An Introduction to Dynamic Macroeconomic Models. Part One: Basic Models And Solution Methods

Transcription

1 The ABCs of RBCs An Introduction to Dynamic Macroeconomic Models George McCandless Preface Introduction Part One: Basic Models And Solution Methods 1. The Basic Solow Model The Basic Model Technological Growth The Golden Rule A Stochastic Solow Model Log-Linear Version of the Solow Model Capital Output 2. Savings in an OLG Model The Basic OLG Model An Example Economy Dynamics A Stochastic Version Matlab Code Used to Produce Figure In nitely Lived Agents A Robinson Crusoe Economy with Fixed Labor Variational Methods A Robinson Crusoe Economy with Variable Labor The General Model Solution for a Sample Economy A Competitive Economy The Second Welfare Theorem An Example Where the Representative Agent Economy and the Decentralized Economy Are Not Equal 4. Recursive Deterministic Models States and Controls The Value Function A General Version Returning to Our Example Economy Another Version of the Same Economy An Approximation of the Value Function An Example with Variable Labor Matlab Code for Figures 4.2 and Recursive Stochastic Models Probability 1

2 A Simple Stochastic Growth Model A General Version The Problem of Dimensionality The Value Function for the Simple Economy Calculating the Value Functions Markov Chains Matlab Code 6. Hansen s RBC Model Hansen s Basic Model Techniques The Basics of Uhlig s Method of Log-Linear Version of Hansen s Model Solution Using Jump Variables Calibration of the Log-Linear Model Variances of the Variables in the Model Hansen s Model with Indivisible Labor Stationary State Log-Linear Version of the Indivisible Labor Model Appendix 1: Solving the Log-Linear Model Appendix 2: Blanchard and Kahn s Solution Method General Version Stochastic Shocks Hansen s Model and Blanchard-Kahn The Generalized Schur Method Matlab Code Solution to Basic Hansen Model Approximating the Variances Code for Appendix 2 7. Linear Quadratic Dynamic Programming Taylor Approximations of the Objective Function The Method of Kydland and Prescott An Example Solving the Bellman Equation Calibrating the Example Economy Adding Stochastic Shocks The Example Economy Calibrating the Example Economy Hansen with Indivisible Labor Impulse response functions Vector Autoregressions An Alternative Process for Technology 2

3 Matlab Code Part Two: Extensions Of The Basic Rbc Model 8. Money: Cash in Advance Cooley and Hansen s Model Finding the Stationary State Solving the Model Using Linear Quadratic Methods Finding a Quadratic Objective Function Finding the Economy Wide Variables Solving the Model Using The Solving the Log-Linear System Seigniorage The Model Log-Linear Version of the Model Appendix 1: CES Utility Functions Appendix 2: Matrix Quadratic Equations Matlab Code for Solving the CES Model with Seigniorage 9. Money in the Utility Function The Model Log-Linear Version of the Model Seigniorage 10. Staggered Pricing Model The Basic Model The Final Goods Firms The Intermediate Goods Firms The Family of the Firm s Problem The Final Goods Pricing Rule The Intermediate Goods Pricing Rule In ation Equation (Phillips Curve) Log Linear Version of the Model Solving the Log Linear Model In ation Adjustment for Nonoptimizing Firms 3

4 Solving the Model 11. Staggered Wage Setting The Labor Bundler First-Order Conditions for Families The Rest of the Model Solving the Model 12. Financial Markets and Monetary Policy Working Capital Households Firms Financial Intermediaries Log Linear Version of the Model Economy with Annual In ation of 100 Percent Comparative Central Banking and Monetary Policy Rules The Model with a Taylor Rule Log-Linear Version and Its Solution Comparing a Taylor Rule to a Friedman Rule 13. Small Open Economy Models The Preliminary Model The Household The Firm Stationary State The Dynamic (Log-Linear) Model Model with Capital Adjustment Costs Closing the Open Economy Interest Rates and Country Risk The Dynamic Version The Closed Open Economy with Money The Open Economy Conditions 4

5 The Household Firms Log-Linear Version of Full Model References Index 5