Current Price Topics

A Comparison of the CPI-U 

and the C-CPI-U

1

Consumer Price Index: Third Quarter 2011

U.S. Bureau of Labor Statistics November 2011 Volume 2, Number 11

Background

Before 1999, the U.S. Consumer Price Index 

(CPI) was viewed by many as overstating a 

cost-of-living index.1

 To understand why this 

was the case, it helps to first understand that 

the CPI is calculated in two stages. At the first 

stage, consumer goods and services are 

partitioned into 211 item categories and 38 

geographic index areas, or 8,018 item-area 

combinations. The sampled prices within 

each of those 8,018 cells are first averaged 

together to form 8,108 basic indexes. Then, at 

the second stage of aggregation, these basic 

indexes are averaged together to form aggregate indexes, such as the All items index. 

Before 1999, both the prices and the basic 

indexes were averaged together using a 

Laspeyres or arithmetic mean formula. The 

Laspeyres formula can overstate a cost-ofliving index by, in effect, assuming that 

consumers purchase the same quantity of 

goods and services when relative prices 

change over time. Under a cost-of-living 

framework, changes in relative prices can 

result in consumers changing their spending 

patterns. The difference between an estimate 

of price change using the Laspeyres formula 

and a cost-of-living index could thus be 

viewed as a bias, in particular, a “consumer 

substitution bias.” When a Laspeyres formula is 

used at the first or lower level of aggregation 

to average the individual prices together, 

lower-level consumer substitution bias results 

to the degree consumers substitute within

those CPI item categories. When a Laspeyres 

formula is used at the second or upper-level 

of aggregation to average the basic indexes 

together, upper-level consumer substitution 

bias results to the degree consumers substitute across CPI item categories.

In 1999, to address the issue of lower-level 

consumer substitution bias, the Bureau of 

Labor Statistics (BLS) adopted a geometric 

mean formula to average the prices together 

within most of the 8,018 item-area cells for 

both the Consumer Price Index for All Urban 

Consumers (CPI-U) and the Consumer Price 

Index for Urban Wage Earners and Clerical 

Workers (CPI-W). While the adoption of the 

geometric mean formula essentially addressed lower-level substitution bias, the 

CPI-U and CPI-W still suffer from upper-level 

substitution bias in that the basic indexes are 

averaged together using a Laspeyres formula.

To address upper-level substitution bias, BLS 

began publication of a new Chained CPI for 

All Urban Consumers (C-CPI-U) in 2002, with 

indexes calculated back to December 1999. 

The C-CPI-U employs a “superlative” formula 

to combine the basic indexes together, to 

reflect the effect of substitution that consum-
2

 CURRENT PRICE TOPICS

ers make across CPI item categories in 

response to changes in relative prices. The 

C-CPI-U does not replace the CPI-U or 

CPI-W; it is, instead, a new, supplemental 

measure of inflation.

Comparing and Contrasting the CPI-U and

the C-CPI-U

In both the CPI-U and the C-CPI-U, the 

prices and the formulas used to average 

those prices together within each CPI 

item-area at the first stage of aggregation 

are the same. It is at the second stage of 

aggregation—the averaging of the basic 

indexes across CPI item categories and 

geographic areas—where the formulas 

used in the CPI-U and C-CPI-U differ. The 

CPI-U continues to use a Laspeyres formula 

to average these basic indexes together. In 

addition, expenditure weights from a 

previous 2-year period are used to calculate 

aggregate indexes. For example, the CPI-U 

for 2010–2011 uses consumer expenditure 

estimates from the 2007–2008 period. 

Similarly, weights pertaining to 2009–2010 

will be used in the CPI-U beginning in 

January 2012.

The final C-CPI-U2

, on the other hand, uses 

expenditures from both the current and 

previous month to combine the basic 

indexes together. Since the final C-CPI-U 

uses both current and base expenditure 

weights in its final form, the formula effectively incorporates the impact of changes 

in consumer spending patterns, and thus 

does not suffer from upper-level substitution bias.

Chart 1 shows the behavior of the All items 

CPI-U and the final C-CPI-U from December 

95

100

105

110

115

120

125

130

135

Dec

1999

Dec 

2000

Dec 

2001

Dec 

2002

Dec 

2003

Dec 

2004

Dec 

2005

Dec 

2006

Dec 

2007

Dec 

2008

Dec 

2009

Index value

CPI-U C-CPI-U

NOTE: CPI-U, U.S. city Average, All Items index values are converted to reflect a base period of December 1999=100. 

SOURCE: U.S. Bureau of Labor Statistics

Chart 1. CPI-U and final C-CPI-U indexes, December 1999–December 2009
3

 CURRENT PRICE TOPICS

1999 through December 2009. (C-CPI-U data for 

2010–2011 are not shown in chart 1 as these data 

are preliminary.) Over this 10-year period, the All 

items CPI-U rose at an annual average rate of 2.5 

percent, compared with an average increase of 

2.2 percent for the C-CPI-U—an annual difference 

of 0.3 percent a year.

Although the differences between the CPI-U and 

C-CPI-U average about 0.3 percent a year, those 

differences vary somewhat by year (See table 1). 

Excluding the relatively large difference in 2000, 

the difference between the CPI-U and C-CPI-U 

average about 0.25 percent a year.

Summary

In both the CPI-U and the C-CPI-U, the prices 

used—and the formulas used to average those 

prices together within each CPI item-area—are 

the same. At the second stage of aggregation—

the averaging of the basic indexes across CPI item 

categories and geographic areas—the CPI-U 

continues to use a Laspeyres formula to average 

these basic indexes together, using expenditure 

weights from a previous 2-year period. In contrast, the final C-CPI-U uses a superlative formula 

to combine the basic indexes together using 

both current and previous monthly expenditure 

data.

In short, the C-CPI-U is designed to be a closer 

approximation to a cost-of-living index than the 

CPI-U. That said, the C-CPI-U is subject to two 

annual revisions, while the CPI-U is deemed final 

when issued. 

All Items

The all items Consumer Price Index for All 

Urban Consumers (CPI-U) increased at a 

4.8-percent seasonally adjusted annual rate 

during the third quarter of 2011. This rise 

Table 1. December-December percent changes, CPI-U and C-CPI-U, 2000–2009

Year CPI-U C-CPI-U Difference

2000 3.4 2.6 0.8

2001 1.6 1.3 0.3

2002 2.4 2 0.4

2003 1.9 1.7 0.2

2004 3.3 3.2 0.1

2005 3.4 2.9 0.5

2006 2.5 2.3 0.2

2007 4.1 3.7 0.4

2008 0.1 0.2 -0.1

2009 2.7 2.5 0.2

SOURCE: U.S. Bureau of Labor Statistics 

Current Price Trends

Energy Prices Jump while 

Food Prices Continue to Rise
4

 CURRENT PRICE TRENDS

follows increases of 6.1 percent and 1.5 percent in the first and second quarters of 2011, 

respectively. For the first 9 months of 2011, 

the index has increased at a 4.1-percent 

annual rate. This compares with a rise of 1.5 

percent in 2010

The food index continued its rise in 2011 after 

more modest increases in 2010, increasing 5.7 

percent in the third quarter. The energy index 

increased 26.6 percent in the third quarter, 

after falling 12.5 percent in the second quarter. The index for all items less food and energy rose 2.1 percent in the third quarter, after 

increasing 2.9 percent in the second quarter. 

The index for all items less food and energy is 

up 2.0 percent over the past year.

Energy

Energy prices continued to be volatile. After 

climbing 42.4 percent in the first quarter and 

falling 12.5 percent in the second quarter, the 

energy index jumped 26.6 percent in the third 

quarter.  The previous 6 months overall have 

seen a slowdown in energy prices, rising 5.3 

percent at a seasonally adjusted annual rate, 

after rising 36.0 percent in the 6 months 

ending in March 2011. The energy index rose 

7.7 percent in 2010.  

The rise in the energy index in the third 

quarter of 2011 was driven by an increase in 

the gasoline index, which rose 45.4 percent in 

the third quarter, after falling 20.5 percent in 

the second quarter of 2011. Fuel oil was down 

11.0 percent, while electricity and natural gas

prices increased 6.0 and 7.4 percent, respectively. Overall, the household energy index 

rose 5.2 percent in the third quarter, after 

falling 0.1 percent in the second quarter.

Crude oil prices—and, subsequently, retail 

gasoline and fuel oil prices—have been quite 

volatile over the past few years. From July 

2007 to July 2008, gasoline prices rose sharply, 

increasing 37.9 percent. After crude oil prices 

peaked in July 2008 at over $134 a barrel, 

prices plummeted during the last 5 months of 

2008, with crude oil prices falling to under $32 

a barrel. At the retail level, gasoline prices fell 

by more than 50 percent. In 2009, pump 

prices turned sharply higher again, increasing 

more than 50 percent, with crude oil prices 

increasing to around $70 by the end of 2009.3

In 2010, gas prices saw a more moderate 

increase of 13.8 percent and are up 25.6 

percent through the first 9 months of 2011.

Food

Food prices rose at a seasonally-adjusted 

annual rate of 5.7 percent in the third quarter 

of 2011, after rising 4.1 percent in the second 

quarter and 7.5 percent in the first quarter. 

The food index increased 1.5 percent in 2010. 

Grocery store food prices were up at a 7.4 

percent annual rate in the third quarter, after 

increasing 4.7 percent in the second quarter 

and 11.2 percent in the first quarter. All six 

major grocery store food groups increased, 

with the dairy and related products group 

leading the way with a 14.1-percent jump. 
5

 CURRENT PRICE TRENDS

Fruits and vegetables were the only other 

grocery store item to see a double-digit 

increase, rising 11.0 percent over the quarter. Cereals and bakery products were up 

7.8 percent, meats, poultry, fish and eggs

rose 5.0 percent, nonalcoholic beverages 

and beverage materials increased 2.7 percent, and other food at home increased 7.0 

percent.

Double-digit increases in price were seen 

almost across the board for major dairy 

items, led by a 22.2-percent jump in the 

price of cheese. Only fresh whole milk

prices saw a single-digit increase of 6.5 

percent. The fresh fruits index increased 

22.5 percent, while the index for processed 

fruits and vegetables increased 7.7 percent. 

Within fresh fruits, the prices of apples and 

oranges increased 47.6 percent and 25.5 

percent, respectively. The prices of processed fruits and vegetables was driven 

partly by an increase of 11.2 percent in 

canned vegetables, which contrasts with a 

relatively small 2.8-percent increase in fresh 

vegetables prices.  The prices of fresh 

vegetables were held down by lettuce  and 

tomatoes, which bucked the trend with 

decreases of 4.0 and 15.6 percent, respectively, over the quarter.

The food away from home index rose at a 

3.4-percent rate in the third quarter, after 

rising at a 3.2-percent rate in the second 

quarter. The food at employee sites and 

schools index jumped 15.5 percent in the 

third quarter, after more modest increases 

earlier in the year, while the prices of food 

from vending machines and mobile vendors were up 9.5 percent.

All Items Less Food and Energy

The index for all items less food and energy  

rose 2.1 percent in the third quarter of 2011, 

slowing down from its 2.9-percent increase 

recorded in the second quarter, but almost 

equal to the 2.0 percent rate in the first quarter. 

The shelter index continued its upward trend 

with an increase of 2.3 percent in the third 

quarter after a 1.9-percent increase in the 

second quarter and 1.3-percent increase in 

the first quarter.  Within shelter, owners’ 

equivalent rent and rent of primary residence

both accelerated in the third quarter, rising 2.4 

percent and 3.5 percent, respectively. Lodging 

away from home, on the other hand, declined 

6.1 percent in the third quarter, after a 

25.8-percent second quarter spike. 

The acceleration in shelter prices stands in 

contrast to decreases observed in recent 

years. The 12-month percent changes in 

shelter ending September 2006, 2007, 2008, 

2009, and 2010 were 4.2, 3.5, 2.4, 0.7, and 

minus 0.4 percent, respectively.  

After nearly across-the-board decreases in the 

first quarter, apparel prices were up 5.0 percent in the third quarter, after an 11.5-percent 

increase in the second quarter. Men’s and 

boys’ apparel prices were up 5.4 percent, 

women’s and girl’s apparel prices were up 5.2 
6

 CURRENT PRICE TRENDS

percent, and infants’ and toddlers’ apparel

prices were up 17.9 percent. Jewelry prices 

were up 1.1 percent—a sharp slowdown 

from previous quarters. 

Household furnishings and operations

increased 1.4 percent in the third quarter of 

2011, the same rate observed in the second 

quarter. The transportation index was up 

13.9 percent over the quarter, driven mostly 

by soaring gas prices but also by higher 

airline fares, which increased 9.1 percent 

after a 14.9-percent drop in the second 

quarter. The index for used cars and trucks

rose 4.4 percent.

Other significant components with increases included the index for other goods and 

services, which rose 2.9 percent, and the 

medical care index, which grew 2.8 percent. 

The index for education and communication rose 1.4 percent in the quarter, though 

communication prices decreased 1.6 percent.  

The recreation index fell 0.2 percent. The 

price of televisions continued to decline, 

falling 21.7 percent in the quarter, after 

decreases of 21.1 percent, 12.4 percent, and 

15 percent in the previous three quarters. 

The index for rental of video or audio discs 

and other media increased 29.5 percent.

The index for all items less food and energy

rose 2.0 percent for the 12 months ending 

September 2011. For the 5-year period from 

September 2005 to September 2010, this 

index also increased at a 2.0-percent annual 

rate.

Price movements described in this text 

reflect data as released on October 19, 

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

4.0

5.0

6.0

J F M A M J J A S O N D J F M A M J J A S O N D J F M A M J J A S O N D J F M A M J J A S

2008 2009 2010 2011

Percent change

All items

All items less food and energy

SOURCE: U.S. Bureau of Labor Statistics

Chart 2. Twelve-month percent change, all items and all items less food and 

energy, January 2008–September 2011
 CURRENT PRICE TRENDS

Notes

1

 A cost-of-living index (COLI) attempts to measure the change in the cost over time of maintaining a fixed standard of living. While 

a true cost-of-living index can only be approximated, it is the measurement objective of the U.S. CPI. As noted in Chapter 17 of the 

BLS Handbook of Methods, at http://www.bls.gov/opub/hom/pdf/homch17.pdf, it is sometimes said that the Laspeyres formula 

provides an “upper bound” on the COLI. 

2

 This description applies only to the “final” C-CPI-U. Unlike the CPI-U, the C-CPI-U is subject to two annual revisions before being issued in final form. This is because expenditure data for the current period are not available until 13-24 months after the current 

month. Since the two preliminary (initial and interim) estimates of the C-CPI-U include only base-period expenditure weights, they 

are not true “superlative” indexes. A complete description of how the C-CPI-U is calculated can be found at

http://www.bls.gov/cpi/super_paris.pdf.

3

 Energy Information Administration; see http://www.eia.gov/dnav/pet/hist/LeafHandler.ashx?n=PET&s=WTOTUSA&f=W.

7

2011. All 12-month and longer percent 

changes reflect not seasonally adjusted 

data except as noted. Percent changes 

covering less than a year are based on 

seasonally adjusted annual rates, unless 

otherwise noted. CPI seasonally adjusted 

indexes and percent changes are subject to 

annual revision.

For more information, contact Jonathan 

Church at (202) 691-5379 or email

church.jonathan@bls.gov.