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 start by describing the foundations of the New Keynesian (NK) model and some of its key policy implications. We will then review the tools for doing econometric analysis and forecasting. The econometric analysis involves Bayesian estimation and estimation of such important economic variables as the output gap and the real interest rate. We then consider financial frictions in the intermediation system and organize the discussion around frictions on the liability and asset sides of financial firm balance sheets. This will allow us to consider various monetary policy questions: how monetary policy should respond to changes in interest rate spreads, what the effect of various types of unconventional monetary policy are, as well as macro prudential policy.  After that, we extend the model to the open economy. 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, gap estimation). We will use the software, Dynare version 4, to do the computations, though no experience with Dynare will be assumed. The course does not require specialized technical knowledge about dynamic, stochastic, general equilibrium (DSGE) models or econometrics. Following is a detailed outline of the course, with handouts and background readings.

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

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 (for lecture notes, see this). 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.

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

2)   Econometric analysis of DSGE models (the handout makes some references to these notes 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)    Derivation of the Kalman filter useful for forecasting and other purposes.

d)   Assignment #9, after question 1 (you also need this).

i)    Examples, to illustrate the power and use of the MCMC algorithm (question 2).

ii)            Two ways to estimate the output gap: (a) using the Kalman smoother with a DSGE model and (b) using the HP filter (question 3).

iii)        Estimating a DSGE model on artificial data: posterior modes, posterior versus prior distributions (question 5).

iv)         Evaluating the accuracy of the Laplace approximation to the posterior distribution. The MCMC algorithm is the right way to go, but in practice it is very time intensive and a short cut for everyday work is useful (question 6).

v) Further study of the output gap and forecasting in Dynare (questions 7-11).

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). Related work: Levin, Natalucci and Zakrajsek.

b)   CSV into a New Keynesian model and the results of Bayesian estimation of the model using US data (CMR, JMCB 2003AER 2014, BGG).

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.

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

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

5)   A small open economy New Keynesian model.

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

b)   Addressing uncovered interest rate parity in the small open economy model.

c)    Extensions to include financial frictions and possible currency mismatch problems.

d)   Version of the model described here, designed to be estimated on actual data.