The distributions shown below are constructed by removing the counts of ACS-1 and ACS-2 areas from the total state distributions.
In computing state based standard qualtiy rents, HUD actually uses data on rent distributions
that are prohibited from public release under Title XIII to protect the
confidentiality of respondents. The distributions used in this demonstration
are rounded versions of the actual, protected data.
The rounding scheme is as follows:
0, count = 0
1 to 7, count = 4
all other counts are rounded to the nearest 5 (e.g., 10, 15, 20, 25, etc.)
CALCULATIONS USING THE ROUNDED DATA MAY NOT PRODUCE THE SAME RESULT AS CALCULATIONS
USING THE PROTECTED DATA. THE DIFFERENCE BETWEEN HUD'S ACTUAL RESULTS AND THOSE
DEMONSTRATED HERE IS INVERSELY RELATED TO THE SIZE OF THE AREA. THAT IS,
THE LARGER THE AREA, THE CLOSER THE CALCULATION BASED ON THE
ROUNDED DATA IS LIKELY TO BE TO THE CENSUS BASE RENT COMPUTED FROM THE PROTECTED DATA.
HUD uses rents for standard quality units to generate update factors. "Standard Quality" units and rents are determined by limiting the
full Census sample by including only responses meeting the following criteria:
a. Occupied rental units paying cash rent
b. Specified renter ? on 10 acres or less
c. with full plumbing
d. with full kitchen
e. built before 1999
f. meals not included in rent
Neither the 2000 Census not the 2005 ACS included a question that could be used to filter public or assisted housing from the rental distributions, however HUD is required to ensure that FMRs exclude non-market rental housing in their computation. Therefore, HUD excludes all units falling below a specified rent level determined from public housing rents in HUD's program databases as likely to be either assisted housing or otherwise at a below-market rent (perhaps due to quality problems not otherwise captured by the survey questions).
The "public housing" rent cut-off in Michigan in 2005 is $248 and the 2000 cut-off rent is $248.
A Microsoft Excel file containing the unsummarized versions of the publicly releasable standard quality 2-bedroom rent distributions from the 2005 ACS for Michigan, excluding ACS-1 and ACS-2 areas, is available here.
A Microsoft Excel file containing the unsummarized versions of the publicly releasable standard quality 2-bedroom rent distributions from the 2000 Census for Michigan, excluding ACS-1 and ACS-2 areas, is available here.
The following table and calculations demonstrate how the 50th percentile 2005 ACS standard quality rent is determined for Michigan using the public distribution of standard quality rents for the state.
| Portion of Standard Quality Rent Distribution | Gross Rent Dollar Range | Number of Units | Percent of Eligible Distribution | Cumulative Percent |
|---|---|---|---|---|
| Units below interval containing public housing rent level of $248 |
$0 to $224 | 4,599 | Not in Distribution | Not in Distribution |
| Units in interval containing public housing rent level of $248 |
$225 to $247 | 977.59 | Not in Distribution | Not in Distribution |
| $248 to $249 | 85.01 | 0.1% | 0.1% | |
| Units below interval containing 50th percentile standard quality rent of $599 |
$250 to $574 | 42,792 | 42.9% | 43.0% |
| Units in interval containing 50th percentile standard quality rent of $599 |
$575 to $599 | 7,316 | 7.3% | 50.3% |
| Units above interval containing 50th percentile standard quality rent of $599 |
$600 or more | 49,530 | 49.7% | 100.0% |
| Total Units Above Public Housing Rent in Standard Quality Rent Distribution | 99,723.04 |
The numbers of units with standard quality rents above and below the Public Housing Rent level of $248 for Michigan are determined using linear interpolation over the 1,063 units in the rent range $225 to $249. Linear interpolation uses the assupmtion that the 1,063 units' rents are uniformly distributed in the rent range around the Public Housing Rent level. Under this assumption, the proportion of the rent interval ($25) that is below the Public Housing Rent level is the same as the proportion of units with rents in the interval (1,063) that have rents below the Public Housing Rent level.
Proportion of rent interval below the Public Housing Rent Level: ($248 - $225) / $25 = 0.9200
Units in the Public Housing Rent Level Interval below the Public Housing Rent Level: 0.9200 x 1,063 = 977.59
The 50th percentile standard quality rent for Michigan is computed by linear interpolation over the 7,316 units in the rent range $575 to $599. Linear interpolation uses the assupmtion that the 7,316 units' rents are uniformly distributed in the rent range around the 50th percentile. Under this assumption, the proportion of the rent interval ($25) that needs to be added to the lower limit of the interval to reach the 50th percentile rent is the same as the proportion of units in the interval that needs to be added to the units in lower rent intervals to reach 50 percent of units in the distribution.
50 percent of units = 0.5 x 99,723.04 = 49,861.52
Units below the 50th percentile rent interval = 42,792.03 + 85.01 = 42,877.04
Units in 50th percentile rent interval needed to reach 50 percent of units = 49,861.52 - 42,877 = 6,984.48
Additional Units as Proportion of Interval = 6,984.48 / 7,316 = 0.9547
Dollars Added to Lower Limit of Interval to reach 50th percentile rent = 0.9547 x $25 = $24
50th percentile standard quality rent = $575 + $24 = $599
The following table and calculations demonstrate how the 50th percentile Census 2000 standard quality rent is determined for Michigan using the public distribution of standard quality rents for the state.
| Portion of Standard Quality Rent Distribution | Gross Rent Dollar Range | Number of Units | Percent of Eligible Distribution | Cumulative Percent |
|---|---|---|---|---|
| Units below interval containing public housing rent level of $248 |
$1 to $224 | 4,894 | Not in Distribution | Not in Distribution |
| Units in interval containing public housing rent level of $248 |
$225 to $247 | 1,132.52 | Not in Distribution | Not in Distribution |
| $248 to $249 | 98.48 | 0.1% | 0.1% | |
| Units below interval containing 50th percentile standard quality rent of $509 |
$250 to $499 | 44,086 | 47.3% | 47.4% |
| Units in interval containing 50th percentile standard quality rent of $509 |
$500 to $524 | 6,800 | 7.3% | 54.7% |
| Units above interval containing 50th percentile standard quality rent of $509 |
$525 or more | 42,283 | 45.3% | 100.0% |
| Total Units Above Public Housing Rent in Standard Quality Rent Distribution | 93,267.48 |
The numbers of units with standard quality rents above and below the Public Housing Rent level of $248 for Michigan are determined using linear interpolation over the 1,231 units in the rent range $225 to $249. Linear interpolation uses the assupmtion that the 1,231 units' rents are uniformly distributed in the rent range around the Public Housing Rent level. Under this assumption, the proportion of the rent interval ($25) that is below the Public Housing Rent level is the same as the proportion of units with rents in the interval (1,231) that have rents below the Public Housing Rent level.
Proportion of rent interval below the Public Housing Rent Level: ($248 - $225) / $25 = 0.9200
Units in the Public Housing Rent Level Interval below the Public Housing Rent Level: 0.9200 x 1,231 = 1,132.52
The 50th percentile standard quality rent for Michigan is computed by linear interpolation over the 6,800 units in the rent range $500 to $524. Linear interpolation uses the assupmtion that the 6,800 units' rents are uniformly distributed in the rent range around the 50th percentile. Under this assumption, the proportion of the rent interval ($25) that needs to be added to the lower limit of the interval to reach the 50th percentile rent is the same as the proportion of units in the interval that needs to be added to the units in lower rent intervals to reach 50 percent of units in the distribution.
50 percent of units = 0.5 x 93,267.48 = 46,633.74
Units below the 50th percentile rent interval = 44,086.00 + 98.48 = 44,184.48
Units in 50th percentile rent interval needed to reach 50 percent of units = 46,633.74 - 44,184 = 2,449.26
Additional Units as Proportion of Interval = 2,449.26 / 6,800 = 0.3602
Dollars Added to Lower Limit of Interval to reach 50th percentile rent = 0.3602 x $25 = $9
50th percentile standard quality rent = $500 + $9 = $509
The difference between the actual 2000 Census Standard Quality Rent of $507 and the demonstration 2000 Census Standard Quality Rent of $509 computed here is due to the effects of rounding on the public distribution as described above.
The 2000 to 2005 update factor is calculated as the ratio of the 2005 ACS standard quality median rent to the 2000 Cesus standard quality median rent for Michigan. Therefore the 2000 - 2005 update factor is:
= 2005 Standard Quality Median Rent / 2000 Standard Quality Median Rent
= $599 / $509
= 1.1768
The difference between the actual 2000 - 2005 update factor of 1.1815 and the demonstration update factor of 1.1768 computed here is due to the effects of computational rounding and the use of the rounding performed on the public distributions as described above.
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Problems or questions? Contact Peter.B.Kahn@hud.gov.