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 (NK) 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. We then
consider financial frictions in the intermediation system and organize the
discussion around frictions on the liability and asset sides of financial firm
balance sheets. This will allow us to consider various monetary policy
questions: how monetary policy should respond to changes in interest rate
spreads, what the effect of various types of unconventional monetary policy
are, as well as macro prudential policy. After that, we extend the model to the open
economy. 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. The course does not
require specialized technical knowledge about dynamic, stochastic, general
equilibrium (DSGE) models or econometrics. Following is a detailed outline of
the course, with handouts and background readings.

**Lectures**

1) The New
Keynesian (NK) model (handout,
manuscript):
basic principles and policy implications.

a) More
detailed version of the handout.

b) Assignment #9,
question 1, explores:

i) Solving
and analyzing models using Dynare.

(1)
A simplified discussion of the solution to
linear expectational difference equations that we
explore with Dynare appears in the class handout.
An evaluation of that solution from the perspective of all possible solutions
to a linear expectational difference equation appears
here.

(2)
For a discussion of methods for solving
nonlinear expectational difference equations, see this.

ii)
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 (see this manuscript
for further discussion).

iii)
News shocks as a source of dynamics.

iv)
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).

c) Extensions not discussed formally in class:

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

ii)
An alternative to perturbation for solving
models is called *the extended path method*,
which – like the perturbation method – has been incorporated into Dynare. A discussion of that method for doing stochastic
simulation appears here (for lecture notes, see this).
Two examples, based on the simple NK model without capital, are considered. In
each case, the zero lower bound on the interest rate is binding. One case
considers the economic effects of a positive technology shock. The other case
considers the welfare and other effects of a government spending shock when it
must be financed by distortionary taxes and the government’s intertemporal budget constraint must be satisfied.

iii)
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).

iv)
A more extensive discussion of Ramsey optimal
policy appears here.
Possible time inconsistency of monetary policy and the timeless perspective are
discussed. The implications of the working capital channel (briefly discussed in
assignment 9) are reviewed.

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

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 (you also need this).

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) Financial
frictions on the asset side of banks’ balance sheets.

a) Micro foundations for
the Costly State Verification (CSV) approach (zip file with code for the computations, and a version of the slides with more extensive derivations). Related work:
Levin,
Natalucci and Zakrajsek.

b) Integrating CSV
into a New Keynesian model and the results of Bayesian estimation of the model
using US data (CMR,
JMCB
2003, AER
2014, BGG).

i) The
model.

ii)
The importance of risk shocks.

iii)
The response of monetary policy to an
increase in interest rate spreads.

iv)
Carefully documented (thanks to Ben
Johannsen) Dynare __code__ for replicating the material in
this presentation.

4) Financial
frictions on the liability side of banks’ balance sheets (background
manuscript).

a) Two-period exposition
of Gertler-Karadi/Gertler-Kiyotaki
model in which the financial frictions stem from bankers’ ability to ‘run away’
(handout).

b)
Dynamic Model in which financial frictions stem
from the fact that to do their job well, bankers must exert costly but
unobserved effort. The environment has the implication that imposing
leverage restrictions on banks can raise social welfare and thus represents a
laboratory for thinking about macro prudential policy (background manuscript).

5) 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) Extensions
to include financial frictions and possible currency mismatch problems.

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