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
Reprise
2. Savings in an OLG Model
The Basic OLG Model
An Example Economy
Dynamics
A Stochastic Version
Reprise
Matlab Code Used to Produce Figure 2.2
3. 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 Decentral-
ized Economy Are Not Equal
Reprise
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
Reprise
Matlab Code for Figures 4.2 and 4.3
5. Recursive Stochastic Models
Probability
1
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
Reprise
Matlab Code
6. Hansens RBC Model
Hansens Basic Model
Log Linearization Techniques
The Basics of Log Linearization
Uhligs Method of Log Linearization
Log-Linear Version of Hansens Model
Solution Using Jump Variables
Calibration of the Log-Linear Model
Variances of the Variables in the Model
Hansens Model with Indivisible Labor
Stationary State
Log-Linear Version of the Indivisible Labor Model
Impulse Response Functions
Reprise
Appendix 1: Solving the Log-Linear Model
Appendix 2: Blanchard and Kahns Solution Method
General Version
Stochastic Shocks
Hansens 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
Reprise
2
Matlab Code
Part Two: Extensions Of The Basic Rbc Model
8. Money: Cash in Advance
Cooley and Hansens 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 Log Linearization
The Log Linearization
Solving the Log-Linear System
Impulse Response Functions
Seigniorage
The Model
The Stationary State
Log-Linear Version of the Model
Reprise
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
Stationary States
Log-Linear Version of the Model
Seigniorage
The Full Model
Stationary States
Log Linearization
Reprise
10. Staggered Pricing Model
The Basic Model
The Final Goods Firms
The Intermediate Goods Firms
The Family
Equilibrium Conditions
The Full Model
The Stationary State
Log Linearization
Log Linearization of the Firms Problem
The Final Goods Pricing Rule
The Intermediate Goods Pricing Rule
Ination Equation (Phillips Curve)
Log Linear Version of the Model
Solving the Log Linear Model
Impulse Response Functions
Ination Adjustment for Nonoptimizing Firms
3
The Stationary State
Log Linearization
Solving the Model
Impulse Response Functions
Reprise
11. Staggered Wage Setting
The Labor Bundler
First-Order Conditions for Families
The Rest of the Model
Equilibrium Conditions
The Full Model
The Stationary State
Log Linearization
Solving the Model
Impulse Response Functions
Reprise
12. Financial Markets and Monetary Policy
Working Capital
Households
Firms
Financial Intermediaries
The Full Model
The Stationary State
Log Linear Version of the Model
Impulse Response Functions
Economy with Annual Ination of 100 Percent
Comparative Impulse Response Functions
Central Banking and Monetary Policy Rules
The Model with a Taylor Rule
Stationary States
Log-Linear Version and Its Solution
Comparing a Taylor Rule to a Friedman Rule
Reprise
13. Small Open Economy Models
The Preliminary Model
The Household
The Firm
Equilibrium Conditions
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 ClosedOpen Economy with Money
The Open Economy Conditions
4
The Household
Firms
Equilibrium Conditions
The Full Model
The Stationary State
Log-Linear Version of Full Model
Reprise
References
Index
5
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