The New Keynesian Model: Computational
and Econometric Tools, and Financial Market Extensions

By Lawrence J. Christiano

**Overview**

The course begins with a review of computational and
econometric tools useful in the analysis of dynamic, stochastic general
equilibrium (DSGE) models. After a very brief review of the basic New Keynesian
model, we discuss extensions of the model to introduce financial market
frictions. Finally, we use a model of financial frictions to discuss the
interaction between monetary policy and stock market volatility. Afternoon
sessions will be devoted to computer exercises using Dynare that illustrate the
points discussed in the lectures.

**Lectures**

1.
Introductory
remarks.

2.
Overview
of tools for solving DSGE models: Perturbation and Projection methods with a
Dynare file
to do the computations reported in the handout.

· The
following exercise
explores perturbation in Dynare (the exercise
contains an extremely simplified discussion of pruning, something that is
discussed in greater detail in this extended
version of the class handout). The assignment requires this zip
file (see also this).

· For
more discussion, see part (1) of this
lecture series.

·
Background readings: Christiano-Fisher (JECD,
2000), Ken Judd’s textbook. A detailed review
of solving linearized systems.

3.
Estimation of
DSGE models (the handout makes some references to these notes
on model solution and here is a note on the appropriate
acceptance rate for the MCMC algorithm).

· A procedure that lies at the heart of
Bayesian methods for econometric inference is the MCMC algorithm. Question 3,
part 2, of Assignment #9
explores the MCMC algorithm.

· James
Hamilton, Time Series Analysis.

· Longer
version of slides that shows how to use the state-space/observer system to
handle mixed frequency data and to map from a DSGE model into the implied VAR
representation for a set of data.

·
Christiano-Trabandt-Walentin, ‘DSGE
Models for Monetary Policy’, chapter in Friedman and Woodford’s Handbook of
Monetary Economics, 2011 (sections 3.3.3 and 5).

4.
Basic New Keynesian model
without capital and with flexible labor markets (zip
file with Dynare code for computations). (For a more
detailed handout, see handout#1
and handout#2
and also my handbook chapter.)

· The lecture focuses the resource
misallocation consequences of price setting frictions and working capital. Some
ideas in the growth literature that motivates these slides are you discussed by
Chad
Jones. The slides are written up in manuscript form here.

· Linearization of NK model: Phillips
curve.

· Ramsey (‘Natural’) equilibrium.

· We will work on assignment 9,
question 1, to explore some economic properties of the NK model. We will then
use these properties as we explore questions 3 and later in assignment 9, which
review techniques of Bayesian inference.

· Specifically, 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 (see
section 3 of handbook chapter).

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).

iii.
Sensitivity of the dynamic properties of the NK model to the type
of persistence in shocks.

· An
alternative approach to solving models is called *the extended path method*, which – like the perturbation method –
has been incorporated into Dynare (lecture notes appear here).
A discussion of extended path 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 for a while and then not binding (this feature of
the example disqualifies the perturbation method as an appropriate model
solution method). The first example considers the economic effects of a
positive technology shock. The second example considers the welfare and other
effects of a government spending shock when it must be financed by
distortionary taxes, subject to satisfying the government’s intertemporal
budget constraint.

· 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.

5.
Introducing financial
frictions into the New Keynesian DSGE Model.

· Microfoundations
for the Costly State Verification (CSV) approach (version of the handout
with more extensive derivations, and associated zip
file).

·
Integrating
CSV into an NK model and the results of Bayesian estimation of the model using
US and EA data.

i.
The model.

ii.
The importance of risk shocks.

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

iv.
Background reading: Bernanke, Gertler and Gilchrist’s classic 1999
paper and Christiano-Motto-Rostagno (AER,
2014). This url has the CMR manuscript, as
well as a carefully documented (by Ben Johannsen) set of codes for reproducing
the main results in the CMR.

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

·
Open economy version
of the model.

6.
Monetary policy and asset
prices. (Christiano-Ilut-Motto-Rostagno, background manuscript;
and section 3.2 of handbook chapter).

· News and inflation targeting.

·
Using Ramsey optimal policy as a
benchmark for evaluating a policy rule.