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Survey of Market Absorption of Apartments (SOMA)
CHARACTERISTICS OF THE DATA
All statistics from the Survey of Market Absorption (SOMA) are limited to apartments in newly constructed buildings with five units or more. Absorption rates are based on the first time an apartment offered for rent is rented after completion, or the first time a condominium or cooperative apartment is sold after completion. If apartments initially intended to be sold as condominium or cooperative units are, instead, offered by the builder or building owner for rent, they are counted as rental apartments. Units categorized as federally subsidized are those built under the two programs of the Department of Housing and Urban Development: Section 8, Low Income Housing Assistance and Section 202, Senior Citizen Housing Direct Loans, and all units in buildings containing apartments in the Federal Housing Administration (FHA) rent supplement program. The data for privately financed units include privately owned housing subsidized by State and local governments. Units categorized as not in the scope of the survey include time-sharing units, continuing care retirement units, and turnkey units (privately built for and sold to local public housing authorities subsequent to to completion).
Tables 1 through 4 are restricted to privately financed, nonsubsidized, unfurnished rental apartments. Table 5 is restricted to privately financed, nonsubsidized, condominium and cooperative apartments, while Table 6 is limited to privately financed, nonsubsidized condominium apartments only. Table 7 covers privately financed, nonsubsidized, furnished, rental apartments and Table 8 is a historical summary table which includes all newly constructed apartments in buildings with five units or more. Estimates published in this report are preliminary and are subject to revision in the H-130, Market Absorption of Apartments annual report.
The SOMA is a sample survey and consequently all statistics are subject to sampling variability. Estimates derived from different samples would likely differ from these. The standard error of a survey estimate is a measure of the variation among the estimates from all possible samples. It allows the construction of an interval with prescribed confidence that the interval includes the average of the estimates from all possible samples. (Estimates of standard errors can be calculated by using Tables A, B and C.)
For all the statements about changes made in this report, 90-percent confidence intervals for statistical comparisons can be constructed by using the 90-percent deviate shown in parentheses after the change; however, when a 90-percent confidence interval contains zero, a change may or may not have occured. In addition, any statistical findings that are not part of the tables or that are derived by collapsing intervals within a table are also provided with a 90-percent confidence interval.
NOTE TO DATA USERS
The SOMA adopted new ratio estimation procedures in 1990 to derive more accurate estimates of completions (see section on ESTIMATION). This new procedure was used for the first time in processing annual data for 1990. Caution must be used when comparing the number of completions in 1990 and later with those in earlier years.
The SOMA is designed to provide data concerning the rate at which privately financed, nonsubsidized, unfurnished units in buildings with five or more units are rented or sold (absorbed). In addition, data on characteristics of the units, such as number of bedrooms and rent or price, are collected.
The buildings selected for the SOMA are drawn from those included in the Census Bureau's Survey of Construction (SOC). For the SOC, the United States is first divided into primary sampling units (PSU's), which are stratified based on population and building permits. The PSUs to be used for the survey are then randomly selected from each stratum. Next, a sample of permit-issuing places is chosen within each of the selected PSUs. Finally, all newly constructed buildings with five units or more within sampled places, as well as a subsample of buildings with one to four units, are included in the SOC.
Each quarter, a sample of buildings with five units or more in the SOC sample reported as completed during that quarter are chosen for the SOMA. Buildings completed in nonpermit-issuing areas are excluded from consideration. Information on the proportion of units absorbed 3, 6, 9, and 12 months after completion is obtained for units in buildings selected in a given quarter in each of the next four quarters.
Beginning with data on completions in the fourth quarter of 1990 (which formed the basis for absorptions in the first quarter of 1991), the estimation procedure was modified. The modified estimation procedure was also applied to data for the other three quarters of 1990 so that annual estimates could be derived using the same methodology for four quarters. No additional re-estimation of the past data has been done.
Before this change in the estimation procedure, unbiased quarterly estimates were formed by multiplying the counts for each building by its base weight (the inverse of its probability of selection) and then summing over all buildings. The final estimate was then obtained by multiplying the unbiased estimate by the following ratio estimate factor for the Nation as a whole:
total units in buildings with five units or more in permit-issuing areas as estimated by the SOC for that quarter divided by total units in buildings with five units or more as estimated by the by the SOMA for that quarter
For the modified estimation procedure, instead of applying a single ratio-estimate factor for the entire nation, separate ratio-estimate factors are computed for each of the four Census regions. The final estimates for regions are obtained by multiplying the unbiased regional estimates by the corresponding ratio estimate factors. The final national estimate is obtained by summing the final regional estimates.
This procedure produces estimates of the units completed in a given quarter which are consistent with unpublished figures from the SOC and reduces, to some extent, the sampling variability of the estimates of totals. Annual absorption rates are obtained by computing a weighted average of the four quarterly estimates.
Absorption rates and other characteristics of units not included in the interviewed group or not accounted for are assumed to be identical to rates for units where data were obtained. The noninterviewed and not-accounted-for cases constitute less than 2 percent of the sample housing units in this survey.
ACCURACY OF THE ESTIMATES
There are two types of possible errors associated with data from sample surveys: nonsampling and sampling errors. The following is a description of the sampling and nonsampling errors associated with the SOMA.
In general, nonsampling errors can be attributed to many sources: inability to obtain information about all cases in the sample, difficulties with definitions, differences in interpretation of questions, inability or unwillingness of the respondents to provide correct information, and errors made in processing the data. These nonsampling errors also occur in complete censuses. Although no direct measurements of the biases have been obtained, the Census Bureau feels that most of the important response and operational errors were detected in the course of reviewing the data for reasonableness and consistency.
The particular sample used for this survey is one of many possible samples of the same size that could have been selected using the same design. Even if the same questionnaires, instructions, and interviewers were used, estimates from each of the different samples would likely differ from each other. The deviation of a sample estimate from the average of all possible samples is defined as the sampling error. The standard error of a survey estimate attempts to provide a measure of this variation among the estimates from the possible samples and, thus, is a measure of the precision with which an estimate from a sample approximates the average result from all possible samples.
As calculated for this survey, the standard error also partially measures the variation in the estimates due to errors in responses and by the interviewers (nonsampling errors), but it does not measure, as such, any systematic biases in the data. Therefore, the accuracy of the estimates depends on the standard error , biases, and some additional nonsampling errors not measured by the standard error. As a result, confidence intervals aroind estimates based on this sample reflect only a portion of the uncertainty that actually exists. Nonetheless, such intervals are extremely useful because they do capture all of the effect of sampling error and, in this case, some nonsampling error as well.
If all possible samples were selected, each of them was surveyed under essentially the same general conditions, there were no systematic biases, and an estimate and its estimated standard error were calculated from each sample, then:
Approximately 68 percent of the intervals from one standard error below the estimate to one standard error above the estimate (i.e., the 68-percent confidence interval) would include the average result from all possible samples.
Approximately 90 percent of the intervals from 1.6 standard errors below the estimate to 1.6 standard errors above the estimate (i.e., the 90-percent confidence interval) would include the average result from all possible samples.
Approximately 95 percent of the intervals from two standard errors below the estimate to two standard errors above the estimate (i.e., the 95-percent confidence interval) would include the average result from all possible samples.
This report uses a 90-percent confidence level as its standard for statistical significance.
For very small estimates, the lower limit of the confidence interval may be negative. In this case, a better approximation to the true interval estimate can be achieved by restricting the interval estimate to positive values, that is, by changing the lower limit of the interval estimate to zero.
The reliability of an estimated absorption rate (i.e., a percentage) computed by using sample data for both the numerator and denominator depends upon both the size of the rate and the size of the total on which the rate is based. Estimated rates of this kind are relatively more reliable than the corresponding estimates of the numerators of the rates, particularly if the rates are 50 percent or more.
Tables A, B and C present approximations to the standard errors of various estimates shown in the report. Table A presents standard errors for estimated totals, and Tables B and C presents standard errors of estimated percentages for rental apartments and condominiums , respectively. In order to derive standard errors that would be applicable to a wide variety of items and could be prepared at moderate cost, a number of approximations were required. As a result, the tables of standard errors provide an indication of the order of magnitude of the standard errors rather than the precise standard error for any specific item. Standard errors for values not shown in Tables A, B, or C can be obtained by linear interpolation.
ILLUSTRATIVE USE OF THE STANDARD ERROR TABLES
Table 2 of this report shows that there were 12,000 one-bedroom apartments built in the Midwest. Table A shows the standard error of an estimate of this size to be approximately 1,730. To obtain a 90-percent confidence interval, multiply 1,730 by 1.6 and add and subtract the result from 12,000 yielding limits of 9,230 and 14,770. The average estimate of these units completed in 1998 in the Midwest may or may not be included in this computed interval, but one can say that the average is included in the constructed interval with a specified confidence of 90 percent.
Table 2 also shows that the rate of absorption after 3 months for these apartmentss in the Midwest is 63 percent. Table B shows the standard error on a 63 percent rate on a base of 12,000 to be approximately 6.9 percent. Multiply 6.9 by 1.6 (yielding 11) and add and subtract the result from 63. The 90-percent confidence interval for the absorption rate of 63 percent is from 52 to 74.
Table 2 shows that the median asking rent for these estimated 12,000 one-bedroom apartments built in the Midwest was $535. The standard error of this median is about $15.
Several statistics are needed to calculate the standard error of a median.
The base of the median -- the estimated number of units for which the median has been calculated. In this example, 12,000.
The estimated standard error from Table B of a 50-percent characteristic on the base of the median (sigma 50%). In this example, the estimated standard error of a 50-percent characteristic with the base of 12,000 is about 7.5 percent.
The length of the interval that contains the median. In this example, the median lies between $450 and $549. The length of the interval is $100.
The estimated proportion of the base falling in the interval that contains the median. In this example, 50 percent. The standard error of the median is obtained by using the following approximation:
Standard error of median = sigma 50% times [length of interval containing the sample median] divided by [estimated proportion of the base falling within the interval containing the sample median]
For this example, the standard error of the median of $535 is:
7.5 X 100/50 = $15
Therefore, 1.6 standard errors equals $24. Consequently, an approximate 90-percent confidence interval for the median asking rent of $535 is between $511 and $559 ($535 plus or minus $24).