New Keynesian DSGE Models, Financial Frictions and Bayesian Estimation

 

Lawrence J. Christiano

  

 

I plan to review the basic New Keynesian model and extensions that take into account financial frictions.  The course is aimed at a broad audience, including people actively doing research with dynamic, stochastic, general equilibrium (DSGE) models, as well as people interested in seeing a review of the structure of these models and what they are used for. Sessions will include lectures as well as hands-on exercises in which participants will use Dynare to analyze, solve and estimate DSGE models.

 

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

 

 

Outline

Introduction

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.

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.) 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 use the model to discuss a `Fisherian’ scenario in which inflation and the nominal interest rate move in the same direction and an `anti-Fisherian’ scenario in which the two variables move in opposite directions. We will discuss how the Volcker disinflation in the US can be understood as a blend of the two scenarios. (See also these notes.)

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)

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).

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)   An informal review of financial frictions literature: frictions arising from problems originating in the non-financial business sector (Christiano-Motto-Rostagno  AER 2014) and frictions arising from problems in the financial sector (Gertler-Kiyotaki AER2015).