2006-37; December 22, 2006
Will Moderating Growth Reduce Inflation?
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The December 12, 2006, statement of the Federal Open
Market Committee (FOMC) said, "Readings on core inflation
have been elevated, and the high level of resource
utilization has the potential to sustain inflation
pressures." The link between "inflation pressures" and
the "level of resource utilization" is formalized
by the Phillips curve, which says that short-term movements
in inflation and unemployment (a measure of labor resource
utilization) tend to go in opposite directions. For
example, when strong economic activity makes the labor
market tight, inflation is likely to increase. Technically, "tightness" in
the labor market means that the unemployment rate is
below its natural (or equilibrium) rate, a measure
that is not directly observable but is derived from
estimates. Pioneering research by economists Edmund
Phelps and Milton Friedman during the 1960s asserted
that monetary policy could not keep the unemployment
rate permanently below the natural rate--a view that
is now universally accepted. Phelps is the most recent
recipient of the Nobel Memorial Prize in economic science.
Friedman was awarded the same prize in 1976.
A much debated question among economists is the usefulness
of the Phillips curve as a tool for forecasting inflation
(see Lansing 2002 for an introduction to this debate).
This Economic Letter presents some quantitative comparisons
between a Phillips curve-based inflation forecast
and an alternative forecast that is constructed as
moving average of past observed rates of inflation.
Methods of forecasting inflation
The Phillips curve is a commonly used framework for forecasting inflation, but difficulties in knowing the true value of the natural rate, together with empirical instabilities in the inflation-unemployment relationship can lead to significant forecast errors. A simple estimated version of a Phillips curve can be obtained by regressing the one-quarter change in (annualized) quarterly inflation on the lagged unemployment rate and a constant term. Inflation is measured using the "core" personal consumption expenditures (PCE) price index, which excludes food and energy components. The estimated coefficient on the unemployment rate is the "slope" of the Phillips curve. The ratio of the estimated constant term to the absolute value of the slope coefficient is an estimate of the natural rate of unemployment.
Figure 1 plots the natural rate estimates obtained
from a series of 10-year rolling regressions. The estimated
value of the natural rate is quite volatile for sample
periods that span the late 1990s. Since 2001, however,
the rolling-regression estimates are more stable and
track reasonably well with the natural rate series
constructed by the Congressional Budget Office (CBO).
Although not shown, the rolling-regression estimates
of the slope coefficient also exhibit a fair amount
of variability--reflecting the fundamental imprecision
of the link between inflation and economic activity.
The magnitude of the estimated slope coefficient has
approached zero in recent decades, suggesting that
the Phillips curve has become less useful for forecasting
inflation. Along these lines, Federal Reserve Bank
of Richmond President Jeffrey Lacker (USA Today 2006,
p. B8) recently stated his view that "Moderating
growth doesn't change inflation. Central banks change
Numerous research studies have demonstrated that
forecasts of U.S. inflation based on empirical Phillips
models can frequently underperform simple alternative
forecasts that only employ data on inflation itself.
A naive random walk forecast says that future inflation
will be the same as current inflation. A study by
Atkeson and Ohanian (2001) showed that a random walk
outperforms a Phillips curve-based inflation forecast
from 1984 onwards.
A random walk forecast uses data only on the most
recent inflation rate. A more general forecasting approach
uses a moving average of past rates of inflation, with
recent data receiving more weight than older data.
This "weighted moving average" forecast is
known to be more accurate when inflation movements
are governed by both temporary and permanent shocks.
The underlying assumption is that temporary shocks
push inflation away from a long-run target rate but
permanent shocks can shift the target over time.
The optimal weights assigned to past inflation in
the forecast rule are governed by a mathematical formula
that depends on the ratio of volatilities of permanent
to temporary shocks. A higher volatility ratio means
that a larger fraction of observed movements in inflation
are viewed as permanent, thus increasing the weight
assigned to recent data in the forecast rule. The volatility
ratio can be identified from the data by measuring
the persistence of one-quarter changes in the inflation
rate, as shown by Lansing (2006). The methodology reveals
a downward trending volatility ratio over the last
decade, indicating a reduced likelihood of a permanent
shift (either upwards or downwards) in the Fed's inflation
target. This evidence is consistent with the idea of "well-anchored
inflation expectations" in describing the current
environment (see, for example, Williams 2006).
Quantitative forecast comparison
Figure 2 plots one-year-ahead inflation forecasts
together with realized inflation data over the period
to 2006:Q3. The distance between the forecasts and
the realized data represents the forecast error.
The metric for assessing forecast accuracy is the mean
squared error of the forecast.
Each quarter, the latest Phillips curve regression
equation is iterated four quarters ahead to compute
a predicted average inflation rate for the coming
year. The predicted trajectory of the unemployment
constructed by assuming that the prevailing unemployment
rate will gradually adjust to the most recent estimate
of the natural rate.
The weighted moving average forecast is constructed
using the weights implied by the volatility ratio
identified from a 10-year rolling sample. Forecasts
quarter are set equal to the one-quarter-ahead prediction,
reflecting the idea that the best forecast of the
future inflation target is the current estimate of
The weighted moving average forecast outperforms
both the Phillips curve and a random walk forecast
over the full data sample that runs from 1975:Q1 to
The weighted moving average also delivers the best performance in two out of
three subperiods, namely, during the volatile inflation era from 1975:Q1 to
1984:Q4 and the stable inflation era from 1996:Q1 to
2006:Q3. The random walk forecast
(not shown) does slightly better than the weighted moving average during the
intermediate period that runs from 1985:Q1 to 1995:Q4. These results are in
line with previous studies which find that simple inflation-based
forecast rules can
routinely outperform Phillips curve-based forecasts.
In Figure 2, the Phillips curve predicts a mild upward
drift in core PCE inflation over the next two years
as the unemployment rate rises towards the natural
The weighted moving average predicts a slight decrease in core PCE inflation
from 2006:Q3 to 2006:Q4, followed by a leveling out thereafter at the current
estimate of the long-run inflation target (which is slightly below 2.4%).
The unemployment "gap" is the percentage-point difference between the
natural rate and the prevailing unemployment rate. In addition to appearing in
Phillips curve models, the gap plays a role in simple Taylor-type policy rules,
which are often used to establish a rough range for judging the appropriate level
of the federal funds rate to achieve a balance between the Fed's competing goals
of keeping inflation low while promoting maximum employment. In Figure 1, the
2006:Q3 unemployment gap is positive using either measure of the natural rate.
Figure 3 plots the predicted level of the federal
funds rate using a Taylor-type rule with a weight of
1.0 on the unemployment gap and a weight of 0.5 on
gap between actual and "desired" inflation. The unemployment gap is
constructed using the less volatile CBO natural rate series. Inflation here is
measured by the four-quarter change in the core PCE price index. In constructing
the figure, two values for the desired inflation target are considered: 1% or
2%, defining what is often viewed as the Fed's "comfort zone." Two
values for the long-run equilibrium real rate of interest are considered: 2%
or 3%, reflecting typical empirical estimates.
As the figure shows, today's 5.25% funds rate is
slightly above the lower bound of the Taylor-type rule
prediction, in contrast to the 2002-2004 period, when
the funds rate was well below the lower bound. Still, the current stance of
could be tightened by more than 100 basis points without exceeding the upper
bound. Given the uncertainty about the true values of the inflation target,
the equilibrium real interest rate, and the natural
rate of unemployment, this exercise
does not say definitively whether policy is too tight or too loose. According
to the December 12 FOMC statement, "The extent and timing of any additional
firming that may be needed to address [inflation] risks will depend on the evolution
of the outlook for both inflation and economic growth, as implied by incoming
Empirical estimates suggest that changes in the level
of labor resource utilization, as measured by the unemployment
gap, appear to be less useful for forecasting
inflation than in the past. If anything, the Phillips curve predicts that core
PCE inflation will drift upward over the next two years, because the prevailing
unemployment rate is below estimates of the natural rate.
A weighted moving average forecast attempts to disentangle
permanent versus temporary movements in the inflation
rate. This decomposition is relevant to current policy
discussions, because some of recent increase in core PCE inflation could be
to temporary factors, such as pass-through from high energy prices and a shift
in the demand for rental housing that affects the shelter-cost component of
core inflation. A retrospective evaluation of forecast
accuracy shows that the weighted
moving average forecast generally outperforms both the Phillips curve and a
random walk forecast in predicting core PCE inflation
one year ahead. The weighted moving
average predicts that core PCE inflation will experience only a slight drop
going forward because the current rate is close to
the estimated inflation target.
Kevin J. Lansing
[URLs accessed December 2006.]
Atkeson, A., and L.E. Ohanian. 2001. "Are Phillips
Curves Useful for Forecasting Inflation?" FRB
Minneapolis Quarterly Review (Winter) pp. 2-11.
Lansing, K.J. 2002. "Can the Phillips Curve Help
Forecast Inflation?" FRBSF Economic Letter 2002-29
Lansing, K.J. 2006. "Time-Varying U.S. Inflation
Dynamics and the New Keynesian Phillips Curve." FRBSF
Working Paper 2006-15.
USA Today. 2006. "Dissenting Fed Official Says
Inflation a Risk." September 6.
Williams, J.C. 2006. "Inflation Persistence in
an Era of Well-Anchored Inflation Expectations." FRBSF
Economic Letter 2006-27 (October 13).
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