Comparing market basket changes and the CPI

Mary Lynn Schmidt, Economist, Bureau of Labor Statistics

The views expressed are those of the author and do not necessarily represent an official position of BLS

Consumer expenditures on specific items

vary widely over time, consumers tend to maintain a

pattern of expenditures for much longer time

periods. The market basket of goods and services

that make up the Consumer Price Index (CPI) is

divided into seven major groups, such as food and

beverages or housing. The pattern of consumer

expenditures at this level changes more slowly than

the components within a group.

A Consumer Price Index is one of the most

widely used economic indicators. It is a measure of

the average change in the prices paid, in the United

States, by urban consumers for a fixed market basket

of goods and services. Knowing that consumers are

constantly offered new items to include in their

market basket, how do changing market baskets

influence the CPI? The answer is not unambiguous

and depends on the importance of the change in

terms of total expenditures by consumers.

When the price of a commodity goes up or

down it is usual to expect consumption of that

commodity to go down or up, respectively, as a

result. In fact, most of us frequently make such

choices every time we go the supermarket. Price

indexes are produced to provide government,

business, and individuals a measure to compare

prices over time and make informed decisions on

economic behavior. Many believe changes in the

Consumer Price Index reflects changes in their

standard of living. Because the CPI is a modified

Laspeyres index and keeps quantities fixed between

revisions, it is a measure of price change not a true

Cost of Living Index.

The base period expenditure weights for the

1987 CPI revision relied on the 1982, 1983 and 1984

Survey of Consumer Expenditures (CE) and the

1980 Census of Population. While there were many

improvements to sampling techniques, data

collection, processing, and estimation associated

with the 1987 revision, it also introduced a “rolling

in” process for new areas replacing discontinued

areas.

The BLS sponsors the Continuing Point of

Purchase Survey (CPOPS) annually to provide an

outlet frame to select outlets in which to price items

for the CPI. This survey is used in combination with

the now ongoing Consumer Expenditure Survey to

select items and outlets in approximately one-fifth of

the geographic areas (defined by the Bureau of the

Census for the Current Population Survey) included

in the CPI each year. Since the 1987 revision, two

years of the most recent Consumer Expenditure

Survey data are used in selecting items being rotated

each year (Marcoot, 1985). New items and outlets

selected for the 1994 CPOPS were based on the 1992

and 1993 Consumer Expenditure Survey data. Thus,

new items and new outlets are being introduced in

twenty percent of the pricing areas annually. The

entry level item reselection has gradually changed

the composition of the entry level items being priced.

Market baskets and price change

Prior to 1945 the CPI was called a “cost of

living” index. Since then the BLS has more

correctly named it the Consumer Price Index.

Because the Consumer Price Index is weighted by

consumer expenditures in a previous time period and

uses a fixed market basket of goods and services, it

represents a ratio of the prices in subsequent time

periods to that of the base period. The CPI is a

measure of price change based on a sample of prices

of food, apparel, housing, transportation, medical

care, entertainment and other goods and services. It

does not include many consumer outlays, for

example, income taxes, charitable contributions,

personal insurance, pensions or investments.

A true Cost of Living index (CLI) is a ratio

of the minimum expenditure required to attain a

particular level of satisfaction in two price situations;

it attempts to measure the price change associated

with a constant standard of living. A Laspeyres

index is identical to a cost of living index if the

consumer preferences do not permit substitution, and

goods and services are purchased in the same

proportion over time. The CPI is estimated using a

fixed market basket to hold the base-period

consumption patterns fixed. It is calculated by using

a modified Laspeyres price index formula which

measures the ratio of the costs of purchasing a basket

of items of constant quality and constant quantity in

two different time periods. As we noted above the

current CPI uses the 1982-84 expenditure weights

from the Consumer Expenditure Survey but they are

updated for price change from the midpoint of the

base period to the introduction of the new weights in

1987; hence, it uses a modified Laspeyres formula.
The Laspeyres price index formula requires the

expenditure base (quantity) and reference periods to

coincide.

To calculate the CPI an estimate of the

expenditure pattern is needed to define and weight

the market basket of goods and services for which

the index is computed. Each expenditure-population

weight is the product of estimates of mean

expenditures per consumer unit derived from the

1982-84 Consumer Expenditure Survey and

estimates of the number of consumer units obtained

from the 1980 census files. Mean expenditures are

calculated using preliminary expenditures and their

relative importance, composite estimated and raked

to minimize the average mean square error of the

relative importance of the total weight for the index.

Two important factors to consider in using a

consumer price index are the formula used to

calculate it and the commodities and services

included. As we noted before, the CPI uses a

modified Laspeyres index formula. It measures the

ratio of the cost of purchasing a basket of items of

constant quality and constant quantity in one period

to the corresponding cost in another period. The

CPI revises the quantities of items consumed in its

basket of goods and services approximately every ten

years.

The Laspeyres formula is known to

represent an upper bound to a true cost of living

index. This occurs because the fixed quantity (base

period relative importances) does not allow for

substitution of goods as prices change. Our common

experience tells us that consumers are likely to

purchase more quantities of items when their prices

go down and fewer quantities when their prices go

up. This implies that consumers attempt to

maximize the utility of purchases. Economic

literature refers to this as the substitution effect as

individuals move along an indifference curve

purchasing more as the price falls; and the income

effect which allows individuals to purchase more as

the price goes down (raising the individual’s

purchasing power) and thereby move to a higher

indifference curve. In the CPI the relative

importance of items at the base period is held

constant and multiplied by the ratio of price change.

When prices of a group of items goes up faster than

average, the CPI continues to give the same

importance to this group even as consumers shift to

lower cost substitutes. Under this condition we can

understand how the CPI may overstate the price

experience of individual consumers.

There have been several attempts to

quantify the difference between a cost-of-living

index and the CPI. Much of the recent literature on

index theory has focused on eliminating or

measuring bias or how to account for quality

changes- defining a true cost of living index.

For the most part consumer price indexes

attempt to measure how much more it would cost to

purchase a set of goods at a point in time compared

to some specified base period. It shows how prices

of a fixed basket of goods and services change over

time. Other studies have found that the amount of

the substitution effect amounted to an average

annual rate of 0.1 to 0.2 percent per year.

(Braithwait, 1980) (Marilyn E. Manser and Richard

J. McDonald 1988) (Aizcorbe and Jackman, 1993)

Effects of updated market baskets on the CPI

For this study we began five years after the

1982-84 current CPI base period, and created

alternative indexes for each subsequent three-year

period using Consumer Expenditure data from 1987

to 1993 (e.g., the base period for Alternative index A

uses CE data from 1987-89; Alternative index B uses

CE data from 1988-90; etc.). The CPI uses three

years of consumption expenditures to smooth out the

variability associated with any one or two years of

data. These alternative indexes are used to compare

potential effects of changes in consumption patterns

with the current CPI. The effects of market basket

changes are compared in five overlapping periods.

Table 1 below shows the relative

importances based on CE data for the seven major

groups of the CPI and a few selected other categories

for each of the alternative index periods. Relative

importance refers to the ratio of expenditure of an

item or a group of items to the total expenditures for

all items. The patterns of expenditures at major

group levels are quite similar over these time

periods.

When we compare relative importances of

consumer expenditures from the official CPI base

period to those of the Alternative indexes, we see

more similarities among the five alternative periods

(which begin five years from the base period of the

current CPI) than any one with the base period of the

current CPI. To capture these movements argues in

favor of using more recent expenditure data to

represent spending patterns in calculating a price

index. We should not negate the importance in

selecting a base period that minimizes the impact of

short-term economic conditions on consumption

patterns. For example, during the alternative index
Table 1. CE Relative Importances for three year averages compared to the base period expenditures used for

the official CPI

Official

CPI

 Alternative Index periods

(Expenditure weight base periods)

1982-84 (1987-89) (1988-90) (1989-91) (1990-92) (1991-93)

 A B C D E

Food and beverages 17.910 16.501 16.506 16.603 16.565 16.460

 Food at home 10.196 9.136 9.210 9.520 9.698 9.895

 Food away from home 7.714 6.150 6.138 5.954 5.746 5.514

Housing 42.087 42.548 42.639 42.801 43.26 43.341

Apparel and upkeep 6.518 6.537 6.516 6.620 6.552 6.432

Transportation 18.874 19.221 18.875 18.182 17.708 17.687

 New vehicles 5.517 6.225 5.865 5.263 4.988 4.991

 Motor fuel 4.847 3.491 3.506 3.338 3.200 3.093

Medical care 5.031 5.198 5.425 5.570 5.709 5.908

Entertainment 4.461 4.759 4.761 4.814 4.773 4.781

Other goods and services 5.119 5.229 5.280 5.412 5.433 5.389

period E (1991-93) food and beverages, apparel

and upkeep, and transportation, are smaller

portions of all expenditures than in the official

CPI while housing, medical care, entertainment,

and other goods and services represents larger

portions of total expenditures. The relative

importance of food away from home in

Alternative E is lower than for any other base

period in Table 1. The portion of consumer

expenditures for food away from home was

highest during the period of the late 1980’s.

The Alternative indexes were updated

for price change to December of each subsequent

year using the price ratios from the official CPI

(see Table 2). These indexes were calculated at

lower-level aggregations using the new weights

based on the more recent consumption patterns.

There are 207 item strata or classes of similar

items used to sample and calculate the CPI.

There are 365 even lower level item categories

where specific items to price for the CPI are

selected. We are not able to discern the market

Table 2. Relative importances of major groups using Alternative indexes updated to December 1994.

Official

 Alternative Indexes

(Expenditure weight base period)

CPI (1987-89) (1988-90) (1989-91) (1990-92) (1991-93)

 1982-84 A B C D E

Food and beverages 17.412 16.397 16.188 16.181 16.126 16.419

 Food at home 9.934 9.255 9.093 9.309 9.466 10.004

 Food away from home 5.904 5.909 5.911 5.720 5.579 5.406

Housing 41.187 41.194 41.814 42.071 42.815 42.834

Apparel and upkeep 5.656 5.938 6.026 6.104 6.138 6.000

Transportation 17.139 19.193 18.589 18.408 17.979 18.076

 New vehicles 5.059 5.988 5.788 5.342 5.073 5.091

 Motor fuel 3.106 3.418 3.055 3.087 2.910 2.831

Medical care 7.266 6.484 6.677 6.479 6.344 6.287

Entertainment 4.335 4.684 4.692 4.761 4.727 4.743

Other goods and services 7.005 6.111 6.013 5.996 5.870 5.640
basket substitutions within an item stratum (e.g.,

the substitutions that occur between Coke and

Pepsi based on price change since both are

contained in the same item stratum; additionally,

lower-fat cookies for more traditionally prepared

cookies).

But, we can observe the market basket

changes in the major groups such as Food and

beverages or more specifically, food at home and

food away from home. The relative importance of

Food and beverages in each of the five threeyear periods is less than in the base period for the

current CPI. The relative share of food away

from home as a portion of total expenditures in

the CPI as of December 1994 is lowest using the

expenditure weights based in 1991-93 updated for

price change. The food at home share was

highest during the same period as compared to

any other period. The reverse is true for

Alternative B. Space limitations prevent further

discussion here, more details are available from

the author.

Table 3 presents the relative differences

between the published U.S. All Items CPI for

Urban Consumers (CPI-U) and each of the

alternative indexes. It begins with the last 12

months of the base period for each alternative

index and includes each 12 month period

following that up to December, 1994. This

difference reflects the change in consumer

purchasing patterns in response to price changes

and all the other factors associated with

individual economic decisions. It is the

percentage difference in the index values between

the published CPI and an alternative index for a

common timespan. Therefore, the first column

shows how much lower the CPI could be if the

alternative index with more recent weights were

in place during the last 12 months of the base

period. The results of the last two alternative

index periods are especially interesting because of

the small amount of the difference. The last

column (6) in Table 3 shows how much lower the

official CPI could be (-0.734 of 1 percent lower in

1994) if consumer expenditure patterns from

1987-89 (Alternative A) were used.

Table 3. Percentage differences between the CPI and alternative indexes with more current base periods1

,

1989-94

Cumulative from the midpoint of the base period to:

Alternative

Last 12

months of

base period2

12 months

from end of

base period

24 months

from end of

base period

36 months

from end of

base period

48 months

from end of

base period

60 months

from end of

base period

 Index (column 1) (column 2) (column 3) (column 4) (column 5) (column 6)

Alternative A - .169 - .353 - .513 - .748 - .809 - .734

Alternative B - .147 - .360 - .437 - .544 - .498

Alternative C - .144 - .366 - .446 - .347

Alternative D - .065 - .187 - .272

Alternative E - .067 - .187

1

 Alternative A, (1987-89 CE data updated for price change); Alternative B, (1988-90 CE data updated for

price change); Alternative C, (1989-91 CE data updated for price change); Alternative D, (1990-92 CE data

updated for price change); Alternative E, (1991-93 CE data updated for price change).

2

 The difference from the midpoint of the base period to the end of the base period (an 18-month period)

was .243 for Alternative A, .186 for alternative B, .283 for Alternative C, .096 for Alternative D, and .096

for Alternative E.

Braithwait pointed out (Braithwait, p.

74) that “it is clear that the size of the bias

(difference) depends on the extent of relative

price change and the amount of commodity

substitution”. The annual increase in the official

CPI-U was 3.1 or lower from 1991 to 1994. This

was the first time since the first half of the 1960s

this occurred in 4 consecutive years.

Coincidentally, it appears that the amount of

market basket changes were lower not only in

Alternative D and Alternative E for both the last

12 months of the base period (.065 and .067,

respectively), but additionally, lower in the first

12 months from the end of the base period
(column 2) than previous periods (.187 for both)

adjusted for price change.

The Consumer Price Index is used as a

measure of price change. The difference between

the index level from one time period to another is

calculated to yield a percent change. Table 4

below shows the 12-month percent changes in the

CPI All Items and each of the Alternative indexes

for the years 1989 to 1994. The price change is

calculated to one decimal point because the CPI is

published at that level. The 12-month percent

change for Alternative A and Alternative C,

shown in Table 4, would be 0.1 percent higher

than that of the official CPI in December, 1994.

While Alternative D and E would be 0.1 percent

lower than that of the official CPI in December,

1994.

Table 4. CPI All Items and Alternative indexes1

, 12-month percent changes, 1989-94

1989 1990 1991 1992 1993 1994

(column 1) (column 2) (column 3) (column 4) (column 5) (column 6)

Official CPI

 (1982-84)

 4.6 6.1 3.1 2.9 2.7 2.7

Alternative A 4.5 6.0 2.9 2.7 2.7 2.8

Alternative B - 6.2 2.9 2.8 2.7 2.7

Alternative C - - 3.0 2.8 2.7 2.8

Alternative D - - - 3.1 2.7 2.6

Alternative E - - - - 2.7 2.6

1 Alternative A, (1987-89 CE data updated for price change); Alternative B, (1988-90 CE data updated for

price change); Alternative C, (1989-91 CE data updated for price change); Alternative D, (1990-92 CE data

updated for price change); Alternative E, (1991-93 CE data updated for price change).

As you can see, one could assert that the

alternative indexes do yield lower percent

changes, but not always. We are not able to

anticipate what to expect next. In the first four

alternative indexes one 12-month period was 0.1

(3 times) or 0.2 (once) percentage point higher

than the official CPI. In 1993 each of the

alternative indexes showed a 12-month percent

change equal to that in the official CPI, not

higher and not lower. The estimates of change

from the CPI and the alternative indexes are

subject to sampling error, thus, the differences in

Table 4 are not necessarily statistically

significant. Research done by Sylvia Leaver and

Rick Valliant found that the CPI estimates of 12-

month price change had standard errors of about

.144 index points during the period 1987-91

(Leaver and Valliant, 1995, Table 28.1).

Assuming a high correlation between the CPI and

an alternative index, the differences in Table 4

would have to be greater than .1 to be statistically

significant.

Conclusion

Earlier we mentioned that consumer

behavior is sensitive to a number of factors other

than price movement. (Much of this discussion is

omitted here because of space limitations)

Because the alternative indexes are built on

different time periods the relative importance of

items during each time period is influenced by all

of these factors. This study has focused on how

alternative weighted indexes updated for price

change would differ from the official CPI and

influence substitutions in the consumer market

basket. We have attempted to address the

question we asked at the beginning, which is:

How do changing market baskets influence the

CPI.

From this analysis we can state that

substitutions in the market basket are less of an

influence during periods of lower rates of

inflation, as noted in the most recent periods.

Taking the cumulative percentage difference

between the official CPI and Alternative A (the

longest period) in this study and dividing it by the

number of years studied, we find the average

annual amount of percentage difference in the

updated market basket would be 0.15 index point

lower than the official CPI. This is consistent

with the studies mentioned earlier including

Braithwait’s estimate of the difference,
approximately one-tenth of one percent per year

(Brathwaite, 1980).

During the course of this century, the

Consumer Price Index has been continually

revised, expanded and improved. New

consumption patterns based on more recent

Consumer Expenditure Surveys have been

introduced approximately every ten years over

several decades. The Bureau of Labor Statistics

is currently developing some test indexes using a

geometric mean of the price changes to calculate

a consumer price index. This method of

calculation is believed by some to combine the

positive points of both the Laspeyres and the

superlative indexes. It is thought that a geometric

mean index would more closely resemble the

superlative indexes without the necessity of

providing current weights for consumer

expenditures.

“The increasingly significant role that

index numbers have been assuming in business

planning and in the formulation of executive

decisions not only puts a tremendous burden on

the statisticians who are responsible for their

construction, but it also presents the businessman

who uses them with the responsibility of using

them intelligently in full awareness of what,

through their strength, they show and, through

their inherent weaknesses and limitations, they

fail to show” (Freund, 1962).

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