A Short Course on

Estimation, Solution and Policy Analysis using
Equilibrium Monetary Models

By

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

•
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

•
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

•
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)