University of Oxford Summer School

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The University of Oxford held a 5-day summer course in July 2021.  

The Essentials course covers basic building blocks of numerical analysis, their use in solving modern macroeconomic models and an introduction into model estimation. Participants use Matlab code to solve and analyse macroeconomic models.
Each day consists of lecture sessions and exercise sessions. Slides and codes are provided below. 

Day 1: Solving and analyzing your first dynamic model (Slides) 

  • State variables, policy rules and impulse response functions  
  • Perturbation analysis  
  • Certainty equivalence  
  • Introduction to Dynare  
  • Exercises (Code) 
  • Additional Material (Slides, Notes)

Day 2: Key tools from the numerical approximation literature and projection methods (Slides) 

  • Numerical integration (Gaussian quadrature) 
  • Function approximation (Splines & Polynomials) 
  • Projection methods 
  • Endogenous grid points 
  • Fixed point iteration 
  • Time iteration 
  • Exercises (Code) 
  • Additional notes (Notes) 

Day 3: Parameterized Expectations Algorithm and Blanchard-Kahn conditions (Slides) 

  • Parameterized expectations algorithm  
  • Value function iteration  
  • Accuracy tests: Euler errors, dynamic Euler equation test, DHM statistic  
  • Occasionally binding constraints and penalty functions  
  • Blanchard-Kahn conditions  
  • Sun spots and self-fulfilling expectations  
  • Exercises (Code) 
  • Additional notes (Notes) 

Day 4: Kalman filter & full information methods (Slides) 

  • Kalman filter  
  • State space form  
  • Maximum Likelihood  
  • Avoiding the singularity problem 
  • Exercises (Code) 
  • Additional notes (Notes) 

Day 5: Bayesian estimation (Slides) 

  • Bayesian estimation  
  • Markov Chain Monte Carlo methods 
  • Metropolis and Metropolis Hastings  
  • Maximum Likelihood, GMM, SMM, idea of calibration 
  • Exercises (Code)