FRBSF Economic Letter
2005-27; October 21, 2005
Estimating the "Neutral" Real Interest Rate
in Real Time
On September 20, the Federal Open
Market Committee, the nation's monetary policymaking body,
raised its target level of the federal funds rate by 25
basis points, the eleventh straight increase over the last fifteen months.
The statement released immediately after the meeting said, "With underlying
inflation expected to be contained, the Committee believes that policy accommodation
can be removed at a pace that is likely to be measured. Nonetheless, the Committee
will respond to changes in economic prospects as needed to fulfill its obligation
to maintain price stability."
The statement clearly implies that the Committee believes
that the real funds rate is below the so-called neutral
real rate. What is the "neutral real rate"? According
to Greenspan (1993), the real funds rate may be said to
be neutral when it is at a level that, "if maintained,
would keep the economy at its production potential over
time." Therefore, if the real funds rate is below
the neutral real rate, policy is accommodative and the
economy expands; if it is above the neutral real rate,
policy is restrictive and the economy shrinks.
The difficulty policymakers face is that it is not obvious
exactly what the level of the neutral real rate is. It
cannot be observed directly. There is no reliable way to
estimate it. And it can change.
This Economic Letter discusses the problems of estimation
using both statistical methods and structural economic models.
It focuses particularly on the vagaries of such estimations
done in "real time," that is, without the benefit
of long and reliable series of data.
Structural estimation
of the neutral real interest rate
 Because the neutral real interest rate is unobservable,
economists have devised several strategies to estimate
it. The simplest approach is to assume that it is equivalent
to the trend real interest rate; this trend can be extracted
from the real interest rate using statistical tools. For
instance, the black line in Figure 1 plots one such measure
by running what is known as a Hodrick-Prescott filter (in
this figure, the real fed funds rate is defined using the
deflator for personal consumption expenditures excluding
food and energy). The estimated neutral real interest rate
varies noticeably during the past four decades, from about
2% in the 1960s to almost 6% in the early 1980s and about
3% in the mid-1990s.
This simple statistical approach may be reasonable over
periods when inflation and output growth are stable, but
it leads to substantial biases when output or inflation
varies significantly. For instance, inflation was rising
during most of the 1970s, suggesting that the trend real
interest rate was, in fact, well below its neutral level.
Similarly, inflation fell rapidly in the early 1980s, suggesting
that the average real interest rate was much higher than
the neutral level. Thus the black line in Figure 1 underestimates
the neutral real rate for the 1970s and overestimates it
for the early 1980s.
 A more robust approach is to combine statistical tools
with structural macroeconomic modeling techniques. Laubach
and Williams (2003) provide a good example. There are three
equations in their structural model: an "IS equation" relating
the output gap (the deviation of actual output from its
potential level) to the neutral real interest rate, a "Phillips
curve" relating inflation to the output gap, and an
equation describing the positive correlations between the
neutral real rate and the trend growth of output, as predicted
by economic theory. Once the macroeconomic model is specified,
one can then estimate the neutral real interest rate through
exploring the correlations between the interest rate, inflation,
and output. For instance, when actual output exceeds trend
output as predicted by the model, part of the unexpected
strength in output will be attributed to a more accommodative
monetary policy, which, in turn, implies that the neutral
real interest rate was higher than otherwise projected.
Figure 2 plots the estimate of the neutral real interest
rate based on the Laubach-Williams model. The estimate
suggests that, since the 1960s, the neutral real interest
rate has fluctuated between 2% and 4%, and in early 2005
it stood around 2.25%. Note that for the 1970s, this estimate
is significantly higher than the one based on the simple
statistical approach, and for the 1980s, it is lower.
Translating the real neutral rate to the nominal neutral
rate, given these estimates, would seem to be an easy exercise.
For someone feeling comfortable with an inflation rate of
2%, for instance, the neutral federal funds rate would be
around 4.25% at the moment. Unfortunately, it is not as easy
as it seems.
Three problems with real-time estimation
Estimates of the neutral real interest rate based on the
structural model can be quite imprecise. A recent study
by Clark and Kozicki (2004) analyzes the difficulties in
estimating today's neutral real rate based on the contemporaneous
data initially released historically (which would be called "real-time" estimates
by economists), and concludes that such estimates "will
be difficult to use reliably in practical policy applications" (p.
4). There are three major kinds of difficulties that arise,
each of which can significantly bias the estimates.
The "one-sided filtering problem." The
first difficulty has to do with the so-called "one-sided
filtering problem." Statistical theory tells us that,
in estimating unobservable variables, such as the neutral
real interest rate, the more observations that are used
in estimation, the more accurate the estimates will be.
In reality, however, we can observe macroeconomic data
only up to today. Therefore, the estimate of today's neutral
real rate based on data that are available today—called
the "one-sided" estimate—will be quite different
from the estimate when we have data beyond today—which
are called the "two-sided" or "smoothed" estimates.
For instance, suppose we were back in 1990 and were trying
to estimate the neutral real interest rate at that time.
We would be able to perform the estimation based only on
the data observed before 1990, since we would not know
what inflation or real GDP growth is in 1991 or afterward.
Now fast-forward to 2005. With the hindsight of an additional
15 years of data, we are able to revise our estimates based
on a much longer sample, and our estimate of the neutral
real interest rate for 1990 as of 2005 (the two-sided estimate)
will be quite different from the one obtained in real time
in 1990 (the one-sided estimate). Similarly, in estimating
the neutral real interest rate in 2005, we are able to
obtain only the one-sided estimate, which will be quite
different from the two-sided estimate, which will take
into account future data over the next decade or so.
 How much can the one-sided estimate differ from the more
accurate two-sided estimate? The discrepancy could be as
large as one to two percentage points, as Figure 3 shows.
The gray line in the figure plots the one-sided estimates
of the neutral real interest rate based on the data as
observed in each quarter in the past 40 years, and the
black line plots the two-sided estimates based on the data
as observed to 2005. For instance, the one-sided estimate
of the neutral real rate in 1990 is about 3.75%, whereas
the two-sided estimate based on the data to 2005 is 2.5%.
Data revisions. Another source of imprecision
comes from the fact that macroeconomic data are often revised,
and sometimes the revisions can be quite substantial. For
instance, consider real GDP growth in the second quarter
of 2001. According to the real-time macroeconomic data
set collected by the Federal Reserve Bank of Philadelphia,
it was initially estimated to be 0.7% at an annual rate;
a few months later, it was revised down to 0.3%; a year
later, it was revised down further to -1.6%; in mid-2003,
it was revised up to -0.6%; as of 2005, it was finally
revised up to 1.2%.
Such substantial revisions to the macroeconomic data will
undoubtedly bias the estimates of both the model parameters
and the neutral real interest rate. And the magnitude of
the biases will depend on the size of the data revisions.
Clark and Kozicki (2004) investigate this problem using
40 years of real-time data for the U.S. and find that such
biases could be as high as one to two percentage points.
Uncertainties about model specification. Our
discussion so far assumes that the macroeconomic model
underlying the estimates of the neutral rate is the correct
one. However, there are alternative ways to model the economy,
and macroeconomists have not reached a consensus about
which one is most reliable.
Different model specifications can generate very different
estimates of the neutral real interest rate. Indeed, Clark
and Kozicki (2004) find that estimates of the neutral real
interest rate are sensitive to model specification and that
these differences can again be as large as one to two percentage
points. Therefore, given all three kinds of uncertainties,
it would not be surprising to have a total bias of two percentage
points or more in estimating the neutral real interest rate.
Conclusion
Economists have highlighted numerous difficulties in
estimating the neutral federal funds rate in real time,
including data and model uncertainty, which can result
in estimates that are off by a couple of percentage points.
These difficulties add to the challenge of conducting monetary
policy, especially when the federal funds target is near
the neutral rate, because policymakers must make their
decisions without the benefit of reliable data. Therefore,
policymakers will be especially attentive at this stage
to incoming data. And, until research finds a solution
to the difficulties of estimating the neutral rate, the
conduct of policy will remain both a science and an art.
Tao Wu
Economist
References
[URLs accessed October 2005.]
Clark, Todd, and Sharon Kozicki. 2004. "Estimating
Equilibrium Real Interest Rates in Real Time." FRB
Kansas City Working Paper 2004-08. http://www.kc.frb.org/Publicat/Reswkpap/RWP04-08.htm
Greenspan, Alan, 1993. Testimony on 1993 Monetary Policy
Objectives to the U.S. Senate, July 20.
Laubach, Thomas, and John Williams. 2003. "Measuring
the Natural Rate of Interest." The Review of Economics
and Statistics 85(4) (November) pp. 1063-1070.
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