monopolistic Competition and Monetary Policy 283.2.1 Environment 283.2.2 The Nonlinear System 333.2.3 Log-Linearization 343.3 Model III: Asset Pricing 383.3.1 Single-Asset Environment 383.3.2 Multi-Asset Environment 393.3.3 Alternative Preference Specifications 40Part II Model Solution TechniquesChapter 4: Linear Solution Techniques 514.1 Homogeneous Systems 524.2 Example Models 544.2.1 The Optimal Consumption Model 544.2.2 Asset Pricing with Linear Utility 554.2.3 Ramsey's Optimal Growth Model 564.3 Blanchard and Kahn's Method 574.4 Sims' Method 614.5 Klein's Method 644.6 An Undetermined Coefficients Approach 66v Chpater 5: Nonlinear Solution Techniques 695.1 Projection Methods 715.1.1 Overview 715.1.2 Finite Element Methods 725.1.3 Orthogonal Polynomials 735.1.4 Implementation 745.1.5 Extension to the l-dimensional Case 785.1.6 Application to the Optimal Growth Model 795.2 Iteration Techniques: Value-Function and Policy-Function Iterations 875.2.1 Dynamic Programming 875.2.2 Value-Function Iterations 895.2.3 Policy-Function Iterations 945.3 Perturbation Techniques 955.3.1 Notation 955.3.2 Overview 975.3.3 Application to DSGE Models 995.3.4 Application to an Asset-Pricing Model 105Part III Data Preparation and RepresentationChapter 6: Removing Trends and Isolating Cycles 1136.1 Removing Trends 1156.2 Isolating Cycles 1206.2.1 Mathematical Background 1206.2.2 Cramer Representations 1246.2.3 Spectra 1256.2.4 Using Filters to Isolate Cycles 1266.2.5 The Hodrick-Prescott Filter 1286.2.6 Seasonal Adjustment 1306.2.7 Band Pass Filters 1316.3 Spuriousness 134Chapter 7: Summarizing Time Series Behavior When All Variables Are Observable 1387.1 Two Useful Reduced-Form Models 1397.1.1 The ARMA Model 1397.1.2 Allowing for Heteroskedastic Innovations 1457.1.3 The VAR Model 1477.2 Summary Statistics 1497.2.1 Determining Lag Lengths 1577.2.2 Characterizing the Precision of Measurements 1597.3 Obtaining Theoretical Predictions of Summary Statistics 162Chapter 8: State-Space Representations 1668.1 Introduction 1668.1.1 ARMA Models 1678.2 DSGE Models as State-Space Representations 1698.3 Overview of Likelihood Evaluation and Filtering 1718.4 The Kalman Filter 1738.4.1 Background 1738.4.2 The Sequential Algorithm 1758.4.3 Smoothing 1788.4.4 Serially Correlated Measurement Errors 1818.5 Examples of Reduced-Form State-Space Representations 1828.5.1 Time-Varying Parameters 1828.5.2 Stochastic Volatility 1858.5.3 Regime Switching 1868.5.4 Dynamic Factor Models 187Part IV Monte Carlo MethodsChapter 9: Monte Carlo Integration: The Basics 1939.1 Motivation and Overview 1939.2 Direct Monte Carlo Integration 1969.2.1 Model Simulation 1989.2.2 Posterior Inference via Direct Monte Carlo Integration 2019.3 Importance Sampling 2029.3.1 Achieving Efficiency: A First Pass 2069.4 Efficient Importance Sampling 2119.5 Markov Chain Monte Carlo Integration 2159.5.1 The Gibbs Sampler 2169.5.2 Metropolis-Hastings Algorithms 218Chapter 10: Likelihood Evaluation and Filtering in State-Space Representations Using Sequential Monte Carlo Methods 22110.1 Background 22110.2 Unadapted Filters 22410.3 Conditionally Optimal Filters 22810.4 Unconditional Optimality: The EIS Filter 23310.4.1 Degenerate Transitions 23510.4.2 Initializing the Importance Sampler 23610.4.3 Example 23910.5 Application to DSGE Models 24110.5.1 Initializing the Importance Sampler 24310.5.2 Initializing the Filtering Density 24510.5.3 Application to the RBC Model 246Part V Empirical MethodsChapter 11: Calibration 25311.1 Historical Origins and Philosophy 25311.2 Implementation 25811.3 The Welfare Cost of Business Cycles 26111.4 Productivity Shocks and Business Cycle Fluctuations 26811.5 The Equity Premium Puzzle 27311.6 Critiques and Extensions 27611.6.1 Critiques 27611.6.2 Extensions 279Chapter 12: Matching Moments 28512.1 Overview 28512.2 Implementation 28612.2.1 The Generalized Method of Moments 28612.2.2 The Simulated Method of Moments 29412.2.3 Indirect Inference 29712.3 Implementation in DSGE Models 30012.3.1 Analyzing Euler Equations 30012.3.2 Analytical Calculations Based on Linearized Models 30112.3.3 Simulations Involving Linearized Models 30612.3.4 Simulations Involving Nonlinear Approximations 30712.4 Empirical Application: Matching RBC Moments 308Chapter 13: Maximum Likelihood 31413.1 Overview 31413.2 Introduction and Historical Background 31613.3 A Primer on Optimization Algorithms 31813.3.1 Simplex Methods 31913.3.2 Derivative-Based Methods 32813.4 Ill-Behaved Likelihood Surfaces: Problems and Solutions 33013.4.1 Problems 33013.4.2 Solutions 33113.5 Model Diagnostics and Parameter Stability 33413.6 Empirical Application: Identifying Sources of Business Cycle Fluctuations 337Chapter 14: Bayesian Methods 35114.1 Overview of Objectives 35114.2 Preliminaries 35214.3 Using Structural Models as Sources of Prior Information for Reduced-Form Analysis 35514.4 Implementing Structural Models Directly 36014.5 Model Comparison 36114.6 Using an RBC Model as a Source of Prior Information for Forecasting 36414.7 Estimating and Comparing Asset-Pricing Models 37314.7.1 Estimates 38014.7.2 Model Comparison 384References 387Index 401