DSGE Models for Macroeconomic Policy Analysis: Solution Methods, Estimation and Analysis

 

Lawrence J. Christiano

  

 

We will begin by reviewing model solution methods. This discussion will focus on the analysis of simple real business cycle models. We will then turn to the modern workhorse in macroeconomics, the New Keynesian model. We will discuss the basic properties and policy implications of a very simple closed economy version of that model (a second week in the course will be devoted to an open economy model). In recent years, much work has been poured into the introduction of financial frictions into the New Keynesian model. I will present a simple overview of some of that work. Finally, if there is time we will discuss vector autoregressions and what it is that we can infer about models from them.

 

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

 

 

Outline

Introduction

1)   Overview of tools for solving DSGE models: Perturbation methods (here is the MATLAB code that generated the last graphs in the handout, and here is a Dynare file that can also be used to solve the model in the handout).

a)   a much more detailed version of the handout, including a discussion of projection methods.

b)   Here is an exercise, which works with a version of the model in the handout that includes hours worked (as in the standard rbc model). The third question shows how to build and simulate a model in which there is nonstationary growth. The material is in this zip file.

c)   Background readings: Christiano-Fisher (JECD, 2000), Ken Judd’s textbook.

2)   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)

e)    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.

3)   Bayesian inference.

a)   Additional material on mixed frequency observations and link between DSGE models and VARs, reading. Code for GDP example in handout.

b)   Exercise. Code for estimation part of exercise. Code for MCMC part of exercise.

c)   Readings: Del Negro and Schorfheide, Zellner’s classic 1971 text, Bernanke and Boivin on ‘Data Rich’ estimation.

d)   Methods to do a Bayesian version of Generalized Method of Moments and to construct more plausible priors for DSGE models.

4)   Introduction to financial frictions: 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).  For more detailed lectures on the GK material see this and this.

5)   Identification and Vector Autoregressions.

a)   Exercise, code. Answers by Sebastian Kohls.

b)   Readings: CEE handbook chapter, ACEL.

c)   Information on material not covered in lectures: for high frequency identification, see Gorodnichenko and Weber; Gertler and Karadi; Nakamura and Steinsson, For sign restrictions see Uhlig; Arias, Rubio-Ramirez and Waggoner.