Formulation, Estimation and Policy Analysis with DSGE Models

By Lawrence J. Christiano

Overview

The objective is to review some basic tools of modern macroeconomic analysis. We will discuss model solution and simulation methods, as well as Bayesian methods of statistical inference. We will develop in detail the basic New Keynesian model and review its key policy implications. For example, we will use the model to explore the motivation for inflation targeting and the interaction between monetary policy and asset prices. We will also explore extensions of the model that integrate financial frictions. There will be computer exercises to give students hands-on experience solving, estimating and analyzing the models discussed in lectures. We will use the software package, Dynare, to do these calculations, but no prior experience with Dynare will be assumed. Following is a detailed outline of the course, with handouts and background readings.

Lectures

1)    Solving and simulating DSGE models.

a)    Review of perturbation and projection methods for solving, simulating and computing impulse response functions for models  (software used to generate the graphs in the handout, a zip file that uses Dynare to do some of the computations).

i)       Do assignment #7, questions 1-3.

ii)    Advanced exercise (only for those who want to dig much deeper).

b)    The application emphasized in (a) is the neoclassical model. Following is an analysis of first and second order perturbations in the simple New Keynesian model without capital.

i)       A simple New Keynesian economy with Rotemberg price adjustment costs. In this model there is no endogenous state variable, and pruning has only a very small effect (see Rotemberg.mod, and the writeup at the beginning of that mod file).

ii)    A simple New Keynesian economy with Calvo price adjustment. In this model there is an endogenous state variable (lagged price dispersion) and pruning has a very substantial effect. Moreover, a second order approximation seems to make a difference over the first order approximation. In particular, the price distortion term, ignored in first order approximations, appears to matter in the second order approximation (see Calvo.mod and the writeup at the beginning of that mod file).

c)     The following code allows you to compare first and second order perturbations (with or without pruning) in a medium-sized New Keynesian model.

d)  Using linearized DSGE models to simulate a fixed interest rate path, either because the zero lower bound is binding or as input to a policy briefing (code).

2)  The New Keynesian model.

a)   The basic foundations of the model (handout: this and this).

b)  Exploring the meaning of the fact that money demand and supply are not included standard presentations of the NK model.

c)    Assignment #9, question 1.

3)  Estimation of DSGE models (the handout makes some references to these 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)    Assignment #9, not question 1.

4)  Introducing financial frictions into the New Keynesian DSGE Model.

a)   Microfoundations for the Costly State Verification (CSV) approach ( zip file with code for the computations).

b)  CSV into an NK model and the results of  Bayesian estimation of the model using US data (forthcoming AER manuscript).

i)     The model.

ii)  The importance of risk shocks.

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 presenation.

c)    Very brief discussion of extending CSV to risky banking (discussion based on papers by Zeng and by Hirakata, Sudo and Ueda.)

d)  An open economy version of the model with financial frictions (Handout).

5)    Implications of the zero lower bound on the nominal rate of interest (manuscript).

a)   The deflation spiral, the government spending multiplier.

b)  Quantitative analysis of the role of the zero bound in the dynamics of US data, 2008 and 2009.

c)    Evidence on the sensitivity of conclusions to having used linearized equilibrium conditions (related material, including exercise).

6)

a)   News and inflation targeting.

b)   Using Ramsey optimal policy as a benchmark for evaluating a policy rule.

Computer Sessions

Apart from giving students hands-on experience with the quantitative analysis of models, computer exercises allow us to discuss the following topics:

1)

a)    Bayesian estimation of DSGE models.

b)    The HP filter as a way to estimate the output gap.

2)    The Taylor principle (see section 3.1 of handbook chapter).

a)    The rationale for the principle in the standard NK model.

b)    Circumstances when things can go awry with the Taylor principle:

i)       An important working capital channel.

ii)    News shocks.

Introduction to model solving with Dynare using the real business cycle model.

Assignment #9

This assignment works heavily with the Clarida-Gali-Gertler model, which is developed.

The text for this assignment, as well as all the necessary software, is included in this zip file.

The assignment explores the dynamics of the model (question #1) and uses the model to explore Bayesian estimation and hp-filtering.

Background readings

The readings for the computational material include: 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).

The main reference for New Keynesian models is my chapter with Trabandt and Walentin, in the Handbook of Monetary Economics, edited by Friedman and Woodford.

The primary reference for financial frictions is Christiano and Ikeda, Government Policy, Credit Markets and Economic Activity.  For an extension of one of the models in this paper to a dynamic setting in which leverage restrictions on banks is studied, see, Christiano and Ikeda, Leverage Restrictions in a Business Cycle Model.

Other references on financial frictions:

Bernanke, Gertler and Gilchrist’s classic 1999 paper.

Christiano, Motto, Rostagno (2003): Using the BGG model to analyze the cause of the US Great Depression, and the reason it lasted so long.

Christiano, Motto, Rostagno (2013): Using the BGG model to understand the causes of economic fluctuations in the EA and the US.

Christiano, Trabandt and Walentin (2009): Financial and labor market frictions in a small open economy model of Sweden. (Handout)