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$fmrtype$ FY 2017 FMR Documentation System -- CPI Update Factor for

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CPI Update Factor for

This page demonstrates how 2014 and 2015 CPI information was used to derive the Annual 2014 to 2015 update factor of $update_factor_display$ for the the FMRs in . CPI data are available through the BLS web site at http://data.bls.gov/cpi/. The CPI data are current as of June 2015 and may be revised by the BLS.

HUD uses the annual change in the "Rent of primary residence" and "Fuels and utilities" indices from the "Housing" component of the CPI to update FMRs. This avoids the effect of any unusual seasonal variation in the data as CPI data are not seasonally adjusted. These annual data are the latest used because they are the last issued before the Final FMRs are set. BLS reports these statistics as index numbers, not actual price levels. The index levels and changes are reported in the table below.

CPI Index Data for
CPI Series Annual
2014
Annual
2015
Change
2014-2015
Rent of Primary Residence -##.#0%
Housing -- Fuels and Utilities -##.#0%

Converting CPI Rent and Utility Data into Gross Rent Change Factors

The FMR is intended to be a measure of gross rent, which means it is supposed to measure the cost of both the contract rent paid to the owner plus the cost of utilities required to make the unit livable (e.g., heating/cooking/hot water fuel, electricity, water and sewer). In some cases, the contract rent paid to the owner includes all relevant utility costs and is therefore the same as the gross rent. In the remaining cases, rent does not include all necessary utilities so contract rent is less than gross rent.

The BLS collects data on the change in contract rents and on the change in costs of utilities. Because utility costs are included in most, but not all rents, BLS's "Rent of primary residence" statistic does not account for all of the effect of changing utility cost on gross rents. At the same time, because BLS's "Rent of primary residence" statistic does include utilities for many cases, it is not a true measure of the change in non-utility rents either. For computational purposes, HUD divides rental units into two categories -- those which have most or all utilities included in the contract rent (defined as "gross rent" units) and those where electricity and heating costs are paid directly by tenants in addition to the contract rent paid (referred to as "shelter rent" units).

In order to filter out the effect of utilities on BLS's "Rent of primary residence" statistic, HUD computes an "Annual Shelter Rent Change Factor," which is combined with BLS's "Fuels and utilities" change factor to compute the "CPI-Based Gross Rent Change". The "Annual Shelter Rent Change Factor" is computed by decomposing BLS's "Rent of primary residence" statistic to remove the influence of utilities. BLS's "Rent of primary residence" is, effectively, a weighted average of the change in area shelter rents and area gross rents (as defined above). Suppose some proportion "A" of tenants in the CPI area pay gross rents, then BLS's "Rent of primary residence" change statistic, "I" can be expressed as:

I = (1 - A) x R + A x (Change in Gross Rents)

where R is the change in shelter rent.

Similarly, the Change in Gross Rents is, effectively, a weighted average of the change in area shelter rents, "R" and the change in utility costs, "U." If "C" is the proportion of gross rent attributable to utilities, then (1-C) is the proportion of gross rent attributable to shelter rent (excluding utilities). Change in gross rents can therefore be expressed as follows:

Change in Gross Rents = (1 - C) x R + C x U.

Substituting this equation into the equation for I above yields:

I = (1 - A) x R + A x [ (1 - C) x R + C x U ].

Solving this equation for R yields the shelter rent change factor equation:

R = [ I - (A x C x U) ] / [ 1 - (A x C) ].

The Bureau of Labor Statistics supplies HUD with a special tabulation of the Consumer Expenditure Survey (conducted in each CPI survey area) showing the proportion of rental units in each CPI survey area where tenants pay for heat as part of their rent. This is used as a proxy for the proportion of tenants paying gross rent -- "A" above.

"C", the proportion of the gross rent attributable to utilities, is calculated using a special tabulation of utility expenses for all housing units in each FMR area where residents pay for electricity and heating from the 2006 American Community Survey (ACS) provided by the Bureau of the Census

2015 CPI Update Factor Data for
I2015 = CPI Annual Rent of Primary Residence Change, 2014 to 2015 A2015 = CEX Percent of Renters with Heat Included in Rent in 2015 U2015 = CPI Annual Utility Change, 2014 to 2015 C2015 = Utility Cost as a Percent of Gross Rent R2015 = Shelter Rent Change Factor
-##.#0% -##.#0% -##.#0% -##.#0% -##.#0%

The 2015 Annual Shelter Rent Change for the is computed as follows:

R2015 = [ I2015 - (A2015 x C2015 x U2015) ] / [ 1 - (A2015 x C2015) ].

= [ -##.#0% - ( -##.#0% x -##.#0% x -##.#0%)] / [1 - (-##.#0% x -##.#0%)]

= [-##.#0% - (-##.##0%)] / [1 - (-##.##0%)]

= -##.##0%/ -##.##0%

= -##.#0%

Computing the CPI Update Factor

The following tables and calculations present how the Shelter Rent Change computed above, and the CPI utility cost data are used by HUD to update the FMRs from 2014 to 2015. The computations used to derive the update factor are demonstrated below the tables.

Components of 2015 CPI Update Factor for
R2015 = Shelter Rent Change Factor (1-C2015) = Shelter Rent as a Percent of Gross Rent U2015 = CPI Annual Utility Change, 2014 to 2015 C2015 = Utility Cost as a Percent of Gross Rent CPI-Based 2015 Gross Rent Update Factor
-##.#0% -##.#0% -##.#0% -##.#0% $update_factor_display$

CPI-Based 2015 Gross Rent Update Factor

= 1 + R2015 x (1-C2015) + U2015 x C2015

= 1 + (-##.#0% x -##.#0%) + (-##.#0% x -##.#0%)

= 1 + (-##.###0) + (-##.###0)

= $update_factor_display$

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