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).

c) Deeper discussion
of first order perturbation (connection to Blanchard-Kahn conditions, sunspots,
others exotic things).

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.

c)
Code
for computing impulse responses and stochastic simulations of first and second
order perturbations on solution to non-linear equilibrium conditions of simple
NK model.

d)
Assignment
#9, questions 1 and 3.

3) Implications of the zero lower bound on the nominal rate of interest (manuscript).

a) The effects of government spending in normal times and in the zero lower bound.

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).