Interarea Consumer Prices

Sherwood” index, the range is somewhat broader,
from 91.0 to 112.9, although the statistical sig-
nificance of these differences has not been
assessed.

Future research

At present, the experimental interarea price in-
dex project has provided indices for food at
home,” professional medical services,'? and
housing, '* Indices for private transportation com-
modities, apparel, and household fuels and utili-
ties are currently in the process of being formed.
When these are completed, coverage will have

Footnotes

been extended to about 85 percent of the average
household’s budget for consumption.'* The re-
sults thus far are consistent with a prior expec-
tations of intercity price differences and with
information from other sources.

The component indices will be aggregated
into an all-items index for those goods and
services in the project sample. This index, and
the information obtained by constructing each of
the component indices, could provide useful
guidelines for adapting the CPI sample of price
information to facilitate interarea as well as
intertemporal comparisons. oO

ACKNOWLEDGMENT: Thanks are due to Kimberly
Zieschang for his helpful comments and to Joseph Pavalone
for assistance with research.

' Mark K. Sherwood, “Family budgets and geographic
differences in price levels,” Monthly Labor Review, April
1975, pp. 8-15.

* Sherwood, “Family budgets,” p. 9.
> pbid., p. 8

* Floyd A. Rabil, “Average retail food prices: a brief
history of methods,” Monthly Labor Review, November
1984, pp. 52-53.

5 See L. Blanciforti, Price Measurement for Interarea
Comparisons, unpublished manuscript (Bureau of Labor
Statistics, November 1986); D. F. Primont and Mary F.
Kokoski, Comparing Price across Cities: A Hedonic Ap
proach, BLS Working Paper 204 (Bureau of Labor Statis-
tics, May 1990); and D, F. Primont and Mary F. Kokoski,
Differences in Food Prices across U.S. Cities: Evidence
from cP Data, BLS Working Paper 209 (Bureau of Labor
Statistics, November 1990).

© See 1. B. Kravis, “Comparative Studies of National
Incomes and Prices,” Journal of Economic Literature 22
(1984): 1-39; 1. B. Kravis, Z. Kennessey, A. Heston, and R.
Summers, United Nations International Comparison
Project: Phase One, a System of International Compari-
sons of Gross Product and Purchasing Power (Baltimore,
the Johns Hopkins University Press, 1975); and R. Sum
mers, “International Comparisons with Incomplete Data,
Review of Income and Wealth, March 1973, pp. |-16.

34 Monthly Labor Review July 1991

7 See W. E, Diewert, “Index Numbers,” in The New
Palgrave Dictionary of Economics, vol. 2, edited by J.
Eatwell, M. Milgate, and P, Newman (New York, Stockton
Press, 1987), pp. 767-80; and L. Drechsler, “Weighting of
Index Numbers in Multilateral International Comparisons,”
Review of Income and Wealth, March 1973, pp. 17-34. The
method was generalized in D. W. Caves, L. R. Christensen,
and W. E. Diewert, “Multilateral Comparisons of Output,
Input, and Productivity Using Superlative Index Num-
bers,” Economic Journal, March 1982, pp. 73-86.

* A self-representing area is an area represented in the
CPI by a sample of price quotes from that area alone, For
further details on the relationship between self-represent-
ing areas and Standard Metropolitan Statistical Areas, see
BLS Handbook of Methods, Bulletin 2285 (Bureau of Labor
Statistics, 1988), pp. 161-162.

° These weights are the same preliminary cost weights
used for the CPI; see BLS Handbook of Methods, p. 168.

"© For more details, see Primont and Kokoski, Differ-
ences in Food Prices.

"Index 4 in Sherwood, “Family budgets,” p. 10

 Primont and Kokoski, Differences in Food Prices

8 Primont and Kokoski, Comparing Price.

“4B. Moulton, Interarea Indexes of the Cost of Shelter
Using Hedonic Quality Adjustment Techniques, unpub-
lished manuscript (Bureau of Labor Statistics, December
1989).

'S See cpy Detailed Report for December 1988 (Bureau
of Labor Statistics, 1989).



Mary F. Kokoski

Mary F. Kokoski is an
economist in the Division
of Price and Index
Number Research, Bureau
of Labor Statistics,

New research on interarea
consumer price differences

An experimental interarea price index project

is under way at BLs and has generated indices
for several components of the consumer’s budget;
the aim of the project is to adapt cpt data

to facilitate interarea cost-of-living comparisons

nterarea comparisons of the cost of living

are of interest to researchers and policy-

makers, as well as to businesses and
households making decisions about where they
should locate or relocate. It is widely perceived
that the cost of goods and services differs across
geographic areas. Published Consumer Price
Index (CPI) series for various geographic areas
measure price changes over time for these areas.
An official, consistently designed index of
interarea price differences does not exist. Re-
search is under way, however, to investigate the
possibility of using the enormous data resources
compiled for the CPI to construct a comprehen-
sive index of interarea prices. Such an index, if
officially produced, would provide an interarea
complement to the CPI.

Among the goods and services included in
this experimental index would be those compos-
ing the food-at-home component of the con-
sumer’s budget. Food at home, which consti-
tuted 10.1 percent of the average household
budget in December 1989, is also an expenditure
of particular interest to policymakers and re-
searchers in the health field. Accordingly, in this
article, an experimental interarea price index for
food at home is analyzed in the context of past
research at the Bureau of Labor Statistics on
geographic differences in prices.

Interarea price measurement

The first official measure of interarea differ-
ences in the cost of living was the standard
budget of the Family Budgets program of the
BLS, developed in the 1940's. Under this pro-

gram, a predetermined standard of living was
translated into a set of hypothetical baskets of
goods and services, and the costs of these bas-
kets were compared across geographic areas.
The standard budget embodied an “income re-
quirements approach,” by assuming that fami-
lies with a given demographic profile had the
same utility function across goods and services,
leisure, and working conditions.’ It did not,
however, take an identical basket of goods and
services as a common denominator to compare
in all areas. Variations in the specific items
included, as well as in the quantities purchased,
were therefore implicit in the interarea compari-
son. As Mark Sherwood pointed out in 1975,
an interarea price index produced from these
budget data would serve as a measure of differ-
ences in the cost of living only under the assump-
tion that a given family would be indifferent
with respect to all the various baskets.? By com-
paring index values from the Family Budgets
program with those generated by a fixed market
basket for all areas, he found that variations in
specification of items and in quantities did have
a large effect on the interarea comparisons for
food and transportation.’

Although the Family Budgets program was
phased out in the 1970’s, price information con-
tinues to be collected in many metropolitan and
nonmetropolitan areas in support of the Con-
sumer Price Index and the Average Prices pro-
gram of the BLS. Unfortunately, these price data
are not readily amenable to interarea compari-
sons. First, the Average Prices program includes
only selected food items in its sample, and there
are variations in the brand and quality of items

Monthly Labor Review July 1991 31


Interarea Consumer Prices

across areas.* Second, average retail prices for
food are reported officially only at the U.S. and
regional levels. Third, the price sample used for
the cpt, although extremely large, is intended to
facilitate intertemporal comparisons and is based
on a probability-sampling methodology. This
means that the specific items priced in each
outlet in each area are those which consumers in
that outlet and area are likely to purchase. Thus,
while a 10-ounce jar of Folger’s crystals will
represent the instant coffee category ina grocery
in Milwaukee, a 2-ounce jar of house-brand
instant coffee will represent the same category in
a grocery in Denver. This diversity of market
baskets makes direct comparison of prices across
areas problematic.

An experimental interarea price index

Recent research has demonstrated that interarea
comparisons can be made using the CPI price
quotes as a resource.’ To accomplish these com-
parisons, a methodology is adopted which ac-
counts for the diversity of items in the sample in
a statistically explicit fashion. Based on the
Country-Product-Dummy method, used in mak-
ing international output comparisons,° this ap-
proach employs a hedonic regression, with each
specific item’s price as the dependent variable
and three sets of independent dummy variables:
one describing the item’s physical characteris-
tics (such as weight and color), asecond defining
the type of outlet in which the item is sold (for
example, a chain supermarket), and a third de-
fining the geographic area in which the item is
sold (for instance, Milwaukee). When the de-
pendent variable is expressed in logarithmic
form, the coefficients of the area dummies can
be interpreted as bilateral interarea price indices,
with one area arbitrarily chosen as the reference
area by excluding its dummy variable from the
regression sample.

When aggregated across commodities, these
bilateral indices, while useful for many applica-
tions, are not, in general, transitive. For ex-
ample, the product of the bilateral index for
Baltimore to New York with that of New York to
Philadelphia will not, in general, equal the direct
bilateral index of Baltimore to Philadelphia.
Also, alternative choices of reference area will
result in different index values for all areas. For
instance, the price differential for Baltimore
versus Milwaukee may be different when Phila-
delphia is taken as the reference area than when
New York is chosen as the reference area. To
overcome these difficulties, the bilateral indices
can be adjusted by a method of constructing a
transitive, multilateral set of index values de-
scribed initially by O. Elteto, P. Koves, and B.

32 Monthly Labor Review July 1991]

Szulc.’ This method, known as the EKS ap-
proach, takes the geometric mean of all areas in
the sample as the reference “area.”

The construction of an EKS index requires
four basic steps. First, hedonic regressions are
run at the most disaggregate level possible of
item classification, the entry-level item. Second,
the regression coefficients are weighted up, to
construct interarea price relatives at a more ag-
gregate level, the item stratum level. The weights
used are the preliminary cost weights from the
Consumer Expenditure Survey. Third, the price
relatives are used to construct a set of bilateral
Térnqvist indices that are aggregated over item
strata to the level of aggregation desired (for
example, all food at home). Fourth, the geomet-
tic mean of the bilateral Térnqvist indices is
obtained. The value of this mean for an area / is
the EKS index value for that area.

Formally, the Térnqvist (transcendental loga-
rithmic) price index is defined as

a) nef = 2S (st) In (4)
n i

=5D (ses) (8B) iam
7

where the summation is over the item strata
composing the aggregate of interest, f is item
stratum n’s share of expenditures for that aggre-
gate in area k, In (n"/ pf) is the difference be-
tween the item stratum-level relative interarea
prices for area i and area j for item stratum n, and
5f is the average of the hedonic regression coef-
ficients for item stratum n in area i. The EKS
index 4; is then defined as a weighted geometric
mean of the Tornqvist bilateral price indices for
area i relative jo every other area j:

au | .
(2) in a->) eet |in af
Prd

LL
Here, 7j4; isexpenditures in areaj, so the weights

are areaj’s share of expenditures in all areas. The
multilateral indices 6;, then, represent the price
level in area i relative to all other areas.

The EKS method has been applied to the food-
at-home component of the CPI to derive a multi-
lateral interarea index for the 44 geographic
areas that have published CPI series. These con-
sist of 32 self-representing areas* and 12 areas
that are aggregates of smaller Standard Metro-
politan Statistical Areas clustered by census
region and population size class. The survey
period July 1988 through June 1989 was chosen
to provide the sample of price quotes. After a
screening of the data for missing information or
errata that could not be corrected, the final sample
comprised 53,459 observations. The regressions



were run at the level of the entry-level item, and
the resulting coefficients were weighted up to
obtain a set of price relatives for the next level of
aggregation, the item stratum level, using the
expenditure weights from the Consumer Expend-
iture Survey.” The EKS index thus derived covers
the aggregate of all food at home, as defined by
the cpi.'°

Index values for selected cities are presented
in the first column of table 1 as the variable tap
(for “Interarea Price”). Unfortunately, computa-
tion of variance estimates for these indices is not
straightforward, a result of imputation proce-
dures required in the aggregation from entry-level
item coefficients to the item stratum level. Re-
search is under way to enhance the procedure.

Interarea indices for food at home

Although they cover different time periods and
were calculated by different methodologies, it is
interesting to compare the interarea index values
from the hedonic Exs method with the values
obtained by Sherwood with a fixed market bas-
ket. Similarities may indicate consistent patterns
of price differences across cities and also lend
some support to the usefulness of the hedonic
method in statistically controlling for differ-
ences in item characteristics. Thus, in table },
column 2 shows the Sherwood index values for
the year 1973, the reference year of his published
study, and column 3 gives a set of “updated
Sherwood” index values for the year 1988, more
comparable to the time period of the 1AP values.
Both of these Sherwood series are based on his
fixed-weight index."

To obtain Sherwood index values compa-
rable to the IAP results, it was first necessary to
identify geographic areas that were the same in
both studies. These are the 25 cities in table 1.
Taking these cities as the relevant sample, the
index values for both Sherwood and LAP were
“teweighted” so that the index base was the
mean index value for this sample for each type of
index. That is, the reference for each column of
indices is the mean of that column of index
values across all cities in table 1. Because of the
15-year time difference between the two studies,
a set of “updated Sherwood” indices was con-
structed by moving the reweighted 1973
Sherwood index values forward by each city’s
cPI for 1973 to 1988. That is, each reweighted
Sherwood index value in column 2 was multi-
plied by a price relative of the 1988 food-at-
home CPI to the 1973 food-at-home CPI, where
the CPI values were specific to each respective
city. The resulting index values were then
reweighted to give them a base value of 100 and
are presented in column 3.

A comparison of the IAP values to the 1973
Sherwood values indicates a different pattern of
cities above and below the mean of interarea
prices for food at home. However, when the
Sherwood index is updated by the CPI, the pat-
tern is quite similar to that of the IAP index. Only
two cities, Boston and Kansas City, deviate from
the common pattern. In the absence of variances
and, thus, tests of statistical significance, this
observation would appear to provide some sup-
port for the hedonic method when identical mar-
ket baskets cannot be compared across areas.
The difference between the 1973 Sherwood val-
ues and the “updated Sherwood” values sug-
gests that interarea price differences are not
consistent over time.

The “updated Sherwood” 1988 and IAP 1988—
89 pattern of price differences shows generally
higher prices for cities in the south and more
cities with below-average prices in the north
central region of the United States. In all index
series, the high price outliers are Anchorage and
Honolulu, which would be expected on the basis
of heuristic evidence. The range of LAP index
values is from 93.4 to 106.8 for cities in the
continental United States; for the “updated

Table 1. Index values for food at home, selected cities
[Average= 100]
city ap,? Sherwood, Updated
1988-89 1973 Sherwood, 1988
Northeast
Boston...... 0.200000 99.3 102.2 102.6
Buttalo veeceees 96.6 96.2 98.8
New York/Northeastern NJ . 105.1 103.2 112.0
Philadelphia . 102.1 99.2 102.2
Pittsburgh ......--.- 66-65 93.3 95.2 91.0
North Centrai
Chicago detec e ween 102.2 102.2 102.3
Cincinnati .. a 106.2 98.2 106.2
Cleveland beeen eee 96.4 95.2 96.0
Detroit........ 98.3 102.2 98.2
Kansas City : 101.3 100.2 99.2
Milwaukee... . 95.9 93.3 94.8
Minneapolis/St. Paul ..... 93.4 96.2 98.7
St. Louis . . 105.7 100.2 103.7
South
Atlanta........ 106.8 103.2 104.1
Baltimore 105.1 101.2 101.6
Dallas . 103.2 94.2 100.5
Houston ..... 102.4 99.2 110.2
Washington 104.1 103.2 112.8
We:
Denver .... 96.5 95.2 90.9
Los Angeles . 100.6 93.3 100.0
San Diego... 97.3 91.3 98.6
San Francisco ........... 102.4 98.2 307.4
Seattle ween en ene 104.3 100.2 100.7
Noncontinental
Honolulu ....... 139.0 116.1 141.3
Anchorage... se 1257 121.0 124.7
‘1aP = interarea price index.
— —

Monthly Labor Review July 1991 33