Analysis and Solution of the New Keynesian Model

 

By Lawrence J. Christiano

  

We will develop the New Keynesian (NK) model from its foundations and discuss model solution methods. Computer exercises will be used to study properties of NK models and obtain experience using Dynare. The applications will focus on the NK model’s implication that the economy may suffer from excess or insufficient aggregate demand.

 

I recommend that you print out a copy of the lecture notes before lecture, and that you write notes on them during the lecture. Also, I will be writing by hand and sometimes adding extra pages as I present the lecture. After each lecture, I will upload my marked-up lecture notes to this website.

 

Background readings: handbook chapter; Journal of Economic Perspectives, interview and this.

 

 

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). Addendum to proof in solution notes of certainty equivalence in first order approximation of neoclassical model.

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

b)   Introduction of uncertainty into `toy example’ in lecture notes (these notes are rough and were written on an inspiration at the last minute).

c)   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).

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

e)   Readings: 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); Schmidt-Grohe and Uribe (perturbation).

2)   Foundations of the New Keynesian model (handout#1 and handout#2). Background: handbook chapter.

a)   The linearized Phillips curve.

b)   Solving the model by linearization.

c)     We can use the linearization solution strategy to demonstrate important properties of the model analytically.

i)     We use the New Keynesian model to discuss a scenario in which the response of the economy to an inflation target shock is ‘Fisherian’ in nature and a scenario in which it is ‘anti-Fisherian’ in nature. In the Fisherian scenario, the way to reduce inflation is to cut the interest rate and the anti-Fisherian scenario has the opposite property.  The New Keynesian model is useful for thinking about these two extreme scenarios, as well as for thinking about actual disinflation scenarios (like the Volcker disinflation) which are more properly thought of as a blend of the two.

ii)    We derive analytically how the Taylor principle helps to stabilize the economy in the linearized solution to the model.

d)   Assignment #9, question 1, accomplishes three things.

i)     Gives students experience with Dynare for solving and simulating models.

ii)    Gets to the heart of the New Keynesian models by exploring its basic underlying economic principles.

iii)  Shows how ‘news’ shocks might cause an inflation targeter to drive the interest rate in the ‘wrong’ direction and inadvertently trigger an inefficient stock market boom (Slides, manuscript; and section 3.2 of handbook chapter.)         Also shows how the Taylor rule can be too weak in its response to more conventional shocks.

e)   Other, related materials.

 

3)   Brief review of literature on modeling covid-19 (the slides will be updated with Peruvian data before the presentation). All background material for the slides I included as links in the lecture slides. The code for generating the pictures in the slides is here. A useful reference.

 

Group photo!