Publishing Consumer Price Indexes to Three Decimal Places:
Questions and Answers
Effective with the release in February 2007 of the January 2007 Consumer Price Index (CPI), the Bureau of Labor Statistics (BLS) will begin to publish its consumer price indexes rounded to three decimal places. Percent changes will be calculated from the three decimal place indexes. Those percent changes will continue to be published to one decimal place.
The questions and answers below provide further information.

What indexes are affected by this change?

Why is BLS making this change?

Can you give me an example?

How often did the monthly published percent change based on indexes rounded to one decimal place differ from percent changes based on unrounded indexes?

Why are the indexes being rounded to three decimal places rather than two decimal places in order to calculate the onedecimal place percent change?

Does this change reduce the sampling error in the CPI?

Why don’t you publish the percent changes to more than one decimal place?

Will you republish historical indexes (i.e., prior to 2007) to three decimal places?

How can I find out more information about this change?

This change will be made to all CPIs calculated by BLS. This includes the All items
consumer price index and all component indexes for the CPIU, CPIW, and CCPIU, for the
U.S. City Average and for all other published areas.

This change will make the published percent changes more precise. Historically,
the CPI published index values rounded to one decimal place. The published percent changes
were derived from those published index values, so that users could replicate the
calculations. Because both the numerator and denominator index values were rounded to one
decimal place, there was a significant probability of obtaining a different percent change
using the published oneplace values than with indexes with more precision. Percent
changes now will be calculated using indexes rounded to three decimal places; the percent
changes will continue to be published to one decimal place.

Suppose an index increased from 203.189 to 203.547. The percent change for that
index will now be published as 0.2 percent, as 203.547/203.189 = 1.00176 = 0.176 percent,
or 0.2 percent when rounded to one decimal place. In contrast, this index historically
would have been published to one decimal place, and would therefore have been published as
203.2 and 203.5, respectively. The published percent change would have been
203.5/203.2 = 1.00148 = 0.148 percent, or 0.1 percent when rounded to one decimal place.

While the answer to this question varies by index series, for the all items index and for the index for all
items less food and energy, the published 1month percent changes based on indexes rounded
to one decimal place differed from 1month changes based on unrounded indexes
approximately 25 percent of the time. Using threedecimal place indexes, the probability
of the published percent change differing from that based on unrounded indexes decreases
to well under 1 percent.

Using twodecimal place indexes, the probability of the percent change differing
from that based on the unrounded indexes would be around 2.5 percent. As noted before, by
basing percent changes on threedecimal place indexes, that probability decreases even
further, to below one percent.

No, it simply makes the published percent changes more precise by better
reflecting the underlying data. The data underlying the CPI are still subject to the same
degree of sampling error, since the index is based upon a sample of prices, not the
complete universe of retail prices. BLS calculates and publishes estimates of variance
and their associated standard errors annually. These data can be used to construct
confidence intervals to determine whether the change in a particular index is
statistically significant. For the latest data, see “Variance Estimates for Changes in
the Consumer Price Index, January 2005  December 2005” in the CPI Detailed Report,
February 2006, which also is available at http://www.bls.gov/cpi/cpivar2005.pdf.

In general, the sampling error associated with published CPI percent changes
suggests that continuing to publish percent changes to one decimal place remains
appropriate.

No. Indexes published before 2007 were published to one decimal place; they
remain the official CPIs for years prior to 2007. BLS will provide unofficial historical
data on a not seasonally adjusted basis calculated to three decimal places for 19872006.
Seasonally adjusted historical data based on threedecimal place indexes will not be
recalculated or made available.

For more information contact Patrick Jackman or Ken Stewart either by telephone
at (202) 6916952 and (202) 6916966, respectively, or by electronic mail at
Jackman.Patrick@bls.gov or Stewart.Ken@bls.gov
Last Modified Date: August 16, 2006
