A Short Course on

Estimation, Solution and Policy Analysis using Equilibrium Monetary Models

By Lawrence J. Christiano

I will discuss the construction and use of dynamic stochastic general equilibrium (DSGE) models in the analysis of monetary policy. We will begin with the estimation of DSGE models, with a special focus on the role that estimated Vector Autoregressions (VAR) can play (we will also touch on maximum likelihood and Bayesian methods for estimation). We will discuss various features that appear in modern DSGE models: sticky prices, sticky wages, adjustment costs in investment, a banking sector, multiple monetary aggregates, financial frictions, and open economy considerations. We will then discuss the application of estimated DSGE models to the analysis of several policy questions: does a low nominal interest rate expose the economy to special risks? What is the appropriate response of monetary policy in the aftermath of a financial crisis? How should monetary policy respond to the stock market? The course is targeted to a range of people. The lectures are designed so that students who have little time outside of class for preparation and study will see the basic ideas. In addition, a set of homework assignments has been prepared for people who want to dig in much deeper. The assignments give students hands-on experience estimating VARs, as well as solving, simulating and analyzing DSGE models.

Participants who wish to do the assignments will need a computer loaded with MATLAB 6.5 and with Scientific Workplace (actually, the latter will only be necessary for the second assignment). I will not assume any familiarity with MATLAB or Scientific Workplace.

The course is organized as follows:

        Part 1: Vector Autoregressions. Topics: estimation of VARs; identification of impulse response functions; confidence intervals for impulse response functions; variance decompositions; diagnostics for VARs; estimation results for post-war US data. (Lecture notes).

        Two Assignments -

        Assignment #1: Analysis of VARs: the impact on impulse response functions of first differencing hours worked, and the impact of alternative choices of sample period.

        Assignment #2: Further analysis of VARs: diagnostics for selecting lag lengths (Akaike and other criteria, multivariate Q statistics); sensitivity to alternative measures of population, productivity, and hours worked; alternative variance decomposition measures.

        Part 2: Introduction to the Linearization Strategy for Solving Models (Lecture notes).

        Code that goes with the discussion in lecture of the two-sector model in Stokey-Lucas, Chapter 6.

        Assignment #3: A first stab at solving a dynamic, general equilibrium model. Analysis of the implications of incorporating variable capital utilization. How to handle unit roots in the data. (Answers.)

        Part 3: An Estimated Monetary General Equilibrium Model (ACEL) (Lecture notes).

        Role of Various Frictions: Investment Adjustment Costs, Habit Persistence, Variable Capital Utilization

        Important Consideration: Degree of Firm-Specificity of Capital (The Degree of Market Power in the Economy is Key to this Discussion. For Some Estimates of the Degree of Market Power in the US Economy, See Bowman.)

        Assignment #4: Analysis of higher-dimensional dynamic general equilibrium models. Substantively, we explore one interpretation of a bubble.

        Assignment #5: Another analysis of a higher-dimensional equilibrium model. Substantively, we evaluate alternative hypotheses of the slow growth experience of Japan in the 1990s.

        Assignment #6: Replicate ACEL Analysis, Including Robustness to Assumptions.

        Part 4: Evaluating Recent Criticisms of VARs. (A preliminary manuscript.)

        Part 5: Introducing Financial Frictions and a Banking Sector Into Analysis (Christiano-Motto-Rostagno), Estimation by Maximum Likelihood Methods (Lecture notes).

        Analysis of US Great Depression

        Estimation Results for US and Euro Area (Notes Will be Posted Later)

        Analysis of the Monetary Policy and Stock Market Bubbles

        Part 6:  Other Monetary Policy Issues

        The Inflation Take-Off of the 1970s. Notes.

         Optimal Monetary Policy in a Sudden Stop (Lecture notes)

         Monetary Policy and a Bubble. (See assignment #4 and Notes)

         Implications for Policy of the Zero Lower Bound on Interest Rates.