FRBSF Economic Letter
2003-32; October 31, 2003
The Natural Rate of Interest
A key question for monetary policymakers, as well as participants
in financial markets, is: "Where are interest rates headed?" In
the long run, economists assume that nominal interest rates will tend
toward some equilibrium, or "natural," real rate of interest
plus an adjustment for expected long-run inflation.
Unfortunately, the "natural" real rate of interest is not
observable, so it must be estimated. Monetary policymakers are interested
it because real rates above or below it would tend to depress or stimulate
economic growth; financial market participants are interested because
it would be helpful in forecasting short-term interest rates many years
into the future in order to calculate the value and, therefore, the yields
of long-term government and private bonds. This Economic Letter describes
factors that influence the natural rate of interest and discusses different
ways economists try to measure it.
Defining the natural rate of interest
In thinking about the natural rate
of interest, economists generally focus on real interest rates. They
believe that movements in those rates,
more so than in nominal rates, influence businesses' decisions about
investment spending and consumers' decisions about purchases of durable
goods, like refrigerators and cars, and new housing, and, therefore,
Over 100 years ago, Wicksell defined the natural rate
There is a certain rate of interest on loans which is neutral
in respect to commodity prices, and tends neither to raise nor to lower
translation from 1898 text, p.102.)
Since then, various definitions of
the natural rate of interest have appeared in the economics literature.
In this Letter, the natural rate
is defined to be the real fed funds rate consistent with real GDP equaling
its potential level (potential GDP) in the absence of transitory shocks
to demand. Potential GDP, in turn, is defined to be the level of output
consistent with stable price inflation, absent transitory shocks to supply.
Thus, the natural rate of interest is the real fed funds rate consistent
with stable inflation absent shocks to demand and supply.
of the natural rate takes a "long-run" perspective
in that it refers to the level expected to prevail in, say, the next
five to ten years, after any existing business cycle "booms" and "busts" underway
have played out. For example, the U.S. economy is still at a relatively
early part of its recovery from the 2001 recession, so the natural rate
refers not to the real funds rate expected over the next year or two,
but rather to the rate that is expected to prevail once the recovery
is complete and the economy is expanding at its potential growth rate.
1 shows what determines the natural rate in a stylized form. The downward-sloping
line, called the IS (investment = saving) curve shows
the negative relationship between spending and the real interest rate.
The vertical line indicates the level of potential GDP, which is assumed
to be unrelated to the real interest rate for this diagram. (In principle,
potential GDP is also a function of the real rate, but this modification
does not affect the basic point.) At the intersection of the IS curve
and the potential GDP line, real GDP equals potential, and the real interest
rate is the natural rate of interest.
Importantly, the natural rate of
interest can change, because highly persistent changes in aggregate supply
and demand can shift the lines.
For example, in a recent paper, Laubach (2003) finds that increases in
long-run projections of federal government budget deficits are related
to increases in expected long-term real interest rates; in Figure 1,
an increase in long-run projected budget deficits would be represented
by a rightward shift in the IS curve and a higher natural rate. In addition,
economic theory suggests that when the trend growth rate of potential
GDP rises, so does the natural rate of interest (see Laubach and Williams
(2003) for supporting evidence).
Measuring the natural rate of interest
Although it is relatively straightforward
to define the natural rate of interest, it is less straightforward to
measure it. If the natural
rate were constant over time, one might estimate it simply by averaging
the value of the real funds rate over a long period. For example, the
average real fed funds rate over the past 40 years has been about 3%,
so if history were a good guide, then one would expect real interest
rates to return to 3% over the next five to ten years.
the natural rate using a long-term average is akin to using a baseball
player's lifetime batting average to predict his batting
average over the next season. This makes sense only if the likelihood
of getting a hit doesn't change much over a career. In reality, the factors
that affect a baseball player's performance—experience, age, and the
quality of opponent pitching—change from year to year. For example,
Barry Bonds's batting average over the past three seasons was well above
his career average, suggesting an important change in the factors that
determine whether Barry gets a hit. The leap in performance is even greater
when looking at his home run hits: over the past three years, he has
hit home runs at a rate over 50% higher than during the rest of his career.
Indeed, Barry Bonds's performance during the 2003 season was much closer
to his record over the past three seasons than his career statistics
would predict, showing that long-term averages can be misleading predictors.
same logic of time variation in batting averages of baseball players
applies to the natural rate of interest. The factors affecting supply
and demand evolve over time, shifting the natural rate around. If these
movements are sufficiently large, the long-term average could be a poor
predictor of the natural rate of interest.
One way to allow for structural
changes that may influence the natural rate of interest is to compute
averages of past values of the real funds
rate while putting
less weight on older data. Figure 2 illustrates such a calculation, taking the
average over the past five years. Other more sophisticated statistical approaches
identify the natural rate by using weighted averages of past data, and they yield
plots similar to those in the figure.
Although such averaging methods tend to
work well at estimating the natural rate of interest when inflation and
output growth are relatively stable, they do not
work so well during periods of significant increases or declines in inflation
when real interest rates may deviate from the natural rate for several years.
For example, during the late 1960s and much of the 1970s, inflation trended steeply
upward, which suggests that the real funds rate was below the natural rate on
average. The averaging approach misses that point, however, and ascribes this
pattern of low real rates to a low natural rate.
Estimating the natural rate of
interest with an economic model
Since the averaging approach does not
work well when interest rates deviate from the natural rate for long
periods, economists also use other economic
to estimate the natural rate. For example, Bomfim (1997) estimated the location
and slope of the IS curve and potential output shown in Figure 1 using the Federal
Reserve Board's large-scale model of the U.S. economy, and thereby derived estimates
of the natural rate of interest. In terms of the baseball analogy, these methods
try to estimate some aspect of a player's abilities, taking into account the
effects of relevant observable characteristics, say, the player's age and the
quality of the opposing pitcher.
Laubach and Williams (2003) use a simple macroeconomic
model to infer the natural rate from movements in GDP (after controlling
for other variables, including
importantly, the real fed funds rate). In their model, if the real fed funds
rate is above the natural rate, monetary policy is contractionary, pulling GDP
down, and, if it is below the natural rate, monetary policy is stimulative, pushing
An important component of their procedure is a statistical technique
known as the Kalman filter; this method works on the principle that you
your estimate of the natural rate of interest based on how far off the model's
prediction of GDP is from actual GDP. If the prediction proves true, you do not
change your estimate of the natural rate. If, however, actual GDP is higher than
predicted, then monetary policy probably was more stimulative than you had thought,
implying that the difference between the real fed funds rate and the natural
rate of interest was more negative than you thought. The estimate of the natural
rate goes up by an amount proportional to the GDP prediction error, or "surprise." If
GDP is lower than predicted, the estimate of the natural rate is lowered. This
procedure is designed to allow for the possibility of a change in the natural
rate and also to protect against overreacting to every short-term fluctuation
The final estimate for the natural rate of interest that Laubach and
Williams get for mid-2002 is about 3%, coincidentally not far from the
of the real funds rate (Figure 2). But, for other periods, the estimates range
from a little over 1% in the early 1990s to over 5% in the late 1960s. The
high estimates in the late 1960s reflect the fact that output was growing
expected, given the history of real interest rates and the prevailing estimates
of the natural rate of interest. The natural rate estimates fell during the
early 1990s owing to the slow recovery from the recession of 1990-1991
even with low
real fed funds rates.
These results show that the procedure for estimating the
natural rate using the Kalman filter was not "fooled" by the
period of the late 1960s and 1970s, but instead recognized it as one
of excessive growth and inflationary
pressures resulting from real rates that lay well below the true natural rate
of interest. Similarly, it was not fooled by the early 1980s into thinking
that the natural rate had increased sharply because policy had tightened;
it recognized that real rates well above the natural rate had contributed to
the slowing of economic activity and, in fact, had little longer-term implications
for real interest rates.
Economists have made progress in estimating the natural rate
of interest in recent years. But they have not yet hit a "home run." For
example, although the Kalman filter has proven its usefulness in this
effort, it is important to
note that the resulting estimates are not very precise; that is, from a statistical
viewpoint, we cannot be confident that these estimates are correct. Furthermore,
as Orphanides and Williams (2002) point out, these estimates are sensitive
to the choice of statistical methods, which further obscures our ability
the natural rate of interest accurately.
John C. Williams
Senior Research Advisor
Bomfim, Antulio. 1997. "The Equilibrium Fed Funds Rate and the Indicator
Properties of Term-Structure Spreads." Economic Inquiry 35(4), pp.
Laubach, Thomas. 2003. "New Evidence on the Interest Rate Effects
of Budget Deficits and Debt." Board of Governors of the Federal
Reserve System, FEDS Working Paper 2003-12 (April).
Laubach, Thomas, and John C. Williams. 2003. "Measuring the Natural
Rate of Interest." The Review of Economics and Statistics 85(4)
Orphanides, Athanasios, and John C. Williams. 2002. "Robust Monetary
Policy Rules with Unknown Natural Rates." Brookings Papers on
Economic Activity, 2, pp. 63-145.
Wicksell, Knut. 1936. Interest and Prices (tr. of 1898 edition by R.F.
Kahn). London: Macmillan.