Order Code RL32293
CRS Report for Congress
Received through the CRS Web
The Chained Consumer Price Index:
How Is It Different?
Updated February 24, 2006
Brian W. Cashell
Specialist in Quantitative Economics
Government and Finance Division
Congressional Research Service ˜ The Library of Congress

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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 actual C-CPI-U and
the CPI seems to be about 0.3 - 0.4 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. The final C-CPI-U is only available two
years after the reference date.
This report will be updated as economic events warrant.

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Contents
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Methodological Differences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
The Current CPI Is a Fixed-Weight Index . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
The Chain-Weighted CPI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Statistical Differences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Policy Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
List of Figures
Figure 1. The CPI-U and the C-CPI-U . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
List of Tables
Table 1. The C-CPI-U, the CPI-U, and the CPI-W . . . . . . . . . . . . . . . . . . . . . . . . 7

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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 the
CPI and made specific recommendations.2
As part of its continuing efforts to construct a better measure of changes in the
cost of living, BLS has introduced the chained consumer price index for all urban
consumers (C-CPI-U). In testimony before the House Budget Committee, 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
services. They are assumed to spend that money in such a way as to get the most
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.
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, Dec. 4, 1996.
3 Testimony of Alan Greenspan before the Committee on the Budget, U.S. House of
Representatives, Feb. 25, 2004. Available on the Federal Reserve Board website at
[http://www.federalreserve.gov/boarddocs/testimony/2004/20040225/default.htm].

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CRS-2
satisfaction possible within the limitations of their budget. But there is no unit of
measure for utility. 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 adequately reflect on-going
changes in buying habits.4 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 overall consumer satisfaction is unchanged once purchasing patterns respond
to changed relative prices, 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 of living. This is referred to as “substitution bias.”5
The Current CPI Is a Fixed-Weight Index
The current CPI is a fixed-weight, or “Laspeyres,” price index. In the simple
case of two periods and two goods, the value of the index in the first period is one.
The index value in the 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
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 2006 CPI, the weights
were updated to reflect spending patterns in the 2003-2004 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, Dec. 1993, pp. 25-33.

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CRS-3
period. The ratios are then summed using expenditure shares in 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:
⎛ pt ⎞
IndexL
= ∑ s1 i
⎜
⎟
[1;t]
i
1
⎝
⎠
i
pi
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:
Beer
Wine
Total
Period
Quantity
Price
Cost
Quantity
Price
Cost
Cost
1
10
4
40
6
10
60
100
2
12
2
24
4
19
76
100
the index for period 1 is 1.000, and the index value for period 2 is:
⎡
⎛ 2⎞ ⎤ ⎡
⎛ 19⎞ ⎤
IndexL = 0 4
⎢ . ×
0 6
.
2
⎝⎜
⎥ + ⎢
×
⎥
⎣
4⎠⎟ ⎦
⎝⎜
⎣
10⎠⎟ ⎦
IndexL = 1 34
.
0
2
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 from BLS about the C-CPI-U is available on the Internet at
[http://www.bls.gov/cpi/superlink.htm].

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CRS-4
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:
⎛ s1+st ⎞
i
i
⎛
⎜⎜
⎟⎟
pt ⎝ 2
⎞
⎠
IndexT
i
=
⎜
⎟
∏
[1;t]
⎝ p1 ⎠
i
i
In this case, for each good (i), the price in the second period (in which case pt is simply
p2) is divided by the price in the first period (p1) 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:
⎛ .40+.24⎞
⎛ .60+.76⎞
⎛ 2 ⎝⎜ 2
⎞
⎠⎟
⎛ 19 ⎝⎜ 2
⎞
⎠⎟
IndexT =
2
⎝⎜ 4⎠⎟
× ⎝⎜ 10⎠⎟
IndexT = 117
.
5
2
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 can not 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. In February of each year the previous
year’s C-CPI-U estimates are revised, again using an alternative formula. This is
referred to as the “interim” release. In the following February, the “final” C-CPI-U
estimates based on the Törnqvist formula are released.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...)

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CRS-5
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 the overall
index 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. 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 actually have a
negative substitution bias. In other words, it assumes that consumers respond to
changes in relative prices more than is actually the case. 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:
s1
⎛ pt i
⎞
IndexG
i
=
⎜
⎟
∏
[1;t]
⎝ p1 ⎠
i
i
Using the same prices and quantities as in the previous example with this formula
gives:
⎛ 2 .4
⎞
⎛ 19 .6
⎞
IndexG =
2
⎝⎜ 4⎠⎟ × ⎝⎜ 10⎠⎟
IndexG = 111
.
4
2
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.
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
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, Oct. 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.

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CRS-6
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. In the case of the release of C-CPI-U data for the month of
January 2006, the initial release occurred in February 2006, the interim release will
occur in February 2007, and the final release will occur in February 2008. The index
base period is December 1999 (i.e., December 1999 equals 100), and that is the
earliest date for which actual data are available.
Statistical Differences
In anticipation of the release of the new series, BLS produced estimates of the
C-CPI-U using a simulation model to determine how much of a difference might be
expected between the C-CPI-U and the CPI-U. These estimates, for the years 1990
to 1995, led BLS to expect that the C-CPI-U would increase by about 0.1 to 0.2
percentage point more slowly than the CPI-U. Subsequently, BLS recalculated those
figures and extended the estimates through 1999. These new estimates showed a
slightly larger difference between the row indexes for the 1990-1995 period, just over
0.2 percentage point. For the 1995-1999 estimates, the difference grew, reaching 0.5
percentage point in 1999.11
One reason for the increase in the difference between the two indexes during the
1990s may have been that in 1999 the marketbasket of the CPI-U was five years old.
Since that time, BLS has begun updating the marketbasket every two years.
Actual data for the C-CPI-U are now available beginning with December 1999.
That is the base period for the C-CPI-U in which it is set equal to 100. Final data are
available through the end of 2004, and interim data are available through the end of
2005. Table 1 presents these data as well as data 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.12
11 See Bureau of Labor Statistics, “Frequently Asked Questions About the Chained
Consumer Price Index for All Urban Consumers (C-CPI-U),” available at
[http://www.bls.gov/cpi/cpisupqa.htm].
12 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.

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CRS-7
Table 1. The C-CPI-U, the CPI-U, and the CPI-W
Percentage Change
12-month period
ending in
C-CPI-U
December of:
CPI-U
CPI-W
Initial
Interim
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
1.6
1.9
1.6
2004
3.0
3.1
N.A.
3.3
3.4
2005
3.0
3.2
N.A.
3.4
3.5
Source: Department of Labor, Bureau of Labor Statistics.
With the exception of the year 2000, the difference between the actual C-CPI-U
and the CPI-U seems to be about 0.3 - 0.4 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 expected 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 the changes in relative prices. BLS found that variability in the component
indexes rose between 1998 and 2000 and contributed to the increase in the gap
between the two indexes.
An important difference between the two indexes is that the CPI-U is not subject
to revision, while the C-CPI-U is subject to two revisions after the initial release.
That the CPI-U is not revised makes it attractive for use in making automatic cost-of-
living adjustments. 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. The final C-CPI-U which
is calculated using the most recent actual expenditure data will only be available two
years after the reference date.
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 amounted to 0.3
percentage point, a fairly large change relative to the difference between the C-CPI-U
and the other CPIs. For the most part, however, it appears that 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.

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CRS-8
Figure 1. The CPI-U and the C-CPI-U
120
119
118
117
116
115
114
113
112
111
110
109
108
107
106
105
104
CPI-U
103
Initial C-CPI-U
102
Interim C-CPI-U
101
Final C-CPI-U
100

2000

2001

2002

2003

2004
2005
Source: Department of Labor, Bureau of Labor Statistics.
Policy Considerations
The publication of the C-CPI-U is part of a continuing effort by BLS to produce
a more accurate measure of inflation.13 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
complication, however is the release schedule. Final C-CPI-U data are not available
13 As part of that effort, BLS recently 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.

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CRS-9
for up to two years after the reference period. The January 2006 Social Security cost-
of-living adjustment was based on the third quarter 2005 CPI data. Final C-CPI-U
data for the third quarter of 2005 will not be available until February 2007. Such a
long time lag makes the final 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. 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. This 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

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