Formulation, Estimation and Policy
Analysis in DSGE Models with Financial Frictions

By Lawrence J. Christiano

**Overview**

We will
review the basic New Keynesian model and its policy implications. We will
consider the pros and cons of inflation targeting, the dangers posed by the
zero lower bound on the nominal rate of interest and rationales for including
credit and/or asset prices in monetary policy interest rate rules. We will also
explore extensions to incorporate financial frictions and to the open economy.
The discussion of financial frictions will allow us to consider aspects of
‘unconventional monetary policy’, such as when and why government purchases of
privately issued assets may help repair a dysfunctional financial system.
Finally, we will use Dynare to solve models and to
estimate them using Bayesian methods. No previous experience with Dynare will be assumed. The course is aimed at a broad
audience, including people actively doing research with dynamic, stochastic,
general equilibrium (DSGE) models, as well as people interested in seeing what
these models are about and what they are used for. A substantial part of the
course (including all analysis with Dynare) will
occur in the afternoon sessions, however, these are not required to follow the
morning lectures.

**Lectures**

1) The New Keynesian (NK) model.

a) The basic foundations of the model (handout
#1, handout
#2).

b) 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).

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. 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.

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

2) 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).

b) Integrating CSV into
a New Keynesian model and the results of Bayesian estimation of the model using
US data (CMR, JMCB 2003, AER2014).

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.

3) Financial frictions on the liability side of
banks’ balance sheets (not covered in class).

a) Two-period exposition of Gertler-Karadi/Gertler-Kiyotaki
model in which the financial frictions stem from bankers’ ability to ‘run away’
(section 3 of reading, 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).

c)
This reading also shows (in two-period
settings) how financial frictions on the liability side of banks’ balance sheet
can arise from adverse selection and costly state verification. We will not
discuss these cases in the lectures.

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

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

*e)
* Discussion of the work of Mihai
Copaciu, addressing the interaction of possible
currency mismatch problems in emerging markets that are anticipated as the US
Federal Reserve implements ‘lift off’.* *

**Afternoon Sessions**

Some lectures will be presented in afternoon sessions and all
computations will be based on assignment #9. Apart from giving students
hands-on experience with the quantitative analysis of models, assignment #9
exercises allow us to discuss the following topics:

1)
Empirical methods (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) 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 (background manuscript).

**Background
readings**

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
on the liability side of banks’ balance sheets 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?

Thinking
about the Great Recessions through the lens of a New Keynesian model:

Christiano,
Eichenbaum and Trabandt
(AEJ-Macro, 2015), ‘Understanding the Great
Recession’.