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)       Derivation of the equilibrium conditions for the basic New Keynesian model.

For a more detailed derivation see. (See, for example, page 33 for a direct proof that the Tack Yun distortion is necessarily less than, or equal to, unity.)

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

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

(2) A more extended discussion of Ramsey optimal policy, including the ‘timeless perspective’, ‘time inconsistency’, ‘deflation bias’ and ‘inflation bias’.

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

c)     This shows that when a network structure of production is introduced into the New Keynesian model, that model provides a serious theory of the cost of inflation and of Total Factor Productivity (manuscript).

d)     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.

e)    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 Material

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.


Here is an interview I gave at the International Monetary Fund on the type of modeling discussed in this course.


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).