Analysis and Solution of the New Keynesian Model

By Lawrence J. Christiano

Morning lectures will develop the New Keynesian (NK) model from its foundations. Afternoon sessions will explore applications of the NK models with a combination of computer exercises and additional lectures. The applications will focus on the NK model’s implication that the economy may suffer from excess or insufficient aggregate demand. In addition, the afternoon sessions will acquaint students with the use of Dynare in the solution and analysis of economic models.

**Lectures and
Handouts**

Introductory
remarks.

1)
Solving and simulating DSGE models (software used to generate the graphs in the
handout…not part of the course requirement).

a)
Review
of perturbation and projection methods for solving models.

b)
Simulating
solutions based on higher-order perturbations: pruning (a zip
file that uses Dynare to do some of the
computations).

i)
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. (not
part of the course requirement).

2)
Foundations of the New Keynesian
model (handout#1 and handout#2).

a)
A simple non-monetary model:
efficient allocations and decentralization.

b)
Monetary, sticky price (i.e., New
Keynesian) version of the above model.

i)
(Ramsey) optimal monetary policy
defined and analyzed in the sticky price model.

Result: under Ramsey
optimal monetary policy, allocations in sticky price model (eventually)
coincide with efficient allocations in non-monetary economy.

ii) Analysis of sticky price model when monetary policy is governed by
the Taylor rule.

3) 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.

4) 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**

The
afternoon sections will involve some lecturing above, as well as hands-on
experience with the quantitative analysis of models. The computational
exercises will explore the following topics:

1)
The
Taylor principle (see section 3.1 of handbook chapter).

a)
The
rationale for the Taylor 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 (this relates to lecture (4)).

2) The Taylor rule versus optimal monetary policy.

a)
Display
several examples in which the Taylor rule is not ‘aggressive enough’ in moving
the interest rate.

b)
Modifying
the Taylor rule so that the Ramsey-optimal monetary policy is implemented.

These
topics will be explored by working on question 2 of an assignment, labeled
assignment 9. Question
2 works with the Clarida-Gali-Gertler
model, which is developed in the handouts above, as well as here. The text for the assignment, as well as all the necessary
software, is included in this zip file.

**Background readings**

The main reference for New
Keynesian models is my chapter with Trabandt and Walentin, in the 2010 Handbook
of Monetary Economics, edited by Friedman and Woodford.

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).