FRBSF Economic Letter
2007-10; April 13, 2007
Do Monetary Aggregates Help Forecast Inflation?
The European Central Bank (ECB) and the Federal Reserve
share a similar goal, price stability, and their strategies
to pursue their goals are similar--with one notable difference.
When considering long-term risks to price stability, the
ECB places an explicit emphasis on the link between prices
and measures of the money supply (also known as monetary
aggregates); the Federal Reserve System, in contrast, does
not specifically emphasize monetary aggregates.
To explore this difference, the ECB held a conference
in November 2006 ("The Role of Money: Money and Monetary
Policy in the Twenty-First Century";
this site also contains links to the papers discussed
below). Fischer et al. showed that including a broad
monetary aggregate
in the ECB's inflation-forecasting model improved its
accuracy. Galí's discussion of that paper argued,
however, that the results were somewhat precarious and
inconsistent
with the more recent experience in the U.S. Furthermore,
Woodford argued that most monetary policy goals can be
obtained without focusing on the money supply; while
he agreed that using monetary aggregates, as the ECB
does,
can have small advantages, he argued that those advantages
come at the cost of losing transparency and accountability
in the conduct of monetary policy. Subsequently, this
latter point was also made by an OECD report (2007),
which concluded,
in addition, that monetary aggregates "appear to
have lost much of their predictive power in the 2000's,
at least
so far" (p. 11).
These differences reflect an ongoing debate among economists.
While the quantity theory of money (notably Friedman
1987) establishes a direct link between monetary aggregates
and
the inflation rate, and still dominates introductory
economics textbooks, modern macroeconomic theory does not
assign
money an important role in the conduct of monetary policy.
To shed some light on this debate, this Economic
Letter investigates one aspect in which monetary aggregates
can contribute to monetary policy, specifically, by providing
better forecasts of future inflation. Our approach compares
the historical predictive value of monetary aggregates
in forecasting inflation in the U.S. and in the euro
area.
Several disclaimers are worth making at the outset. Our
forecasting exercises are not meant to replicate the
forecasting models at the ECB or the Federal Reserve. In
addition,
the forecasting evaluation is done on historical data
and contains no predictions about future inflation. Finally,
we steer clear of theoretical economic justifications
in
favor of or against monetary aggregates as these were
presented eloquently in several of the ECB conference papers.
With
these caveats in mind, the predictive evaluation reported
here provides compelling evidence that monetary aggregates
have negligible predictive power for U.S. inflation,
although the evidence is more mixed for the euro area.
The forecasting exercise
Our objective is simple: to evaluate whether forecasts
of inflation improve when monetary aggregates are included
in a model with well-known predictors of inflation. To
forecast inflation, say, six months into the future,
we examine how historical observations of inflation correlate
with these predictors observed six months prior. If the
underlying structure of the economy is the same, the
historical
average of these correlations will approximately characterize
the correlation between the economic variables today
and inflation six months hence.
In judging the validity of any statistical test, there
are pitfalls to watch for. One is that results showing
that the monetary aggregates do improve forecast accuracy
may be dubious because it is possible that our model
does not include genuinely predictive variables or because
our
model is too unsophisticated. Either case increases the
chances of finding variables that are spuriously good
predictors. For example, if we were forecasting the fall
harvest of
grapes in the Napa Valley, and we omitted winter rainfall
but included winter sales of umbrellas, the latter would
look like a good predictor. Thus, it would be more definitive
to find that monetary aggregates are a poor predictor
of inflation than that they improve the accuracy of the
forecast.
Another pitfall is that we may include too many variables,
in that some will be good predictors simply by chance,
making our forecasts more uncertain. For example, consider
what happened to Powerball officials in the March 30,
2005, drawing. The chances of getting five out of six numbers
correct are about one in three million. Given the number
of tickets sold across 29 states, officials expected
four
or five second place claims but got 110 instead. Why?
Because many players had chosen their numbers from fortune
cookies
that came from the same factory in New York. While the
fortune cookie numbers happened to be good "predictors" of
the winning combination once, they are unlikely to be so
again.
A third issue in evaluating the accuracy of a forecast
is its "path dependence." Because current inflation
is correlated with past inflation, so are long-run forecasts
with short- and medium-run forecasts. Therefore, when comparing
the accuracy of different forecasts, one should evaluate
their predictive power simultaneously at short, medium,
and long horizons. By analogy, we may be quite uncertain
whether a train leaving Washington, D.C., is headed for
Boston or Miami but it would not make sense to predict
that if it is headed for Miami, it will have intermediate
stops in Philadelphia and New York. For this reason, we
focus on comparing forecast paths (train lines) rather
than forecasts at particular horizons (train stations).
With these three features in mind, our interest is out-of-sample
predictive ability; that is, our experiments reserve
part of the sample for estimation and then use the remaining
sample to compare our forecasts with actual core inflation.
In the U.S., we save the last three years of data for
out-of-sample
comparisons; in the euro area, we reserve only the last
18 months because the sample is shorter. We examine forecast
paths over the following one, three, six, nine, and twelve
months.
 We use the following data: core CPI inflation (excluding
food and energy), measures of M2, M3 money stock, and
M3C, a corrected version of M3 for the euro area; industrial
production in the U.S. and real GDP in the euro area;
the
federal funds rate for the U.S. and the 4-month Euribor
for the euro area. All variables are available monthly,
except for the euro area real GDP, which is quarterly.
The U.S. sample is January 1985-January 2007 (M3 is available
only until February 2006); the euro area sample is January
1997-September 2006 (M3C is available only since January
1999).
Results
We first look at the overall out-of-sample differences
between forecasts that include and exclude different
measures of monetary aggregates. Therefore, we take the
average
deviation of the forecasts from actual core inflation
over the entire forecast path by adjusting for the correlation
of forecasts across horizons (like the correlation of
stations
in a rail line). Generally, we find that the forecast
gains of including monetary aggregates are concentrated
toward
shorter prediction horizons, six months or less; over
nine and twelve months, such forecasts become more imprecise.
Meanwhile, whereas the differences in forecasting accuracy
for the U.S. are extremely small (usually less than 3%),
those for the euro area can be quite large with gains
as
big as 54% and losses as extreme as 142%.
As an example, Figure 1 illustrates the twelve-month
forecasts made by including and excluding M2, and the actual
path
of inflation between February 2006 and January 2007.
For the U.S., the forecasts with and without M2 are very
close
to each other (although they both miss the run-up in
inflation in the middle of the period). For the euro area,
the forecasts
with and without M2 differ significantly. This forecast
is a bit like the "fortune cookie" example: including
M2 does seem to result in a more accurate forecast even
though on average across all dates in the evaluation sample,
including M2 results in a forecasting loss for twelve-month-ahead
forecasts. These results suggest that monetary aggregates
provide, at best, a very small refinement in U.S. inflation
forecasts, the picture being considerably murkier for the
euro area.
 In order to avoid the "fortune cookie" pitfall,
therefore, a more formal statistical metric is needed.
That is, we must ask: What proportion of out-of-sample
forecasts made by excluding monetary aggregates (either
M2 or M3) is statistically indistinguishable from forecasts
made by including these monetary aggregates in the forecasting
model? Figure 2 offers some answers. Not surprisingly,
for the U.S., about two-thirds of one-month-ahead forecasts
that excluded monetary aggregates and virtually all forecasts
at longer horizons are equivalent to forecasts that included
monetary aggregates. For the euro area, the proportion
of forecasts with significant differences between including
and excluding monetary aggregates is higher, especially
for the uncorrected measure of M3. However, usually these
differences occur because forecasts that include monetary
aggregates are less accurate, not more.
Conclusions
Our results for the U.S. accord well with Galí's
and Woodford's arguments and suggest that there is no predictive
power to monetary aggregates when forecasting inflation:
whatever information monetary aggregates have seems to
be already contained in measures of past inflation, economic
activity, and interest rates. Evidence for the euro area
is far more ambiguous. Over some horizons (usually in the
short run, but not the long run), there appear to be benefits
to including monetary aggregates in the forecasting model,
although it is probably too early (in terms of the depth
of our analysis and the scarcity of data) to tell whether
monetary aggregates are the "umbrellas" or the "rainfall" of
the euro area's inflation harvest. Overall, our analysis
provides little reason to dispute current practices at
either central bank.
Galina Hale
Economist, FRBSF
Òscar Jordà
Associate Professor, UC Davis,
and Visting Scholar, FRBSF
References
[URLs accessed April 2007.]
Fischer, B., M. Lenza, H. Pill, and L. Reichlin. 2006. "Money
and Monetary Policy: The ECB Experience 1999-2006." Unpublished
manuscript.
Friedman, Milton. 1987. "Quantity Theory of Money." In
The New Palgrave: A Dictionary of Economics, v. 4,
pp. 3-20. London: Palgrave Macmillan.
Galí, J. "Discussion
of 'Money and Monetary Policy: The ECB Experience 1999-2006.'"
OECD.
2007. Economic
Survey of the Euro Area 2007. Paris: OECD. Woodford, Michael. 2006. "How
Important Is Money
in the Conduct of Monetary Policy?" Unpublished manuscript.
Opinions expressed in this newsletter
do not necessarily reflect the views of the management
of the Federal Reserve Bank of San Francisco or of the
Board of Governors of the Federal Reserve System. Comments?
Questions? Contact
us via e-mail or write us at:
Research Department
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