Formulation,
Estimation and Policy Analysis with DSGE Models

By Lawrence J.
Christiano

**Overview**

The objective is to review some basic tools of modern
macroeconomic analysis. We will start by describing the foundations of the New Keynesian
model and some of its key policy implications. We will then review the tools
for doing econometric analysis and forecasting. The econometric analysis
involves Bayesian estimation and estimation of such important economic
variables as the output gap and the real interest rate. After that we address
the problem of optimal policy in a model. This approach can yield important
insight about policy questions. It even offers a practical framework for the
conduct of monetary policy, one that is pursued in various degrees in several
countries. After that, we extend the model to the open economy. This discussion
forces us to address the so-called uncovered interest rate parity puzzle.
Although most of the course focuses on monetary policy, there will be a discussion
about fiscal policy and policy rules. There will be computer exercises to give
students hands-on experience solving, estimating and analyzing the models
discussed in lectures. In addition, computer sessions will be used to review
several important policy-relevant properties of the NK model (e.g.,
Ramsey-optimal policy, the Taylor principle, the timeless perspective, gap
estimation). We will use the software, Dynare version 4, to do the
computations, though no experience with Dynare will be assumed. Following is a detailed outline of the course, with
handouts and background readings.

**Lectures**

1) The New Keynesian model.

a) The basic foundations of the model (handout: this and this).

b) Exploring the
meaning of the fact that money demand and supply are not included standard
presentations of the NK model.

c) Assignment #9,
question 1, explores:

i) the rationale for and possible pitfalls of the
Taylor principle/inflation targeting. Pitfalls will be shown to be possible if
there is a significant working capital channel or if ‘news’ shocks are
important.

ii) the optimality of using the natural rate of
interest (especially if news shocks are important) to guide policy, and
identifying measurable proxies for it
(see background manuscript).

d) Code
for exploring different models and investigating, for example, the relative
performance of first and second order perturbation methods for solving the
model. Here is a simple (no capital,
closed economy) New Keynesian economy with Rotemberg
price adjustment costs. Here is a simple New
Keynesian economy with Calvo price adjustment. Here
is code for
analyzing a medium-sized New Keynesian model.

e) Using
linearized DSGE models to simulate a fixed interest rate path,
either because the zero lower bound is binding or as input to a policy briefing
(code).

2) Econometric
analysis of DSGE models (the handout makes some references to these notes on
model solution and here is a note on the
appropriate acceptance rate for the MCMC algorithm.

a) State space representation of a model.

b) Elements of Bayesian inference (Bayes’ rule, MCMC algorithm).

c) Derivation of the Kalman filter useful for forecasting and other purposes.

d) Assignment #9, after question 1.

i) Examples, to illustrate the power and use of
the MCMC algorithm (question 2).

ii) Two ways to estimate the output gap: (a) using
the Kalman smoother with a DSGE model and (b) using the
HP filter (question 3).

iii) Estimating a DSGE model on artificial data:
posterior modes, posterior versus prior distributions (question 5).

iv) Evaluating the accuracy of the Laplace
approximation to the posterior distribution. The MCMC algorithm is the right way
to go, but in practice it is very time intensive and a short cut for everyday
work is useful (question 6).

v) Further study of the output gap and
forecasting in Dynare (questions 7-11).

3) Optimal policy in the New Keynesian model (i.e., the policy
strategy pursued at the Riksbank and the Norges Bank).

a) Ramsey-optimal
monetary policy and the timeless perspective (lecture handout, and longer
handout)

b) Assignment
#8.

c)
Dynare is useful for computing optimal
policy, but here is some
software that is also useful.

4) A small open economy New Keynesian model.

a) Computer code for
exploring the properties of the model.

b) Addressing uncovered interest rate
parity in the small open economy model.

c) Version of the model described
here, designed to be estimated on actual data.

5) Analysis of fiscal
rules, a brief introduction.

a)
Government spending under lump sum
taxes.

b)
Analysis of a tax rule.

6)
Possible discussion of macro
prudential policy (background manuscript).

** **

**Background readings**

The
main reference is my chapter
with Trabandt and Walentin, in the Handbook of Monetary Economics, edited by
Friedman and Woodford.