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.

1. What indexes are affected by 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 CPI-U, CPI-W, and C-CPI-U, for the U.S. City Average and for all other published areas.

2. Why is BLS making this change?

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 one-place 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.

3. Can you give me an example?

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.

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

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 1-month percent changes based on indexes rounded to one decimal place differed from 1-month changes based on unrounded indexes approximately 25 percent of the time. Using three-decimal place indexes, the probability of the published percent change differing from that based on unrounded indexes decreases to well under 1 percent.

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

Using two-decimal 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 three-decimal place indexes, that probability decreases even further, to below one percent.

6. Does this change reduce the sampling error in the CPI?

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 www.bls.gov/cpi/cpivar2005.pdf.

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

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

8. Will you re-publish historical indexes (i.e., prior to 2007) to three decimal places?

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 1987-2006. Seasonally adjusted historical data based on three-decimal place indexes will not be recalculated or made available.