Planned Change In The Consumer Price Index Formula April
16, 1998
The Bureau of Labor Statistics announced today its decision to
use a new formula for calculating the basic components of the
Consumer Price Index for all Urban Consumers (CPIU) and the
Consumer Price Index for Urban Wage Earners and Clerical Workers
(CPIW). This change will become effective with data for January
1999.
The new formula, the geometric mean estimator, will be used in
index categories that comprise approximately 61 percent of total
consumer spending represented by the CPIU. The remaining index
categories, which are shown in the attached table, will continue
to be calculated as they are currently. Based upon BLS research,
it is expected that planned use of the new formula will reduce
the annual rate of increase in the CPI by approximately 0.2
percentage point per year.
The research that BLS 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 following presents a summary of the factors that led BLS
to consider use of the new formula, the empirical research that
BLS conducted in evaluating the new formula, and the specific
decisions BLS has reached for using it in the CPI. A more
detailed description of the analysis underlying the decisions
will be released later this year.
The possibility of using the geometric mean formula to
calculate basic indexes in the CPI was first raised by BLS
researchers in 1993. One initial motivation for this research was
the problem of functional form bias (sometimes referred to as
"formula bias" or "elementary index bias")
then present in the CPI. The functional form bias occurred
because of technical problems involved in using observed
expenditure information to estimate the quantity weights used in
the index formula. Because the geometric mean formula does not
require quantity data, it does not suffer from this problem.
Functional form bias in the CPI was eliminated in a series of
steps, beginning in January 1995 and ending in July 1996, using
an approach that did not involve the use of the geometric mean
formula. BLS, however, continued research on the formula and
development of 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 item categories in the CPI. This
recommendation was based upon the belief that a geometric mean
formula would help to correct what the Commission called
"substitution bias." 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
lowerpriced goods or services. Consequently, the current CPI,
when compared with a measure that reflects this substitution
effect, tends to overstate the rate of price increase consumers
experience.
In contrast to the fixed quantity weights of the current CPI
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. It is, in part, this property of the geometric
mean estimator that led to the Boskin Commission recommendation
of its use in the CPI.
The CPI is constructed as an aggregation of basic indexes
computed for approximately 200 item categories, 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 only to average prices within the itemarea strata.
Consequently, the use of the formula will address only the issue
of consumer substitution within strata.
Substitution can take several forms corresponding to the types
of item and outletspecific prices used to construct the basic
indexes:
 Substitution among brands of products, for example,
between brands of ice cream;
 Substitution among product sizes, 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 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 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 from the ice cream
brand to a specific alternative dessert item, such as cupcakes or
apples, that is in another CPI category. This latter form of
substitution, although across CPI categories, would still have
the effect of reducing the quantity consumed of the higherpriced
ice cream brand relative to the quantities of other items within
the ice cream stratum. Like the other forms of substitution, this
is implicitly addressed by use of the geometric mean formula.
Note, however, that overall substitution across
categories, such as between ice cream products in general and
apples in general, is not addressed by the geometric mean
formula. The geometric mean formula will not be used to combine
the basic indexes in the CPI, like 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.
It should also be noted that the formula is only allowing 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 items’ relative prices
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, BLS began issuing an experimental CPI that used
the geometric mean estimator in the calculation of all basic
components of the index. This experimental index was issued to
provide users with a quantitative estimate of the impact that use
of a geometric mean formula at the lowest level of index
construction would have on the performance of the CPI. At that
time, it was stated that BLS would continue research on the
question of using a geometric mean estimator in the CPI. 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 comprise 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, a limited number of individual item
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, this evidence did not provide definitive
support concerning 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
item categories because of limited data availability.
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 market place. The geometric mean
estimator, as was stated earlier, can better reflect the effects
of such changes in consumer spending than can the current CPI
formula. Use of the geometric mean estimator at the basic level
of index calculation in the CPI thus can be expected to produce
an overall CPI that better reflects the impact that changing
prices have on the average consumer. Consequently, BLS 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
rationales for these exceptions are presented below.
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 CPIU and 25.500 percent in the CPIW.
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 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. These six categories had a total relative
importance of 7.067 percent in the CPIU and 7.347 percent in the
CPIW, 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 geometricmean and
arithmeticmean 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, nonetheless, 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 CPIU and 3.484 percent in the
CPIW, 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 use of the geometric mean estimator, three within
Shelter and three within Fuels and utilities. Within 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 BLS 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 bias
that affected the current formula before special, corrective
procedures were implemented in 1995 and 1996. Use of the
geometric mean estimator as outlined above obviates the need to
use 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 Laspeyres index.
The geometric mean estimator will be introduced in both the
CPIU and the CPIW effective with data for January 1999, in
accord with the past practice of introducing methodological
changes at the beginning of a calendar year. BLS will continue to
publish "overlap" CPIU and CPIW series using the
current calculation method for the first six months of 1999.
These indexes will not be published regularly for months
subsequent to June 1999, but will be available upon request.
The experimental CPIUXG, using the geometric mean estimator
in the calculation of all basic indexes, 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 CPIUXG relative to the CPIU during 1998
may not be indicative of the future impact of the geometric mean
formula in the CPI.
1. Selected shelter
services: 

A) Rent of primary residence 
B) Owners' equivalent rent
of primary residence 
C) Housing at school,
excluding board 






2. Selected utilities and
government charges: 

A) Electricity 
C) Residential water and
sewerage maintenance 
E) Telephone services, local
charges 



B) Utility natural gas
service 
D) State and local
registration, license, and motor vehicle property tax 
F) Cable television 






3. Selected medical care
services: 

A) Physicians' services 
C) Eyeglasses and eye care 
E) Hospital services 
B) Dental services 
D) Services by other medical
professionals 
F) Nursing homes and adult
daycare 






Last Modified Date: October 16, 2001