Preface
Preface to the First Edition
Part I Introduction
1 Background and Overview
1.1 Background
1.2 Overview
2 Casting Models in Canonical Form
2.1 Notation
2.1.1 Log-Linear Model Representations
2.1.2 Nonlinear Model Representations
2.2 Linearization
2.2.1 Taylor Series Approximation
2.2.2 Log-Linear Approximations
2.2.3 Example Equations
3 DSGE Models: Three Examples
3.1 Model I: A Real Business Cycle Model
3.1.1 Environment
3.1.2 The Nonlinear System
3.1.3 Log-Linearization
3.2 Model II: Monopolistic Competition and Monetary Policy
3.2.1 Environment
3.2.2 The Nonlinear System
3.2.3 Log-Linearization
3.3 Model III: Asset Pricing
3.3.1 Single-Asset Environment
3.3.2 Multi-Asset Environment
3.3.3 Alternative Preference Specifications
Part II Model Solution Techniques
4 Linear Solution Techniques
4.1 Homogeneous Systems
4.2 Example Models
4.2.1 The Optimal Consumption Model
4.2.2 Asset Pricing with Linear Utility
4.2.3 Ramsey's Optimal Growth Model
4.3 Blanchard and Kahn's Method
4.4 Sims' Method
4.5 Klein's Method
4.6 An Undetermined Coefficients Approach
5 Nonlinear Solution Techniques
5.1 Projection Methods
5.1.1 Overview
5.1.2 Finite Element Methods
5.1.3 Orthogonal Polynomials
5.1.4 Implementation
5.1.5 Extension to the/-dimensional Case
5.1.6 Application to the Optimal Growth Model
5.2 Iteration Techniques: Value-Function and Policy-Function Iterations
5.2.1 Dynamic Programming
5.2.2 Value-Function Iterations
5.2.3 Policy-Function Iterations
5.3 Perturbation Techniques
5.3.1 Notation
5.3.2 Overview
5.3.3 Application to DSGE Models
5.3.4 Application to an Asset-Pricing Model
Part III Data Preparation and Representation
6 Removing Trends and Isolating Cycles
6.1 Removing Trends
6.2 Isolating Cycles
6.2.1 Mathematical Background
6.2.2 Cramtr Representations
6.2.3 Spectra
6.2.4 Using Filters to Isolate Cycles
6.2.5 The Hodrick-Prescott Filter
6.2.6 Seasonal Adjustment
6.2.7 Band Pass Filters
6.3 Spuriousness
7 Summarizing Time Series Behavior When All Variables
Are Observable
7.1 Two Useful Reduced-Form Models
7.1.1 The ARMA Model
7.1.2 Allowing for Heteroskedastic Innovations
7.1.3 The VAR Model
7.2 Summary Statistics
7.2.1 Determining Lag Lengths
7.2.2 Characterizing the Precision of Measurements
7.3 Obtaining Theoretical Predictions of Summary Statistics
8 State-Space Representations
8.1 Introduction
8.1.1 ARMA Models
8.2 DSGE Models as State-Space Representations
8.3 Overview of Likelihood Evaluation and Filtering
8.4 The Kalman Filter
8.4.1 Background
8.4.2 The Sequential Algorithm
8.4.3 Smoothing
8.4.4 Serially Correlated Measurement Errors
8.5 Examples of Reduced-Form State-Space Representations
8.5.1 Time-Varying Parameters
8.5.2 Stochastic Volatility
8.5.3 Regime Switching
8.5.4 Dynamic Factor Models
Part IV Monte Carlo Methods
9 Monte Carlo Integration: The Basics
9.1 Motivation and Overview
9.2 Direct Monte Carlo Integration
9.2.1 Model Simulation
9.2.2 Posterior Inference via Direct Monte Carlo Integration
9.3 Importance Sampling
9.3.1 Achieving Efficiency: A First Pass
9.4 Efficient Importance Sampling
9.5 Markov Chain Monte Carlo Integration
9.5.1 The Gibbs Sampler
9.5.2 Metropolis-Hastings Algorithms
10 Likelihood Evaluation and Filtering in State-Space
Representations Using Sequential Monte Carlo Methods
10.1 Background
10.2 Unadapted Filters
10.3 Conditionally Optimal Filters
10.4 Unconditional Optimality: The EIS Filter
10.4.1 Degenerate Transitions
10.4.2 Initializing the Importance Sampler
10.4.3 Example