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Consumer Price Index

## 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.

Table 1: 12-month percent changes in CPI-U, U.S. city average series for all items with different bases
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.

Table 2: Rebasing the CPI-U, U.S. city average series for all items
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.