The Chained Consumer Price Index: How Is It Different?

The Chained Consumer Price Index:
How Is It Different?
Updated February 21, 2008
Brian W. Cashell
Specialist in Macroeconomic Policy
Government and Finance Division

The Chained Consumer Price Index:
How Is It Different?
Summary
The Bureau of Labor Statistics (BLS) of the Department of Labor publishes two
important measures of inflation: the consumer price index for all urban consumers
(CPI-U), and the consumer price index for urban wage earners and clerical workers
(CPI-W). The CPI-W is used to adjust Social Security benefit payments, and the
CPI-U is used to adjust the personal income tax brackets to keep up with inflation.
As is the case with most economic indicators, the two CPIs are not without their
flaws.
One of the difficulties in estimating changes in the cost of living is that
consumer spending patterns change continuously. Spending patterns change because
of changing tastes and also because of changes in relative prices. Over time, as
prices change, consumers will tend to buy more of those goods and services whose
prices are rising slower than average and fewer of those goods and services whose
prices are rising faster than average. This substitution is believed to result in a CPI
that overstates the effect of inflation on consumer well-being.
As part of the continuing effort to improve measures of change in the cost of
living, BLS introduced a supplemental measure known as the chained consumer
price index for all urban consumers (C-CPI-U). The C-CPI-U does not replace either
of the current CPIs, and has not affected any current indexing provisions of federal
government programs. The aim of the C-CPI-U is to produce a measure of change
in consumer prices that is free of substitution bias.
Actual data for the C-CPI-U are now available beginning with December 1999.
With the exception of the year 2000, the difference between the “final” C-CPI-U and
the CPI seems to range from 0.1 to 0.5 percentage point. In 2000, the increase in the
C-CPI-U was 0.8 percentage point less than the CPI-U.
That the CPIs are not revised makes them attractive for use in making automatic
cost-of-living adjustments. The C-CPI-U is subject to two revisions after its initial
release. If the C-CPI-U were to be used instead, either the adjustment would have
to wait until the final number was available, or the adjustment would have to rely on
a number that could change after the fact. Depending on the month, the final C-CPI-
U will not be available for as long as two years after the reference date.
This report will be updated as economic events warrant.

Contents
In troduction ......................................................1
Methodological Differences..........................................2
The Current CPI Is a Fixed-Weight Index...........................2
The Chain-Weighted CPI........................................3
Statistical Differences..............................................7
Policy Considerations..............................................8
List of Figures
Figure 1. The CPI-U and the C-CPI-U..................................8
List of Tables
Table1. Number of Months After Reference Month That Data Are Released...6
Table 2. The C-CPI-U, the CPI-U, and the CPI-W........................7

The Chained Consumer Price Index:
How Is It Different?
Introduction
The consumer price index (CPI) is probably the most important measure of
inflation published by the federal government. Published by the Bureau of Labor
Statistics (BLS) of the Department of Labor, it is used to adjust Social Security
benefit payments as well as personal income tax brackets to keep up with inflation.¹
Nonetheless, it has been subject to criticism. For example, in 1996, a group
commissioned by the Senate Finance Committee issued a report that examined the²
CPI and identified a number of weaknesses and made specific recommendations.
As part of its continuing efforts to construct a better measure of changes in the
cost of living, BLS introduced the chained consumer price index for all urban
consumers (C-CPI-U). In testimony before the House Budget Committee in 2004,
then Federal Reserve Board chairman Alan Greenspan suggested that Congress might
consider replacing the CPI with the C-CPI-U to make automatic cost-of-living
adjustments to federal programs.³ He pointed out that, at that time, if the C-CPI-U
had been used instead of the CPI over the previous 10 years that the federal debt
would have been about $200 billion less. This report explains how the C-CPI-U is
calculated, and discusses how it differs from the existing CPI.
Ideally, a price index would measure changes in the cost of living. A true cost-
of-living index would measure the change in income that would be required for
consumers to maintain a constant level of satisfaction, or “utility.” But there are a
number of practical complications that make constructing such an index difficult.
The concept of utility is pervasive in economic theory. With a given level of
income, which constrains their choices, consumers decide how to spend their money
based on the utility, or satisfaction, yielded by the various available goods and

¹ Actually, there are two CPIs. The consumer price index for all urban consumers (CPI-U)
and the consumer price index for urban wage earners and clerical workers (CPI-W). Social
Security benefits are indexed to the CPI-W, and income tax brackets are indexed to the CPI-
U. See CRS Report RL34168, Automatic Cost-of-Living Adjustments: Some Economic and
Practical Considerations, by Brian W. Cashell.
² See Toward a More Accurate Measure of the Cost of Living, Final Report to the Senate
Finance Committee from the Advisory Commission to Study the Consumer Price Index,
Michael Boskin, Chairman, December 4, 1996.
³ Testimony of Alan Greenspan before the Committee on the Budget, U.S. House of
Representatives, February 25, 2004. Available on the Federal Reserve Board website at
[ ht t p: / / www.f e der a l r eser ve .gov/ boar ddocs/ t e st i mony/ 2004/ 20040225/ def a ul t .ht m] .

services. They are assumed to spend that money in such a way as to get the most
satisfaction possible within the limitations of their budget. But since there is no unit
of measure for utility, any measure of change in the cost of living must be based on
what consumers actually spend. Any numerical measure that attempts to
approximate changes in the cost of a given standard of living depends on a number
of assumptions and has numerous practical limitations.
One of the difficulties in estimating changes in the cost of living is that
consumer spending patterns change continuously. Spending patterns change because
of changing tastes and also because of changes in relative prices. Over time, as
prices change, consumers will tend to buy more of those goods and services whose
prices are rising slower than average and fewer of those goods and services whose
prices are rising faster than average. This substitution is believed to cause the CPI
to overstate the effect of inflation on consumer well-being.
Methodological Differences
Because the CPI is a fixed-weight index, it does not entirely reflect ongoing⁴
changes in buying habits. As the overall level of prices rises, relative prices change
as well. Some prices rise faster than average and some prices rise more slowly than
average. When goods are reasonably close substitutes, consumers can change their
spending patterns and buy relatively more of those goods whose prices are rising
slowly, and fewer of those goods whose prices are rising rapidly.
If these changes in consumer spending patterns have no effect on overall
consumer satisfaction, then a price index based on a fixed marketbasket of goods and
services will overstate the increase in cost of a given standard of living. Because the
CPI does not take into account consumers’ ability to insulate themselves, albeit to a
limited extent, from inflation by changing their spending patterns, it overestimates
how much they would need to raise total spending to maintain a constant standard of⁵
living. This is referred to as “substitution bias.”
The Current CPI Is a Fixed-Weight Index
The current CPI is a fixed-weight, or “Laspeyres,” price index. To see how a
fixed-weight index is calculated, consider the simple case of two time periods and
two goods. In the first period, the value of the index is one. The index value in the

⁴ The CPI is, strictly speaking, a modified fixed-weight price index, in that the marketbasket
is periodically updated. Until recently, however, those updates occurred only about once
every 10 years. With the release of CPI data for January 2002, the marketbasket was
updated to reflect spending patterns in the 1999-2000 period, and BLS now plans to update
the marketbasket every two years. With the release of the January 2008 CPI, the weights
were updated to reflect spending patterns in the 2005-2006 period. While the marketbasket
may not be allowed to get too far out of date, it is always somewhere between two and four
years out of date.
⁵ Ana M. Aizcorb and Patrick C. Jackman, “The Commodity Substitution Effect in CPI
Data, 1982-91,” Monthly Labor Review, December 1993, pp. 25-33.

second period is a function of the quantities in the first period and the prices in the
two periods. It is a weighted sum. The first step is to calculate, for each good, the
ratio of the price in the second period to the price in the first period. The ratios are
then summed using expenditure shares in only the first period as weights. To see
how a fixed-weight price index is calculated, see Box 1.
Box 1. Calculating a Fixed-Weight Price Index
To illustrate, consider the formula:
p^L¹ⁱ^t⎛ ⎞
Index s^1tⁱ¹^[;^] = ⎜ ⎟∑
pⁱⁱ⎝ ⎠
where i refers to the good, t refers to the period, and s¹ refers to the expenditure share for
each good in the first period, and the following hypothetical values for prices and
quantities:
BeerWine
Total
Cos tPeriod Quantity Pr ice Cost Quantity Pr ice Cost
11044061060100
21222441976100
the index for period 1 is 1.000, and the index value for period 2 is:

2 19^L ⎛ ⎞⎡ ⎤ ⎛ ⎞⎡ ⎤

Inde x 0 4 06² =×⎝⎜ ⎠⎟⎢ ⎥ +×⎝⎜ ⎠⎟⎢ ⎥. .

4 10⎣ ⎦ ⎣ ⎦

Index 1 340²^L = .
Using expenditure weights from the first period (in the case of beer, the expenditure
weight is 40 ÷ 100 = 0.40, and for wine it is 60 ÷ 100 = 0.60), yields an index value in the
second period of 1.340 which indicates an overall increase in the price of this
marketbasket of 34.0%. In this case, the measure of price change does not take into
account the fact that the hypothetical consumer bought more beer and less wine because
of the change in relative prices.
The Chain-Weighted CPI
As part of the continuing effort to improve measures of change in the cost of
living, BLS introduced a supplemental measure known as the chained consumer
price index for all urban consumers (C-CPI-U).⁶ The C-CPI-U does not replace the
current CPI, and has not affected any current indexing provisions of federal

⁶ Information about the C-CPI-U is available at [http://www.bls.gov/cpi/superlink.htm].

government programs. The aim of the C-CPI-U is to produce a measure of change
in consumer prices that is free of substitution bias.
The “final” release of the C-CPI-U will be calculated using a “Törnqvist” index
formula.⁷ This formula uses expenditure weights in both periods, and thus it reflects
both changes in prices and changes in the composition of the marketbasket. To see
how a Törnqvist price index is calculated, see Box 2.
Box 2. Calculating a Törnqvist Price Index
The Törnqvist index formula looks like this:
^ssⁱ¹ⁱ^t⁺^⎛^⎜^⎞^⎟
p^Tⁱ^t²⎛ ⎞^⎝^⎜^⎠^⎟
Index^1t¹^[;^] = ⎜ ⎟∏
pⁱⁱ ⎝ ⎠
In this case, for each good (i), the price in the second period (in which case p^t is simply²¹
p) is divided by the price in the first period (p) and the exponent applied to that ratio is
the average of the expenditure weights of that good in the two periods. In this formula,
the J symbol indicates that each of the weighted price ratios for the goods in the
marketbasket are multiplied together. Continuing with the same hypothetical numbers
from the previous example and using the Törnqvist formula gives:
⁴⁰²⁴⁶⁰⁷⁶⁺^⎛^⎜^⎞^⎟⁺^⎛^⎜^⎞^⎟^..^..

2 19^T²²⎛ ⎞ ⎛ ⎞^⎝^⎠^⎝^⎠

Index² = ⎝⎜ ⎠⎟ × ⎝⎜ ⎠⎟
410
Index 1 175²^T = .
Using the Törnqvist formula yields an index value for the second period of 1.175,
indicating an increase in the price of this hypothetical marketbasket of 17.5%.
Because the Törnqvist index requires data on expenditures in both time periods,
it cannot be published concurrently with existing CPIs. Expenditure data are not
available in time. However, BLS publishes an “initial” estimate of the C-CPI-U
based on an alternative formula. The release of this initial estimate will coincide
with the release of other CPI data each month. Every February, the estimates for all
of the months in the previous calendar year’s C-CPI-U estimates are revised, again
using an alternative formula. This first revision referred to as the “interim” release.
In the following February, the “final” C-CPI-U estimates based on the Törnqvist
formula are released for all of those same months.⁸

⁷ The Törnqvist price index formula was developed at the Bank of Finland in the 1930s.
⁸ Neither the CPI-U nor the CPI-W is subject to revision. That the C-CPI-U will be subject
(continued...)

The “initial release” and the first revision, or “interim” release of the C-CPI-U,
will be based on the same expenditure weights used for the CPI-U but these indexes
will be based on a geometric mean formula.⁹ In contrast with the Laspeyres index in
which the quantities are held constant in both periods, the geometric mean index
formula holds expenditure shares (price times quantity) constant. It assumes a
particular consumer response to the change in relative prices. That means that if the
price of a good rises the quantity consumed implicitly falls. Some research has
suggested that the geometric mean based price index may have a negative
substitution bias if consumers are assumed to respond to changes in relative prices
more than they actually do. To see how a geometric mean index is calculated, see
Box 3.¹⁰
Box 3. Calculating a Geometric Mean Price Index
The formula for a geometric mean price index looks like this:
^sⁱ¹⎛ ⎞
p^Gⁱ^t
Index^1t¹^[;^] = ⎜ ⎟∏
pⁱⁱ ⎝ ⎠
Using the same prices and quantities as in the previous example with this formula
gives:
⁴⁶^..

2 19^G ⎛ ⎞ ⎛ ⎞

Inde x² = ⎝⎜ ⎠⎟ × ⎝⎜ ⎠⎟
410
Index 1 114²^G = .
Using the geometric mean approach to calculating the price index for period 2 yields an
increase of 11.4% between the two periods, less than either of the other two measures.

⁸ (...continued)
to revision may make it less attractive for indexing purposes.
⁹ A geometric mean is the root of a product of a set of numbers. The geometric mean of two
numbers is the square root of their product. The current CPI already makes use of geometric
means in calculating some of the component indexes. Geometric means were adopted for
the CPI-U in January 1999 for use in aggregating some of the component indexes, where
goods in a given category were relatively close substitutes. At the time, it was estimated that
the change would result in a 0.2 percentage point drop per year in measured consumer price
inflation. Kenneth V. Dalton, John S. Greenlees, and Kenneth J. Stewart, “Incorporating
a Geometric Mean Formula into the CPI,” Monthly Labor Review, October 1998, pp. 3-7.
¹⁰ See Matthew D. Shapiro and David W. Wilcox, “Alternative Strategies for Aggregating
Prices in the CPI,” Federal Reserve Bank of St. Louis Review, May/June 1997, pp.113-125.

In estimating the initial and interim releases of the C-CPI-U, which will be
calculated using the geometric mean formula, an adjustment is made to the numbers
based on the historical differences between the geometric mean index and the
Törnqvist index, so that the initial and interim release will be closer to the final index
number.
Although the C-CPI-U may be superior to the CPI in some respects, final data
are far from timely. For example, in the case of the release of C-CPI-U data for the
month of January 2008, the initial release occurred in February 2008, the interim
release will occur in February 2009, and final data will not be released until February
2010. Final data for all of the months in calendar 2008 will be released in February

2010. Thus the wait for the final release of any January C-CPI-U is 25 months. But,

because all of the months in a given calendar year are revised at the same time, the
wait for the final release of any December C-CPI-U is only 14 months. Table 1
shows how many months after the reference month (the month for which the data are
reported) that the various releases are published.
Table1. Number of Months After Reference Month
That Data Are Released
C-CPI-U
Re f erence CP I - U/ W
Month Initial Interim Final
Release Release Release
January111325
February111224
March111123
April111022
May11921
June11820
July11719
August11618
September11517
October11416
November11315
December11214
^Source:^D^e^part^m^eⁿ^t^of^L^a^{bor, Bu}^reau^of^L^a^{bor S}^t^atⁱ^s^tⁱ^c^s^.

Statistical Differences
Data for the C-CPI-U are now available beginning with December 1999. That
is the base period for the C-CPI-U, for which it is set equal to 100. Final data are
available through the end of 2006, and interim data are available through the end of

2007. Table 2 compares the various C-CPI-U releases as well as those for the CPI-

U, and the consumer price index for urban wage earners and clerical workers (CPI-
W), which is the index used to calculate Social Security cost-of-living adjustments.¹¹
Table 2. The C-CPI-U, the CPI-U, and the CPI-W
Percentage Change
12-Month Period
Ending inC-CPI-U
December of:CPI-UCPI-W
Initial Int erim Final
2000 N.A. N.A. 2.6 3.4 3.4
2001 N.A. N.A. 1.3 1.6 1.3
2002 N.A. 2.3 2.0 2.4 2.4
2003 1.6 1.5 1.7 1.9 1.6
2004 3.0 3.1 3.2 3.3 3.4
2005 3.0 3.2 2.9 3.4 3.5
2006 2.7 2.4 2.3 2.5 2.4
2007 3.4 3.6 N.A. 4.1 4.3
^Source:^D^e^part^m^eⁿ^t^of^L^a^{bor, Bu}^reau^of^L^a^{bor S}^t^atⁱ^s^tⁱ^c^s^.
With the exception of the year 2000, the differences between the actual C-CPI-U
and the CPI-U have ranged from 0.1 to 0.5 percentage point. In 2000, the increase
in the C-CPI-U was 0.8 percentage point less than the CPI-U. BLS examined the
underlying data and found that increased variability in the component indexes may
have led to the larger than usual difference. The difference between the two indexes
is determined, in part, by the extent to which component indexes rise at varying rates
and the degree to which consumers shift their spending habits as a result of changes
in relative prices.
The short history of the C-CPI-U makes it difficult to say with any confidence
how large future revisions are likely to be. In 2002, the change between the interim
and final release amounted to 0.3 percentage point, a significant change. The initial
estimate for 2006 actually indicated a larger increase in the cost of living than either
the CPI-U or CPI-W. The final estimate was revised downwards by 0.4 percentage
point, and the increase in it was smaller than either the CPI-U or CPI-W. Most of

¹¹ The CPI-W differs from the C-CPI-U not only because the C-CPI-U corrects for
substitution bias, but also because the CPI-W represents a different marketbasket of goods
and services.

the other revisions to the C-CPI-U have been small. Figure 1 plots the monthly
index numbers for the CPI-U and all three versions of the C-CPI-U.
Figure 1. The CPI-U and the C-CPI-U

^Source:^D^e^part^m^eⁿ^t^of^L^a^{bor, Bu}^reau^of^L^a^{bor S}^t^atⁱ^s^tⁱ^c^s^.
Policy Considerations
The publication of the C-CPI-U is part of a continuing effort by BLS to produce¹²
a more accurate measure of inflation. If it is widely seen as superior to the CPI it
will at least provide policymakers with a better measure of inflation.
The CPI is important, not only as an economic indicator, but also because it has
significant implications for the budget through the indexing of the tax brackets and
Social Security benefits. If the CPI overstates the effect of inflation on consumers,
then Social Security benefits are rising more rapidly than necessary to preserve the
living standards of beneficiaries. Similarly, the income tax brackets are rising faster
than necessary to avoid “bracket creep,” whereby, with progressive tax rates, income
is taxed at a higher rate even though it is simply keeping up with rising prices.
If the C-CPI-U is a better measure of changes in the true cost of living, and the
goal of indexing is strictly to reflect changes in the cost of living, then the C-CPI-U
might be considered as a measure on which to base those adjustments. A major
¹² As part of that effort, BLS sponsored a panel of experts to examine the CPI and make
specific recommendations. The Panel on Conceptual, Measurement, and Other Statistical
Issues in Developing Cost-of-Living Indexes was chaired by Charles L. Schultze. Their
report was published in 2002 by the National Academy Press under the title At What Price?
Conceptualizing and Measuring Cost-of-Living and Price Indexes.

complication, however is the release schedule. Final C-CPI-U data are not available
for up to two years after the reference period. The January 2008 Social Security cost-
of-living adjustment was based on the third quarter 2007 CPI data. Final C-CPI-U
data for the third quarter of 2007 will not be available until February 2009. Such a
long time lag might make the final C-CPI-U number a poor candidate as an index for
automatic adjustments. Whether the initial or interim estimates might be attractive
alternatives may depend on whether they are biased relative to the final number, or
if the revisions tend to be significant. If there is a tendency for the final index to rise
faster than the initial or interim indexes that might make the preliminary indexes
unpopular with those who would be affected.
The C-CPI-U is likely to continue rising more slowly than either the CPI-U or
the CPI-W as they are now calculated. That could generate opposition to changing
current indexing provisions, and basing future cost-of-living adjustments on the C-
CPI-U, from some Social Security beneficiaries and taxpayers