The Chained Consumer Price Index: A Brief Explanation
CRS Report for Congress
The Chained Consumer Price Index:
A Brief Explanation
Brian W. Cashell
Specialist in Quantitative Economics
Government and Finance Division
The consumer price index (CPI) is probably the most important measure of
inflation published by the federal government. It is used to adjust Social Security
benefit payments as well as personal income tax brackets to keep up with inflation.
Nonetheless, it has been subject to criticism. Because the CPI does not take into account
consumers’ ability to insulate themselves 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.” As part of the
continuing effort to improve the CPI, the Bureau of Labor Statistics (BLS) is introducing
a supplemental measure which will be known as the chained consumer price index for
all urban consumers (C-CPI-U). The C-CPI-U uses continuously updated expenditure
weights, and thus reflects changes both in prices and in the composition of the consumer
marketbasket. Because the new C-CPI-U will be subject to revision, with the final
release two years after the reference date, it is an unlikely alternative for automatic
indexing provisions. This report will not be updated.
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.2
The Current CPI Is a Fixed-Weight Index
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 In 1996, a group commissioned by the Senate Finance Committee issued a report which
examined the CPI and made specific recommendations. See: Toward a More Acurate 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.
Congressional Research Service ˜ The Library of Congress
One of the criticisms, in particular, is that because the CPI is a fixed-weight index
it does not adequately reflect changing buying habits.3 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.”4
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 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.
3 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. Thus, 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.
4 Ana M. Aizcorb and Patrick C. Jackman, “The Commodity Substitution Effect in CPI Data,
Box 1. Calculating a Fixed-Weight Price Index
To illustrate, consider the formula:
pL 1 it
Index s1t i 1[;] = ∑
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
CostPeriod Quantity Price C ost Quantity Price C ost
the index for period 1 is 1.000, and the index value for period 2 is:
Inde x 0 4 062 =× +× . .
Index 1 3402L = .
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 New Chain-Weighted CPI
As part of the continuing effort to improve the CPI as a measure of changes in the
cost of living, BLS is introducing a supplemental measure which will be known as the
chained consumer price index for all urban consumers (C-CPI-U).5 The C-CPI-U will
5 Information from BLS about the C-CPI-U is available on the internet at:
not replace the current CPI, and will not affect 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.
The “final” release of the C-CPI-U will be calculated using a “Törnqvist” index
formula.6 This formula uses expenditure weights in both periods, 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:
pT it 2
Index 1t 1[;] = ∏
In this case, for each good (i), the price in the second period (in this 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 expenditure weight of that good in both 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 7 6+ + .. ..
Index 2 = ×
Index 1 1752T = .
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 will publish 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
[http://www.bls.gov/ cpi/superlink.htm] .
6 The Törnqvist price index formula was developed at the Bank of Finland in the 1930s.
other CPI data each month. In February of each year the previous year’s C-CPI-U
estimates will be revised, again using an alternative formula. This will be referred to as
the “interim” release. In the following February, the C-CPI-U estimates based on the
Törnqvist formula will be released.7
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.8 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. To see how a geometric mean index is
calculated, see Box 3.
Box 3. Calculating a Geometric Mean Price Index
The formula for a geometric mean price index looks like this:
Index 1t 1[;] = ∏
Using the same prices and quantities as in the previous example with this formula
Inde x 2 = ×
Index 1 1142G = .
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
7 Neither the CPI-U nor the CPI-W is subject to revision. That the C-CPI-U will be subject to
revision may make it less attractive for indexing purposes.
8 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.
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.9
In estimating the initial and interim releases of the C-CPI-U, which will be calculated
using the geometric mean formula, an adjustment will be 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.
In the case of the first release of C-CPI-U data for the month of July 2002, the initial
release will occur in August 2002, the interim release will occur in February 2003, and
the final release will occur in February 2004. The earliest data available will be for
January 2000, and the index base period will be December 1999 (i.e., December 1999 will
The expectation is that the C-CPI-U will indicate a slightly slower rate of increase
in prices than the CPI-U. Historical estimates suggest that the difference could be about
The publication of the C-CPI-U is part of a continuing effort by BLS to produce a
more accurate measure of inflation.11 At a minimum, the C-CPI-U should yield a better
estimate of the extent of substitution bias in the existing CPI. Its immediate practical use,
however, may be limited. 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. If it turns
out that revisions to the C-CPI-U are very small, then it might become the preferred
measure of inflation for those simply keeping track of overall economic conditions. But
because it will be revised, and because the revisions will take some time, it may be an
impractical measure of inflation to use for indexing.
It seems unlikely that the methodology of the C-CPI-U will be incorporated into the
existing CPIs any time soon. The methodology of all the price indexes published by BLS
is entirely within BLS’ discretion, and the methodology of the existing CPI will likely
continue to change as it has over the years. But one aspect of the existing CPI that seems
unlikely to change is that it is not usually subject to revision once it has been published.
That is one reason why the existing CPI is attractive for indexing. Given the time it takes
to get the data for calculating the final C-CPI-U, it would not be possible to incorporate
the C-CPI-U methodology into the existing CPI without also making it subject to revision.
9 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.
11 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.