A review of recent improvements to the CPI’s housing age-bias adjustment

This article presents in great detail the process used to estimate age-bias adjustment factors for the U.S. Bureau of Labor Statistics (BLS) Consumer Price Index (CPI). First, I provide an overview of housing, CPI housing-related indexes, and quality adjustments in housing. Next, I present a review of the historical evolution of age-bias adjustment factors, from their introduction in 1988 through the 2007 updates of estimating these factors. I then describe the step-by-step process of estimating age-bias adjustment factors. In these sections, I describe more recent updates to the estimation process and improvements to the regression model. I comment on model fit statistics used in 2022 and the age-bias adjustment factors used in 2023. Finally, I describe the application of these factors in the BLS calculations of unit-level price relatives and the estimated effect of age-bias adjustment factors on aggregate indexes.

Background

Housing is the largest of the eight major groups in the CPI in terms of relative importance. In December 2022, housing, which consists of shelter, residential utilities, and household goods like appliances and furniture, had a relative importance of 44.4 percent in the CPI for All Urban Consumers (CPI-U).¹ The two largest components of housing are rent of primary residence (rent) and owners’ equivalent rent (OER) of primary residence. Also in December 2022, rent and OER, combined, accounted for 31.6 percent of the relative importance in the all-items U.S. city average CPI-U and 71.1 percent of the housing major group.

Chart 1 illustrates that the overall percent changes in the rent and OER index levels from January 2018 to December 2022 were similar. Each index increased between 21.3 and 22.5 percent over the period. The rent and OER indexes showed little volatility; each index stayed within a narrow range of 0.2- and 0.4-percent change per month throughout 2018 and 2019. This growth range declined to 0.1 and 0.2 percent between April 2020 and April 2021, which coincided with the first year of the COVID-19 pandemic. In late 2022, the indexes for rent and OER rose at rates rarely observed in the CPI during the last 40 years. The rent and OER indexes each increased 0.8 percent in December 2022.

To calculate the rent and OER indexes, economists at the U.S. Bureau of Labor Statistics (BLS) need two values: rents and expenditure weights. The source for rents for the indexes is the CPI Housing Survey. BLS collects data on rents for about 8,000 housing units within 75 areas throughout the United States each month. The data include how much the tenant paid that month to occupy the unit, whether the current occupant of the unit is the same occupant when the unit was last surveyed, what utilities (if any) are included in the rent, and whether the amount the tenant paid includes any nonmandatory charges such as fees for pets or an extra parking space. The cost of shelter for renter-occupied housing is rent. OER is the implicit rent that owner occupants would have to pay if they were renting their homes, without furnishings or utilities. The rent and OER indexes are both estimated from virtually the same universe of housing units by using rents collected from renter-occupied units.²

The primary source for expenditure weights is the American Community Survey (ACS) from the U.S. Census Bureau.³ The ACS provides the number of renters, the average rents, and the number of owners by block group. An additional source used by BLS to estimate expenditure weights for owners’ implicit rents is the Consumer Expenditure Surveys (CE), which include both homeowners and renters. In 2021, 65 percent of respondents to the CE were homeowners.⁴ However, owned housing units are not themselves in the CPI market basket. BLS views owned housing units as assets rather than as consumption items. Consequently, spending to purchase and improve homes is considered investment, not consumption. Instead, BLS designs the CPI to capture what the consumer spends on the service that housing units provide to their occupants: shelter. In the CE, homeowners are asked to estimate a shelter cost by the following question: “If someone were to rent your home today, how much do you think it would rent for monthly, unfurnished and without utilities?”⁵ The responses of homeowners provide the data used to derive the expenditure weight for the OER index.⁶ The basic weight attached to a particular unit, however, varies between the rent and OER indexes and partially depends on the level of homeownership in the immediate area.

The treatment of rent and OER in the CPI has important differences compared with pricing goods and services.⁷ Goods and services are collected on a monthly or bimonthly basis and, in most cases, represent prices for items available for sale at the time of data collection. By contrast, rents in the CPI Housing Survey are collected for the same unit every 6 months and, in most cases, represent the amounts tenants actually paid in the reference month to occupy a housing unit. One notable characteristic that each survey has in common, however, is the need to apply adjustments when the quality of goods and services changes. Conceptually, the CPI measures the change in cost for urban consumers of a constant-quality market basket of goods and services over time. However, some item varieties in the sample come and go from the marketplace, which makes it difficult to collect prices for the same item variety for long periods of time. In such cases, data collectors may substitute a replacement item. The goal of quality adjustment is to remove any price differential attributed to a change in quality between the item that is no longer available and the replacement item.

Hedonic quality adjustment is one technique often used to adjust for quality change in the CPI.⁸ Hedonic quality adjustment is the analysis of an item as the sum of its features, and an implicit price is estimated for each feature. When an old item exits the marketplace and a replacement item is identified and priced, then the value of any differences in features between the items is measured and added to the price of the exiting item. Stated differently, BLS economists estimate what the price of the entering item would have been if it had been in the CPI sample in the month that the exiting item was last available.

Although there are no item replacements in the CPI Housing Survey, hedonic quality adjustments are also employed to calculate constant-quality price change in shelter indexes. Some adjustments are applied in specific circumstances. For example, if a bedroom or bathroom is added to a housing unit in the 6 months between the collections of rents, an adjustment is made for a structural change. Or if the landlord decreases the number of window air-conditioning units provided from 2 to 1, then a value for that difference in physical quality, called a facilities adjustment, is applied.

Rent adjustments due to changes in facilities and structural characteristics, however, occur infrequently. From 2017 to 2022, less than 1 percent of housing units used in the rent index included either of these rent adjustments. In contrast, another quality adjustment, called an age-bias adjustment, is always applied in the process of calculating a constant-quality price relative for a housing unit. Age-bias adjustment accounts for the depreciation of housing stock within a CPI pricing area in the 6 months between collection of data on rents.

However, BLS economists need to determine the values of housing quality adjustments. And, like commodities in other major groups in the CPI such as apparel or recreation, hedonic quality-adjustment values must be estimated for a particular good or service. These models are updated periodically. For example, new characteristics might be introduced to a service, or long-standing features of a good may become obsolete. Estimating age-bias adjustment factors requires a similar approach. Housing unit-level and neighborhood information are used to estimate quality-adjustment values, and these values are used to calculate unit-level relatives and rent and OER indexes. Also, the model used to estimate the factors must be examined and improved over time.

Background for the age-bias adjustment

BLS first introduced an age-bias adjustment with the release of the January 1988 CPI. The motivation for such an adjustment arose from research findings that the CPI was downward biased because it did "not control for quality change that results from systematic physical depreciation of rental housing.”⁹

The hedonic regression model developed in the 1980s to estimate age-bias adjustments forms the basis for the process still used today. BLS economists blended census tract data from the 1980 Census of Housing with information on about 10,000 housing units collected in the CPI Housing Survey. The model consisted of variables for structural characteristics, neighborhood, services included in the rent, and the age of the dwelling. The model was used to estimate the effect of housing unit depreciation. The final adjustments were the average value of the depreciation variables in each CPI pricing area. Initially, the adjustment was applied to the percent change in the rent and OER indexes in each month of the year. The average yearly depreciation rates estimated at the U.S. level were 0.31 percent for units used in the rent index and 0.44 percent for units used in the OER index.

The hedonic model used to estimate the age-bias adjustment was first updated in 1999. Some of the modifications were necessitated by changes to the survey over time. The CPI Housing Survey had been shortened since the model was first specified in 1988 and, thus, data for some of the structural variables in the initial model were no longer available. Additionally, beginning in 1999, BLS economists began using a new housing sample for the CPI, which replaced the housing sample used since 1987. The new housing sample was based on the 1990 census, whereas the original age-bias model was based on the 1980 census. To allow for units built after 1990 to be included in the model, BLS economists matched census data to housing units by zip code rather than by census tract.

Another change made in the early 2000s stemmed from the importance of obtaining the age of a housing unit in the model. The CPI Housing Survey consists entirely of renter-occupied units. The year a unit was built is a specification of the unit that is collected the first time a collector interviews a respondent. Thereafter, this question is asked again about every 2 years, but this is done only if the respondent at the first interview did not know the year a unit was built. Renters, however, often do not know when their home was built. Consequently, a year-built value was missing for more than half of the units in the sample. To increase the number of units that could potentially be used in the regression model, BLS staff made a special effort in the early 2000s to obtain an exact year built for housing units in the CPI sample. As a result, the number of units with a value for year built increased from 45 to 89 percent.¹⁰

Additional updates were made to the process in 2007. In this iteration, BLS economists expanded the method of imputing a year-built value and added new variables. These new variables included the length of occupancy of the current tenant and zip-code-level income data from the Internal Revenue Service (IRS). Also in the 2007 iteration, a decision was made to remove two types of units from the dataset used in the regression model. First, rent-controlled units were removed because these units typically do not reflect market rents.¹¹ Second, units built before 1900 were excluded because research showed that these units had different depreciation effects.¹² Removing both sets of units improved model fit. Also, a change was made to estimate the coefficients used to calculate age-bias factors at the unit level rather than basing that factor on an average for a pricing area.

The current process of estimating age-bias adjustments

Age-bias and structural-change adjustments for rent and OER indexes are estimated annually for the January index and remain constant for 1 calendar year. Age-bias adjustments and structural-change adjustments are estimated using the same process described below. However, the focus henceforth will be on age-bias adjustments.

The first step in the process of estimating age-bias adjustments is to compile the data. The housing units used in the modeling process are those that were collected during the past 6 months and during the month that is 6 months prior. Units that were collected for the first time during the past 6 months are excluded from the age-bias estimation process. Other exclusions are rent-controlled units and units built before 1900, as mentioned earlier. Units for which the rent was imputed (this includes vacant units and units for which the respondent could not be contacted) are also excluded. Finally, units with extreme price declines are also excluded. This final criterion of excluding units with extreme price declines was adopted for calendar year 2021 adjustments and is described in more detail below.

The second step is to merge the CPI Housing Survey data with information from the U.S. Census Bureau and the IRS. Demographic and housing data from the Census Bureau—the latest 5-year estimates from the ACS—are joined to housing units by block group.¹³ Block groups are contiguous divisions within census tracts and are generally defined to contain between 600 and 3,000 people.¹⁴ The smallest geographic entity that the ACS releases data for are block groups.¹⁵ Income data from the IRS are the most recently published statistics and include the total adjusted gross income and number of returns by zip code.¹⁶ All external data used in the estimation process are available to the public. These data sources supplement the information collected in the CPI Housing Survey with variables found to have a statistically significant effect on rent levels.

The third step is imputation of year-built values. This step involves identifying housing units for which the year the structure was built is unknown and approximating a year for those units using known values from other housing units in the same CPI pricing area. Year-built imputation is an iterative process. The initial phase in the process is taken if the year built is unknown but the decade in which the structure is built—another question in the CPI Housing Survey—is known. The next phase of the process is taken for units for which neither the year nor the decade in which it was built is known. Each successive imputation phase is less geographically restrictive than the one before it. The results of the estimation process in January 2023 showed that year-built values were known for 76 percent of units and were imputed for the remaining 24 percent. Table 1 displays the percentage of units that retained or were imputed a year-built value at each stage in the process.

The fourth step is recoding variables with binary responses as dummy variables. Dummy variables are assigned a value of 1 if one of the designated conditions is met and 0 otherwise. For example, if the type of structure is observed to be a mobile home, then the variable Mobilehome equals 1. If the type of structure is something other than a mobile home, then the variable Mobilehome is set to 0. (See table 2 for descriptions of each independent variable.)

The fifth step is to divide the housing units into various datasets by location: four datasets by census region and nine datasets by census division. As a result, each unit is assigned to a regional and a divisional dataset. Once the datasets are created, BLS economists run the same regression model for each region and division. All variables are included in each regression, regardless of their level of statistical significance.

The sixth step is to calculate two values for each housing unit: a region age factor and a division age factor. The model coefficients Age, Age2, Age3, Ageallrm, Agedtchd, and Ageold are used in the formula to calculate each statistic. See the formula in the appendix and the definition of these coefficients in table 2. The result is an age factor that generally slopes downward with age; this means that newer structures have a higher age-bias adjustment than older structures. A combined value is calculated as the average of the region and division age factors.

The seventh step is to calculate two averages for each CPI pricing area. The averages are weighted by a modified weight for the unit’s segment when used in the index during the past 6 months. The modified weight is 20 percent of the weight in rent and 80 percent of the weight in OER. The modified weight is multiplied by the previously collected rent for the unit. One of the weighted averages is then multiplied by the exponentiated value of 6 times the combined age-bias value for each unit. Finally, the age-bias adjustment for each CPI pricing area is calculated as the log of the combined-unit sum divided by the combined-unit weighted sum and divided by 6 to get a monthly value. (See the appendix for the formulas used in the final stages to calculate age-bias adjustments for each CPI pricing area.)

(See Source Data for the data and calculations used to produce the 2023 age-bias factor for the Meridian, MS, pricing area.)

Recent model updates

In 2020, BLS completed another round of improvements to the age-bias adjustment estimation process. These improvements resembled the modifications made in the mid-2000s but were also motivated by market conditions. As the economic fallout from the COVID-19 pandemic spread throughout the country, the pace of growth in the shelter indexes decelerated in mid-2020. Contributing to this slowdown in rent growth were units with abnormally steep price declines. BLS data collectors were finding more instances of tenants who did not pay rent during the month that data were being collected. In cases in which the landlord forgave the rent or did not receive rent and was unsure about the future, data collectors recorded a rent of $0.¹⁷ These extreme rent declines were used in the rent and OER indexes. However, for purposes of estimating age-bias factors in January 2021 and thereafter, BLS excluded units with extreme rent declines. The rationale was that a zero or near-zero rent for a unit did not represent a rent that could be explained by its location or physical characteristics.

Additionally, as with the effort in the early 2000s described above, data collectors completed a special round of data collection to obtain year-built values for housing units where this information was unknown. The age of a housing unit, calculated as the current year less the year the construction of the housing unit was completed, is a key component in the multivariate model. Age is used not only as a standalone variable but also as a component of interaction terms involving five other variables that compose a set of depreciation variables.¹⁸ In addition, an observation that is missing a value for age—or a value for any other variable—would be excluded from the regression model.

To compensate for units that lack a known year-built value, BLS economists use an estimation process that has always included a multistage procedure for imputing a year-built value. This procedure is explained in detail in the previous section, but, in general, units for which the year built is unknown have a value imputed from units in the same CPI pricing area with a known value. To reduce the level of imputation and increase confidence in the accuracy of age-bias adjustment factors, BLS initiated a special collection in September 2020. Over a 4-month period, data collectors used tax-assessment data and other resources to obtain year-built values for 7,100 housing units. Consequently, the number of units with a known year-built value increased from 57 to 75 percent.

The special collection in 2020 proved to be worthwhile. In January 2021, the level of imputation for calendar year 2021 factors was reduced, and the imputation was more accurate compared with the estimation of calendar year 2020 factors in January 2020. Economists at BLS compared the imputed year-built values with the actual year-built values collected from respondents either through the special collection in 2020 or through regular collection conducted in later years. In 2020, the standard deviation was approximately 30 years, and the average difference was 4.90 years. In 2021, the standard deviation was approximately 20 years, and the average difference was 1.89 years.

In mid-2021, BLS initiated another round of improvements to age-bias adjustment estimation. Although the 2020 improvements made better use of variables already in the model, the focus in 2021 was on improving the model itself. When age-bias adjustments were estimated in January 2021, BLS economists included 30 continuous and discrete variables in the model. The adjusted R-squared statistics—the ability of the independent variables to explain the variation in the dependent variable, the natural logarithm of rent—ranged from 66.4 percent in the Midwest to 73.0 percent in the West.

To improve the age-bias estimation model, economists at BLS began postestimation analysis by examining variables in the model. Several structural variables are used directly to calculate age-bias adjustments after the regression models are estimated. These variables were retained out of necessity, regardless of how well each performed in the model. Other variables were retained because of their highly statistically significant power to explain variations in rent. For example, the variables for income, length of occupancy, and percentage of the population with some college education are each statistically significant at the 99-percent confidence level across all census regions and divisions. Ultimately, two variables were removed from the model. The first variable removed was one for “other heating fuel.” This variable had become limited in scope because of changes to the CPI Housing Survey; only housing units with alternate fuels such as solar, geothermal, or firewood were coded as having an “other heating fuel” as a primary heating source. Second, a demographic variable from the ACS related to race was also removed because it tended to be not statistically significant in the Midwest and West regions.

BLS economists also investigated new data that could be introduced into the model. The research began with identifying data being collected for the CPI Housing Survey that were not already included in the model. Using data collected in the first 6 months of 2021, BLS economists tested variables that indicated if the rent was subsidized by a government agency or included free, off-street parking. A variable about leasing, which is based on new questions added to the CPI Housing Survey in October 2020, was also tested. Ultimately, four variables directly collected in the CPI Housing Survey were added to the model. These variables signify whether the rent includes nonmandatory charges, the occupant is a new tenant that moved into the unit since the last collection, the structure includes an elevator, and the unit is a mobile home. In testing, BLS economists found that the first three variables have consistently positive and statistically significant effects on rent, and the indicator for mobile home was found to have a consistently negative and a statistically significant effect on rent.

Another variable added to the model identifies if a unit is in a senior-care community, such as an independent-living or a continuing-care retirement community. This variable is coded indirectly using responses to the CPI Housing Survey. Units in which occupants receive assistance with activities of daily living (ADLs), such as bathing and eating, are ineligible for the CPI Housing Survey. In these situations, it becomes too difficult to determine the true price for the service provided by shelter. Services provided for ADLs also become likely to overlap with services for nursing homes and adult day services that are accounted for in other segments of the CPI. However, units in senior-care communities where the occupant does not receive assistance with ADLs are eligible for the CPI Housing Survey. BLS economists found that the model consistently underpredicted the level of rent for eligible units in senior-care communities. The actual rent levels are likely higher than predicted because, even though occupants do not receive assistance with ADLs, the rent still includes services such as light housekeeping and up to three meals per day. Testing showed that this variable was highly statistically significant in all regions. Moreover, the coefficients ranged from 0.87 to 1.11, the highest of any variable in the tested model, which indicates a strong and positive effect on rent.

BLS economists also looked outside the CPI Housing Survey for new data to include in the model. They examined crime data, but they found it was not consistently available and did not include enough geographic detail to be useful. BLS economists tested data from the Census Bureau on commute times, the percentage of households with nonrelatives living in the home, and the unemployment rate. Ultimately, BLS added two variables from the Census Bureau data to the model.

The first variable added from the Census Bureau is the percentage of the population enrolled in college. On the surface, this variable may appear like a variable already in the model indicating “some college education.” These variables are distinguished, however, by a technical definition. The “some college education” variable includes only the population 25 years of age and over, while the “population enrolled in college” includes the population 3 years of age and over currently enrolled in undergraduate, graduate, or professional school. Theoretically, the variable “population enrolled in college” should indicate a housing unit in student-heavy areas near college and university campuses where landlords often lease units by the bedroom. Testing showed that this variable consistently had a statistically significant effect, although the effects on rent were mixed by region. The partial effect of the percentage of population enrolled in school was positive in the Northeast and negative in all other regions.

The second variable added from the Census Bureau is a continuous variable for population density. This variable is calculated as the log of total population in a census block group divided by the land area of the block group. Testing showed that the population density variable consistently had a statistically significant and positive effect on rent. The implication is that rents tend to be higher in areas with denser populations, holding all other factors equal.

With two variables removed and seven added, the final model has 35 variables (excluding the dummy variables for location within a specific CPI pricing area). (See table 2 for a list of variables and a description for each.) The variables in the final model are described below, along with the source for each:

    ·             6 depreciation variables that each depend on the age of a housing unit (CPI Housing Survey)

    ·             13 variables related to a housing unit’s structural characteristics (CPI Housing Survey)

    ·             2 variables that describe how long the occupant has lived in the unit (CPI Housing Survey)

    ·             2 variables to indicate which utilities were included in the rent (CPI Housing Survey)

    ·             1 variable to indicate if the rent includes optional, extra charges (CPI Housing Survey)

    ·             1 variable to indicate if the unit is in a senior-living community (CPI Housing Survey)

    ·             9 neighborhood variables (Census Bureau)

    ·             1 income variable associated with a unit’s zip code (IRS)

    ·             Dummy variables for all CPI pricing areas included within the census region or division¹⁹

Model fit statistics

The model statistics in January 2022 showed a substantial improvement in model performance in most regions. The adjusted R-squared, which penalizes the addition of variables that are irrelevant to the dependent variable, increased despite the net addition of five variables. In the Midwest, Northeast, and South regions, the adjusted R-squared increased between 0.06 and 0.1 percentage point from 2021 to 2022. (See table 3.) The increase was more modest in the West region.

All 7 of the newly added variables for 2022 (Mobilehome, Elevator, Extracharges, New_tenant, In_senior_cmmty, Density, and PCT_COLLEGE, and see table 2 for definitions) were statistically significant in all regions at the 99-percent confidence level. Tables 4 to 7 display the parameter estimates for units in each of the regional models in January 2023. The largest nonintercept parameter estimate in all models is for the newly added variable for units in senior-living communities (In_senior_cmmty). These estimates indicate that rents for units in senior-living communities are approximately double the rents for units not in senior-living communities, holding all other factors constant. Neighborhood variables with the strongest positive effects on rent include educational attainment and relative level of income. Structural characteristics with the strongest positive effects include the number of bedrooms, the number of bathrooms, and the presence of central air-conditioning.

Table 4. Parameter estimates in the U.S. Census Bureau Northeast region in January 2023

Table 5. Parameter estimates in the U.S. Census Bureau Midwest region in January 2023

Table 6. Parameter estimates in the U.S. Census Bureau South region in January 2023

Table 7. Parameter estimates in the U.S. Census Bureau West region in January 2023

Models for each region and division included dummy variables to indicate the CPI pricing area in which a unit was located. In each model, the CPI pricing area with the highest average rent was left out of the model to avoid the dummy variable trap. Consequently, parameter estimates for location indicators are negative because rents in these areas tend to be lower than the excluded, or reference, pricing area.

Multicollinearity is not a cause for concern with these models. Variance inflation factors, a measure of multicollinearity, are relatively high for interaction variables. This structural multicollinearity is expected. For example, the Agedtchd variable is highly correlated with Detached because it is a product of age and the detached dummy variable. For variables that are not interacting with other variables, variance inflation factors are acceptably low. Relatively high levels of multicollinearity appear between population density and areas of high renter occupancy levels, the number of bedrooms and the number of bathrooms, relative income levels and educational attainment, and units with an elevator and the percentage of units in areas with large buildings. The highest absolute level is between the Gasheat and Elecheat variables, as these values are mutually exclusive. However, no levels of correlation are concerning.

Comments on age-bias adjustments for 2023

Age-bias adjustments effective for calendar year 2023 range from 0.000042 in the urban Honolulu, HI, pricing area to 0.000544 in the Charlotte, NC, pricing area. In percentage terms, age-bias adjustments subtract between 0.0 and 0.3 percent from the rent collected for a unit 6 months prior to use in an index. An age-bias adjustment of 0 means that rents for all units in the CPI pricing area are compared directly with the rents for the same units 6 months ago. In other words, the passage of 6 months between collection periods has no impact on the quality of services provided by rent in these areas. Age-bias adjustments for each CPI pricing area can be found in table 8.

Application of age-bias adjustments

The age-bias adjustment is included in the formula for calculating the price relatives of housing units. Age-bias adjustments are applied equally to all units that are in the same CPI pricing area. The same within-area average value is used in order to minimize variance that would otherwise occur if unit-level adjustments were applied. The 6-month relative for a housing unit used in the rent index is calculated as the economic rent in the current month divided by the economic rent 6 months ago plus the age-bias adjustment effective in the current period. The economic rent is the payment in exchange for all services the landlord provides as well as the value of certain reductions such as government subsidies. A pure rent, rather than the economic rent, is used in the OER index. The pure rent excludes the value of any utilities included in the rent. The 6-month relative for a housing unit used in the OER index is calculated as the pure rent in the current month divided by the pure rent 6 months ago plus the age-bias adjustment effective in the current period.

For example, rent data for a housing unit in the Washington, DC, pricing area is collected in July 2022. At that time, the respondent reported a rent of $2,000. In January 2023, 6 months later, when the unit was collected again, the rent was also $2,000. The economic rent in January 2023 is the monthly rent of $2,000 less any adjustments for changes in who pays for utilities, changes to the structure, and any changes to facilities, such as the number of window air-conditioning units provided by the landlord. In this example, no such changes occurred, so the economic rent in January 2023 is $2,000.

The value of the age-bias adjustment is calculated and subtracted from the rent 6 months ago using the formula below:

Economic rent 6 months ago × (exp(–6 × age – bias adjustment) – 1).

The formula is shown below with the values from the Washington, DC, CPI pricing area example:

$2,000.00 × (e^{(-6.00 × 0.000171)}  – 1.00) = –$2.05.

Put another way, the economic rent 6 months ago is “aged into the current period” by adding the age-bias adjustment effective in the current month. The 6-month relative is then calculated as the economic rent in January 2023 divided by the age-bias-adjusted economic rent in July 2022:            

$2,000.00 ÷ ($2,000.00 – $2.05) = 1.00103.

The age-bias-adjusted economic rent from July 2022 is $1,997.95 in January 2023, or 0.1 percent less than the $2,000 that was collected for the unit in July 2022.

The 6-month rent relative for a housing unit used in the OER index is calculated as the pure rent in the current period divided by the pure rent 6 months ago plus the age-bias adjustment effective in the current period. A pure rent is the value left over after subtracting the estimated costs of utilities and furnishings from the contract rent. Because owners always pay for utilities and furnishings directly, the utility costs that are included in the rent are removed from the contract rent in the OER index. This avoids double counting in the CPI because prices for utilities and furnishings are collected in the CPI Commodities and Services Survey.

For example, rent data for a housing unit in the Chicago, IL, CPI pricing area is collected in July 2022, and the respondent reported a rent of $1,500. In January 2023, 6 months later the rent was also $1,500. The pure rent in July 2022 is the collected rent of $1,500 less the estimated cost of utilities that same month of $44.05, or $1,455.95. Likewise, the pure rent in January 2023 is the collected rent of $1,500 less the estimated cost of utilities that same month of $45.30, or $1,454.70. The pure rent in July 2022 is then “aged into” January 2023 using the age-bias adjustment effective in January 2023. The value of the age-bias adjustment is calculated using the formula below:

Pure rent 6 months ago × (exp(–6 × age – bias adjustment) – 1).

The formula is shown below with the values from the Chicago, IL, CPI pricing area example:

$1,454.70 × (e^{(-6.00 × 0.000276)}  – 1.00) = –$2.40.

The 6-month relative is then calculated as the pure rent in January 2023 divided by the age-bias-adjusted pure rent in July 2022:

$1,454.70 ÷ ($1,455.95 – $2.40) = 1.000791.

The age-bias-adjusted pure rent from July 2022 is $1,453.55 in January 2023, or 0.2 percent less than the $1,500.00 that was collected for the unit in July 2022 less the estimated cost of utilities ($44.05) included in the rent.

In each of these examples, the unit-level rent relatives with no age-bias adjustment applied would be 1. However, with the age-bias adjustment, the 6-month economic and pure-rent relatives are slightly above 1.

Effect of age-bias adjustment on aggregate indexes

The formulas above show the impact of the age-bias adjustment on the calculation of unit-level rent relatives. However, these relatives are not used directly to calculate the rent and OER indexes. Instead, the sum of the weighted current-period rents for each usable unit within a segment is divided by the sum of the weighted rents 6 months earlier.²⁰ The age-bias adjustment, in effect, subtracts from the sum of rents in the 6 months earlier period. Tables 9 and 10 display the effects of the age-bias adjustment for a hypothetical segment within the Moses Lake, WA, pricing area in January 2023.

As an extension of age-bias modeling, BLS economists created a research series for the rent and OER indexes that removes the application effects of age-bias adjustment factors. From December 2014 to December 2020, the 12-month-percent changes in the indexes without the age-bias adjustments were approximately 0.3 percentage point lower than the published indexes. Charts 2 and 3 display the published and research indexes for both rent and OER.

Summary

This article highlights the importance of the rent and the owners’ equivalent rent (OER) indexes in the All-Items Consumer Price Index for All Urban Consumers (CPI-U). The various adjustments applied in the CPI Housing Survey to account for quality change are described, with a focus on the age-bias adjustment. The evolution of how age-bias adjustment is calculated and applied, since its introduction in January 1988, is explained. The steps involved in calculating the age-bias adjustment are explained in detail.

Details are given about recent updates to the age-bias estimation process. In 2020, economists at the U.S. Bureau of Labor Statistics (BLS) began excluding units with abnormally high declines in rent, and data collectors completed a special collection to obtain year-built values for thousands of housing units. In 2021, BLS economists made improvements to the model itself, which resulted in higher explanatory power of the independent variables in all U.S. Census Bureau regions.

The article provides examples of how age-bias adjustments affect the calculation of unit-level price relatives in both the economic rent used in the rent index and the pure rent used in the OER index. Finally, the estimated impact of age-bias adjustments on aggregate indexes is presented. From December 2014 through December 2020, the 12-month-percent changes in the indexes without the age-bias adjustments were approximately 0.3 percentage points lower than the published indexes.

As long as there are substantial changes in consumer buying habits or shifts in population distribution or demographics, BLS will monitor and make the necessary changes to its methodology. This is just one example of how BLS is trying to improve its data.

Appendix

Region and division factors formula:

Final age-bias factor for CPI pricing areas formulas:

     cusum + (cfswl × rntnm × 6 × exp(6 × cvalue))

     cuwtsum + (cfswl × rntnm × 6)

     cuaverage = log(cusum ÷ cuwtsum) ÷ 6