The following information provides details on how the 2017 ACS 5-Year Adjusted Standard Quality 40th Percentile Rent of $780 was developed for Grand Rapids-Wyoming, MI MSA using the publicly releasable distributions from the 2017 ACS.
The Standard Quality Gross Rents that HUD uses in generating FMRs are derived from 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.
"Standard Quality" units and rents are determined by limiting the full ACS sample by including only responses meeting the following criteria:
The 2017 ACS did not 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 for Grand Rapids-Wyoming, MI MSA in 2017 is $324.
The following table and calculations demonstrate how the 40th percentile 2017 ACS Standard Quality Gross Rent is determined for Grand Rapids-Wyoming, MI MSA using the public distribution of Standard Quality Gross Rents.
| Portion of Standard Quality Gross Rent Distribution | Gross Rent Dollar Range | Number of Units | Percent of Eligible Distribution | Cumulative Percent |
|---|---|---|---|---|
| Units below interval containing public housing rent level of $324 |
$0 to $300 | 665 | Not in Distribution | Not in Distribution |
| Units in interval containing public housing rent level of $324 |
$301 to $323 | 153.60 | Not in Distribution | Not in Distribution |
| $324 to $349 | 166.40 | 0.4% | 0.4% | |
| Units below interval containing 40th percentile Standard Quality Gross Rent of $779 |
$350 to $749 | 13,430 | 33.1% | 33.5% |
| Units in interval containing 40th percentile Standard Quality Gross Rent of $779 |
$750 to $799 | 4,525 | 11.1% | 44.6% |
| Units above interval containing 40th percentile Standard Quality Gross Rent of $779 |
$800 or more | 22,485 | 55.4% | 100.0% |
| Total Units Above Public Housing Rent in Standard Quality Gross Rent Distribution | 40,606.40 |
The numbers of units with Standard Quality Gross Rents above and below the Public Housing Rent level of $324 for Grand Rapids-Wyoming, MI MSA is determined using linear interpolation over the 320 units in the rent range $301 to $349. Linear interpolation uses the assupmtion that the 320 units' rents are uniformly distributed in the rent range around the Public Housing Rent level. Under this assumption, the proportion of the rent interval ($49) that is below the Public Housing Rent level is the same as the proportion of units with rents in the interval (320) that have rents below the Public Housing Rent level.
Proportion of rent interval below the Public Housing Rent Level: ($324 - $301) / $49 = 0.4694
Units in the Public Housing Rent Level Interval below the Public Housing Rent Level: 0.4694 x 320 = 150.20
The 40th percentile Standard Quality Gross Rent for Grand Rapids-Wyoming, MI MSA is computed by linear interpolation over the 4,525 units in the rent range $750 to $799. Linear interpolation uses the assupmtion that the 4,525 units' rents are uniformly distributed in the rent range around the 40th percentile. Under this assumption, the proportion of the rent interval ($50) that needs to be added to the lower limit of the interval to reach the 40th 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 40 percent of units in the distribution.
40 percent of units = .4 x 40,606.40 = 16,242.56
Units below the 40th percentile rent interval = 13,430.00 + 166.40 = 13,596.40
Units in 40th percentile rent interval needed to reach 40 percent of units = 16,242.56 - 13,596 = 2,646.16
Additional Units as Proportion of Interval = 2,646.16 / 4,525 = 0.5848
Dollars Added to Lower Limit of Interval to reach 40th percentile rent = 0.5848 x $50 = $29
40th percentile Standard Quality Gross Rent = $750 + $29 = $779
The difference between the actual 2017 ACS Standard Quality Gross Rent of $780 and the demonstration 2017 ACS Standard Quality Gross Rent of $779 computed here is due to the effects of rounding on the public distribution as described above.
Prepared by the Economic and Market Analysis Division, HUD. Technical Problems or questions? Contact Us.