New Keynesian DSGE Models, Financial Frictions and Bayesian
Estimation

By Lawrence J. Christiano

**Overview**

This is a
graduate-level course on tools for macroeconomics. It is geared to people interested
in applying the tools in situations not necessarily considered previously in
the literature. For this reason, the course will not shy away from the
technical details. At the same time, there will be a constant focus on the
intuition.

We begin by
describing the basic New Keynesian closed economy model with no capital. The
simplicity of this model will allow us to highlight core principles that apply
more generally across models with price-setting frictions. It will also allow
us to focus on a core technical problem in the New Keynesian model, how to
aggregate across heterogeneous firms.

We then turn
to a discussion of the econometric tools for estimating dynamic, stochastic,
general equilibrium models like the New Keynesian model.

Finally, we
consider financial frictions. We will examine in detail the consequences of
incorporating financial frictions on the asset side of banks’ balance sheets.
We will also discuss, at a more informal level, financial frictions on the
liability side of banks’ balance sheets.

Computer
exercises will give students hands-on practice in the use of Dynare to solve, estimate and analyze dynamic models.

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

**Outline**

1. The simple New Keynesian (NK) model without capital. We will build the model (almost) from its foundations and describe its properties and implications for policy. Most of the implications for policy will be ‘discovered’ in MATLAB exercises. (2.5 days)

a) First,
we (i) derive carefully the model’s equilibrium
conditions; (ii) talk about the classical dichotomy and how it does not occur
when there are sticky prices; (iii) discuss the apparent absence of `money’
from New Keynesian models; (iv) define the natural equilibrium, a benchmark for
policy analysis.

b) Second,
we derive the log-linearized equilibrium conditions around a zero-inflation
steady state. (Though we will not do a detailed derivation of the linearized
Phillips curve, that is covered here.
A more in-depth discussion appears here.) We will then do the series of Dynare
exercises described in NK_exercise.pdf, which accomplish three things (you can
find the pdf file, as well as the associated Dynare code,
cgg.mod, here):

i) Convey basic intuition about the
working of the New Keynesian model.

ii) Show how under ‘news’ shocks,
inflation targeting might 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).

iii)
This
Dynare code contains the seven non-linear equilibrium
conditions of the Simple New Keynesian model. It can be used to show how Dynare handles this case, and to investigate the accuracy
of the linearization strategy used in parts (i) and
(ii).

c) Third,
we will show how the model can be used with simple pencil and paper methods to
put structure on two debates among economists and policymakers:

i) The debate between Fisherians and anti-Fisherians over how to get inflation down when it is too
high (or, up when it is too low). We’ll see how a blend of the two viewpoints
can be used to understand the dynamics of the Volcker disinflation in the US in
the 1970s;

ii) Discussions of the so-called forward guidance puzzle which has
been used to motivate proposals for modifying the type of NK model studied in this
course.

d) Finally,
we will use the model to discuss three types of conditional forecasting
situations. They allow one to answer questions like `what will happen if we
keep the interest rate high over the next year’, or `what will happen to our
economy if the world economy begins to weaken?’

i) How
to compute Odyssean forecasts. The code
for this can also be used for other things, such as quantifying the forward
guidance puzzle or studying the impact on the government spending multiplier
when the interest rate is held constant (say, because the effective zero lower
bound is binding). Application: characterizing `forward guidance puzzle’ (see
this code,
as well as the commentary at the start of the code; see also the second topic
covered in this handout.).

ii) How
to compute two more standard types of conditional forecast. The code in (i) above can be used to compare all three types of
conditional forecasts.

2. Estimation of DSGE
models (the handout makes some references to this note on model
solution and here is a note on the
appropriate acceptance rate for the MCMC algorithm). (1.5 days)

a) State space representation of a model.

b) Elements of Bayesian inference (Bayes’ rule, MCMC algorithm).

c) A simple example
to illustrate Bayes’ rule.

d) Exercise that illustrates the MCMC algorithm is in the pdf file,
MCMC_exercise that can be found in the zip file found
here).

e) We will
use Dynare to estimate a version
of the closed economy model using macroeconomic data from India. We will use
the estimated model to do conditional forecasting.

3.
Financial frictions originating
outside banking sector: Costly State Verification in Business Cycles. (0.75
day)

a) Micro foundations for the Costly State Verification (CSV)
approach (zip file with code for the computations, and a version of the slides with more extensive
derivations). The CSV model is used as a friction on the asset side of a
bank’s balance sheet.

b)
Integrating
CSV into a New Keynesian model and the results of Bayesian
estimation of the model using US data (CMR, JMCB 2003, AER 2014, longer
version of handout). Here is carefully documented (thanks to Ben
Johannsen) Dynare code for
replicating the material in this presentation.

4. Financial
frictions originating inside the banking sector: an informal review.
(0.25 day) Summary of Gertler-Kiyotaki AER2015
(here is a more extended set of lecture notes).
The focus here will be on shadow banking, which grew very large
in the US in the 2000s. Here
is a three period version of the model which explores some of the implications
for macro prudential policy.