Formulation, Estimation and Policy
Analysis with DSGE Models

By Lawrence J. Christiano

**Overview**

We start by
reviewing the New Keynesian model and its policy implications. We use the model
as a platform for much of the rest of the course. We will review the tools of
Bayesian econometrics, and use the simple New Keynesian model to explore
hands-on computer exercises to illustrate the main points. We will show how to
use Dynare to solve, estimate and analyze dynamic
models. We then turn to the study of financial frictions and how they are
integrated into macroeconomic models. 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. Time permitting, we will be able to discuss
macro-prudential policy and extensions of the closed economy New Keynesian
model to the open economy.

**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. 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) 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.

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).

i) A
microeconomic approach.

Related empirical paper: Levin,
Natalucci and Zakrajsek.

ii)
Introducing the frictions into a neoclassical
growth model (BGG, 1999).

(1)
Linear aggregation.

(2)
The ‘financial friction wedge'.

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).

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.

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

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

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) The 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.

*5) **A small open economy New
Keynesian model.*

*a) **Extending the simple model to the
open economy, following the approach of Adolfson-Laséen-Lindé-Villan**
**(**RAMSES I).*

*i)
**Computer code for
exploring the properties of the model.*

*ii) **Further extensions to bring the
model to the data.*

*b) **Incorporating financial frictions
into the model, following the approach of Christiano-Trabandt-Walentin (RAMSES II).*

*i)
**A
discussion of the work of Mihai Copaciu addressing
the interaction of possible currency mismatch problems in emerging markets and
the US Federal Reserve’s eventual ‘exit strategy’.*

*ii) **A slightly simplified version of the
CTW model is described here (the relatively complicated labor
market part of CTW is replaced by a standard sticky wage setup). You can see
how the model is estimated on Swedish data. There are instructions for
replacing the Swedish data with another country’s data and using the code to
analyze that.*

**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)

An extensive applications of the methods described in the course,
to understand recent events in the US:

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