Formulation, Estimation and Policy Analysis with DSGE Models

By Lawrence J. Christiano

Overview

We start by reviewing the New Keynesian model and its policy implications. We use the model as a platform for much of the rest of the course. We will review the tools of Bayesian econometrics, and use the simple New Keynesian model to explore hands-on computer exercises to illustrate the main points. We will show how to use Dynare to solve, estimate and analyze dynamic models. We then turn to the study of financial frictions and how they are integrated into macroeconomic models. The discussion of financial frictions will allow us to consider aspects of ‘unconventional monetary policy’, such as when and why government purchases of privately issued assets may help repair a dysfunctional financial system. Time permitting, we will be able to discuss macro-prudential policy and extensions of the closed economy New Keynesian model to the open economy.

Lectures

1) The New Keynesian (NK) model (handout, manuscript): basic principles and policy implications.

a) More detailed version of the handout.

b) Assignment #9, question 1, explores:

i) Solving and analyzing models using Dynare.

(1) A simplified discussion of the solution to linear expectational difference equations that we explore with Dynare appears in the class handout. An evaluation of that solution from the perspective of all possible solutions to a linear expectational difference equation appears here.

(2) For a discussion of methods for solving nonlinear expectational difference equations, see this.

ii) The rationale for, and possible pitfalls of, the Taylor principle/inflation targeting. Pitfalls will be shown to be possible if there is a significant working capital channel or if ‘news’ shocks are important (see this manuscript for further discussion).

iii) News shocks as a source of dynamics.

iv) The optimality of using the natural rate of interest (especially if news shocks are important) to guide policy, and identifying measurable proxies for it (see background manuscript).

c) Extensions not discussed formally in class:

i) Code for exploring different versions of the NK model and investigating, for example, the relative performance of first and second order perturbation methods for model solution. Here is a simple (no capital, closed economy) NK economy with Rotemberg price adjustment costs. Here is a simple NK economy with Calvo price adjustment. Here is code for analyzing a medium-sized NK model.

ii) An alternative to perturbation for solving models is called the extended path method, which – like the perturbation method – has been incorporated into Dynare. A discussion of that method for doing stochastic simulation appears here. Two examples, based on the simple NK model without capital, are considered. In each case, the zero lower bound on the interest rate is binding. One case considers the economic effects of a positive technology shock. The other case considers the welfare and other effects of a government spending shock when it must be financed by distortionary taxes and the government’s intertemporal budget constraint must be satisfied.

iii) 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).

iv) A more extensive discussion of Ramsey optimal policy appears here. Possible time inconsistency of monetary policy and the timeless perspective are discussed. The implications of the working capital channel (briefly discussed in assignment 9) are reviewed.

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

2) 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.

3) Financial frictions on the asset side of banks’ balance sheets.

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).

i) A microeconomic approach.

Related empirical paper: Levin, Natalucci and Zakrajsek.

ii) Introducing the frictions into a neoclassical growth model (BGG, 1999).

(1) Linear aggregation.

(2) The ‘financial friction wedge'.

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).

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 presentation.

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

4) Financial frictions on the liability side of banks’ balance sheets.

a) Two-period exposition of Gertler-Karadi/Gertler-Kiyotaki model in which the financial frictions stem from bankers’ ability to ‘run away’ (section 3 of reading, handout).

b) Dynamic Model in which financial frictions stem from the fact that to do their job well, bankers must exert costly but unobserved effort. The environment has the implication that imposing leverage restrictions on banks can raise social welfare and thus represents a laboratory for thinking about macro prudential policy (background manuscript).

c) The reading also shows (in two-period settings) how financial frictions on the liability side of banks’ balance sheet can arise from adverse selection and costly state verification. We will not discuss these cases in the lectures.

5) A small open economy New Keynesian model.

a) Extending the simple model to the open economy, following the approach of Adolfson-Laséen-Lindé-Villan
(RAMSES I).

i) Computer code for exploring the properties of the model.

ii) Further extensions to bring the model to the data.

b) Incorporating financial frictions into the model, following the approach of Christiano-Trabandt-Walentin (RAMSES II).

i) A discussion of the work of Mihai Copaciu addressing the interaction of possible currency mismatch problems in emerging markets and the US Federal Reserve’s eventual ‘exit strategy’.

ii) A slightly simplified version of the CTW model is described here (the relatively complicated labor market part of CTW is replaced by a standard sticky wage setup). You can see how the model is estimated on Swedish data. There are instructions for replacing the Swedish data with another country’s data and using the code to analyze that.

Background readings

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 on the liability side of banks’ balance sheets 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 (2009): 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)

An extensive applications of the methods described in the course, to understand recent events in the US:

Christiano, Eichenbaum and Trabandt (forthcoming, AEJ-M), ‘Understanding the Great Recession’.