Changes in concepts and methods being readied for the 1998 revision should smooth the process of index production for shelter services
The Consumer Price Index (CPI)
currently consists of seven major categories, with the large aggregate grouping called
housing representing 41 percent of the total index. Within the
housing category, most of the relative importance belongs to the index for
owners equivalent rent, also known as rental equivalence,
and that for residential rent, for which data are obtained through the Housing
survey. These two items represent 20 percent and 6 percent, respectively, of the total
CPI. The remaining 15 percent accounted for by the housing group consists of
many indexes, which are handled through the Commodities and Services survey. (For more
detail see "Changing the item structure of the Consumer Price
In addition to data on residential rents used to calculate changes in rents for the rent index, the Housing survey also collects data for owned homes for use, in conjunction with the rent data, in calculating of changes in the rental value of owned homes for the rental equivalence measure. Clearly, the rental value of owned homes is not an easily determined dollar amount, and Housing survey analysts have spent considerable time and effort in estimating this value. As a result, determining 'rental equivalence' is an important issue in the upcoming 1998 revision of the CPI.
The revision has provided a window of opportunity to initiate an extensive redesign of the Housing survey. Beginning in 1999, the CPI for rent and for rental equivalence will be based on a new sample design and estimation methodology. Major technological advances and improvements in the operational processes also will be implemented in the survey. More specifically, these changes include:
This article describes the systems, data bases, and procedures that are being developed for the upcoming revision of the Housing survey, and explains the advantages to be derived from each.
equivalence approach to measuring price change for owner-occupied housing was
implemented for the CPI for All Urban Consumers (CPI-U) in January 1983, and for the CPI
for Urban Wage Earners and Clerical Workers (CPI-W) in January 1985. In essence,
rental equivalence measures the change in the amount a homeowner would pay to
rent, or would earn from renting, his or her home in a competitive market. It is a measure
of the change in the price of the shelter service provided by owner-occupied housing. When
initially introduced, the rental equivalence index was moved (that is, changes
were applied) by reweighting the rent sample to represent owner-occupied units. The
preferred methodology would have been to match owner units to renter units and use those
more specific rent changes to calculate changes in the rental value of owner units. The
reweighting approach was taken because an owner sample could not be selected and available
for use before the CPI was last revised in 1987.
Since January 1987 (the 1987 revision), the rental equivalence index movement has been based on changes in the implicit rent of owner units. These implicit rents are moved by the changes in the pure rents (which exclude the cost of any utilities included in the rent contract) of matched rental units. The implicit rents are estimated by the owners in the CPI owner sample, and those implicit rents are then moved by the specific rent changes for renter units with similar characteristics (owner/renter matching). The characteristics include location, structure type, and other general traits such as age, number of rooms, and type of air conditioning.
The rent index measures the changes in rents, specifically "contract rents," paid by tenants or received by landlords. "Contract rents" are the payments for all services the landlord provides in exchange for the rent. For example, if the landlord provides electricity, it is considered part of the contract rent. The data collected for the rent index consists of rent, rent reductions, extra charges, and information concerning the utilities, facilities, and services received for the rent.
In any properly designed
statistical study, samples are selected to support the estimation process that is planned.
The 1987 revision Housing sample was selected to support the estimation of the
rental equivalence index through the use of implicit rents for owner-occupied
units and the movement of the implicit rents through owner/renter matching.
For purposes of the upcoming 1998 revision, the decision was made to drop the owner sample and return to the methodology that was used for the rental equivalence index when it was first introducedthat is, the reweighting of the rent sample to represent owner-occupied units. This decision was made for several reasons:
Geographic stratification.Research performed by BLS using 1980 and
1990 census data indicates that geographic location is the most important variable (that
is, it accounts for most of the variance) in determining rent change. Once geography is
taken into account, only rent level is significant in predicting rent change. The percent
of owner-occupied units in a neighborhood, which was a key stratification variable in the
1987 sample selection process, proved to be of little importance in explaining change.
Geographic software, which was not available for the 1987 revision, allowed stratification by geography for the 1998 revision. The geographic stratification accomplished five goals:
The Housing sample for the 1998
revision is a stratified cluster sample, which represents housing units built before 1990.
Housing units built after 1989 are handled through the New Construction survey, as
described later in this article. Using data from the 1990 Census of Population and
Housing, CPI analysts divided the primary sampling units1
(PSUs) into geographic neighborhoods (segments). The segments are small contiguous groups
of census blocks (sectors). The segments contain at least 50 housing units in the larger
PSUs and at least 30 units in the smaller PSUs. These segments are stratified by location
within the PSU. Six geographic strata were formed in each PSU. Once geography is taken
into account, only rent level is significant in predicting rent change, so the
stratification boundaries were determined using information about population and median
In the first step of the stratification process, a box is found in the geographic center of the PSU, so that about one-third of the population is contained inside the box. The box is then split into two strata. Whether the split is by latitude or longitude is determined by rent level. The split that maximizes the difference in median rent level determines strata 1 and 2. Then, the four noncentral strata are determined iteratively in a similar fashion. The entire noncentral part of the PSU is split into two parts, either by latitude or longitude. Once the first noncentral split is determined, a split perpendicular to the first split is made within each half.
Exhibit 1 shows the six geographic strata in the St. Louis, MO-IL PSU. According to this map, the central box was split by longitude, and then the entire noncentral part was split by longitude, with each half then split by latitude. While rent level, as well as population, was used to determine the geographic strata boundaries, the resulting strata are purely geographic divisions of the PSU. Two of the strata correspond roughly to the most densely populated part of the PSU, and the other four strata correspond to surrounding suburban areas.2
Weighting during segment sample selection.CPI analysts then selected
segments in the strata to represent housing units constructed before 1990. In the 1987
revision, segments had been selected with probability proportional to size, the size
measure being the number of housing units in the segment. When the number of units is used
as the size measure, smaller, less expensive housing units (in apartment complexes, for
example) have the same probability of selection as more expensive single-family units.
Because the rent and rental equivalence indexes are measures of
the change in the price of the shelter service provided by renter-occupied and
owner-occupied housing, it was felt that higher expenditures (rent levels) should have a
higher probability of selection. In the 1998 revision, therefore, segments were again
selected with probability proportional to size, but the size measure was estimated expenditures.
In the segment selection process, the segments are ordered within each stratum by county and then by segment rent level within county. Because the segment selection is systematic, this guarantees that not all high-rent or low-rent segments are chosen.
Each segment has a probability of selection within the stratum (Ps) that is the ratio of the cost of housing in the segment relative to the cost of housing in the stratum. Therefore,
S = stratum; and
TCs is defined below.
Each segment also has a weight (Ws), which is the reciprocal of the probability of selection. Therefore,
The cost of housing in the segment is the cost of rented housing in the segment (RCs) plus the cost of owned housing in the segment (OCs). The RCs is the number of rented housing units in the segment (Rs) times the average rent value within the segment (RRs). The OCs is the number of owned housing units in the segment (Os) times an estimated average owner equivalent rent value within the segment (IRs). This gives segments with higher-valued units (that is, higher rent levels) a higher probability of selection and a lower segment weight. The relationship among these variables is given by:
The estimated average owner equivalent rent value (IRs) was determined by a nonlinear regression of the 1990 census owner value within census blocks on the 1990 census average rent value within the same census block:
y = b0 * (1-exp(-b1 * x)) + e
where y = average rent;
x = average owner value; and
z = average implicit rent.
The actual regression coefficients (b0 and b1) were determined uniquely within each PSU.
Because rents are not volatile, the Housing sample is divided into panels; one panel is priced each month and each panel is priced twice a year. For example, panel 1 is priced in January and July, panel 2 in February and August, and so on through panel 6. The segments within the strata are assigned to these panels. These assignments are made such that each panel has a representative subsample of the PSU. Because each panel is representative of the entire sample and there is never an off-cycle month for the Housing survey, a panel of data provides sufficient information for monthly publication of the rent and rental equivalence indexes. Primary segments were selected within the PSUs in multiples of 36, so that each combination of stratum and panel had the same sample size.
Other segment sample selection outputs.About 10,000 segments have
been selected in the PSUs and the 1998 revision Housing unit sample is designed to consist
of approximately 50,000 rental units. CPI analysts have computed sampling rates for each
segment, so that the sample design will be realized after the listing, sampling, and
screening processes, as described below, are completed. These sampling rates will be used
during the listing process to select the addresses that will be screened for use in the
Segment-level information from the selected segments will be provided to the mapping system. This information allows the production of all maps required by field staff to locate the segments within the PSUs.
New construction augmentation.The augmentation of the Housing sample with newly constructed housing units is not part of the segment sample selection process, but it is discussed here because these housing units will fit neatly into the geographic stratification of the Housing sample. The Census Bureau will supply to BLS a sample of address records from building permits, representing housing units built after 1989. (BLS calls this list of address records the New Construction sample.) BLS expects to receive about 1,000 address records per year from the Census Bureau, with 20 percent of these yielding usable renter-occupied units after they have gone through the screening process. Once they receive the new construction sample, CPI analysts will assign each address record to one of the six geographic strata based on the zip code. They then will allocate the new construction sample among the segments, using the census sample design and zip code.
Mapping system.Sets of maps are needed to help field staff locate the sectors within the segments that must be recorded in the listing process described below. In previous CPI revisions, maps with PSU, segment, and sector identifiers, along with street names and boundary information, were produced by hand in Washington and provided to the field staff. Because corrections to the maps were entered and kept by the field staff, the BLS Washington Office did not maintain an updated set of maps for all PSUs, segments, and sectors. For the 1998 revision, the CPI systems staff has developed a system to produce sets of maps, using the Census Bureaus Topologically Integrated Geographic Encoding and Referencing (TIGER) data and commercial, "off-the-shelf" Geographic Information System (GIS) software. The process of segment sample selection and use of the Sample Maintenance and Control System (SMCS) described below will provide the information necessary to accurately specify the selected segments within each PSU/stratum and each sector within those segments. The mapping system will yield accurate, reproducible sets of maps with all necessary information for the field staff and will extract the defined limits (boundary information) for each sector from the TIGER data. These boundary data will be provided to the SMCS portion (see below) of the Housing data base for use in the listing process. The sets of maps will include:
Corrections and additions will be entered on the maps by the field staff, usually during the listing process, and a copy of the corrected map will be sent to the Washington Office, where the changes will be entered in the mapping data base by cartographers. New maps will be supplied to the field staff before pricing begins. This process will allow the Washington Office to produce updated maps upon request for all PSUs, segments, and sectors.
Sample Maintenance and Control System (SMCS). Previously, much of the sample information for the CPI Housing survey was maintained separately from the rest of the Housing data base, a situation that complicated sample administration. It also was hard to analyze the current sample using the Housing data base due to its panel structure. With the 1998 revision, however, sample information will become an important part of the Housing data base. The SMCS is a new, consolidated system that will be used to control the Housing Sample. It has five major functions:
Computer-assisted data collection.A key element of the 1998 revision is the conversion of all data collection and transmission to electronic systems.
Housing review and correction preprocessing system.The review and
correction preprocessing system consists of various functions that must be performed
before a unit can be used in index calculation. Upon receipt of the data, the system
determines how to proceed (which functions are to be performed) based on selected
variables, such as the scope status and the schedule status.
This system handles the micro data preprocessing required for the review and correction functions performed by the analysts. Some of these functions currently are performed as part of the existing price relative calculation (see below), so the analyst is not able to review all inputs to the calculation. As a result, the analysts occasionally have had to enter additional corrections, because the initial result of the calculation was not as expected. The new system also will complete all unit-level computations, so that the analyst will be able to review all micro data and price relative calculation inputs much earlier in the processing cycle. Once the calculation is run, the analyst will have to review only the results of aggregation and imputation.
The Housing review and correction preprocessing system will prepare all micro data necessary for the revised Housing price relative calculations for the rent and rental equivalence indexes. These computations include:
These data are then made available to the analysts through the review and correction instrument. This instrument is a subsystem of the review and correction preprocessing system and handles the interactive review and correction functions. The review and correction preprocessing system also permits the interactive derivation of dependently derived micro data, so that the analysts may immediately observe the results of their corrections.
The Housing and the Commodities and Services programs do not directly calculate indexes. Instead, they produce "price relatives," which are used in the index estimation system for basic index calculation. Price relatives are ratios of price change from the previous month (T1) to the current month (T), and basic index calculation updates the last months indexes (T1) into the current month (T). (As explained above, a decision was made for the revision that the renter sample would be reweighted to represent owner units in the same segment.)
Weighting during the price relative calculation.The renter and owner costs of housing in the segment (see "Weighting during segment sample selection" above) become the basis of the renter and owner weights used by the price relative calculation for the segment.
To derive the total renter weight in the segment (RWs ), the segment weight (Ws) must be adjusted by the proportion of renter cost in the segment (RAs) and the expectation of selecting a renter in the segment (RPs).
The proportion of renter cost in the segment (RAs) is the renter cost (RCs) divided by the total cost (TCs).
The expectation of selecting a renter in the segment (RPs) is the number of sampled housing units in the segment (SUs) divided by the total number of housing units in the segment (HUs).
The total renter weight for the segment (RWs), therefore, is the segment weight (Ws) times the renter cost proportion (RAs) adjusted by the proportion of sampled renters (RPs).
To derive the total owner weight in the segment (OWs), the segment weight (Ws) must be adjusted by the proportion of owner cost in the segment (OAs) and the expectation of selecting a renter in the segment (RPs). Because owners are not being sampled and the renters are being reweighted to represent owners, the RPs is used in both derivations.
The proportion of owner cost (OAs) is the owner cost (OCs) divided by the total cost (TCs).
The total owner weight for the segment (OWs), therefore, is the segment weight (Ws) times the owner cost proportion (OAs) adjusted by the proportion of sampled renters (RPs).
The renter and owner weights are ratios of expenditures, not expenditures themselves, so there is no need to convert them into quantities by dividing them by base rents or base implicit rents. In addition, the renter and owner weights are being derived from 1990 census data, while the first rent data will be collected no earlier than 1997, so there should be no autocorrelation effects. In short, there appears to be no fear of formula bias in the rent and rental equivalence estimators.
The rent and rental equivalence estimators.The
rent estimator is based on the change in the "economic rent," which
is basically the "contract rent," adjusted for any changes in the quality of the
housing unit. Because of the panel structure used in the Housing sample, the current
economic rents for sampled, renter-occupied units within a segment, weighted by the renter
weight, are divided by the previous (T6) economic rents for sampled,
renter-occupied units within a segment, weighted by the renter weight. The result
represents the 6-month change in rent for all renter-occupied units in the segment.
In a parallel calculation, the current pure rents (which exclude the cost of any utilities included in the rent contract) for sampled, renter-occupied units within a segment, weighted by the owner weight, are divided by the previous (T6) pure rents for sampled, renter-occupied units within a segment, weighted by the owner weight. This is used as a proxy for the 6-month change in the equivalent rent for all owner-occupied units in the segment.
The functions of the price relative calculation have been designed to make use of the parallel rent and rental equivalence computations. In general, the calculation aggregates the weighted rents for the units (i) in the index area (A) for the current period (T) and for the period 6 months earlier (T-6), and then computes the price relatives:
When the calculation is run for Rent, economic rents (ERi) and renter weights (RWs) are used. That is,
When the calculation is run for rental equivalence,4 pure rents (PRi) and owner weights (OWs) are used. That is,
Because the index estimation system needs a 1-month price relative, rather than a 6-month price relative, the 6th root of the is derived:
and then passed to the estimation system for basic index computation for the rent and rental equivalence item strata.
The rent and rental equivalence item strata have not been changed in the 1998 revision item structure, but the revision area structure and the basic aggregation weights will be brought into the CPI in late 1997. The revision price relative calculation and the revision Housing sample will not be ready for use in the revised CPI until January 1999. During 1998, the current Housing sample will be priced, and the current price relative calculation will provide price relatives through December 1998. A Concordance program is being developed to map the price relatives for the current area structure to the revision area structure.
|Exhibit 1. Segment sample selection for St Louis, MO-IL|
1 Primary sampling units are the metropolitan and nonmetropolitan areas defined as the CPI area sample. (See Janet Williams, "The redesign of the CPI geographic sample".)
2 Eugene F. Brown and William H. Johnson, "Comparison of Stratification Designs for the Housing Sample of the Consumer Price Index," 1994 Proceedings of the Section on Survey Research Methods, American Statistical Association.
3 Two examples of out-of-scope addresses are units occupied by owners or relatives of the landlord. Because the owner sample is being dropped, owner-occupied units are out of scope. In the case of relatives, it has been determined that, if the tenant is a relative of the landlord, it is very difficult to collect data on market rents. Because the relative usually gets some type of rent reduction that cannot easily be determined, the units are considered out of scope.
4 The price relative calculation also will handle the estimation of price relatives for the official Laspeyres index and the Geometric Means index. The same economic and pure rents, but different renter and owner weights, will be used for the Geometric Means index.
Frank Ptacek is the chief of the Housing Section, Division of Consumer Prices and Price Indexes, and Robert M. Baskin is a mathematical statistician, Division of Price Statistical Methods, both at the Bureau of Labor Statistics.
Last Modified Date: October 16, 2001