Economics 416
Spring, 2009
Specification, Estimation, Solution and Analysis of Equilibrium Models.
Recent years have witnessed the econometric estimation of equilibrium models, and their use for monetary policy analysis. Policy analysis involves the study of the operating characteristics of various policy rules, the study of Ramsey-optimal rules and the study of economies in which the policy authorities do not have the ability to commit to future policies. The aim of this course is to review these developments, and to explore extensions.
The best reference for the econometrics part of the course is James Hamilton, Time Series Analysis.
The course grade will be determined by a midterm Wednesday May 6, a final and homeworks. People have the option to submit a term paper instead of the final, but this needs to be discussed with me in the week after the midterm. The midterm will be in the regular lecture May 6. There is no class Monday, May 4, and that class will be rescheduled for another day.
Homework #1, due April 9.
Homework #2, due April 17.
Homework #3, due May 1.
Homework #4, due May 1.
Homework #5, due May 11.
Homework #6, due May 19.
Homework #7, due May 28.
1. Methods for solving equilibrium models and for computing their implications for Ramsey policy.
a. Log-linearization strategy and standard models.
i. General issues in solving linear expectational difference equations.
ii. Strategy for finding minimal state variable solutions (see also).
iii. Ramsey-optimal policy (here, we only consider optimal monetary policy when there are lump-sum taxes. For a broader overview of the analysis of Ramsey policy, see).
iv. Application: analysis of government spending multiplier when the zero lower bound on the nominal rate of interest is binding.
b. More general discussion of solution strategies.
i. Log-linearization strategy as first order perturbation.
ii. Second and higher-order perturbations (handout, lecture notes).
c. Projection Methods.
2. Dropping the assumption of commitment in the analysis of government policy.
a. Analysis of a model without commitment.
b. Solution strategies.
3. Financial Frictions.
b. Bernanke-Gertler-Gilchrist. (lecture notes)
c. Kiyotaki-Moore.
d. Other models.
1. Estimation of linearized equilibrium models.
a. Putting a model into state space/observer form.
i. Smoothing and filtering.
ii. Mixed monthly and quarterly data.
iii. Connection between equilibrium models and vector autoregressions.
iv. Impulse response functions.
v. Connection between equilibrium models and vector autoregressions.
b. Maximum Likelihood Estimation.
c. Bayesian inference.
i. Basic idea.
ii. MCMC algorithm.
iii. Laplace approximation to posterior distribution.
iv. Evaluating model fit using the marginal likelihood.
2. Learning about equilibrium models using vector autoregressions.
i. Identification and impulse response functions.
ii. Diagnostics.
iii. Decomposition of the data into shocks.
iv. Variance decompositions.
v. Fiscal shocks.
vi. A recent controversy about VARs (background), lecture notes.
b. Estimating an equilibrium model by matching impulse response functions.
i. The econometrics of the strategy.
ii. Basic features of the model: habit persistence, investment adjustment costs, variable capital utilization.
iii. Sketch of extensions of the model to a small open economy, introducing Mortensen-Pissarides search and matching into the labor market and financial frictions.
c. Mortensen -Pissarides search and matching in the labor market.
d. Open economy.
3. Monetary Policy and Stock Market Volatility
a. Work with Ilut, Motto and Rostagno
b. Technical observations on learning and a model of overoptimism.
4. Information frictions and new directions for equilibrium models. See Mendes and Lorenzoni.