MODELING THE REALIZED OUTLET SAMPLE FOR THE COMMODITIES AND SERVICES

COMPONENT OF THE U.S. CONSUMER PRICE INDEX.

William H. Johnson, Sylvia G. Leaver and Thomas S. Benson, U.S. Bureau of Labor Statistics

2 Massachusetts Avenue, NE, Room 3655, Washington, DC 20212

KEY WORDS: simulation, sample design, sample size

Any opinions expressed in this paper are those of the

authors and do not constitute policy of the Bureau of

Labor Statistics.

The U.S. Consumer Price Index (CPI) is made up of

two large components, commodities and services

(C&S) and housing. Each year approximately 25% of

the sample for commodities and services is rotated in

order to introduce new items into the sample for the

CPI and to select a set of outlets which better reflects

current expenditures among outlets. The variance and

cost of the sample for commodities and services are

modeled so that a sample design can be found which

minimizes the variance of the estimator for the

commodities and services component of the CPI. In

order to do this, it is necessary to ascertain the number

of distinct outlets that arise under repeated sampling of

the outlet frames for distinct item categories.

This paper documents the method used to estimate the

actual number of unique outlets as a function of the

number of outlets specified to be selected and attempts

to evaluate the effectiveness of this methodology.

1. The Design of the Commodities and Services

sample

The U.S. Consumer Price Index measures the change in

the cost of a fixed market basket of goods and services.

The commodities and services component of the CPI

accounts for 72.5% of the expenditure weight in the

CPI. The sample for the commodities and services

component is derived from two stages of samples.

The first stage of the design is the selection of primary

sampling units (PSUs) which are used for both the

housing and commodities and services components of

the CPI. A PSU is a geographic area composed of

counties, or minor civil divisions in the northeast

United States. There are 87 PSUs of which 31 are

metropolitan statistical areas selected with certainty and

56 are smaller non-self representing areas.

At the second stage of sampling for commodities and

services there are two independent samples drawn

within each PSU. A sample of outlets is drawn from

frames constructed from the Telephone Point of

Purchase Survey (TPOPS). Commodities and services

is represented by 217 TPOPS categories and 16 nonPOPS categories. Roughly 25% of the categories are

rotated each year. In the Telephone Point of Purchase

Survey, consumers are sampled using random digit

dialing. The selected consumers are then asked from

which outlets they bought items within a subset of the

TPOPS categories and how much money was spent in

each outlet for each TPOPS category within a given

recall period ranging from one week to five years. The

set of the reported outlets make up the frames for the

TPOPS categories.

Separately a sample of item strata is selected. An item

stratum is a fairly small set of items or services such as

bananas or canned fruits and vegetables or laundry and

dry cleaning services. The item strata are clustered into

item groups and the sample design specifies the total

number of item strata selections per item group. Each

item stratum corresponds to one or more TPOPS

categories. Each time an item stratum is selected, one

of the corresponding TPOPS categories is selected with

probability proportional to the relative importance of

the TPOPS category within the item stratum. The

relative importance for a TPOPS category is the sum of

the relative importances of the entry level items (ELIs)

which are mapped to the TPOPS category. The ELI

level relative importances within an item stratum are

determined from the Consumer Expenditure survey

(CE). This produces a sample of item strata and

associated TPOPS categories. Once the samples of

outlets and item strata are selected they are merged by

TPOPS category to give a sample of outlets and items

within outlets.

2. The model of the Commodities and Services

sample

The total variance of price change is a weighted sum of

variances of index area – group of item strata price

changes. An index area here is a self representing PSU

or a collection of non-self-representing PSUs of the

same size class and in the same Census region.

The variance of an index area - group of item strata

price change is decomposed into three or four

components; a component of variance attributable to

variation across outlets, a component of variance

attributable to variation across item strata, a residual

component of variance and if there are multiple PSUs

in the index area, a component of variance attributable
to variance across PSUs within the index area. The

variance due to variation in price change across outlets

is modeled as 

total number of unique outlets

unit outlet

2

s ,

where 2 sunit,outlet is the unit component of variance

attributable to variation across outlets for the index area

– item group combination. Thus we need to know the

number of unique outlets within the index area for each

group of item strata in order to estimate these index

area – item group level price change variances.

The cost model is broken apart into outlet related costs

and quote related costs. The quote related costs depend

on the number of quotes but not upon the number of

unique outlets in which these quotes are found.

However, the outlet related costs require a measure of

the number of unique outlets across all groups of item

strata. This is because an outlet associated cost such as

traveling to an outlet or obtaining non quote related

information from an outlet are independent of the

number of groups of item strata from which quotes are

to be priced or initiated. For details of the variance and

cost models for the commodities and services sample

see Leaver et al (1996).

3. The particular choice of model

Estimates of the number of unique outlets within each

index area and item group and of the number of unique

outlets across item groups within each index area are

achieved by modeling the number of unique outlets

against the number of outlets selected. The model

chosen is a quadratic polynomial with zero intercept

M unique a * M b * M

2

= + where M is the

designated outlet sample size. The intercept is taken as

zero because if zero outlets are selected then zero

unique outlets will be in the selected sample. This

model has been used historically since the optimization

of the commodities and services sample for the 1987

CPI revision. The quadratic coefficient is almost

always small, but in a check of 286 cases, the quadratic

coefficient was significantly different from zero at the

0.05 level in 260 of those instances.

In the future alternative models may be considered to

determine if a more suitable model exists.

4. Difficulties in determining the coefficients of the

model

The sample for the commodities and services is

currently derived primarily from two separate sources.

Through 1996, frames of outlets for rotation were

derived from the Continuing Point of Purchase Survey

(CPOPS). CPOPS collected data for all item categories

within a subset of PSUs and each PSU was rotated

about once every five years. Collection was done by

the Census Bureau using household personal

interviews. Currently the frames of outlets are derived

from the Telephone Point of Purchase Survey (TPOPS).

TPOPS surveys consumers about a subset of all item

categories and is designed so that about 25% of item

categories are rotated each year in all PSUs. Currently

the outlet sample is a mixture of sample derived from

frames from CPOPS sources and from frames from

TPOPS sources, but outlets to be initiated are only from

frames derived from TPOPS.

In case the allocation of items and outlets couldn’t be

revised between sample selections based on more

recently available data it was decided to model the

allocation as though one quarter of the categories within

each group of item strata would be rotated each year in

each PSU.

Outlets that are currently in the sample can be selected

again from new TPOPS based frames. Thus we end up

having to measure the number of unique outlets for a

sample derived partly from CPOPS based frames and

partly from TPOPS based frames. This will continue

for several years until the commodities and services

outlet sample has been completely replaced by sample

from TPOPS based frames.

As noted earlier, samples of outlets are merged with

samples of item strata by POPS category. The CPOPS

categories were revised in 1996 so frames from old

CPOPS categories had to be mapped into new frames

for newer CPOPS categories.

PSUs are divided into 12 groups for the purposes of

TPOPS. The same set of item categories are rotated for

all of the PSUs within each of these groups. Currently

only the first four of these groups of PSUs has had any

frames derived from TPOPS. The TPOPS categories

are divided into 16 groups. During this transition from

a CPOPS based sample to a TPOPS based sample the

TPOPS categories have been introduced on a staggered

basis, e.g., PSU group 1 has TPOPS based frames for

the first seven groups of TPOPS categories, PSU group

2 has TPOPS based frames for the first six groups of

TPOPS categories, PSU group 3 has TPOPS based

frames for the first five groups of TPOPS categories

and PSU group 4 has TPOPS based frames for the first

four groups of TPOPS categories. Thus, the mixture of

CPOPS and TPOPS frames from which the totality of

the sample for a PSU are drawn varies from PSU to

PSU depending on which TPOPS group of PSUs it

belongs to.
Finally, we usually had to work from frames that

differed from the final frames used to select the actual

sample. This is because the frames of outlets may

contain duplicate outlets with different descriptive

information or the outlets may now be known to be out

of business. The process of sending out the frames to

the individual PSUs to eliminate duplicate and out-ofbusiness outlets occurs fairly late in the sample

selection process and it was only in designing the

sample for the August 1999 TPOPS rotation that we

have had the final refined frames from which to do the

simulations. In preparing to do the sample design for

the February 1999 TPOPS rotation, we went through a

subset of frames and refined them using information

available on the internet and a street atlas program.

Comparing the final regression coefficients obtained

using the unrefined and refined frames for February and

August 1999 showed almost no difference. Thus it

appears that the effect of frame refinement itself is

minimal.

5. The procedure for obtaining the coefficients

In order to see what the final realized sample would be,

the three processes of drawing a sample of outlets, a

sample of item strata and associated POPS categories

and merging these into a sample of outlets and items

within outlets were simulated.

To select outlet samples it was first determined for each

PSU what was to be the source of frames for the totality

of item categories. This mixture of sources for frames

changes with each rotation as further sample based on

TPOPS frames is introduced. Outlet samples of size

two through twelve were drawn independently with

outlets being selected with probability proportional to

the expenditures within outlet for the POPS category.

The range of sample sizes used was intended to reflect

the range in which we expected the final specified

number of outlets per POPS category to fall. There was

some variation in the maximum sample size used

ranging from six through twelve. Comparisons of the

final model coefficients obtained based on differing

maximum outlet sample sizes showed very little

difference.

The above process was repeated from six to fifteen

times in order to provide additional datapoints for

determining the model coefficients. The number of

times the process was repeated varies in part because of

time restrictions for some of the times that the sample

design was revised. However the primary reason for

the variation is due to the unequal clustering of PSUs

into groups of PSUs in order to simplify the

optimization problem.

Next the item samples were selected. One input needed

is the number of selections of each item stratum. For

the purposes of the simulation we used the number of

item stratum selections from the most recent sample

selection. From having used multiple sets of item

stratum selections and examining the resulting model

coefficients it appears that the model coefficients are

quite insensitive to this particular input.

Each item stratum is associated with one or more POPS

categories. For instance items in item stratum AA01,

which contains men’s suits, outer wear, sports coats and

tailored jackets, come from outlets in TPOPS categories

A01 (Men’s suits or sports coats) and A02 (Men’s

outerwear) for PSUs in TPOPS PSU group 1. Each

POPS category has a relative importance within the

item stratum and this relative importance varies

depending on Census region. For instance, the relative

importance of POPS category A01 within item stratum

AA01 is 0.626 in Census region 1, the northeast United

States, but the relative importance is 0.728 for Census

region 3, the southern United States.

For each item stratum, a number of POPS categories

were selected with probability proportional to relative

importance with the number of POPS category

selections being the specified number of selections for

the item stratum. A POPS category is allowed to be

selected multiple times and there is the possibility that a

given POPS category won’t be selected at all. Enough

samples were selected in order to have a separate

sample to match up with each of the outlet samples and

separate samples were drawn for each region. The

process was also repeated for each of the five

combinations of CPOPS and TPOPS categories which

occur in our current set of PSUs.

Now for each PSU, item samples drawn using the

relative importances for the region where the PSU is

located are matched up to the outlet samples which

have been drawn for that PSU by POPS category which

yields a sample of outlets and item strata to be collected

in those outlets.

For each sample one now needs to determine two

different measures of the unique number of outlets. For

the variance model the number of unique outlets within

a group of item strata is needed. This is done by

unduplicating the list of outlets in each sample for each

item group and counting the number of remaining outlet

records.

For the cost model a different measure of uniqueness is

needed. This is because the fixed costs of visiting an

outlet do not depend on the items to be priced or
initiated within the outlet. It is still necessary to

apportion these fixed outlet related costs across the

groups of item strata. This was done by treating the

outlet as contributing 

n

1

 outlets to each of the n groups

of item stratum for which there is at least one item

stratum within the outlet. Other possibilities exist such

as apportioning the fixed outlet cost based on the

percentage of item stratum selections within the outlet

in each group of item strata. Thus the number of

unique outlets associated with each PSU group j and

item group i is

∑ =

=

ni j

k

i j

of item groups outlet ijk is in

U

,

1

,

#

1

where ni, jis the number of unique outlets in item

group i and index area group j.

With these two measures of unique outlets within a

group of item strata one now has a collection of

specified outlet sample sizes per POPS category and

two numbers of unique outlets for each group of item

categories. The unique numbers of outlets are then

regressed against the specified number of outlet

selections and the square of the specified number of

outlet selections.

6. How good are the models?

There are some changes that are necessitated by the

conversion to TPOPS based frames. Previously the

number of unique outlets per CPOPS category was

modeled as a function of the number of outlet selections

per CPOPS category. The number of unique outlets

predicted was then multiplied by the number of CPOPS

categories to get an estimate of the number of unique

outlets per group of item strata from the number of

outlet selections specified per CPOPS category.

With the current sample being a mixture of sample

derived from TPOPS and CPOPS based frames, there is

no longer a well defined number of POPS categories

per group of item strata and there won’t be a well

defined number until the sample has converted entirely

to being based on TPOPS frames. This is because the

categories were changed considerably when switching

to TPOPS and are usually more refined than

comparable CPOPS frames. Thus, it was necessary to

absorb the number of POPS categories into the model

itself and predict the number of unique outlets per

groups of item strata as a function of the specified

number of outlet selections per POPS category.

It was desired to conduct as pure a test as possible. As

selected outlets have their outlet code renamed it is

impossible to determine overlap between outlets

selected from old CPOPS based frames and the outlets

selected in simulations from TPOPS frames. Thus it

was decided to perform a test of the methodology using

the actual selected but not yet initiated outlets for

TPOPS categories which are part of the February 1999

TPOPS rotation. Six A-sized PSUs were selected for

test based on their being contained entirely in the first

TPOPS PSU group and thus having a full five quarters

of TPOPS frames to work with.

The procedure described above was applied to just the

TPOPS frames for these six PSUs through the first

quarter of 1998 and the regression coefficients were

computed at the individual PSU level.

First is a summary of the comparison of the predicted

number of unique outlets within a group of item strata

to the actual realized sample size within the same group

of item stratum.

Group of item

strata

Mean

realized

outlets

Mean

predicted

outlets

Mean

 of

ratios

Overall 20.4 20.5 0.996

Food staples 18.8 18.6 0.992

Fruits and

vegetables

9.0 8.8 0.964

Other food 21.2 20.6 0.976

Household 39.2 41.4 1.057

Apparel 21.1 20.8 0.978

Transportation 4.8 4.9 1.002

Education and

communication

12.5 12.4 0.998

Entertainment

and other

33.9 34.0 1.001

Next is a summary of the comparison of the predicted

number of unique outlets across all groups of item

strata to the actual realized number of unique outlets

across all groups of item strata as distributed among

groups of item strata.
Group of item

strata

Mean

realized

outlets

Mean

predicted

outlets

Mean

 of

ratios

Overall 18.8 18.7 0.958

Food staples 16.3 15.9 0.972

Fruits and

vegetables

7.4 6.7 0.770

Other food 17.9 17.7 0.973

Household 37.4 39.1 1.050

Apparel 19.4 18.8 0.921

Transportation 4.8 4.9 1.002

Education and

communication

12.5 12.2 0.977

Entertainment

and other

32.3 32.4 1.009

Thus it appears that the regression formulas generated

by these frames do a good job of predicting the unique

number of outlets within a group of item strata and they

do only slightly worse for predicting the number of

unique outlets across groups of item strata with the

likelihood that the estimates produced are slightly too

low.

7. The effect of switching from a CPOPS based

sample to a TPOPS based sample.

It is of interest to determine how much effect the

introduction of frames for new TPOPS categories has

on the unique outlet predicting function. This was done

by comparing regression coefficients for all A-sized

cities in TPOPS PSU group one using frames from the

first quarter of 1997 through the third quarter of 1998 to

ones using frames from the first quarter of 1997

through the second quarter of 1998 as well as the ones

for the A-sized PSUs in TPOPS PSU group 2 using all

of the frames through the third quarter of 1998. This

allows examining the effect of the introduction of one

quarter of TPOPS frames for PSUs in TPOPS PSU

group one, the PSUs with the most TPOPS based

frames available, and it allows one to compare two sets

of PSUs that have the same total set of frames. Of

interest are the groups of item stratum in which there

were new associated TPOPS categories in the third

quarter 1998 frames for TPOPS PSU group one.

TPOPS group 1 Q983

Group of item strata Linear

coefficient

Quadratic

coefficient

Food staples 7.68 -0.24

Other food 15.49 -0.45

Apparel 18.65 -0.44

Entertainment and

other

26.50 -0.68

TPOPS group 1 Q982

Group of item strata Linear

coefficient

Quadratic

coefficient

Food staples 8.65 -0.23

Other food 15.49 -0.42

Apparel 19.71 -0.47

Entertainment and

other

29.94 -0.75

TPOPS group 2 Q983

Group of item strata Linear

coefficient

Quadratic

coefficient

Food staples 3.95 -0.03

Other food 11.94 -0.26

Apparel 15.96 -0.47

Entertainment and

other

23.77 -0.76

As shown in this comparison, while there is some

change in the model coefficients due to the introduction

of new TPOPS categories, this amount of change is

smaller than the difference in model coefficients using

the same set of TPOPS categories but different PSUs.

8. Conclusions

It appears that the quadratic models used to estimate the

number of unique outlets do a reasonable job of

approximating the final realized outlet sample sizes.

There is some effect on the coefficients of the quadratic

models due to the introduction of frames for TPOPS

categories over time, but it appears that there is more

variation in the coefficients across PSUs. The

refinement of frames seems to have little effect on the

coefficients of the quadratic model. Due to the changes

produced by the introduction of new TPOPS based

frames with each rotation it is advisable to re-estimate

the coefficients for each rotation if possible.

9. Acknowledgments

The authors would like to thank Janet Williams for her

careful reading of this paper and her helpful comments.

In addition, we would like to thank Owen Shoemaker

for his thoughts on this particular problem.

10. References

Leaver, S., Johnson, W. H., Baskin, R., Scarlett, S., and

Morse, R. (1996) "Commodities and Services Sample

Redesign for the 1998 Consumer Price Index

Revision," Proceedings of the Section on Survey

Research Methods, American Statistical Association,

Vol. I, pp. 239-244.