Formulation,
Estimation and Policy Analysis with DSGE Models

By Lawrence J.
Christiano

**Overview**

The objective is to review the basic tools of modern
macroeconomic analysis. This includes model solution and simulation methods, as
well as methods for estimating and testing models using aggregate data. We will
develop in detail the basic New Keynesian model and review its key policy
implications. For example, we will use of the model to analyze the risks posed
by the zero lower bound on the interest rate and what to do when the zero lower
bound binds. We will also explore extensions of the model that integrate
financial frictions. We will also discuss the theoretical and empirical aspects
of introducing unemployment into the model. 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). 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) 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)
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).

4)
Financial
frictions in the intermediation sector, exposited in two-period settings
(sections 3, 4, and *maybe* 5 of reading, handout).

a)
Two approaches
based on moral hazard.

i)
Two-period
version of Gertler-Kiyotaki financial friction
model, (section 3) .

ii)
Hidden action and
implications for macro-prudential policy (section 4).

A dynamic, New Keynesian version of the model is described and
analyzed here.

b)
Adverse selection
(section 5).

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)
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.

7)
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.

8)
Consensus, medium sized New Keynesian (NK) DSGE
model.

9) Wage
setting frictions in the New Keynesian model: the role they play, with
implications for employment and unemployment (background manuscript and
handbook chapter). See this Dynare mod file for the code corresponding to the model developed here. For further discussions of the implications of
sticky wages for unemployment, see this and this. For additional readings that take one beyond
the developments emphasized here, see:

a)
The search, matching and Nash
bargaining approach to the labor market (i.e., for an excellent introduction, see).

b) Alternating offer bargaining (see this and this).

10)
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.

Explores Ramsey-optimal policy in the Rotemberg model. (For an alternative software, useful for example when you want to
do Ramsey with higher order approximations, see).

**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 #2) 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 Daisuke, Government Policy, Credit
Markets and Economic Activity.

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 (2012): 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)

Government spending and the zero bound:

Christiano,
Eichenbaum and Rebelo (JPE, 2011) When is the Government
Spending Multiplier Large?