Formulation, Estimation and Policy Analysis with DSGE Models

By Lawrence J. Christiano




The objective is to review the basic tools of modern macroeconomic analysis. This includes model solution and simulation methods, as well as methods for estimating and testing models using aggregate data. We will develop in detail the basic New Keynesian model and review its key policy implications. For example, we will use of the model to analyze the risks posed by the zero lower bound on the interest rate and what to do when the zero lower bound binds. We will also explore extensions of the model that integrate financial frictions. We will also discuss the theoretical and empirical aspects of introducing unemployment into the model. There will be computer exercises to give students hands-on experience solving, estimating and analyzing the models discussed in lectures. In addition, computer sessions will be used to review several important policy-relevant properties of the NK model (e.g., Ramsey-optimal policy, the Taylor principle, the timeless perspective). We will use the software, Dynare version 4, to do the computations, though no experience with Dynare will be assumed. Following is a detailed outline of the course, with handouts and background readings.





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)  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)  Integrating 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).

4)  Financial frictions in the intermediation sector, exposited in two-period settings (sections 3, 4, and maybe 5 of reading, handout).

a)  Two approaches based on moral hazard.

i)    Two-period version of Gertler-Kiyotaki financial friction model, (section 3) .

ii)  Hidden action and implications for macro-prudential policy (section 4).

A dynamic, New Keynesian version of the model is described and analyzed here.

b)   Adverse selection (section 5).

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)  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.

7)  Optimal policy in the New Keynesian model (i.e., the policy strategy pursued at the Riksbank and the Norges Bank).

a)  Ramsey-optimal monetary policy and the timeless perspective (lecture handout, and longer handout)

b)  Assignment #8.


8)  Consensus, medium sized New Keynesian (NK) DSGE model.


9)  Wage setting frictions in the New Keynesian model: the role they play, with implications for employment and unemployment (background manuscript and handbook chapter).  See this Dynare mod file for the code corresponding to the model developed here.  For further discussions of the implications of sticky wages for unemployment, see this and this.  For additional readings that take one beyond the developments emphasized here, see:

a)  The search,  matching and Nash bargaining approach to the labor market (i.e., for an excellent introduction, see).

b)  Alternating offer bargaining (see this and this).

10)      Monetary policy and asset prices. (Background manuscript)

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)   Empirical methods

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.


Assignment #7

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


Assignment #8

Explores Ramsey-optimal policy in the Rotemberg model. (For an alternative software, useful for example when you want to do Ramsey with higher order approximations, see).


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 #2) 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 Daisuke, Government Policy, Credit Markets and Economic Activity.


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 (2012): 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)


Government spending and the zero bound: 

Christiano, Eichenbaum and Rebelo (JPE, 2011) When is the Government Spending Multiplier Large?