Andrew T. Levin

English

Research Papers in Economics

FEDERAL RESERVE BANK OF ST. LOUIS REVIEW JULY/AUGUST 2008 301
Commentary
Andrew T. Levin
ronment in which the central bank faces a set of
competing models and uses incoming information
to update its probability assessments regarding
which model is the best representation of the
actual economy. Moreover, because private sector
expectations play a key role in determining eco-
nomic outcomes, the optimal policy not only
characterizes the central bank’s current actions
but also involves a complete set of commitments
regarding which future actions will be taken under
every possible contingency. Given this approach,
the analysis is made tractable—and very elegant—
by the use of Markov jump-linear-quadratic
methods.
In this environment, the Bayesian optimal
policy is influenced by an “experimentation”
motive, because the central bank recognizes that
its current policy actions can influence the flow
of incoming information and thereby affect the
degree of model uncertainty in subsequent peri-
ods. In effect, experimentation is a form of public
investment that incurs a short-run cost (in terms
of greater macro volatility) in exchange for the
medium-run benefit of a more precise estimate
of the structure of the economy that will thereby
facilitate better stabilization policies. Thus, the
paper also makes a valuable contribution by com-
paring the Bayesian optimal policy with an
“adaptive optimal control” strategy (in which
the central bank updates its probability assess-
ments of the competing models but does not
engage in experimentation) and with the case of
O
ver the past decade or so,
researchers at academic institutions
and central banks have been active
in specifying and estimating
dynamic stochastic general equilibrium (DSGE)
models that can be used to analyze monetary
policy.1 Although the first-generation models
were relatively small and stylized, more recent
models typically embed a much more elaborate
dynamic structure aimed at capturing key aspects
of the aggregate data.2 Indeed, several central
banks now use DSGE models in the forecasting
process and in formulating and communicating
policy strategies.3 In following that approach,
however, it is crucial to investigate the sensitivity
of the optimal policy prescriptions of a given
model—that is, comparing the policy implica-
tions of alternative specifications of the behav-
ioral mechanisms or exogenous shocks—and to
identify policy strategies that provide robust per-
formance under model uncertainty.
The authors’ paper (Svensson and Williams,
2008) makes an important contribution in analyz-
ing Bayesian optimal monetary policy in an envi-
1 Pioneering early studies include King and Wolman (1996, 1999),
Goodfriend and King (1997), Rotemberg and Woodford (1997, 1999),
Clarida, Galí, and Gertler (1999), and McCallum and Nelson (1999).
2 See Christiano, Eichenbaum, and Evans (2005), Smets and Wouters
(2003), Levin et al. (2006), and Schmitt-Gröhé and Uribe (2006).
3 Examples include the Bank of Canada, the Bank of England, the
European Central Bank, and the Sveriges Riksbank. Recent DSGE
model development at the Federal Reserve Board is described in
Erceg, Guerrieri, and Gust (2006) and Edge, Kiley, and Laforte
(2007).
Andrew Levin is a deputy associate director in the Division of Monetary Affairs, Board of Governors of the Federal Reserve System.
Federal Reserve Bank of St. Louis Review, July/August 2008, 90(4), pp. 301-305.
© 2008, The Federal Reserve Bank of St. Louis. The views expressed in this article are those of the author(s) and do not necessarily reflect the
views of the Federal Reserve System, the Board of Governors, or the regional Federal Reserve Banks. Articles may be reprinted, reproduced,
published, distributed, displayed, and transmitted in their entirety if copyright notice, author name(s), and full citation are included. Abstracts,
synopses, and other derivative works may be made only with prior written permission of the Federal Reserve Bank of St. Louis.“no learning” (in which the central bank never
changes its probability assessments).
Interestingly, this analysis reaches conclusions
regarding the role of experimentation that are
broadly similar to those obtained in earlier studies
such as Wieland (2000, 2006). In particular, the
experimentation motive has relatively modest
effects on the characteristics of the Bayesian
optimal policy, and welfare comparisons indicate
fairly minimal costs of using adaptive optimal
control. Indeed, as John Taylor described in a
recent interview (Leeson, 2007), he arrived at
essentially the same conclusions several decades
ago when he applied Bayesian optimal control
to a small structural macro model: “My Ph.D.
thesis...problem was to find a good policy rule
in a model where one does not know the param-
eters and therefore had to estimate them and con-
trol the dynamic system simultaneously. My main
conclusion...was that in many models, simply
following a rule without special experimentation
features was a good approximation [to the optimal
policy].”
In the remainder of this commentary, I discuss
a few conceptual issues regarding the formulation
of model uncertainty, the characterization of
optimal policy under commitment, and the speci-
fication of how the private sector’s information
set differs from that of the central bank.
CHARACTERIZING MODEL
UNCERTAINTY
In analyzing the monetary policy implications
of model uncertainty, it seems reasonable to
assume that there will never be any single “true”
model, because every macro model is merely a
stylized approximation of reality. Moreover, on-
going progress in economic theory and empirical
analysis not only shifts policymakers’ probability
assessments about which existing model is the
best approximation, but it also inevitably gener-
ates a winnowing process whereby new model-
ing mechanisms are developed while obsolete
models are completely discarded. Over the past
few decades, for example, many central banks
have undergone a sequence of transitions from
traditional Phillips curve models (which implied
a positive long-run relationship between output
and inflation) to structural macro models embed-
ding rational expectations—most recently to
DSGE models with formal microeconomic founda-
tions. Furthermore, it seems reasonable to antici-
pate that this process of model development and
refinement will continue at a similar pace in the
years ahead.
From this perspective, a stationary Markov
process does not seem to be the ideal approach
to represent the sort of model uncertainty that is
relevant for monetary policymaking. In the pres-
ent analysis, each competing model corresponds
to a specific node or “state” of the Markov process;
hence, model uncertainty is represented by the
policymaker’s assessments of the probability
that each of these nodes is the correct model of
the economy, and the learning process is repre-
sented by how these probability assessments are
updated in response to incoming information.
Thus, if the economy switches from one node to
another, this implies that the “true” model of the
economy has suddenly shifted. Such shifts may
well occur, but it seems doubtful that the process
is stationary: that is, the true economy does not
shift back and forth among the members of the
set of competing models.
For example, a recent study of an empirical
DSGE model of the U.S. economy found that two
alternative specifications of the structure of nomi-
nal wage contracts—namely, Calvo-style contracts
with random duration versus Taylor-style con-
tracts with fixed duration—have markedly differ-
ent implications for optimal monetary policy
and welfare (Levin, Onatski, J. Williams, and
N. Williams, 2006). The analytical framework of
this paper can easily be used to characterize the
Bayesian optimal policy for this specification
uncertainty: One node would correspond to the
Calvo-style contract structure, and the other node
would correspond to the Taylor-style contract
structure. But it does not seem plausible to specify
this uncertainty as a stationary Markov process—
after all, that would imply that the economy
occasionally shifts back and forth between Calvo-
style contracts and Taylor-style contracts!
Levin
302 JULY/AUGUST 2008 FEDERAL RESERVE BANK OF ST. LOUIS REVIEWOf course, a stationary Markov regime–
switching specification may well be useful for
representing occasional shifts in the state of the
economy, such as stochastic transitions between
low growth and high growth. But in the case of
model uncertainty, it seems reasonable to specify
a diagonal structure for the Markov transition
matrix: that is, the true economy never shifts
between competing models. In that case, the
policymaker has prior beliefs that assign some
positive weight to each of these models; these
priors are then updated in response to incoming
information. Alternatively, one might consider a
triangular Markov transition matrix with very
small off-diagonal elements, representing the
notion that the true structure of the economy
might experience very rare shifts but would never
revert to its original structure.
CHARACTERIZING OPTIMAL
POLICY UNDER COMMITMENT
The “timeless perspective” is an appealing
approach to characterizing optimal policy under
commitment in a stationary environment
(Woodford, 2003). This approach is equivalent
to assuming that the government agency estab-
lished a complete set of state-contingent policy
commitments at some point in the distant past
(that is, time t = –￿), and that the economy has
converged to its stationary steady state under that
regime by now (t = 0). Moreover, in the general
case in which this steady state is not Pareto opti-
mal, the quadratic approximation of household
welfare depends on the steady-state values of the
Lagrange multipliers of the original policymaking
problem (Benigno and Woodford, 2005).
In contrast, for the reasons described here
previously, an environment of model uncertainty
may be viewed as implying that the economy
has not yet reached any stationary steady state,
and hence that policy should not be characterized
from a timeless perspective. Indeed, in this con-
text it might be more natural to characterize opti-
mal policy from the Ramsey perspective, that is,
assuming that the policymaker is prepared to
establish a complete set of state-contingent com-
mitments starting in the present period (that is,
as of time t = 0), where these commitments would
reflect the anticipation that incoming informa-
tion in future periods will gradually enable the
policymaker to learn which model correctly rep-
resents the economy. Of course, that specification
would raise further computational issues: Under
the Ramsey policy (as opposed to the timeless
perspective), the Lagrange multipliers correspon-
ding to the implementation constraints cannot
be substituted out of the problem but remain as
essential state variables of the linear-quadratic
approximation.
CHARACTERIZING THE PRIVATE
SECTOR’S INFORMATION
Finally, it is worthwhile to consider the
assumptions used in this analysis regarding the
information available to private agents:
1. In the benchmark case of Bayesian optimal
control, the analysis of this paper proceeds
under the assumption that neither private
agents nor the policymaker know which
model is true. Unfortunately, this assump-
tion is somewhat problematic in the context
of DSGE models with explicit microeco-
nomic foundations, because those models
are formulated under the assumption that
each household is aware of its own prefer-
ences and that each firm is aware of its own
production technology and the character-
istics of consumer demand.
For example, in New Keynesian DSGE
models with monopolistic competition and
staggered price contracts, it is assumed
that each firm sets the price of its product
with full knowledge of its own production
function and the elasticity of demand for
its product. Nevertheless, econometricians
may be unable to make precise distinctions
regarding the extent to which aggregate
price-setting behavior is influenced by
factors such as firm-specific inputs and
quasi-kinked demand; hence, there may
be a strong motive for designing a monetary
policy strategy that is robust to this source
Levin
FEDERAL RESERVE BANK OF ST. LOUIS REVIEW JULY/AUGUST 2008 303of model uncertainty (Levin, Lopez-Salido,
and Yun, 2007).
Similarly, DSGE models typically
involve a consumption Euler equation
that is derived from a particular specifica-
tion of household preferences for consump-
tion and leisure—and of course, each
individual household is assumed to have
full knowledge of its own preferences in
making decisions about spending, labor
supply, etc. Nevertheless, the available
data may be insufficient to enable econo-
metricians to resolve uncertainty regard-
ing several competing specifications of
household preferences. Therefore, the
central bank may wish to follow a policy
strategy that is robust to this source of
model uncertainty (Levin et al., 2008).
2. In the case of adaptive optimal control, the
analysis proceeds under the more restric-
tive assumption that neither private
agents nor the policymaker observe the
current vector of shocks—an assumption
that precludes consideration of most (if
not all) existing DSGE models. In many
such models, for example, shocks to total
factor productivity play a key role as a
source of aggregate volatility in output
and employment. But it is by no means
clear how an individual firm could deter-
mine its own production if the firm did
not have contemporaneous knowledge of
its own productivity.
3. The case of “no learning” assumes that
neither private agents nor the policymaker
can recall any of the data that were observed
in previous periods. In many DSGE models,
however, these data do enter explicitly
into agents’ decision rules. For example,
in specifications with habit persistence in
consumption, the household’s current
spending decision partly reflects its spend-
ing in previous periods. Similarly, when
investment in physical capital is subject to
adjustment costs, each individual firm’s
decision regarding its current level of
investment depends explicitly on its prior
investment decisions.
Evidently, in analyzing optimal policy under
model uncertainty in the context of DSGE models
with explicit micro foundations, further progress
is needed to distinguish between the information
available to the central bank and the information
that is available to individual households and
firms.
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An Estimated Dynamic Stochastic General Equilibrium Model of the Euro

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Interest and Prices: Foundations of a Theory of Monetary Policy.

Macroeconometric Equivalence, Microeconomic Dissonance, and the Design of Monetary Policy.”

Monetary Policy and Uncertainty about the Natural Unemployment Rate: BrainardStyle Conservatism versus Experimental Activism.”

Monetary Policy, Parameter Uncertainty,

Natural Rate Measures in an Estimated

Nominal Rigidities and the Dynamic Effects of a Shock to Monetary Policy.”

Optimal Fiscal and Monetary Policy in a Medium-Scale Macroeconomic Model,”

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Performance of Operational Policy Rules in an Estimated Semi-Classical Structural Model,”

SIGMA: A New Open Economy Model for Policy Analysis.”

What Should the Monetary Authority Do When Prices Are Sticky?”

Commentary on "Optimal monetary policy under uncertainty: a Markov jump-linear-quadratic approach"

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Commentary on "Optimal monetary policy under uncertainty: a Markov jump-linear-quadratic approach"

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