Monthly Labor Review October 1998 3

T his article describes an important improvement in the calculation of the ConsumerPrice Index (CPI). The Bureau of Labor Statistics plans to use a new geometric mean formula for calculating most of the basic components of the Consumer Price Index for all Urban

Consumers (CPI-U) and the Consumer Price Index for Urban Wage Earners and Clerical Workers (CPI-W). This change will become effective

with data for January 1999.1

The geometric mean formula will be used in

index categories that make up approximately 61

percent of total consumer spending represented

by the CPI-U. The remaining index categories,

which are shown in exhibit 1, will continue to be

calculated as they are currently. On the basis of

BLS research, it is expected that the use of the

new formula will reduce the annual rate of increase in the CPI by approximately 0.2 percentage point per year.

Background

The Bureau of Labor Statistics has a long tradition of research and operational innovation regarding the measurement of prices. In the past

few years, the Bureau has made a series of improvements that reflect the agency’s ongoing

commitment to keeping its measures on changes

in consumer prices as accurate and up to date as

possible.

In 1995 and 1996, for example, steps were

taken to resolve the problem of “functional form

bias” in the CPI.

2 This upward bias was a technical problem that tied the weight of a CPI sample

item to its expected price change. The flaw was

effectively eliminated by changes to the CPI

sample rotation and substitution procedures and

to the functional form used to calculate changes

in the cost of shelter for homeowners. In 1997, a

new approach to the measurement of consumer

prices for hospital services was introduced.3 Pricing procedures were revised, from pricing individual items (such as a unit of blood or a hospital inpatient day) to pricing the combined sets of

goods and services provided on selected patient

bills, facilitating the measurement of price change

in an area in which the products and services

available are undergoing significant change. Effective with the data for January 1998, the Bureau instituted a number of important changes

associated with the 1998 CPI revision.4 Expenditure weights are now based on 1993–95 consumer

spending patterns, a new sample of geographic

areas was introduced that better represents the

current distribution of the U.S. population, and a

new classification structure was incorporated that

better reflects the categories of goods and services consumers buy. In January 1998, the Bureau also improved its treatment of changes in

the quality of personal computers.5

The Bureau plans further improvements to the

CPI as well. A hedonic model to adjust television

prices for changes in quality is slated to begin in

January 1999, as is a change in the way utility

rebates are treated in the index.6 The Bureau also

Beginning in January 1999, a new geometric mean

formula will replace the current Laspeyres formula

in calculating most basic components

of the Consumer Price Index; the new formula will better

account for the economic substitution behavior of consumers

Kenneth V. Dalton,

John S. Greenlees,

and

Kenneth J. Stewart

Kenneth V. Dalton is

Associate Commissioner for Prices and

Living Conditions;

John S. Greenlees is

Assistant Commissioner for Consumer

Prices and Price

Indexes; and Kenneth

J. Stewart is an

economist in the

Division of Consumer

Prices and Price

Indexes, Bureau of

Labor Statistics.

Incorporating a geometric

mean formula into the CPI

Calculating the CPI
4 Monthly Labor Review October 1998

Calculating the CPI

plans to improve the timeliness of future CPI revisions. In this

regard, the size of the Consumer Expenditure (CEX) Survey,

which is used as the source of the market basket weights for

the CPI, will expand by approximately 50 percent, and the lag

between the collection of information on expenditures and

the introduction of the market baskets into the CPI will decrease.7 Further, in addition to supporting more timely updates of CPI expenditure weights, the expanded sample for the

CEX Survey will support the publication of production-quality

superlative indexes. Under certain conditions, superlative indexes account for substitution across CPI item categories in

response to relative price changes. Finally, the Bureau plans

to improve its procedures for selecting outlet and item samples,

to allow for more frequent sample updates for those consumer

markets undergoing rapid change.8

The geometric mean formula

The CPI currently is constructed using a set of constant, or

fixed, implicit quantity weights. Thus, the index does not reflect the fact that consumers can—and do, to some degree—

insulate themselves from the impact of higher prices by adjusting their spending to favor relatively lower priced goods

or services. Consequently, compared with a measure that reflects this substitution effect, the current CPI tends to overstate

the rate of price increase consumers experience.

In contrast to the fixed quantity weights of the current CPI

arithmetic mean formula, the geometric mean estimator employs a set of fixed expenditure proportions as weights to be

used in averaging the prices of individual items within a CPI

basic index. Fixing the relative expenditure proportions, rather

than the relative quantities, implies that consumers can alter

the quantities of goods and services they buy—albeit within

the narrow range of a CPI category—when the relative prices

of those goods and services change.

The CPI is constructed as an aggregation of basic indexes

computed for approximately 200 categories of items, such as

“ice cream and related products,” in each of 38 geographic

areas. Within each of these index components, or strata, prices

for specific items in a sample of outlets (stores) are combined

to produce a basic index. As noted above, the geometric mean

formula will be used solely to average prices within the itemarea strata. Consequently, the use of the formula will address

only the issue of consumer substitution within strata.9

The research the Bureau has conducted over the past few

years strongly suggests that the use of the geometric mean

estimator at the basic level of index construction in the CPI

will produce a measure that more accurately reflects the impact that changing prices have on the average U.S. household. The remainder of this article presents (1) a summary of

the factors that led the Bureau to consider using the new formula, (2) the empirical research the Bureau conducted in evaluating the formula, and (3) the specific BLS decisions that were

reached in regard to using the formula in the CPI.

The possibility of using the geometric mean formula to

calculate basic indexes in the CPI was first raised by BLS researchers in 1993.10 One initial motivation for research into

this area was the problem of functional form bias (sometimes

referred to as formula bias or elementary index bias) then

present in the CPI. Functional form bias occurred because of

technical problems involved in using observed expenditure

information to estimate the quantity weights employed in the

index formula. Because the geometric mean formula does not

require quantity data, it does not suffer from this problem. As

noted above, functional form bias was eliminated from the CPI

in a series of steps, beginning in January 1995 and ending in

July 1996, using an approach that did not involve the geometric mean formula. The Bureau, however, continued research

on the formula and developed an experimental geometric mean

index, in part due to a recognition that the formula offered a

means of reflecting consumer substitution behavior.

In December 1996, the Advisory Commission to Study the

Consumer Price Index, commonly known as the Boskin Commission, recommended the use of the geometric mean formula

for the aggregation of prices within all categories of items in

the CPI.

11 This recommendation was based upon the belief that

a geometric mean formula would help to correct what the Commission called “substitution bias.”

Substitution can take several forms, corresponding to the

types of item- and outlet-specific prices used to construct the

basic indexes:

Exhibit 1. Components of the CPI retaining the

 arithmetic mean (Laspeyres) formula

 Selected shelter services

Rent of primary residence

Owner’s equivalent rent of primary residence

Housing at school, excluding board

 Selected utilities and government charges

Electricity

Maintenance of residential water and sewerage

Telephone services, local charges

Utility natural gas service

State and local registration, license, and motor

 vehicle property tax

Cable television

 Selected medical care services

Physicians’ services

Eyeglasses and eye care

Hospital services

Dental services

Services by other medical professionals

Nursing homes and adult day care
 Monthly Labor Review October 1998 5

• Substitution among brands of products, for example,

between brands of ice cream

• Substitution among sizes of products, for example,

between pint and quart packages of ice cream

• Substitution among outlets, for example, between a

brand of ice cream sold at two different stores

• Substitution across time, for example, between purchasing ice cream during the first or the second week

of the month

• Substitution among types of items within the category, for example, between ice cream and frozen

yogurt

• Substitution among specific items in different index categories, for example, between ice cream and

cupcakes

Thus, in response to an increase in the price charged by a

store for a certain brand of ice cream, a consumer could respond by redistributing his or her purchases along any of several dimensions represented by other priced items in the category: to another brand of ice cream whose price had not risen,

to a larger package of ice cream with a smaller price per ounce,

to ice cream at a different store where ice cream is on sale, or to

a brand of frozen yogurt. The consumer also could respond by

postponing the ice cream purchase until a later date. (Prices for

CPI items are collected throughout the month and then averaged.)

Finally, the consumer could substitute a specific alternative dessert item, such as cupcakes or apples, that is in another CPI category. This form of substitution, although across

CPI categories, would still have the effect of reducing the quantity consumed of the higher priced brand of ice cream relative

to the quantities consumed of other items within the ice cream

stratum. Like the other forms of substitution, such cross-category substitution is implicitly addressed by the use of the

geometric mean formula. Note, however, that the formula does

not address overall substitution across categories, such as between ice cream products in general and apples in general.

Thus, the geometric mean formula will not be used to combine the basic indexes in the CPI, such as those for ice cream

products and apples, into the overall index. In the same way,

the use of the geometric mean formula within categories does

not address the issue of whether consumers can, or do, respond to a general increase in the price of ice cream products

by, for example, forgoing dessert altogether.

Note also that the formula only allows for a degree of substitution by consumers as a group: while the formula implicitly assumes that at least some customers will change their

purchasing patterns when the relative prices of items change,

it is not inconsistent with some individual consumers continuing to purchase their favorite products even when they

become relatively more expensive.

In April 1997, the Bureau began issuing an experimental

CPI that used the geometric mean estimator in the calculation

of all basic components of the index. This experimental index, called the CPI-U-XG, afforded a quantitative estimate of

the impact that the use of a geometric mean formula at the

lowest level of index construction would have on the performance of the CPI. At that time, the Bureau stated that it would

continue research on the question of using a geometric mean

estimator in the CPI.

12 This research would entail a thorough

review of the theoretical literature concerning different index

number formulas, a review of the practices of other countries

and the justifications for their choices of formula, and a systematic and comprehensive analysis of available data to evaluate the appropriateness of using the geometric mean formula

in the construction of each basic component of the CPI.

One of the principal objectives of the BLS research on geometric means was to determine, for each of the basic index

categories that make up the CPI, the extent to which consumers can be expected to alter their spending when relative prices

change. Three types of evidence were examined in this effort:

(1) highly detailed supermarket scanner data on prices charged

for, and quantities sold of, items in a limited number of categories; (2) measures of the extent of substitution at index

calculation levels above the basic level, which can be viewed

as providing indirect evidence concerning the likelihood of

substitution behavior within item categories; and (3) estimates

of the magnitude and prevalence of the substitution effect derived from a survey of the relevant empirical literature. For a

variety of reasons, none of the three types of evidence provided definitive support regarding the existence and magnitude of the substitution effect in each of the basic index categories. For example, although analysis of the detailed data

on prices and quantities strongly indicated the existence of a

significant substitution effect, the analysis was possible for

only a few categories of items because of limited availability

of the data.

Taken in its entirety, however, the evidence unambiguously

supported the proposition that consumers can, and do, alter

their purchasing behavior in response to changes in the array

of prices that they confront in the marketplace. As stated earlier, the geometric mean estimator can better reflect the effects of such changes in consumer spending than can the current CPI formula.

Incorporating the formula into the CPI

On the basis of the preceding analysis of the evidence, the use

of the geometric mean estimator at the basic level of index

calculation in the CPI can be expected to produce an overall

index that better reflects the impact that changing prices have

on the average consumer. Consequently, the Bureau plans to

use the geometric mean estimator in most CPI basic indexes,

beginning with data for January 1999. The basic indexes that

will continue to be calculated as they are now represent important exceptions to this general rule. The excepted indexes
6 Monthly Labor Review October 1998

are shown in exhibit 1 and fall into three general categories,

the rationales for whose exclusion are presented next.

Selected shelter services. The total residential housing stock

changes slowly. Thus, consumers as a group cannot freely alter their purchases of housing services in response to changes

in the relative prices of different rental units. Consequently,

the item categories of residential rent, owner’s equivalent rent,

and housing at school will not employ the geometric mean

estimator. As of December 1997, these three categories together had a relative importance of 27.315 percent in the CPI-U

and 25.500 percent in the CPI-W.

Selected utilities and government charges. The services in

these categories are provided primarily by governments or by

regulated monopolies. Although CPI pricing samples within a

basic index may include different service providers, in most

cases consumers can substitute between these providers only

by moving into a different service area. The BLS analysis of the

substitution effect above the basic index level supports the

continued use of the current formula in the utilities sector. Additionally, estimated utility demand elasticities obtained from

the economics literature mentioned before are low, at least in

the short run, and thus argue for maintaining the current approach. The six categories under selected utilities and government charges had a total relative importance of 7.067 percent

in the CPI-U and 7.347 percent in the CPI-W, as of December

1997. (These relative importance totals include the prorated

weight of two unpublished indexes, unsampled motor vehicle

fees and unsampled video and audio, whose movements will

be imputed by a mixture of geometric mean and arithmetic

mean indexes.)

Selected medical care services. The decision to retain the

current formula for professional and hospital medical care services is based largely on the results of the survey of demand

elasticities in the economics literature. The relatively large elasticities for some prescription drugs contrast with low elasticities for hospital and professional services. Insurance firms and

health plans, acting as agents for consumers, may be more sensitive to relative price changes than are consumers themselves,

who pay only a share of the cost directly. It is therefore difficult to justify the proposition that consumers are highly responsive to relative prices in their direct purchases of health

care services. The six excluded medical care categories (along

with corresponding unpublished health insurance indexes) had

a total relative importance of 4.159 percent in the CPI-U and

3.484 percent in the CPI-W, as of December 1997.

These exclusions leave three major groups of the CPI—food

and beverages, apparel, and other goods and services—that

will use the geometric mean formula exclusively in the calculation of basic indexes. The other major groups each will have

one or more excepted categories. Within the transportation

group, State and local registration, license, and motor vehicle

property tax charges will continue to use the current formula.

Within the recreation group, the cable television index will

continue to be calculated as it now is, as will the telephone

services local charges index within the education and communication group. The housing group will have six important

exceptions to the use of the geometric mean estimator, three

within the shelter category and three within fuels and utilities.

In the medical care group, the medical care commodities indexes will employ the geometric mean formula, while most

indexes for medical care services will continue to use the current formula.

It is important to note that, in addition to the evidence described above, the Bureau considered other factors in reaching its decisions on the use of the geometric mean estimator.

Two of these additional considerations are worthy of mention.

First, the geometric mean estimator does not suffer from the

persistent functional form bias that affected the current formula before the special, corrective procedures were implemented in 1995 and 1996. Use of the geometric mean estimator as outlined above obviates the need to employ these special procedures in all but the several basic indexes that will

continue to use the current formula. Largely eliminating the

need for special procedures will, for the most part, make unnecessary the continued monitoring of how well they are achieving their intended objective. Second, index calculation formulas often are evaluated with respect to how well they satisfy

certain performance criteria, often referred to as tests. Within

the context of the list of tests generally imposed on price indexes, the geometric mean formula performs at least as well as

the current, Laspeyres index.

The geometric mean estimator will be introduced into both

the CPI-U and the CPI-W effective with data for January 1999, in

accord with the past practice of introducing methodological

changes at the beginning of a calendar year. The Bureau will

continue to publish “overlap” CPI-U and CPI-W series using the

current calculation method for the first 6 months of 1999. These

indexes will not be published regularly for months subsequent

to June 1999, but will be available upon request.

The experimental CPI-U-XG, using the geometric mean estimator in the calculation of all basic indexes and issued since

April 1997, will be calculated through data for December 1998.

Users of this series are reminded that the implementation of

the geometric mean formula in 1999 will not apply to all basic

indexes. Therefore, the movements of the CPI-U-XG relative to

the CPI-U during 1998 may not be indicative of the future impact of the geometric mean formula in the CPI. 

Footnotes

1 See, for example, “Improving CPI sample rotation procedures,” Consumer Price Index Detailed Report (Bureau of Labor Statistics, October 1994),

pp. 7–8.

Calculating the CPI
 Monthly Labor Review October 1998 7

2

 Elaine M. Cardenas, “Revision of the CPI hospital services component,”

Monthly Labor Review, December 1996, pp. 40–48. 3

 John S. Greenlees and Charles C. Mason, “Overview of the 1998 revision of the Consumer Price Index,” Monthly Labor Review, December 1996,

pp. 3–9. 4

 “Using a hedonic model in the CPI to adjust personal computer prices

for changes in quality,” Consumer Price Index Detailed Report (Bureau of

Labor Statistics, June 1997), p. 18. 5

 See “Using a hedonic model to adjust television prices in the Consumer Price Index for changes in quality,” Consumer Price Index Detailed

Report (Bureau of Labor Statistics, June 1998), p. 5; and “Improvements to

CPI procedures for handling utility refunds,” Consumer Price Index Detailed

Report (Bureau of Labor Statistics, July 1998, p. 5. 6

 Testimony of Katharine G. Abraham, Commissioner of Labor Statistics, before the Subcommittee on Human Resources of the House Committee on Government Reform and Oversight, Apr. 29, 1998. 7

 Robert Cage, “New methodology for selecting CPI outlet samples,”

Monthly Labor Review, December 1996, pp. 49–61. 8

 Recent empirical analyses of substitution across strata are presented

in, for example, Ana M. Aizcorbe and Patrick C. Jackman, “The commodity

substitution effect in CPI data, 1982–91,” Monthly Labor Review, December

1993, pp. 25–33; and Matthew D. Shapiro and David W. Wilcox,

“Mismeasurement in the Consumer Price Index: An Evaluation,” in Ben S.

Bernanke and Julio J. Rotemberg, eds., NBER Macroeconomics Annual, 1996

(Cambridge, MA, MIT Press, 1996), pp. 93–142. 9

 Brent R. Moulton, “Basic components of the CPI: estimation of price

changes,” Monthly Labor Review, December 1993, pp. 13–24. Among other

recent papers that propound theoretical or empirical results concerning the

geometric mean formula are W. Erwin Diewert, Axiomatic and Economic

Approaches to Elementary Indexes, Working Paper No. 5104 (Cambridge,

MA, National Bureau of Economic Research, May 1995); Marshall B.

Reinsdorf and Brent R. Moulton, “The Construction of Basic Components

of Cost-of-Living Indexes,” in Timothy F. Bresnahan and Robert J. Gordon,

eds., The Economics of New Goods (Chicago, University of Chicago Press,

1997); and Brent R. Moulton and Karin E. Smedley, “A Comparison of Estimators for Elementary Aggregates of the CPI.” Paper presented at the Western Economic Association International Conference, San Diego, July 7, 1995. 10 Advisory Commission to Study the Consumer Price Index, Toward a

More Accurate Measure of the Cost of Living, Final Report to the Senate

Finance Committee, Dec. 4, 1996. 11 The Experimental CPI Using Geometric Means (CPI-U-XG) (Bureau of

Labor Statistics, Apr. 10, 1997).

Bureau of Labor Statistics Internet

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a range of data on consumer and producer prices, employment and unemployment, occupational compensation, employee benefits, workplace injuries and

illnesses, and productivity. The homepage, at http://stats.bls.gov can be accessed using any Web browser.

Also, some data can be accessed through anonymous FTP or Gopher at

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