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 review the solution and estimation of DSGE models. We will review the use of maximum likelihood and Bayesian estimation methods, methods that make use of estimated Vector Autoregressions (VAR), as well as methods based on single equation 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, search and matching models of unemployment and open economy considerations. We will then review the use of estimated DSGE models in the formulation of monetary policy. Here, we will focus on the operating characteristics of monetary policy rules as well as the implementation of Ramsey-optimal monetary policy. The notes below review additional particular 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 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: Introduction to the linearization strategy for solving and estimating models, and for deducing the implications of models for optimal monetary policy

        Simple examples, based on the RBC model and the Clarida-Gali-Gertler new-Keynesian (‘basic’) (lecture notes).

1.   Code that goes with the discussion in example #1 in the lecture notes of the two-sector model in Stokey-Lucas, Chapter 6.

2.   Code that goes with the discussion of example #5 in the lecture notes.

3.   Code for other examples in the lecture notes.

4.   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.)

5.   Assignment #7: Uses Dynare to solve the models in examples #3 and #5 in the lecture notes.

        Extensions of the basic model to the open economy, to include search and matching in the labor market and to include financial frictions (code used in the calculations in part one of these notes…..uses Dynare, version 3.)

        Ramsey-optimal monetary policy (here, we only consider optimal monetary policy when there are lump-sum taxes. For a broader overview of the analysis of Ramsey policy, see Part 5 below).

        Assignment #8: Uses Dynare to compute optimal monetary policy in example #3 (the Rotemberg sticky price model) of the lecture notes on Ramsey-optimal policy. The assignment shows that optimal monetary policy is sensitive to how distortions in the labor market are treated. For additional discussion and code for optimal monetary policy, see.

        Estimation methods covered include matching VAR impulse response functions, maximum likelihood and Bayesian maximum likelihood.

1.   Assignment #9: Uses Dynare version 4 to (i) estimate the parameters of a model by maximum likelihood and/or Bayesian methods, (ii) estimate unobserved variables like the output gap; (iii) compute forecasts and forecast uncertainty. The assignment devotes a special effort to understanding the MCMC algorithm, because analysis of the posterior distribution of parameters is central to Bayesian inference and the MCMC algorithm is the standard tool for approximating that.


        Part 2: Bayesian estimation of a model for US aggregate data and implications for monetary policy (handout).

        This is an application of all the issues discussed in part 1. In addition,

1.   We specify a model of technology in which signals about technology movements arrive in advance. We then estimate the model in US data.

2.   Based on the estimated model, we argue that monetary policy may inadvertently have played a role in stock market boom-busts. 


        Part 3: 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; decomposition of historical data into shocks. (Lecture notes).

        For a recent debate about VARs, one that we will probably not have time to discuss, see.

        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 4: An Estimated Monetary General Equilibrium Model (CEE, ACEL) (Lecture notes).

        This lecture stresses the value of VARs as a source of guidance for constructing general equilibrium models. An alternative strategy is proposed by CKM. For a discussion and evaluation, see.

        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’ (code).

        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.

        Extension of CEE model to incorporate financial frictions and a banking sector (Christiano, Motto, Rostagno, 2003, 2007).

        Extension of CEE model to incorporate labor market search (Christiano, Ilut, Motto and Rostagno, 2007).

        Extension of CEE model to small open economy (Adolfson, Laseen, Linde, Villani (2007))

        Extension of CEE model to small open economy, and to include financial frictions and search and matching in the labor market (Christiano-Trabandt-Walentin (2007))

        A more recent version of the lecture notes, which places some stress on extensions to financial frictions.


        Part 5: Optimal monetary and fiscal policy (lecture notes).

        Here we address monetary policy in the plausible scenario that there are no lump sum taxes. We consider environments where all taxes distort some margin, such as labor or capital investment. This requires being explicit about the array of taxes available to the fiscal authorities and casting the optimal policy problem within the context of a single intertemporal government budget constraint. We start with the most basic question: ‘what is the optimal monetary policy?’ To make the discussion interesting, we present it in the context of a debate that occurred between Milton Friedman and Edmund Phelps. The former argued that optimal monetary policy sets the nominal rate of interest to zero, to minimize the distortions associated with economizing on cash balances. The latter argued that this conclusion does not hold up when account is taken of the fact that the government must finance its expenditures with distorting taxes. In an environment like this, argued Phelps, it is desirable to spread distortions over many different economic decisions, including the decision to hold money. Phelps suggested this would involve some inflation and, hence, positive nominal interest rates. We will address the Friedman-Phelps debate using the tools of public finance, by taking the primal approach to the study of Ramsey equilibria. We will do so in a model economy (the Lucas-Stokey cash-credit good model) that incorporates the features emphasized by both Friedman and Phelps in their debate. This model does not incorporate sticky prices. We will also review the implications for optimal monetary policy of price-setting frictions. Finally, we will relate the present discussion of optimal monetary policy to the discussion in part I of this course, where we did not have to worry about the government’s intertemporal budget constraint. This is because, implicitly, that discussion assumed the presence of lump sum taxes. Some readings on the analysis of part 5 of the course can be found here. Item 1 in these readings is the most relevant for this course.


        Part 6: The operating characteristics of simple policy rules.

        We will analyze the operating characteristics of alternative monetary policy rules, without modeling explicitly the optimization problem of the monetary authority. We will in particular emphasize the recent literature on Taylor rules. This is a monetary policy strategy under which the monetary authority raises the interest rate when expected inflation is high, and reduces it when it is low. We will discuss the reasons why people have proposed this rule, as well as some of the pathologies associated with it. For example, we will explore the argument that a Taylor rule which assigns insufficient weight to inflation laid the groundwork for the ‘Great Inflation’ of the 1970s. We will also explore the possibility that a Taylor rule which assigns too much weight to inflation may inadvertently contribute to a stock market boom-bust cycle such at the ones experienced in the US in the 1920s or the 1990s. We will explore the idea that a policy of monitoring the monetary aggregates may reduce the likelihood of pathologies associated with the Taylor rule. We will explore the idea that a commitment to low inflation could, in conjunction with the zero lower-bound on the nominal interest rate, expose the economy to falling into a ‘liquidity trap’. Finally, time permitting we will explore the relationship between monetary policy and a stockmarket boom-bust cycle.


        lecture notes on 1970s and Taylor rule pathologies (Readings); lecture notes on boom-bust cycle (see Assignment #4); Implications for Policy of the Zero Lower Bound on Interest Rates (lecture notes).


        Part 7: Monetary policy in a financial crisis.

        Considerable attention has been given to the appropriate monetary policy in a ‘Sudden Stop’. These are financial crises experienced by several emerging market economies in which domestic output and employment collapse and the current account swings sharply from negative to positive. We will review one model of a ‘Sudden Stop’, according to which it is triggered by a tightening of collateral constraints on foreign borrowing. The economic collapse is brought on by the resulting inability to finance crucial foreign intermediate inputs. The monetary policy question is how best to set the domestic nominal interest rate under these circumstances. In practice, countries in a ‘Sudden Stop’ initially raise the domestic interest rate sharply, and then reduce it. We will explore what features of the environment make such a policy optimal. At a technical level, the analysis will expose the student to a standard small open economy model with a traded and non-traded goods sector. In addition, we will discuss how the presence of binding collateral constraints may profoundly affect the nature of the monetary transmission mechanism.

         Optimal Monetary Policy in a ‘Sudden Stop’ (Lecture notes)