March 24, 1999 (The Editor’s Desk is updated each business day.)
New CPI estimator expected to lower
inflation rate by 0.2 percent
Effective with January 1999 data, the Bureau
of Labor Statistics began using a "geometric mean" formula to calculate indexes
that make up about 61 percent of the Consumer Price Index (CPI-U). Research based on an
experimental all-geometric version of the CPI (CPI-U-XG in the chart) suggests the new
formula will reduce the annual rate of increase in the CPI-U by about 0.2 percentage point
per year.
![CPI using arithmetic and geometric means](https://webarchive.library.unt.edu/web/20120925101934im_/http://www.bls.gov/opub/ted/images/1999/Mar/wk4/art03.gif)
[Chart data—TXT]
The old "arithmetic mean" formula measured changes in the cost of fixed
quantities of items. The new "geometric mean" formula is a better measure of
changes in the cost of living when people reduce consumption of items whose prices have
risen relatively rapidly, and increase consumption of items whose prices have not.
Let’s look at an example. Start with a market basket containing a pound of fresh
carrots and a pound of fresh peas, both at $1.00 a pound. Suppose the price of peas goes
to $1.50 per pound. In the old formula, spending for the basket would rise from $2.00 to
$2.50, representing a price index increase of 25 percent: [($1.00 X 1 pound of carrots +
$1.50 X 1 pound of peas)]/[($1.00 X 1 pound of carrots + $1.00 X 1 pound of peas)] =
$2.50/$2.00 = 1.25. The quantities bought remained the same; the consumer just paid the
higher price, and shelled out the $2.50.
The new geometric mean formula would look like this: [(1.00/1.00) 0.5 of spending
always on carrots] X [(1.50/1.00) 0.5 of spending always on peas]= 1.0 X
1.225 = 1.225, representing a price index change of 22.5 percent. Here, the spending
shares remain the same, so the consumer implicitly buys 0.816 pounds of peas at a
buck-fifty and 1.225 pounds of carrots at a dollar, and spends only $2.45 in total. That
is, the CPI now reflects the fact that people will adjust some of their spending habits to
account for rising or declining prices.
This information is a product of the Consumer Price
Index program. For more information see "Incorporating a geometric mean formula into the CPI," Monthly
Labor Review, October 1998. In their simplest forms, the geometric mean of a set of
N numbers is obtained by taking the Nth root of their product, while the arithmetic mean
is obtained by dividing the sum of the numbers by N. The application of these basic
concepts to the construction of the CPI is considerably more complex. For more
information see, "The Experimental CPI using
Geometric Means (CPI-U-XG)."
Of interest
Spotlight on Statistics: National Hispanic Heritage Month
In this Spotlight, we take a look at the Hispanic labor force—including labor force participation, employment and unemployment, educational attainment, geographic location, country of birth, earnings, consumer expenditures, time use, workplace injuries, and employment projections.
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