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 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. After that we address the problem of optimal policy in a model. This approach can yield important insight about policy questions. It even offers a practical framework for the conduct of monetary policy, one that is pursued in various degrees in several countries. After that, we extend the model to the open economy. This discussion forces us to address the so-called uncovered interest rate parity puzzle. Although most of the course focuses on monetary policy, there will be a discussion about fiscal policy and policy rules. 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. Following is a detailed outline of the course, with handouts and background readings.

Lectures

1) 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, explores:

i) 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.

ii) 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).

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

e) 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) 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.

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) 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.

c) Dynare is useful for computing optimal policy, but here is some software that is also useful.

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

5) Analysis of fiscal rules, a brief introduction.

a) Government spending under lump sum taxes.

b) Analysis of a tax rule.

6) Possible discussion of macro prudential policy (background manuscript).

Background readings

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