Structural change is a central
theme in virtually any explanation of the exceptional performance
of the U.S. economy over the past several years. Structural
changes of uncertain magnitude and timing have increased the
difficulty in forecasting, undermined confidence in our
understanding of the structure of the economy, and increased the
risk of measurement error with respect to key variables.

In my remarks, I will offer a
bridge from today's discussion of structural changes to the
implications for monetary policy, the subject of tomorrow's
agenda. In my view, the most important challenges to monetary
policy related to structural change in this episode arise from
possible changes in aggregate supply--specifically in the
non-accelerating inflation rate of unemployment (NAIRU) and in
trend growth. The key challenge for monetary policymakers during
this period, in my view, has been to allow the economy to realize
the full benefits of the new possibilities while avoiding an
overheated economy. More fundamentally, the challenge has been to
adapt the strategy of monetary policy in light of the
uncertainties associated with structural change. My focus is
therefore not on structural change per se but rather on the
uncertainty about key parameters likely to be heightened during a
period of structural change.

However, the key structural
change during this episode--an increase in the underlying
productivity growth trend--has also set in motion a complex of
effects on inflation, interest rates, equity prices, and aggregate
demand. Even if we knew the precise value of the higher
productivity trend, we would likely remain uncertain about the
size and persistence of many of its effects. As a result, adapting
monetary policy to a higher trend rate of productivity growth
would be a challenge, especially in an interest-rate setting
regime, even if there were no uncertainty about the new underlying
growth trend.

**Perspectives on Monetary
Policy Strategy**

There are, in my view, two fundamental requirements of a prudent
monetary policy. First, monetary policy should impose a nominal
anchor, pinning down the long-run inflation rate. Second, monetary
policy should lean against the cyclical winds. The second
requirement contributes to the first and also to smoothing
fluctuations in output around full employment. This view of the
mission of monetary policy is consistent with both the dual
mandate for the Federal Reserve in the Federal Reserve Act and
with flexible inflation targeting regimes in many countries.

The key to the practice of
monetary policy is to develop a strategy for the discretionary
conduct of policy that meets these requirements. A constructive
way to describe such a strategy is to formalize it in terms of an
explicit rule. John Taylor has offered an attractive and simple
form of such a rule. But perhaps equally important, John's
approach has encouraged a wider acceptance of the study of rules
by emphasizing that the objective is to inform discretionary
monetary policy decisions rather than to replace discretion by a
rule.

I find the Taylor rule
attractive because it is closely aligned both with the objectives
of monetary policy and with the model that governs inflation
dynamics. That is, the rule responds directly to deviations from
the Federal Reserve's objectives--price stability and an
equilibrium utilization rate. And it incorporates a preemptive
response to inflation that is consistent with models that assign
an important role to unemployment or output gaps in inflation
dynamics. However, implementing this strategy requires knowledge
of the output gap and the equilibrium real interest
rate--variables that appear to have been affected by structural
change. As a result, there has been increased focus on how
Taylor-type rules should be adjusted in light of the uncertainties
associated with structural change.

**Uncertainty and Monetary
Policy Strategy**

Given uncertainty about the output gap, for example, should we
attenuate the response to the output gap or even entirely abandon
the output gap as a guide to adjustment in monetary policy? Given
the related difficulty in forecasting during a period of
structural change, should we be less forward-looking and hence
less preemptive? If we are less preemptive, should we compensate
by being more aggressively reactive to recent inflation? Or should
we more fundamentally change the specification of the policy rule
when confronted with these uncertainties? For example, would we
minimize the damage from mis-estimates of the NAIRU and trend
growth using a nominal income rule instead of a Taylor rule? Or
should we allow for a nonlinear instead of a linear policy
response to movements in output and inflation?

There is, of course, a
well-developed literature on the effect of uncertainty on policy.
Until recently, I viewed the literature as delineating two simple
types of uncertainty, typically referred to as additive
uncertainty and multiplicative or parameter uncertainty. Recently,
the literature has focused on uncertainty associated with
imperfect or noisy observation of the economy in ways that do not
neatly fall into the two simple bins.

Certainty equivalence holds in
the case of simple specifications of additive uncertainty. When
certainty equivalence holds, it is optimal for policymakers to
respond to the expected values of their targets as if they held
these values with complete certainty. In a sense, uncertainty has
no effect on policy in this case, though it results in some
decline of its effectiveness. Additive uncertainty and certainty
equivalence are perhaps best seen as devices to allow the
incorporation of some stochastic elements into a model without the
complications that arise in more meaningful encounters with
uncertainty.

In the case of multiplicative
uncertainty, the most well known result is William Brainard's
conclusion that policy should be somewhat more cautious in this
case. Assuming policymakers don't like uncertainty, they become
less aggressive with their policy instruments, because bolder use
of policy adds to uncertainty about outcomes. However, some recent
evidence (Arturo Estrella, Rick Mishkin, and Glenn Rudebusch)
suggests that this type of uncertainty may have a relatively
modest quantitative effect on the policy outcome. Also, newer
theoretical results, such as Tom Sargent's, question the
conclusion that parameter uncertainty would make policy more
cautious.

The newer entry into the
uncertainty literature relates to imperfect or noisy observation
of the economy, although concern about this problem certainly
predates the recent studies. For example, by examining the
historical record at the Federal Reserve, Athanasios Orphanides
uncovered substantial and persistent measurement error associated
with estimates of the output gap--one of the measures we sometimes
identify with "excess demand." This uncertainty starts
by looking a lot like additive uncertainty, but its policy
implications often end up similar to the Brainard result of more
cautious policy, with policy response attenuated at least with
respect to movements in variables about which there are noisy
observations.

The literature supporting this
attenuation result has at least two strands. One consists of
theoretical models based on signal extraction, as in the work that
Eric Swanson and Lars Svensson and Michael Woodford are presenting
at this conference tomorrow. Suppose, as in Swanson's work, that
inflation depends on an unobservable variable we call "excess
demand" and policy responds to the unemployment rate, which
is only an imperfect indicator of "excess demand." Since
the unemployment rate is a noisy indicator of what the policymaker
is interested in--the unobservable "excess demand"--the
weight the policymaker will give this variable will vary with its
reliability as an indicator for excess demand. Specifically, the
less reliable the indicator becomes, the smaller its weight will
be in the optimal policy rule and the more weight will be placed
on the other indicators about which uncertainty has not changed.
In the current context, that means that the weight on the
unemployment rate is decreased, while the weight on inflation is
increased. In effect, as policy becomes less preemptive in
stabilizing inflation, it becomes more aggressive in reacting to
recent inflation.

The second strand of the
literature that supports the attenuation result is based on
simulation results, as reflected in the work of Orphanides,
Rudebusch, Frank Smets, and others. This work employs simple
empirical models and a simple rather than an optimal rule and
examines how policymakers should adjust the parameters of the
simple rule in light of the uncertainty about the measurement of
the output gap. It finds that policymakers should attenuate their
response to changes in the output gap and, indeed, should move
very cautiously when the confidence with which sure measures can
be constructed is low. In contrast with the conclusions based on
signal extraction models, the simulations results using simple
rules generally finds that increased uncertainty about the output
gap may call for attenuation in the response to both the gap
variable and inflation.

In some cases, certainty
equivalence continues to hold, even with noisy observations. In
Swanson's work, for example, optimal policy still displays
certainty equivalence when policy is related to the unobservable
excess demand. In the paper that Svensson and Woodford will
present tomorrow, where the model relates inflation directly to
the observed unemployment gap, certainty equivalence holds
provided that the estimate of the gap is updated on the basis of
all available data and the true model. This structure and result
are also present in the work by Orphanides.

So the question is: How general
or special is the attenuation result? This question appears
particularly relevant to the uncertainties that monetary
policymakers are wrestling with today, and I am sure we will have
a lot of discussion about this conclusion tomorrow. I suspect the
result is a general one for the following reasons. First, I
believe part of the challenge today is finding a proxy for the
unobservable excess demand, especially given the divergent
movements in the unemployment and capacity utilization rates.
Therefore, in my view, Swanson's conclusion that certainty
equivalence holds when policy is expressed in terms of the
unobservable "excess demand" is dominated by his
conclusion that attenuation holds when policy is made in terms of
observables. Put simply, policy authorities are mortals and hence
are unable to observe unobservables. Second, given that we don't
know the true model, policymakers might look at simple rules
rather than try to derive optimal rules for guidance. This leads
me to question the practical significance of certainty
equivalence, which requires that policymakers know the true model,
use an optimal rule, and update their optimal estimate of the
NAIRU based on the true model.

I draw the following conclusions
from this research. First, policymakers should continuously update
their estimates of the NAIRU and the output gap, using all
available information, particularly the realizations of
unemployment, output, and inflation. Such updating will not
entirely erase the problems associated with noisy observations,
but it will mitigate them. In my view, policymakers today update
their estimates of the output gap and the NAIRU more
systematically and more frequently than they once did. This view
suggests some caution in deriving the degree of attenuation from
historical evidence of revisions to the NAIRU and potential
output.

Second, policymakers should
adjust the aggressiveness of their response to the gaps between
actual and target variables in light of the uncertainty about
their measurement. Specifically, policymakers should attenuate
their response to movements in the unemployment or output gap.
There is an important complication in applying this principle.
Simulation results suggest that the optimal response to the output
gap in the absence of uncertainty might be considerably more
aggressive than the parameter in the Taylor rule. The attenuation
might therefore result in a response parameter closer to or lower
than the Taylor rule value.

Third, the literature is less
clear about whether policymakers should offset any attenuation in
the response to the output gap with a more aggressive response to
movements in realized inflation. My instinct tells me that, as
policy becomes less preemptive, it should become more aggressively
reactive. Taking the second and third conclusions together, the
relative weights on the gap variable and inflation should vary,
depending on the degree of uncertainty about the output gap. The
higher coefficient on the inflation rate might be justified by the
fact that inflation has become a better indicator of the excess
demand compared with the output gap when there is heightened
uncertainty about the measurement of the output gap.

The focus of the literature has
been on uncertainty about the unemployment or output gap, but a
shift in trend productivity growth also results in uncertainty
about the equilibrium real interest rate. In this case, a
Taylor-type rule should also incorporate some mechanism for
updating the estimate of this rate.

**A Nonlinear Taylor Rule under
Uncertainty about Key Parameters**

The literature on noisy observations has focused on adjustments in
the parameters of linear Taylor-type rules. But I believe that a
nonlinear rule may dominate a linear specification in this case. I
have suggested a nonlinear rule that would attenuate the response
to the unemployment rate in a region around the best estimate of
the NAIRU but would cause a gradual return to the more aggressive
marginal response appropriate under certainty equivalence once the
unemployment rate had moved sufficiently below the best estimate
of the NAIRU.

Such a nonlinear rule could be
justified either by nonlinearities in the economy or by a
non-normal distribution of policymakers' prior beliefs about the
NAIRU. It is certainly easy to believe that there are
nonlinearities in the economy in general and with respect to the
Phillips curve in particular. For example, to the extent that the
effect on inflation becomes disproportionately larger as the
unemployment or output gap increases, the policy response should
become more aggressive with each incremental increase in the gap.
However, I'm not persuaded that there is a strong case for a
nonlinear Phillips curve. So I am inclined to emphasize the
possibility of a non-normal distribution of prior beliefs about
the NAIRU as the basis for a nonlinear policy rule.

An example of a non-normal
probability distribution for the NAIRU that would justify the
nonlinear policy response I have suggested is one with a uniform
probability distribution around the best estimate for the NAIRU.
For example, policymakers might have a prior of 5 percent for the
NAIRU, but a uniform probability distribution over the range
between 4 � percent and 5 � percent for the unemployment rate.
Because policymakers are so uncertain about the NAIRU within this
interval, they might be very willing to revise their estimate of
the NAIRU about in line with the observations of the unemployment
rate within it. As a result, movements of the unemployment rate
within this range would have little effect on the estimate of the
unemployment gap and, therefore, on the target interest rate.
However, if the unemployment rate moved outside this range,
policymakers might assign an increasingly smaller fraction of each
increment of the unemployment rate to the NAIRU as the
unemployment rate moved still further from policymakers' best
estimate of the NAIRU. In this case, the policy response is
attenuated around the best estimate of the NAIRU, but it gradually
becomes larger, ultimately converging to the marginal response
under certainty equivalence.

**Monetary Policy's Adjustment
to Uncertainty about Key Parameters**

Is the recent monetary policy response consistent with the lessons
I have drawn from the literature on uncertainty associated with
noisy observations? The following discussion draws on the
evolution of my own thinking, as well as on the policy actions,
including the announced tilts in policy and the text of the
announcements that accompanied policy actions.

I pick up this episode in the
middle of 1996, when I joined the Board. It seems to me that
initially monetary policy was consistent with a backward-looking
Taylor rule (although that is sometimes difficult to distinguish
from a forward-looking Taylor rule). We were faced with two
surprises: faster-than-expected growth (resulting in a
higher-than-expected estimated output gap) and lower-than-expected
inflation. These had offsetting effects on the nominal funds rate,
yielding a nearly unchanged policy until the fall of 1998 and a
policy that closely tracked the Taylor rule prescription, at least
allowing for updates of the estimated unemployment or output gaps
along the way. Alternatively, this policy could be viewed as
allowing a passive rise in the real rate that turned out to be
well calibrated to the rise in the output gap.

As the episode progressed, more
questions were raised--both inside and outside the Federal
Reserve--about the values of the NAIRU and trend growth. The staff
continually adjusted its estimates of these parameters in response
to incoming data.

In the fall of 1998, monetary
policy responded both to the financial market distress and to the
abrupt change in the forecast for growth (and hence utilization
rates) in the United States. I put more weight on the forecast and
less on recent observations in the context of a Taylor rule, a
stance I thought was justified by the abrupt change in the
forecast and by the unusually sharp contrast between the forecast
and the still-strong incoming data.

Once it became apparent that the
U.S. economy was maintaining its momentum despite weaker foreign
growth and that financial markets had returned toward normal, the
growing uncertainty about the output gap--reflecting the
continuing contradiction of declining inflation and rising output
gaps--made monetary policymakers cautious about aggressively
reversing their policy actions. But through early 1999 we remained
somewhat concerned about the degree of recovery in both financial
markets and foreign economies. The net result was that the nominal
funds rate remained constant during this phase, instead of
tightening in line with the Taylor rule prescription. In effect,
policymakers could be interpreted as attenuating their response to
the unemployment and output gap in line with the theoretical
models and empirical results I have talked about.

Beginning in mid-1999, with the
estimated output gap increasing further and growth shifting to a
still-higher gear, policymakers became more concerned about the
possibility of overheating and, hence, the risks of higher
inflation. The tightenings in 1999 could be interpreted as
unwinding the earlier easings, once the factors that motivated the
easings had themselves reversed. Of course, every policy action
needs to be defended in terms of its contribution in the future to
achieving the objectives of monetary policy. In this spirit, I
interpreted the tightening moves as preemptive attempts to limit
inflation risks.

Why did policymakers tolerate
for a while further increases in the output gap, and why did they
subsequently become more concerned about the inflation risks from
further increases in the output gap? I think the change can be
rationalized in terms of my discussion of the case for a nonlinear
policy response under uncertainty. As the unemployment rate fell
farther below the best estimates of the NAIRU and the risk of
overheating increased, policymakers became less tolerant of
continued above-trend growth.

**Monetary Policy Strategy in
Light of the Uncertainties Associated with Structural Change**

Looking backward, I think we can find at least a hint of
attenuation of the response to changes in the unemployment rate
and, more recently, a hint of a nonlinear policy response. What
does this suggest about monetary policy strategy going forward?
The current strategy can, I believe, be viewed as a two-step
process. The first step is, preemptively, to slow growth to trend.
If successful, this step would limit, though not necessarily
remove, the threat of overheating, if output has already advanced
beyond potential. The second step is to respond reactively to
higher inflation, should the prevailing output gap prove to be
inconsistent with stable inflation.

The first step is a continuation
of the strategy underlying the recent policy tightenings. In my
judgment, the unemployment rate has already declined to a
sufficiently low level relative to my estimate of the NAIRU that
we should no longer be attenuating the marginal policy response to
further declines. But the current policy is, in my view, also an
aggressive version of such a strategy because it is not a
nonlinear response to further declines in the unemployment rate,
but a forward-looking attempt to prevent further tightening of the
labor market. I think that one of the subtleties of policy is
sometimes being content to respond incrementally to the incoming
data and sometimes becoming more aggressive and responding to
forecasts. It is best that the policymakers are transparent about
such shifts in the relative weight on the forecast in their policy
decisions.

Once growth has slowed to trend
and the output gap stabilizes, monetary policy may become more
reactive, given the continued uncertainty about the levels of the
NAIRU and the output gap. That is, policymakers might be prepared
to slow the economy to trend growth to avoid the risk of higher
inflation associated with still-lower unemployment rates and
higher output gaps, but might be reluctant to reduce the perceived
output gap without evidence from realized inflation that the
prevailing gap is unsustainable.

Under such a policy, the
response to inflation should, in my view, be more aggressive than
it would otherwise be, for example, in the Taylor rule under
certainty. This is an example of offsetting the attenuation in the
response to the output gap with a more aggressive response to
inflation realizations. In effect, the policy setting at trend
growth and at the prevailing level of the output gap is presumed
to be consistent with stable inflation. An increase in inflation
(specifically in core inflation) would be evidence that the output
gap is not in fact sustainable. As a result, the increase in
interest rates should be the combined response to a slight
increase in the estimate of the NAIRU and to an increase in the
inflation rate at an unchanged estimate of the NAIRU.

A final component of the
strategy, in my view, should be that policy should tighten
further--above and beyond what is presumed to be necessary to slow
the economy to trend--to the extent that efforts to stabilize the
output gap fall short. For example, let us assume that growth
ultimately moves to trend but, in the interim, the continued
above-trend growth increases the output gap still further. In
response, policy should tighten incrementally, encouraging below
trend-growth and hence unwinding the further increase in the
output gap.

The strategy I have described
would reduce the prospects of policy responding to noise is
estimates of key real-side variables in the economy and would
increase the prospects of allowing the economy to realize the full
benefits of the recent improvements in aggregate supply. However,
it does risk allowing excess demand to build until it shows up in
inflation and may ultimately require a more aggressive response of
interest rates, if the range of attenuation does not in fact
correspond to a decline in the NAIRU.

**Conclusion**

Structural change complicates the task of monetary policy. Of
course, it is not difficult to put up with this additional burden
when the structural change takes the form of a decline in the
NAIRU and an increase in trend productivity growth. It would not
be easy for monetary policy to turn such good fortune into poor
macroeconomic performance. But the uncertainties about the nature
and degree of structural change confront policymakers with the
task of striving to realize the benefits of a decline in the NAIRU
and an increase in trend growth while trying to avoid the
inflationary consequences of overtaxing the new limits. Recent
work on signal extraction models and on the implications of noisy
observations provides some important guidance about how to adjust
the strategy of monetary policy in the face of the new
uncertainties. This conference provides a timely opportunity to
assess what we have learned and how it might be applied to
monetary policy today, as well as to point to areas that may
deserve further exploration.

**References**

Brainard, W. "Uncertainty and the Effectiveness of
Policy," *American Economic Review,* vol. 57 (1967), pp.
411-25.

Estrella, A., and F. Mishkin.
"Rethinking the Role of NAIRU in Monetary Policy:
Implications of Model Formulation and Uncertainty," in J.B.
Taylor, ed., *Monetary Policy Rules.* Chicago: NBER and
University of Chicago Press, 1999.

Orphanides, A. *Monetary
Policy Evaluation with Noisy Information,* Finance and
Economics Discussion Series No.1998:50. Washington, D.C.: Board of
Governors of the Federal Reserve System, November 1998.

Rudebusch, G. "Is the Fed
Too Timid? Monetary Policy in an Uncertain World," mimeo,
Federal Reserve Bank of San Francisco, April 1999.

Sargent, T. "Discussion of
'Policy Rules for Open Economics' by Lawrence Ball," in J.B.
Taylor, ed., *Monetary Policy Rules.* Chicago: NBER and
University of Chicago Press, 1999.

Smets, F. *Output Gap
Uncertainty: Does It Matter for the Taylor Rule?* BIS Working
Paper No.60, November 1998.

Svensson, L., and M. Woodford.
"Indicator Variables for Monetary Policy," mimeo,
Princeton University, February 2000.

Swanson, E. "On Signal
Extraction and Non-Certainty Equivalence in Optimal Monetary
Policy Rules," mimeo, Board of Governors of the Federal
Reserve System, March 2000.