U.S. Bureau of Labor Statistics

Consumer Price Index

An Introductory Look at the Chained Consumer Price Index

Price Index Number Formula

• The C-CPI-U will be a new supplemental index, and will not replace the CPI-U and CPI-W.

• The C-CPI-U will use a different price index number formula from that used in the current CPI-U and CPI-W.
  
• The CPI-U and CPI-W use a Laspeyres formula to average indexes together. The C-CPI-U will use a "superlative" Tornqvist formula.

There are limits on publishing the C-CPI-U in real-time, because expenditure data is only available with a two year lag. We will publish an Initial C-CPI-U index in real time that is subject to revision. We will publish a revised Interim index in February of the following year. We will publish a Final C-CPI-U in February of the second year. The initial and interim indexes will approximate a superlative index with the information available at the time of publication. The final C-CPI-U will use prices and expenditure weights from the measurement period.

Initial Release

• indexes will be calculated using a geometric mean formula
• the geometric mean indexes will be adjusted using historical information on the ratio of the Tornqvist formula index to the geometric mean formula index.
• The expenditure weights will be those used by the CPI-U.

Interim Release

• indexes will be calculated using a geometric mean formula

• the geometric mean indexes will be adjusted using historical information on the ratio of the Tornqvist formula index to the geometric mean formula index.
• The expenditure weights will be those used by the CPI-U.

Final release

• indexes will be calculated using the Tornqvist formula
• both expenditure weights and prices will correspond to the measurement period.

Formulas are shown in the Technical Appendix available from http://www.bls.gov/cpi/super_cpi.pdf

The chart below shows the timing of C-CPI-U revisions.

TIMING OF C-CPI-U REVISIONS
		2003	2004	2005
	2003	INITIAL		FINAL
	2004		INITIAL
	2005			INITIAL

Cost-of-Living Indexes

As stated in the BLS Handbook of Methods, "The CPI provides an approximation to a Cost-of-Living Index as a measure of consumption costs." – Appropriate reflection of consumer substitution behavior can help provide an even closer approximation.

Appropriate reflection of consumer substitution behavior can help provide an even closer approximation.

Laspeyres formula

• uses spending behavior in previous periods
• assumes fixed quantity proportions
• does not reflect substitution

Geometric mean formula

• uses spending behavior in previous periods
• assumes fixed budget shares
• reflects substitution

Superlative formulas (such as Tornqvist formula)

• uses spending behavior in both the current and a previous period (consumer behavior observed, not assumed
• reflects observed substitution

Superlative indexes incorporate both current period and previous-period spending behavior. Under certain assumptions, they will more closely approximate a Cost-of Living index more closely than either a Laspeyres or a geometric mean index.

The following example shows simple examples of index construction of all three types:

Month 2

• Movie ticket price increases 60%
• Video rental price increases 0%
• Movie ticket quanity decreases 33%
• Video rental quantity decreases 10%

For Lower-level index aggregation, CPI-U, CPI-W and C-CPI-U use a "Hybrid " approach:

• The Laspeyres formula is used for some items, such as electricity, rent, and hospital services. Zero substitution within an item category is implicitly assumed.
• The Geometric Mean formula is used for most items, such as apples, jewelry, and admissions. Unitary substitution within an item category is implicitly assumed.

For Upper-level aggregation, the CPI-U and CPI-W use a Laspeyres formula, and assume zero substitution across items. The C-CPI-U will use a superlative formula, and will reflect substitution across items.

The "Chained" in the title refers to the frequency of expenditure base-period updates. Currently, the CPI-U and CPI-W are updated every two years; the C-CPI-U will be updated every month.

Last Modified Date: March 14, 2002