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 discuss model solution and simulation methods, as
well as Bayesian methods of statistical inference. We will develop in detail
the basic New Keynesian model and review its key policy implications. For
example, we will use the model to explore the motivation for inflation
targeting and the interaction between monetary policy and asset prices. We will
also explore extensions of the model that integrate financial frictions. There
will be computer exercises to give students hands-on experience solving,
estimating and analyzing the models discussed in lectures. We will use the
software package, Dynare, to do these calculations, but no prior experience
with Dynare will be assumed. Following is a
detailed outline of the course, with handouts and background readings.

**Lectures**

1) Solving and simulating DSGE models.

a) Review of
perturbation and projection methods for solving, simulating and computing
impulse response functions for models (software used to generate the graphs in the
handout, a zip file that uses Dynare to do some of the computations).

i)
Do assignment #7, questions 1-3.

ii)
Advanced exercise (only for
those who want to dig much deeper).

b) The
application emphasized in (a) is the neoclassical model. Following is an
analysis of first and second order perturbations in the simple New Keynesian
model without capital.

i)
A simple New
Keynesian economy with Rotemberg price adjustment costs. In this model there is
no endogenous state variable, and pruning has only a very small effect (see
Rotemberg.mod, and the writeup at the beginning of
that mod file).

ii)
A simple New
Keynesian economy with Calvo price adjustment. In
this model there is an endogenous state variable (lagged price dispersion) and
pruning has a very substantial effect. Moreover, a second order approximation
seems to make a difference over the first order approximation. In particular,
the price distortion term, ignored in first order approximations, appears to
matter in the second order approximation (see Calvo.mod and the writeup at the beginning of that mod file).

c) The
following code
allows you to compare first and second order perturbations (with or without
pruning) in a medium-sized New Keynesian model.

d) 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) 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.

3) Estimation of DSGE
models (the handout makes some references to these note 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) Assignment #9, not question 1.

4) Introducing financial
frictions into the New Keynesian DSGE Model.

a) Microfoundations for
the Costly State Verification (CSV) approach ( zip file with
code for the computations).

b) Integrating CSV into an NK model and the results of Bayesian estimation
of the model using US data (forthcoming AER manuscript).

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 presenation.

c) Very brief discussion of extending CSV
to risky banking (discussion based on papers by __Zeng__ and by Hirakata, Sudo and Ueda.)

d) An open economy __version__
of the model with financial frictions (Handout).

5) Implications
of the zero lower bound on the nominal rate of interest (manuscript).

a) The deflation spiral, the government
spending multiplier.

b) Quantitative analysis of the role of
the zero bound in the dynamics of US data, 2008 and 2009.

c)
Evidence
on the sensitivity of conclusions to having used linearized equilibrium
conditions (related
material, including exercise).

6) Monetary policy and asset
prices. (Background
manuscript)

a)
News and inflation
targeting.

**b) **Using Ramsey optimal policy as a
benchmark for evaluating a policy rule. ** **

**Computer Sessions**

Apart from giving students hands-on experience with the
quantitative analysis of models, computer exercises allow us to discuss the
following topics:

a) Bayesian
estimation of DSGE models.

b) The
HP filter as a way to estimate the output gap.

2) The
Taylor principle (see section 3.1 of handbook chapter).

a) The
rationale for the principle in the standard NK model.

b) Circumstances
when things can go awry with the Taylor principle:

i) An
important working capital channel.

ii)
News shocks.

Introduction to model solving with Dynare using the
real business cycle model.

**Assignment #9**** **

This assignment works heavily with the Clarida-Gali-Gertler model, which is developed.

The text for this assignment, as
well as all the necessary software, is included in this zip file.

The assignment explores the
dynamics of the model (question #1) and uses the model to explore Bayesian
estimation and hp-filtering.

**Background readings**

The readings for the computational material include: Judd’s
textbook (perturbation and projection), Christiano-Fisher
(JEDC,2000) (projection), Kim-Kim-Schaumburg-Sims
(JEDC, 2008) (pruning), den
Haan-de Wind (2009) (perturbation and
projection), Lombardo
(2011) (perturbation).

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

The primary reference for
financial frictions is Christiano and Ikeda, Government Policy, Credit
Markets and Economic Activity.
For an extension of one of the models in this paper to a dynamic setting
in which leverage restrictions on banks is studied, see, Christiano and Ikeda, Leverage Restrictions in a
Business Cycle Model.

Other references on financial frictions:

Bernanke, Gertler and
Gilchrist’s classic 1999
paper.

Christiano,
Motto, Rostagno (2003): Using the BGG model to analyze the
cause of the US Great Depression, and the reason it lasted so long.

Christiano,
Motto, Rostagno (2013): Using the BGG model to understand
the causes of economic fluctuations in the EA and the US.

Christiano,
Trabandt and Walentin (2009): Financial and labor market
frictions in a small open economy model of Sweden. (Handout)