Economics 416
Spring, 2008
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 April 30, a final and homeworks. The midterm will be in class, Wednesday April 30. There is no class Monday, April 28, and that class will be rescheduled for another day. Students can opt out of the final by doing a term project. In case you are interested, we should discuss that in advance.
Homework #1, due April 16.
Homework #2, due April 23.
Homework #3, due May 2.
Homework #4, due May 7.
1. Methods for solving equilibrium models and for computing their implications for Ramsey policy.
a. Log-linearization strategy and standard models.
i. Simple examples that illustrate the fundamental ideas. The examples culminate in the ‘basic’ model with Calvo sticky prices.
ii. Extensions of the basic sticky price model: open economy, search and matching in the labor market and financial frictions.
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. QZ decomposition (for technical discussion and references, see the documentation in MATLAB, by typing doc qz at the command prompt. See also.)
b. More general discussion of solution strategies.
i. Log-linearization strategy as first order perturbation.
ii. Second and higher-order perturbations (handout, lecture notes).
iii. Projection Methods.
2. 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.
i. MCMC algorithm.
ii. Laplace approximation to posterior distribution.
iii. Evaluating model fit using the marginal likelihood.
d. Generalized Method of Moments.
i. Sampling theory for second moments.
ii. Estimating individual equations of an equilibrium model.
iii. Sampling theory for comparing different models based on their forecasting properties.
3. 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.
4. Extensions
a. Financial Frictions.
ii. Bernanke-Gertler-Gilchrist.
iii. Other models.
b. Mortensen -Pissarides search and matching in the labor market.
c. Open economy.
5. Analysis of models without commitment.
a. Analysis of a model without commitment.
b. Solution strategies.
6. Information frictions and new directions for equilibrium models. See Mendes and Lorenzoni.