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

    1. The Basic Model
    2. Technological Growth
    3. The Golden Rule
    4. A Stochastic Solow Model
    5. Log-Linear Version of the Solow Model
      • Capital
      • Output
    6. Reprise

    2. Savings in an OLG Model

    1. The Basic OLG Model
      • An Example Economy
    2. Dynamics
    3. A Stochastic Version
    4. Reprise
    5. Matlab Code Used to Produce Figure 2.2

    3. Infinitely Lived Agents

    1. A Robinson Crusoe Economy with Fixed Labor
      • Variational Methods
    2. A Robinson Crusoe Economy with Variable Labor
      • The General Model
      • Solution for a Sample Economy
    3. A Competitive Economy
    4. The Second Welfare Theorem
      • An Example Where the Representative Agent Economy and the Decentralized Economy Are Not Equal
    5. Reprise

    4. Recursive Deterministic Models

    1. States and Controls
    2. The Value Function
    3. A General Version
    4. Returning to Our Example Economy
      • Another Version of the Same Economy
    5. An Approximation of the Value Function
    6. An Example with Variable Labor
    7. Reprise
    8. Matlab Code for Figures 4.2 and 4.3

    5. Recursive Stochastic Models

    1. Probability
    2. A Simple Stochastic Growth Model
    3. A General Version
      • The Problem of Dimensionality
    4. The Value Function for the Simple Economy
      • Calculating the Value Functions
    5. Markov Chains
    6. Reprise
    7. Matlab Code

    6. Hansen’s RBC Model

    1. Hansen’s Basic Model
    2. Log Linearization Techniques
      • The Basics of Log Linearization
      • Uhlig’s Method of Log Linearization
    3. Log-Linear Version of Hansen’s Model
      • Solution Using Jump Variables
      • Calibration of the Log-Linear Model
      • Variances of the Variables in the Model
    4. Hansen’s Model with Indivisible Labor
      • Stationary State
      • Log-Linear Version of the Indivisible Labor Model
    5. Impulse Response Functions
    6. Reprise
    7. Appendix 1: Solving the Log-Linear Model
    8. Appendix 2: Blanchard and Kahn’s Solution Method
      • General Version
      • Stochastic Shocks
      • Hansen’s Model and Blanchard-Kahn
      • The Generalized Schur Method
    9. Matlab Code
      • Solution to Basic Hansen Model
      • Approximating the Variances
      • Code for Appendix 2

    7. Linear Quadratic Dynamic Programming

    1. Taylor Approximations of the Objective Function
    2. The Method of Kydland and Prescott
      • An Example
      • Solving the Bellman Equation
      • Calibrating the Example Economy
    3. Adding Stochastic Shocks
      • The Example Economy
      • Calibrating the Example Economy
    4. Hansen with Indivisible Labor
    5. Impulse response functions
      • Vector Autoregressions
    6. An Alternative Process for Technology
    7. Reprise 178
    8. Matlab Code

    Part Two: Extensions Of The Basic Rbc Model

    8. Money: Cash in Advance

    1. Cooley and Hansen’s Model
    2. Finding the Stationary State
    3. Solving the Model Using Linear Quadratic Methods
      • Finding a Quadratic Objective Function
      • Finding the Economy Wide Variables
    4. Solving the Model Using Log Linearization
      • The Log Linearization
      • Solving the Log-Linear System
      • Impulse Response Functions
    5. Seigniorage
      • The Model
      • The Stationary State
      • Log-Linear Version of the Model
    6. Reprise
    7. Appendix 1: CES Utility Functions
    8. Appendix 2: Matrix Quadratic Equations
    9. Matlab Code for Solving the CES Model with Seigniorage

    9. Money in the Utility Function

    1. The Model
    2. Stationary States
    3. Log-Linear Version of the Model
    4. Seigniorage
      • The Full Model
      • Stationary States
      • Log Linearization
    5. Reprise

    10. Staggered Pricing Model

    1. The Basic Model
      • The Final Goods Firms
      • The Intermediate Goods Firms
      • The Family
      • Equilibrium Conditions
      • The Full Model
    2. The Stationary State
    3. Log Linearization
      • Log Linearization of the Firm’s Problem
      • The Final Goods Pricing Rule
      • The Intermediate Goods Pricing Rule
      • Inflation Equation (Phillips Curve)
      • Log Linear Version of the Model
    4. Solving the Log Linear Model
      • Impulse Response Functions
    5. Inflation Adjustment for Nonoptimizing Firms
      • The Stationary State
      • Log Linearization
      • Solving the Model
      • Impulse Response Functions
    6. Reprise

    11. Staggered Wage Setting

    1. The Labor Bundler
      • First-Order Conditions for Families
      • The Rest of the Model
      • Equilibrium Conditions
      • The Full Model
    2. The Stationary State
    3. Log Linearization
    4. Solving the Model
      • Impulse Response Functions
    5. Reprise

    12. Financial Markets and Monetary Policy

    1. Working Capital
      • Households
      • Firms
      • Financial Intermediaries
      • The Full Model
      • The Stationary State
      • Log Linear Version of the Model
      • Impulse Response Functions
      • Economy with Annual Inflation of 100 Percent
      • Comparative Impulse Response Functions
    2. 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
    3. Reprise

    13. Small Open Economy Models

    1. The Preliminary Model
      • The Household
      • The Firm
      • Equilibrium Conditions
      • Stationary State
      • The Dynamic (Log-Linear) Model
    2. Model with Capital Adjustment Costs
    3. Closing the Open Economy
      • Interest Rates and Country Risk
      • The Dynamic Version
    4. The “Closed” Open Economy with Money
      • The Open Economy Conditions
      • The Household
      • Firms
      • Equilibrium Conditions
      • The Full Model
      • The Stationary State
      • Log-Linear Version of Full Model
    5. Reprise
    • References
    • Index
  • Cover: The ABCs of RBCs
  • A photo of the author

Photo by Patricio Gatti

George McCandless is an economist at the Central Bank of Argentina.