Census Base Rent Calculation for
Independence County

The 2000 Census Base Rent for Independence County used by HUD is $396.

This rent is the 40th percentile recent mover rent for Independence County, AR.

User Note

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.

Recent Mover and Standard Quality Rents

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 Independence County, AR 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 Independence County, AR is $204.

40th Percentile Recent Mover Rent

The following table and calculations demonstrate how the 40th percentile Census 2000 recent mover rent is determined for Independence County, AR using the public distribution of recent mover rents for the FMR area.

The numbers of units with recent mover rents above and below the Public Housing Rent level of $204 are determined using linear interpolation over the 4 units in the rent range $200 to $224. Linear interpolation uses the assupmtion that the 4 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 (4) that have rents below the Public Housing Rent level.

Proportion of rent interval below the Public Housing Rent Level: ($204 - $200) / $25 = 0.1600

Units in the Public Housing Rent Level Interval below the Public Housing Rent Level: 0.1600 x 4 = 0.64

The 40th percentile recent mover rent for Independence County, AR is computed by linear interpolation over the 35 units in the rent range $375 to $399. Linear interpolation uses the assupmtion that the 35 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 617.36 = 246.94

Units below the 40th percentile rent interval = 219.00 + 3.36 = 222.36

Units in 40th percentile rent interval needed to reach 40 percent of units = 246.94 - 222.36 = 24.58

Additional Units as Proportion of Interval = 24.58 / 35.00 = 0.7024

Dollars Added to Lower Limit of Interval to reach 40th percentile rent = 0.7024 x $25 = $18

40th percentile recent mover rent = $375 + $18 = $393

The difference between the actual 2000 Census Recent Mover Rent of $396 and the demonstration 2000 Census Recent Mover Rent of $393 computed here is due to the effects of rounding on the public distribution as described above.

40th Percentile Standard Quality Rent

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 Independence County, AR using the public distribution of standard quality rents for the FMR area.

The numbers of units with standard quality rents above and below the Public Housing Rent level of $204 are determined using linear interpolation over the 4 units in the rent range $200 to $224. Linear interpolation uses the assupmtion that the 4 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 (4) that have rents below the Public Housing Rent level.

Proportion of rent interval below the Public Housing Rent Level: ($204 - $200) / $25 = 0.1600

Units in the Public Housing Rent Level Interval below the Public Housing Rent Level: 0.1600 x 4 = 0.64

The 40th percentile standard quality rent for Independence County, AR is computed by linear interpolation over the 105 units in the rent range $375 to $399. Linear interpolation uses the assupmtion that the 105 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 1,210.36 = 484.14

Units below the 40th percentile rent interval = 400.00 + 3.36 = 403.36

Units in 40th percentile rent interval needed to reach 40 percent of units = 484.14 - 403 = 80.78

Additional Units as Proportion of Interval = 80.78 / 105 = 0.7694

Dollars Added to Lower Limit of Interval to reach 40th percentile rent = 0.7694 x $25 = $19

40th percentile standard quality rent = $375 + $19 = $394

Since the standard quality rent of $394 is not higher than the recent mover rent of $396, the recent mover rent of $396 is the 2000 Census Base Rent for Independence County, AR.

Problems or questions? Contact Peter.B.Kahn@hud.gov.