Topic 1. Macroeconomic models: analysis of equilibrium
1) The neoclassical stochastic growth model. The planner's problem.
2) Characterizing optimal choice by means of dynamic programming. Bellman equation and value function.
3) Markov equilibrium. Characterizing the equilibrium by using first order conditions. Euler equation.
4) Steady state and near-steady-state dynamics.
5) .Decentralizing the social optimum. Competitive equilibrium.
6) Two benchmark models of the real business cycle literature:
• the divisible-labor model by Kydland and Prescott (1982);
• the indivisible-labor model by Hansen (1985).
7) Long-run growth and technological progress.
Topic 2. Numerical analysis of macroeconomic models.
1) Time series of actual economies. First and second moments. The stylized facts.
2) Hodrick-Prescott filter.
3) Calibration of macroeconomic models.
4) Global solution methods for computing equilibrium in models with uncertainty :
• Value function iteration;
• Generalized stochastic simulation algorithm.
5) What our benchmark models can and cannot explain.
Topic 3. Local solution methods.
1) General ideas. Taylor series. Implicit function theorem. Regular perturbation.
2) Log-linearization in the non-stochastic optimal growth model.
3) Log-linearization in the stochastic optimal growth model.
5) Dynare automated software.
6) Shortcomings of perturbation methods and how the literature corrects them.
Topic 4. Monetary policy.
1) The Clarida-Gali-Gertler (`basic') new Keynesian model.
• Formulating the model. Deriving the equilibrium conditions.
• Two ways to close the model: Ramsey-optimal and exogenous policy.
• Solving a linearized version of the model with Dynare.
• Solving a nonlinear version of the model with Dynare. Versions of the model with capital, adjustment cost, and sticky wages.
2) Optimal monetary policy.
• Toy example.
• A more general discussion. Rotemberg model.
• The Clarida-Gali-Gertler model.
3) Unconventional monetary policy.
• Forward guidance;
• Quantitative easing.