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Consumer Price Index
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Rebasing an index
It is sometimes necessary to use index values on a reference base that is not published. Common examples include adjusting a contract which was written to use an index with a discontinued historical base period or making a graph which shows the index values of series which have different base periods.
One alternate base is published for the Consumer Price Index for all urban consumers (CPI-U) in addition to the standard 1982-1984=100 base. It is the 1967=100 base. The December-December 12-month percent changes of the CPI-U U.S. city average all items series for these two bases over the period from 2000 to 2005 are shown in table 1.
| Year | Old base: 1967=100 (CUUR0000AA0) | Current base: 1982-1984=100 (CUUR0000SA0) |
|---|---|---|
|
2000 |
3.4 | 3.4 |
|
2001 |
1.6 | 1.6 |
|
2002 |
2.4 | 2.4 |
|
2003 |
1.9 | 1.9 |
|
2004 |
3.3 | 3.3 |
|
2005 |
3.4 | 3.4 |
Comparing the percent changes of these two series illustrates an important point: the only difference between series is the year we set to 100, the rate of change is exactly the same. Using this fact, we can adjust the base period of any index series for which we have data. First, we must find the relative for each data point in the series by dividing it by the previous data point. Then, we can select any period to set equal to 100 (the new base) and chain the relatives from that value by multiplying the previous month’s index value by the current month’s index relative. An example of this process is given in table 2.
| Month | Published index value (CUUR0000SA0) | Index relative | Relative value | Rebased index (January 2015=100) | Rebased index value (January 2015 =100) |
|---|---|---|---|---|---|
|
January 2015 |
233.707 | 100 | 100.000 | ||
|
February 2015 |
234.722 | 234.722 / 233.707 = | 1.00434 | 100 * 1.00434 = | 100.434 |
|
March 2015 |
236.119 | 236.119 / 234.722 = | 1.00595 | 100.434 * 1.00595 = | 101.032 |
|
April 2015 |
236.599 | 236.599 / 236.119 = | 1.00203 | 101.032 * 1.00203 = | 101.237 |
|
May 2015 |
237.805 | 237.805 / 236.599 = | 1.00510 | 101.237 * 1.0051 = | 101.753 |
|
June 2015 |
238.638 | 238.638 / 237.805 = | 1.00350 | 101.753 * 1.0035 = | 102.110 |
|
July 2015 |
238.654 | 238.654 / 238.638 = | 1.00007 | 102.11 * 1.00007 = | 102.117 |
|
August 2015 |
238.316 | 238.316 / 238.654 = | 0.99858 | 102.117 * 0.99858 = | 101.972 |
|
September 2015 |
237.945 | 237.945 / 238.316 = | 0.99844 | 101.972 * 0.99844 = | 101.813 |
|
October 2015 |
237.838 | 237.838 / 237.945 = | 0.99955 | 101.813 * 0.99955 = | 101.768 |
|
November 2015 |
237.336 | 237.336 / 237.838 = | 0.99789 | 101.768 * 0.99789 = | 101.553 |
|
December 2015 |
236.525 | 236.525 / 237.336 = | 0.99658 | 101.553 * 0.99658 = | 101.206 |
|
January 2016 |
236.916 | 236.916 / 236.525 = | 1.00165 | 101.206 * 1.00165 = | 101.373 |
|
February 2016 |
237.111 | 237.111 / 236.916 = | 1.00082 | 101.373 * 1.00082 = | 101.457 |
|
March 2016 |
238.132 | 238.132 / 237.111 = | 1.00431 | 101.457 * 1.00431 = | 101.893 |
|
April 2016 |
239.261 | 239.261 / 238.132 = | 1.00474 | 101.893 * 1.00474 = | 102.376 |
|
May 2016 |
240.229 | 240.229 / 239.261 = | 1.00405 | 102.376 * 1.00405 = | 102.791 |
|
June 2016 |
241.018 | 241.018 / 240.229 = | 1.00328 | 102.791 * 1.00328 = | 103.128 |
|
July 2016 |
240.628 | 240.628 / 241.018 = | 0.99838 | 103.128 * 0.99838 = | 102.961 |
|
August 2016 |
240.849 | 240.849 / 240.628 = | 1.00092 | 102.961 * 1.00092 = | 103.056 |
|
September 2016 |
241.428 | 241.428 / 240.849 = | 1.00240 | 103.056 * 1.0024 = | 103.304 |
|
October 2016 |
241.729 | 241.729 / 241.428 = | 1.00125 | 103.304 * 1.00125 = | 103.433 |
|
November 2016 |
241.353 | 241.353 / 241.729 = | 0.99844 | 103.433 * 0.99844 = | 103.272 |
|
December 2016 |
241.432 | 241.432 / 241.353 = | 1.00033 | 103.272 * 1.00033 = | 103.305 |
When new base years are introduced, BLS recalculates each index back to the beginning of that series to provide a consistent stream of data. Using the official series will minimize rounding differences occasionally caused by rebasing.
Last modified date: February 9, 2023