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. There will
be afternoon homework sessions, which are not required to follow the lectures.
The purpose of the homework sessions is to give students hands-on experience
solving, estimating and analyzing the models discussed in lectures. In
addition, the homework 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. The following outline for the course is designed to
only provide an indication of the course material to be covered. The outline
and lecture notes will be refined in the weeks before the course.

**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.

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)
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)
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
and EA data (code).

i)
The model

ii)
The importance of risk shocks.

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

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.

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).

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)
More on the New Keynesian model.

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

b)
Assignment
#8.

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

d) Dynare code,
for computing impulse responses in a medium-sized New Keynesian model with the
option of doing first or second order perturbations, pruning, or not, etc.

8) 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. ** **

**Afternoon Sessions**

Apart from
giving students hands-on experience with the quantitative analysis of models,
homework 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 just-released
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 (2009): 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?