An analysis concluding that inflation measures based on median price changes are a better indicator than measures based on mean price changes.Inflation (Finance) ; Consumer price indexes

Christopher J. Pike

Michael F. Bryan

English

Research Papers in Economics

December 1. 1991
eCONOMIG
COMMeNTORY
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 rel-
ative 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 mon-
etary phenomenon that determines the
underlying level of all price changes; it
has virtually nothing to do with the trans-
mission of market information. Indeed,
one fundamental problem with infla-
tion is that it can be confused with rela-
tive price movements, obscuring the
transmission of market information and
reducing market efficiency.
Distinguishing between inflation and
relative price movements is also impor-
tant 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 ad-
justment to a new set of prices. By not
reacting to changes in the inflation rate,
they might allow unnecessary price-
level fluctuations.
People who are interested in the cur-
rent 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
Consumer Price Index (CPI), compiled
monthly by the Bureau of Labor Statis-
tics. The CPI measures the average price
of an array of goods and services pur-
chased by households, but because it is
constructed as a weighted mean of all
consumer prices, it does not discriminate
between relative price changes and infla-
tion. 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 well-
defined and easily computed alternative
— median price changes — as a better
signal of current monetary inflation.
• Inflation and Price Changes
A common textbook definition of infla-
tion 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 ultimate-
ly defines the prosperity of an economy.
If this were the only consideration,
the CPI would be a reasonably accu-
rate indicator of inflation. Commodities
The course of economic history is
replete with substantial price distur-
bances. Whenever such disturbances
have occurred, two different explana-
tions have been offered. One, common
to all disturbances, is that the price
movements reflect changes in the
quantity of money.... The other ex-
planation has been in terms of some
special circumstances of the particular
occasion: good or bad harvests; disrup-
tions in international trade;... and so
on in great variety.
Milton Friedman
included in the CPI are weighted ac-
cording to their share of total house-
hold 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 house-
hold's current cost of living.
4
But the strength of the inflation signal
in goods and services prices is not neces-
sarily 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 theoreti-
cally the same as that in the price of
ISSN 0428-1276shoe 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 move-
ments in the prices of the others.
• The Core Rate of Inflation
To accurately gauge the economy's cur-
rent 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 ob-
ject of this modified index is to clarify
the inflation signal in the price data, be-
cause 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 in-
fluenced by special factors. This intro-
duces 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
TABLE 1 ALTERNATIVE CONSUMER PRICE
MEASURES, JULY TO OCTOBER 1990
Component
Annualized
Percent
Change
Share of Household
Expenditures
(percent)"
Apparel and upkeep
Food and beverages
Other goods and services
Entertainment
Housing
Medical care
Transportation
Mean change (equal-weighted)
CPI (expenditure-weighted)
CPI excluding energy
Median price change
2.3
3.7
4.0
4.9
5.7
10.2
27.9
8.4
9.1
4.5
4.9
6.1
17.9
6.3
4.4
42.0
6.2
17.1
—
—
—
—
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 immedi-
ately following Iraq's invasion of Ku-
wait last year. Table 1 lists, in ascend-
ing 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 sim-
ple 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 an-
nualized aggregate price change over
the sample period was 8.4 percenL Note,
however, that prices in five of the sev-
en components rose at a substantially
lower rate, as the average was heavily
influenced by the huge rise in transpor-
tation costs brought about by soaring
energy prices. Because transportation
costs command a disproportionate
share of total household expenditures
(17.1 percent), the expenditure-
weighted 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 mon-
etary 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 infla-
tionary 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 larger-
than-expected harvest Medical care
costs, on the other hand, were charac-
terized 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.I KJDKK I MONTHLY CONSUMER PRICE CHANGES
Percent change, annual rate
-5-
-10
1970 1975 1980 1985 1990
FIGURE 2 TWELVE-MONTH CONSUMER PRICE CHANGES
Twelve-month average percent change
1b
10
5
0
Mean A
[A
11 it
• Vy Median
••
* i
i
' A.
.•If
CPI
1
\\
\ A
1970 1975 1980 1985 1990
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 in-
tuition that the monetary influence on
the price level is relatively stable from
month to month.
8
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
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 infla-
tion acceleration of 1973-74, the CPI
and the median change followed similar
patterns, while the mean change was sub-
stantially larger. In this instance, the dis-
tribution of price changes was promi-
nently skewed by a large relative price
increase brought on by a droughl-
induced 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.)
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 meas-
ures have tracked more closely. Neverthe-
less, movements in the median change
have continued to display considerably
less monthly volatility than the mean-
derived 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 distor-
tion 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.
• 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 in-
flation because it minimizes, in a non-
subjective way, the influence of these
transitory relative price movements.
Whether the median change is an accu-
rate long-run inflation measure is an
entirely different matter— one that de-
pends in part on whether monetary in-
flation 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 dif-
ferent times. If fluctuations in the dis-
tribution of price changes are predomi-
nately monetary in origin, then what
economists commonly disregard as rel-
ative price noise may actually be lead-
ing (or lagging) indicators of a more
broadly transmitted monetary inflation.
Unfortunately, without a better under-
standing 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 in-
dexes, rather than consumer price in-
dexes, for a reliable long-run measure
of monetary inflation.
• 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, how-
ever, would cause more problems than it
would solve, since in the process of repress-
ing 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 meas-
ure of central location. Mathematically, the
median minimizes the mean absolute deviation
of the data ( SI Xi — ml / n), while the mean min-
imizes 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 pur-
poses, a larger, more diverse array of prices
(including producer prices) would be desir-
able. 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 influ-
ence of this definitional inconsistency was
found to be minimal, however.
8. The annualized monthly standard devia-
tion 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 disap-
pear as the price level stabilizes.
10. For a historical perspective on this rela-
tionship, 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 Fed-
eral Resene Bank of Cleveland or of the
Board of Governors of the Federal Reserve
System.
Federal Reserve Bank of Cleveland
Research Department
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Median price changes: an alternative approach to measuring current monetary inflation

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Median price changes: an alternative approach to measuring current monetary inflation

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