ECON8022 Macroeconomic Theory

Lecture Notes

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• 1. Purpose
  • 1.1. Expectations
• 2. A Quick Tutorial in Python Tools
  • 2.1. Getting started
  • 2.2. Data Types
    • 2.2.1. Floats
    • 2.2.2. Integers
    • 2.2.3. Boolean
    • 2.2.4. Strings
  • 2.3. Python Lists, Indexing and Slicing
  • 2.4. Python dictionaries
  • 2.5. NumPy and SciPy libraries
    • 2.5.1. NumPy Lists, Indexing and Slicing
  • 2.6. Plotting with MATPLOTLIB
  • 2.7. Useful Python and Numpy functions
  • 2.8. Conditionals
  • 2.9. Loops
  • 2.10. Statistics
  • 2.11. More Python resources for the economist
• 3. A Brief History
• 4. Economies as Dynamical Systems
  • 4.1. Reduced-form representation
  • 4.2. Recursive maps by example
  • 4.3. Linear stochastic difference equation systems
  • 4.4. Markov Chains
    • 4.4.1. Time-homogeneous and finite-state Markov chains
    • 4.4.2. Conditional probabilities
    • 4.4.3. Unconditional probability distributions
    • 4.4.4. Stationary distributions
    • 4.4.5. Asymptotic stability
  • 4.5. Postscript
• 5. Solow-Swan: Before and After
  • 5.1. Empirical Regularities
  • 5.2. Population Growth
    • 5.2.1. Technology
    • 5.2.2. Saving
    • 5.2.3. Characterizing Solution
    • 5.2.4. Technology and equilibrium
  • 5.3. Decentralized Economy
  • 5.4. Exogenous Growth
  • 5.5. Golden Rule
• 6. Optimal Growth and General Equilibrium
  • 6.1. Digging deeper
  • 6.2. Ramsey-Cass-Koopman’s Economy
    • 6.2.1. Finite Horizon
    • 6.2.2. Infinite Horizon
  • 6.3. Solving The RCK Economy
  • 6.4. Competitive Equilibrium
    • 6.4.1. Model Primitives
    • 6.4.2. Two stories of competitive equilibrium
      • 6.4.2.1. Date-\(0\) centralized markets
      • 6.4.2.2. Sequential competitive equilibrium I
      • 6.4.2.3. Sequential competitive equilibrium II
  • 6.5. Recursive Competitive Equilibrium
• 7. Dynamic Programming
  • 7.1. Infinite Horizon Program
    • 7.1.1. The value function, histories and strategies
    • 7.1.2. From value function to Bellman functionals
    • 7.1.3. Existence of optimal strategy
    • 7.1.4. A small technical detour
    • 7.1.5. A fixed-point theorem for the Bellman equation
    • 7.1.6. Optimal strategies
    • 7.1.7. Stationary optimal strategies
    • 7.1.8. Optimality and stationary strategies
    • 7.1.9. Existence of a unique continuous value function
    • 7.1.10. Existence of stationary optimal strategy
    • 7.1.11. Total discounted payoff under stationary optimal strategy
  • 7.2. Example
    • 7.2.1. The deterministic optimal growth problem
    • 7.2.2. Existence of optimal strategies
    • 7.2.3. Uniqueness of optimal strategy
    • 7.2.4. Characterizing optimal strategies
    • 7.2.5. Computing optimal strategies
  • 7.3. Stochastic Dynamic Programs
    • 7.3.1. The Bellman principle of optimality
    • 7.3.2. Numerical example
• 8. Individual Risk, Insurance and Complete Markets
  • 8.1. Reading List
  • 8.2. Introduction
  • 8.3. Timing and market structure
  • 8.4. Notion of an equilibrium
  • 8.5. Preferences and endowments
  • 8.6. Social planner’s problem
  • 8.7. Arrow-Debreu competitive equilibrium
    • 8.7.1. Computing a competitive equilibrium
    • 8.7.2. Equilibrium relative price system
    • 8.7.3. Asset-pricing implications
      • 8.7.3.1. Pricing redundant assets
      • 8.7.3.2. Pricing tail assets
      • 8.7.3.3. Pricing one-period returns
  • 8.8. Sequential markets and Arrow securities
    • 8.8.1. A state variable in the sequential economy
    • 8.8.2. Debt limits
    • 8.8.3. Sequential trading
    • 8.8.4. Equivalence in equilibrium allocations
    • 8.8.5. Discussions
  • 8.9. Recursive competititive equilibria
    • 8.9.1. Endowments with Markov property
    • 8.9.2. Equilibrium inherits Markov property
    • 8.9.3. Recursive formulation
  • 8.10. Asset pricing with Markovian economies
    • 8.10.1. \(j\)-step ahead pricing kernel
    • 8.10.2. Arbitrage-free pricing and redundant assets
  • 8.11. Incomplete markets and asset pricing
• 9. Real Business Cycle
  • 9.1. Reading List
  • 9.2. Part I
  • 9.3. Introduction
  • 9.4. Endogenous aggregate state variables
  • 9.5. Pareto optimality in the stochastic growth model
    • 9.5.1. Planner’s problem
      • 9.5.1.1. Preferences
      • 9.5.1.2. Technology
      • 9.5.1.3. Resource constraint
      • 9.5.1.4. Pareto problem
  • 9.6. Competitive equilibrium in the stochastic growth model
    • 9.6.1. Time-0 trading
      • 9.6.1.1. Household
      • 9.6.1.2. Type I Firm
      • 9.6.1.3. Type II Firm
      • 9.6.1.4. Equilibrium prices and quantities
      • 9.6.1.5. A first fundamental welfare theorem
      • 9.6.1.6. Implied wealth dynamics
    • 9.6.2. Sequential trading economy
      • 9.6.2.1. Household
      • 9.6.2.2. Type I Firm
      • 9.6.2.3. Type II Firm
      • 9.6.2.4. Equilibrium prices and quantities
      • 9.6.2.5. Why conjecture \(A=0\) is correct
  • 9.7. A recursive stochastic growth model
    • 9.7.1. Recursive planning problem
    • 9.7.2. Recursive competitive equilibrium with sequential markets
      • 9.7.2.1. Household
      • 9.7.2.2. Type I Firm
      • 9.7.2.3. Type II Firm
    • 9.7.3. Recursive competitive equilibrium
  • 9.8. Part II
  • 9.9. An example recursive economy
    • 9.9.1. Exogenous forcing process
    • 9.9.2. Preferences
    • 9.9.3. Technology
    • 9.9.4. Recursive competitive equilibrium
    • 9.9.5. Computing a sample equilibrium
      • 9.9.5.1. Method of undetermined coefficients
  • 9.10. Appendix A
  • 9.11. Linear Stochastic Difference Equations
  • 9.12. Setup
  • 9.13. Moments of the LSDE
    • 9.13.1. Covariance stationary mean
    • 9.13.2. Covariance stationary covariances
  • 9.14. Impulse response functions
  • 9.15. Forecasting
  • 9.16. Real Business Cycle References
• 10. Keynesian Business Cycles and Inflation
  • 10.1. Introduction
  • 10.2. A simple version of the NK model
    • 10.2.1. Household problem
      • 10.2.1.1. Optimal intertemporal decision
      • 10.2.1.2. Optimal intratemporal decisions
    • 10.2.2. Firms’ optimal production and pricing
      • 10.2.2.1. Optimal production
      • 10.2.2.2. Optimal pricing
    • 10.2.3. Market clearing and competitive equilibrium
    • 10.2.4. Log-linear approximations
      • 10.2.4.1. Natural level of output, interest and output gaps
  • 10.3. Departure from fundamental welfare theorems
    • 10.3.1. Monopolistic distortion
    • 10.3.2. Sticky price distortion
  • 10.4. Specifying the interest rate process
    • 10.4.1. Creating a nontrivial monetary problem
    • 10.4.2. Simple policy rule
    • 10.4.3. Optimal policy
      • 10.4.3.1. Commitment to ex ante optimal policy
      • 10.4.3.2. Ex post optimal policy
      • 10.4.3.3. An anatomy of the Markov equilibrium
  • 10.5. Numerical solution and policy simulation
  • 10.6. Effect of inflation on relative price dispersion across industries
  • 10.7. Keynesian Business Cycles and Inflation References
• 11. Search Matching
  • 11.1. Introduction
  • 11.2. The McCall one-sided search model
    • 11.2.1. Defining the wage offer distribution
    • 11.2.2. One-sided intertemporal job search
    • 11.2.3. Detour on mean-preserving spreads
    • 11.2.4. Effect of mean preserving spreads in the McCall model
    • 11.2.5. Allowing quits
    • 11.2.6. Waiting times
    • 11.2.7. Layoffs
    • 11.2.8. Lake Model
  • 11.3. A simple two-sided search model
  • 11.4. Appendix A
  • 11.5. Well-defined probability measures
  • 11.6. Search Matching References