The 2000 Census Base Rent for Navajo County used by HUD is $488.
This rent is the 40th percentile recent mover rent for Navajo County, AZ.
In computing 2000 Census Base 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 FMR 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 recent movers in standard quality units to set the
2000 Census Base Rent. "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
"Recent Mover" rents are determined by further limiting the "Standard Quality" sample with the following
additional criterion:
g. moved in within the last two years
A Microsoft Excel file containing the unsummarized versions of the publicly releasable recent mover and standard quality 2-bedroom rent distributions for Navajo County, AZ is available here.
The 2000 Census did not include 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 Census questions). The "public housing" rent cut-off in Navajo County, AZ is $323.
The following table and calculations demonstrate how the 40th percentile Census 2000 recent mover rent is determined for Navajo County, AZ using the public distribution of recent mover rents for the FMR area.
| Portion of Recent Mover Rent Distribution | Gross Rent Dollar Range | Number of Units | Percent of Eligible Distribution | Cumulative Percent |
|---|---|---|---|---|
| Units below interval containing public housing rent level of $323 |
$1 to $299 | 220 | Not in Distribution | Not in Distribution |
| Units in interval containing public housing rent level of $323 |
$300 to $322 | 23.00 | Not in Distribution | Not in Distribution |
| $323 to $324 | 2.00 | 0.3% | 0.3% | |
| Units below interval containing 40th percentile recent mover rent of $488 |
$325 to $474 | 235 | 37.2% | 37.5% |
| Units in interval containing 40th percentile recent mover rent of $488 |
$475 to $499 | 30 | 4.7% | 42.2% |
| Units above interval containing 40th percentile recent mover rent of $488 |
$500 or more | 365 | 57.8% | 100.0% |
| Total units Above Public Housing Rent in Recent Mover Rent Distribution | 632.00 |
The numbers of units with recent mover rents above and below the Public Housing Rent level of $323 are determined using linear interpolation over the 25 units in the rent range $300 to $324. Linear interpolation uses the assupmtion that the 25 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 (25) that have rents below the Public Housing Rent level.
Proportion of rent interval below the Public Housing Rent Level: ($323 - $300) / $25 = 0.9200
Units in the Public Housing Rent Level Interval below the Public Housing Rent Level: 0.9200 x 25 = 23.00
The 40th percentile recent mover rent for Navajo County, AZ is computed by linear interpolation over the 30 units in the rent range $475 to $499. Linear interpolation uses the assupmtion that the 30 units' rents are uniformly distributed in the rent range around the 40th 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 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 = 0.4 x 632.00 = 252.80
Units below the 40th percentile rent interval = 235.00 + 2.00 = 237.00
Units in 40th percentile rent interval needed to reach 40 percent of units = 252.80 - 237.00 = 15.80
Additional Units as Proportion of Interval = 15.80 / 30.00 = 0.5267
Dollars Added to Lower Limit of Interval to reach 40th percentile rent = 0.5267 x $25 = $13
40th percentile recent mover rent = $475 + $13 = $488
Before using the recent mover rent as the Census 2000 Base Rent, HUD checks the standard quality rent for the area to ensure that the recent mover rent is high enough to reach the 40th percentile standard quality unit. The recent mover rent may be below the standard quality rent in areas where rental housing markets are particularly stressed such that recent mover rents will not cover the expenses of operating standard quality units.
The following table and calculations demonstrate how the 40th percentile Census 2000 standard quality rent is determined for Navajo County, AZ using the public distribution of standard quality rents for the FMR area.
| 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 $323 |
$1 to $299 | 580 | Not in Distribution | Not in Distribution |
| Units in interval containing public housing rent level of $323 |
$300 to $322 | 73.60 | Not in Distribution | Not in Distribution |
| $323 to $324 | 6.40 | 0.4% | 0.4% | |
| Units below interval containing 40th percentile standard quality rent of $462 |
$325 to $449 | 520 | 35.9% | 36.3% |
| Units in interval containing 40th percentile standard quality rent of $462 |
$450 to $474 | 115 | 7.9% | 44.2% |
| Units above interval containing 40th percentile standard quality rent of $462 |
$475 or more | 809 | 55.8% | 100.0% |
| Total Units Above Public Housing Rent in Standard Quality Rent Distribution | 1,450.40 |
The numbers of units with standard quality rents above and below the Public Housing Rent level of $323 are determined using linear interpolation over the 80 units in the rent range $300 to $324. Linear interpolation uses the assupmtion that the 80 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 (80) that have rents below the Public Housing Rent level.
Proportion of rent interval below the Public Housing Rent Level: ($323 - $300) / $25 = 0.9200
Units in the Public Housing Rent Level Interval below the Public Housing Rent Level: 0.9200 x 80 = 73.60
The 40th percentile standard quality rent for Navajo County, AZ is computed by linear interpolation over the 115 units in the rent range $450 to $474. Linear interpolation uses the assupmtion that the 115 units' rents are uniformly distributed in the rent range around the 40th 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 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 = 0.4 x 1,450.40 = 580.16
Units below the 40th percentile rent interval = 520.00 + 6.40 = 526.40
Units in 40th percentile rent interval needed to reach 40 percent of units = 580.16 - 526 = 53.76
Additional Units as Proportion of Interval = 53.76 / 115 = 0.4675
Dollars Added to Lower Limit of Interval to reach 40th percentile rent = 0.4675 x $25 = $12
40th percentile standard quality rent = $450 + $12 = $462
The difference between the actual 2000 Census Standard Quality Rent of $460 and the demonstration 2000 Census Standard Quality Rent of $462 computed here is due to the effects of rounding on the public distribution as described above.
Since the standard quality rent of $460 is not higher than the recent mover rent of $488, the recent mover rent of $488 is the 2000 Census Base Rent for Navajo County, AZ.
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