View original document

The full text on this page is automatically extracted from the file linked above and may contain errors and inconsistencies.

December 1. 1991

Federal Reserve Bank of Cleveland

Median Price Changes: An
Alternative Approach to Measuring
Current Monetary Inflation
by Michael F. Bryan and Christopher J. Pike

Xrice movements are the channel
through which market information is
transmitted. An increase in one price relative to others is the signal that directs
resources and rations consumption. In
other words, markets operate through the
' distribution of prices.
Inflation, on the other hand, is a monetary phenomenon that determines the
underlying level of all price changes; it
has virtually nothing to do with the transmission of market information. Indeed,
one fundamental problem with inflation is that it can be confused with relative price movements, obscuring the
transmission of market information and
reducing market efficiency.
Distinguishing between inflation and
relative price movements is also important for the conduct of monetary policy.
Without a clear distinction between the
two, policymakers may inadvertently
react to relative price changes and
thereby complicate the economy's adjustment to a new set of prices. By not
reacting to changes in the inflation rate,
they might allow unnecessary pricelevel fluctuations.
People who are interested in the current rate of inflation, either for practical
or for academic reasons, can consult a
variety of measures or price indexes.
By far the most popular of these is the

ISSN 0428-1276

Consumer Price Index (CPI), compiled
monthly by the Bureau of Labor Statistics. The CPI measures the average price
of an array of goods and services purchased by households, but because it is
constructed as a weighted mean of all
consumer prices, it does not discriminate
between relative price changes and inflation. Indeed, the CPI may rise when the
price of just one commodity increases.
This Economic Commentary discusses
the limitations of mean price statistics as
inflation indicators and suggests a welldefined and easily computed alternative
— median price changes — as a better
signal of current monetary inflation.
• Inflation and Price Changes
A common textbook definition of inflation is "a rise in the general level of
prices." Despite its outward simplicity,
this description is a bit vague: The
prices of what? And what constitutes a
"general" price rise?
The issue of what items to include in an
inflation index has been considered at
length. The consensus is that measures
of inflation should be based on prices of
consumer goods and services, since it is
the utility arising from these that ultimately defines the prosperity of an economy.
If this were the only consideration,
the CPI would be a reasonably accurate indicator of inflation. Commodities

The course of economic history is
replete with substantial price disturbances. Whenever such disturbances
have occurred, two different explanations have been offered. One, common
to all disturbances, is that the price
movements reflect changes in the
quantity of money.... The other explanation has been in terms of some
special circumstances of the particular
occasion: good or bad harvests; disruptions in international trade;... and so
on in great variety.
Milton Friedman

included in the CPI are weighted according to their share of total household expenditures in some base period,
so that changes in the index from one
period to the next are broadly reflective
of changes in the representative household's current cost of living.4
But the strength of the inflation signal
in goods and services prices is not necessarily related to an item's share of the
typical household budget As a monetary
phenomenon, inflation should influence
the price of all goods and services
equally. The inflationary signal in the
price of a new pair of shoes is theoretically the same as that in the price of

shoe leather or, for that matter, in t..- ir :e
of cows. Tliere is no reason to expect
movements in the price of one to be a
clearer indicator of inflation than movements in the prices of the others.
• The Core Rate of Inflation
To accurately gauge the economy's current inflationary momentum, we must
somehow disentangle relative price
"noise" from the inflation signal. (It may
be that inflation also temporarily affects
the distribution of price changes. We will
return to this subject in the final section.)
The most common way to reduce the
influence of relative price fluctuations
on the price index is simply to subtract
those goods thought to be affected by
temporary or otherwise special factors.
The CPI excluding food and energy
goods, the index's two most volatile
components, is often referred to as the
core rate of inflation. Clearly, the object of this modified index is to clarify
the inflation signal in the price data, because removing food and energy goods,
which account for roughly 25 percent
of the CPI, substantially alters the
index's implied weights and limits its
usefulness as a cost-of-living measure.
The problem with this approach is
guessing which prices are being influenced by special factors. This introduces more than a little subjectivity
into the inflation-monitoring process.
Besides, all goods and services prices
reflect relative price changes to some
degree, and it is impossible to know
how persistent these changes will be.
We suggest an alternative statistic —
the median consumer price change.
The median of a set of data is the value
of the middle observation when all
items are arranged in either ascending
or descending order of magnitude. In
effect, the median consumer price
change is the CPI less everything but
the price change that lies in the middle
of the continuum. Since only the order,
not the values, of the various price
changes is used in its calculation, the
median is a central tendency statistic
that is largely independent of the data's
distribution. The median also has the


Apparel and upkeep
Food and beverages
Other goods and services
Medical care
Mean change (equal-weighted)
CPI (expenditure-weighted)
CPI excluding energy
Median price change


Share of Household





a. CPI relative importance. December 1989.
SOURCE: U.S. Department of Labor, Bureau of Labor Statistics.

intuitively appealing property of lying
closer to the majority of price changes
than does any alternative measure.
• The Mean versus the Median
A Recent Example. To illustrate the
usefulness of the median as an inflation
indicator, consider the distribution of
price changes that occurred immediately following Iraq's invasion of Kuwait last year. Table 1 lists, in ascending order, the annualized percentage
price changes in the CPI's seven major
components between July and October
1990. Rates of price increase varied
widely during this three-month period,
from a low of 2.3 percent for apparel
and upkeep to a high of 27.9 percent
for transportation.
We computed three measures of central
tendency from these price data: a simple average (in which each of the seven
components was weighted equally), an
expenditure-weighted average (as used
to calculate the CPI), and the median
price change.
In the case of a simple average, the annualized aggregate price change over
the sample period was 8.4 percenL Note,
however, that prices in five of the seven components rose at a substantially
lower rate, as the average was heavily
influenced by the huge rise in transportation costs brought about by soaring

energy prices. Because transportation
costs command a disproportionate
share of total household expenditures
(17.1 percent), the expenditureweighted average price change was an
even higher 9.1 percent.
The high CPI increases recorded during
this period were widely dismissed as a
relative disturbance, not a persistent monetary inflation, because the rise in prices
originated in energy commodities. Thus,
analysts pointed to the CPI less energy
goods, at an annualized 4.5 percent, as a
better indicator of the economy's inflationary momentum.
Yet while the influence of the energy
component was obvious, relative price
disturbances were at work in all of the
CPI's components, though to a lesser
degree. For example, apparel prices
during this period were reported to be
temporarily depressed by seasonal
changeovers, while food prices were
said to be down as a result of a largerthan-expected harvest Medical care
costs, on the other hand, were characterized as rising relatively quickly due
to escalating insurance expenses.We
can minimize the impact of these and
other relative price fluctuations on the
inflation statistic by disregarding all
but the median price change. In our
example, this would be entertainment
costs, which rose at a 4.9 percent rate.



Percent change, annual rate






Twelve-month average percent change
* i
Mean A


' A.



11 it






V y Median






Although we offer the median price
change statistic as a simple and direct
way to track monetary inflation in the
short run, it is also interesting to note its
longer-term patterns. Figure 2 maps the
12-month trend in the CPI, in the

High relative price increases were also
seen during the late 1970s, although
the distribution of these increases was
more balanced (that is, the mean and
the median price changes followed
more comparable trends). In this case,
however, a jump in housing costs,
which are weighted at about 20 percent
of the CPI, pushed the change in the
overall index considerably higher than
the mean and median price changes.
Over the past 10 years, these three measures have tracked more closely. Nevertheless, movements in the median change
have continued to display considerably
less monthly volatility than the meanderived alternatives. Since 1984, the CPI's
annual growth rate has ranged from a low
of 1'/» percent in 1986 to a high of more
than 6 percent in 1990, as fluctuations in
oil prices introduced an important distortion to our interpretation of inflation as
measured by the overall index. The
median price change, on the other hand,
has oscillated within a very narrow 3[A to
4 Vi percent band over the last six and a
half years.


SOURCES: U. S. Department of Labor, Bureau of Labor Statistics: and Federal Reserve Bank of Cleveland.

A Historical Perspective. Figure 1
plots monthly changes in the CPI
against the median consumer price
change (calculated from 35 items) for
the January 1970 to July 1991 period.7
Note that the median price change was
substantially less volatile than the CPI,
a characteristic that conforms to our intuition that the monetary influence on
the price level is relatively stable from
month to month.8

increase brought on by a droughlinduced surge in food prices. (In 1973.
food prices rose at their fastest rate in
more than 50 years, accounting for
roughly half of the uptick in the CPI.)

median consumer price change, and in
the equal-weighted mean consumer
price change since January 1971.
Recall that differences between the CPI
and the mean change largely reflect the
influence of the CPI's expenditure
weights on the measurement of inflation,
while differences between the mean and
the median changes show the degree to
which consumer price movements are
unevenly distributed. During the inflation acceleration of 1973-74, the CPI
and the median change followed similar
patterns, while the mean change was substantially larger. In this instance, the distribution of price changes was prominently skewed by a large relative price

• Conclusion
Differences between changes in the
CPI and the median consumer price
change underscore the impact of the
distribution of price movements on our
monthly interpretation of inflation. The
median price change is a potentially
useful indicator of current monetary inflation because it minimizes, in a nonsubjective way, the influence of these
transitory relative price movements.
Whether the median change is an accurate long-run inflation measure is an
entirely different matter— one that depends in part on whether monetary inflation causes, or otherwise perpetuates,
relative price fluctuations. This is an
important area of research that needs to
be investigated more thoroughly.

It may be that mon "" . 'nflalion and
relative price changes aic related.
One possible linkage may be through a
monetary transmission mechanism,
whereby changes in the quantity of
money influence all prices, but at different times. If fluctuations in the distribution of price changes are predominately monetary in origin, then what
economists commonly disregard as relative price noise may actually be leading (or lagging) indicators of a more
broadly transmitted monetary inflation.
Unfortunately, without a better understanding of how money affects relative
prices, we will be unable to recognize
and exploit such early warning signals.
Moreover, if a monetary transmission
mechanism exists, then the CPI is also
a biased measure of long-run monetary
inflation, since it includes only current,
not future, consumption prices.
Under these conditions, economists
may need to consider asset price indexes, rather than consumer price indexes, for a reliable long-run measure
of monetary inflation.

Federal Reserve Bank of Cleveland
Research Department
P.O. Box 6387
Cleveland, OH 44101

Address Correction Requested:
Please send corrected mailing label to
the above address.

Material may be reprinted provided that
the source is credited. Please send copies
of reprinted materials to the editor.

• Footnotes
1. From Milton Friedman, The Optimal
Quantity of Money and Other Essays. Chicago:
Aldine Publishing Company, 1969, p. 171.
2. A zero inflation policy, then, is not one
that prevents any price movement. The
government could simply adopt such a policy
through wage and price controls. This, however, would cause more problems than it
would solve, since in the process of repressing inflationary signals, relative price signals
are also tost.
3. See, for example, Pierre Fortin, "Do We
Measure Inflation Correctly?" in Richard G.
Lipsey, ed., Zero Inflation. Toronto: CD.
Howe Institute, 1990, pp. 109-30.
4. The current base period is 1982-84.
5. In statistical terms, this is referred to as a
modified average.
6. While the mean can be thought of as a
measure of central value, the median is a measure of central location. Mathematically, the
median minimizes the mean absolute deviation
of the data ( SI Xi — ml / n), while the mean minimizes the mean squared deviation of the data
( £[ jr, — jf ] In), where m is the median and
I is the mean, for a number of observations, n.
7. These calculations are intended primarily
as an illustration. For actual monitoring purposes, a larger, more diverse array of prices
(including producer prices) would be desirable. Moreover, the CPI is a weighted mean
of prices, not of price changes, so deviations
between the percentage changes in the CPI
and the mean consumer price change statistic
are not entirely due to weighting. The influence of this definitional inconsistency was
found to be minimal, however.

8. The annualized monthly standard deviation of the medi n price change was about 1.9
percent, compared with 3.3 percent for the CPI.
9. By accurate, we mean unbiased. It may
be that if skewness in the price data is a
consequence of the inflationary process, the
median price change could provide a biased
estimate of inflation under certain conditions.
If so, we would expect such a bias to disappear as the price level stabilizes.
10. For a historical perspective on this relationship, see Daniel R. Vining, Jr. and
Thomas C. Elwertowski, "The Relationship
between Relative Prices and the General
Price Level," American Economic Review,
vol. 66 (September 1976), pp. 699-708.
11. This idea is discussed at length in
Armen A. Alchian and Benjamin Klein, "On
a Correct Measure of Inflation," Journal of
Money, Credit and Banking, vol. 5 (February
1973), pp. 173-91.

Michael F. Bryan is an economic advisor and
Christopher J. Pike is a senior research
assistant at the Federal Reserve Bank of
Cleveland. The authors wish to thank David
Altig, John Carlson, and William Gavin for
comments on an earlier draft of this article.
The views stated herein are those of the
authors and not necessarily those of the Federal Resene Bank of Cleveland or of the
Board of Governors of the Federal Reserve

U.S. Postage Paid
Cleveland, OH
Permit No. 385