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Analysis of Simple New Keynesian Model and Extension to Include Financial Frictions

By Lawrence J. Christiano

We will develop the basic New Keynesian (NK) model from its foundations and discuss its properties, both analytically and using computer exercises. After that, we will consider a particular approach to financial frictions and discuss how these frictions, when introduced into a medium-sized NK model, help to better understand business cycle fluctuations.

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.

Lectures and Handouts

1)   Foundations of the New Keynesian model (handout#1 (day1, day2, day3, day4_before_break, day4_after_break, day5, day6) and handout#2 (day6)). Background: handbook chapter.

a)   The linearized Phillips curve (we probably will not go through this in detail, but it is the most tricky step in linearizing the NK model and may be useful to review).

b)   Solving a model by linearization (this is a somewhat abstract review of what you have seen in earlier courses, perhaps from a slightly different perspective and different notation).

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 (essentially all policymakers in the world adopt the anti-Fisherian perspective).  The New Keynesian model is useful for thinking about these two extreme scenarios, as well as for thinking about actual disinflation scenarios (like the US disinflation in the 1980s) which are more properly thought of as a blend of the two.

ii)    We derive analytically the so-called forward guidance puzzle associated with the New Keynesian model.

iii)  We can show analytically that the Taylor principle by itself is not sufficient to fully stabilize fluctuations about the natural rate (we will probably not cover this explicitly and will instead do it during assignment #9 below).

d)   Assignment #9 (day7), 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.

2)   Financial Frictions in Nonfinancial Firms Useful for Thinking About Business Cycles:

a)    Partial equilibrium model for the Costly State Verification (CSV) approach (zip file with code for the computations, and a version of the  slides with more extensive derivations). Related empirical paper: Levin, Natalucci and Zakrajsek.

b)   CSV into a New Keynesian model and the results of Bayesian estimation of the model using US data (CMR, JMCB 2003AER 2014).

i)     The model.

ii)    The importance of risk shocks and news on risk.

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

iv)  Carefully documented (thanks to Ben Johannsen) Dynare code for replicating the material in this presentation.