An Introductory Look at the Chained Consumer Price Index

C-CPI-U Key Features

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.

Chaining Interval

  • The CPI-U and CPI-W are chained (that is, they use updated expenditure weights) every two years. The C-CPI-U will be chained monthly
  • C-CPI-U Publication Policy

    • Inaugural publication of C-CPI-U will occur in August 2002. The monthly index series will begin with January 2000 numbers; the reference base will be December 1999=100.
    • A limited set of urban population, U.S. city average, not seasonally adjusted indexes will be published. Indexes will be published for the US, for the categories listed below.
    • Published C-CPI-U Index Series
      SA0 All items SAM   Medical care
      SAF   Food and beverages SAM1     Medical care commodities
      SAF1     Food SAM2     Medical care services
      SAF11       Food at home SAR   Recreation
      SEFV       Food away from home SAE   Education and communication
      SAF116     Alcoholic beverages SAE1     Education
      SAH   Housing SAE2     Communication
      SAH1     Shelter SAG   Other goods and services
      SAH2     Fuels and utilities SAS Services
      SAH3     Household furnishings SAC Commodities
      SAA   Apparel SAD   Durables
      SAT   Transportation SAN   Nondurables
      SAT1     Private transportation SA0L1E All items less food and energy
      SETG     Public transportation SA0E Energy

      C-CPI-U Revision Policy

      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.

      C-CPI-U Indexes—calculation formulas

      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

       

      ccpi2b.gif (1401 bytes)

      2003 2004 2005
      ccpi2a.gif (1065 bytes) 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.

      Price Index formulas

      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:

      Consumer Substitution

      Consumer Substitution
      2-Good, 1-Consumer Example

      Good

      Month 1

      Month 2

      Price

      Quantity

      Cost

      Price

      Quantity

      Cost

      Movie Ticket $5 6 $30 $8 4 $32
      Video Rental $2 10 $20 $2 9 $18
        $50   $50

      Month 2

      • Movie ticket price increases 60%
      • Video rental price increases 0%
      • Movie ticket quanity decreases 33%
      • Video rental quantity decreases 10%
      Laspeyres index increases 36.0% $68
      Superlative (Tornqvist) increases 33.8% $67
      Geometric Mean index increases 32.6% $66

      Construction of the C-CPI-U for lower level aggregations

       

      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.

      movement of C-CPI-U in simulation

      continued movement of C-CPI-U in simulation

      Year

      Simulated
      Biennially
      Updated
      CPI-U

      Simulated
      C-CPI-U
      1990 3.64 3.52
      1991 3.76 3.69
      1992 2.90 2.58
      1993 2.80 2.67
      1994 2.58 2.49
      1995 2.76 2.46
      Average annual percent change 3.07 2.90
      Percentage difference per annum   0.17
      C-CPI-U and CPI-U Contrasted

      CPI-U

      C-CPI-U

      Initial Interim Final
      Lower-level Index Formula Hybrid Hybrid Hybrid Hybrid
      Upper-level Index Formula Laspeyres Adjusted
      Geometric
      Mean
      Adjusted
      Geometric
      Mean
      Tornqvist
      Expenditure base-period:

      Even-year Indexes

      Biennial,
      Lagged 2-3
      years
      Biennial,
      Lagged 2-3
      years
      Biennial,
      Lagged 1-2
      years
      Previous
      Month

      Odd-year Indexes

      Biennial,
      Lagged 3-4
      years
      Biennial,
      Lagged 3-4
      years
      Biennial,
      Lagged 2-3
      years
      Previous
      Month
      Expenditure current-period: none none none Current
      Month
      Weight Update Frequency Biennial Biennial Biennial Monthly
      Publication Schedule 1 Month Lag 1 Month Lag 2 to 13
      Month Lag
      14 to 25
      Month Lag

       

      Last Modified Date: March 14, 2002