BLS WORKING PAPERS

U.S. Department of Labor

U.S. Bureau of Labor Statistics

Office of Prices and Living Conditions

Changing the Housing Share of Poverty Thresholds for the 

Supplemental Poverty Measure and Equivalence Scales:

Does Consumer Unit Size Matter?

Trudi Renwick, U.S. Census Bureau

Thesia I. Garner, U.S. Bureau of Labor Statistics

Working Paper 527

July 30, 2020
2

Changing the Housing Share of Poverty Thresholds for the Supplemental Poverty Measure

and Equivalence Scales: Does Consumer Unit Size Matter? 

Trudi Renwick, Assistant Division Chief

Economic Characteristics

Social, Economic and Housing Statistics 

Division

U.S. Census Bureau, Room 7H179

Washington, DC

Office 301.763.5133 

trudi.j.renwick@census.gov

Thesia I. Garner, Division Chief

Division of Price and Index Number 

Research

Office of Prices and Living Conditions

Bureau of Labor Statistics, Room 3105

Washington, DC 20212

Office 202.691.6576 

garner.thesia@bls.gov

JEL Categories: C6, C8, D12, I3

Key Words: Equivalence Scales, Expenditure Based Poverty Thresholds 

July 30, 2020

(previously approved for presentation at the Southern Economics Association Annual Meetings 

November 2016; an earlier version published as a Census Bureau working paper 2018: SEHSD Working 

Paper 2018-06)

_____________________________________________________________________________________________

Disclaimer

The views expressed in this research, including those related to statistical, methodological, technical, or operational 

issues, are solely those of the authors and do not necessarily reflect the official positions or policies of the Bureau of 

Labor Statistics, Census Bureau, or the views of other staff members within these agencies. The authors accept 

responsibility for all errors. This paper is released to inform interested parties of ongoing research and to encourage 

discussion of work in progress. This research was presented previously at the Southern Economics Association 

Annual Meetings in November 2016 and as SEHSD Working Paper 2018-06 and is also available on the DPINR 

SPM web page: https://www.bls.gov/pir/spm/rwck-gnr-sea-2016.pdf.
1

Abstract

In producing the Supplemental Poverty Measure (SPM) thresholds and subsequent 

statistics, it is assumed that all consumer units, regardless of size and composition, share the 

same fraction of the thresholds on housing (shelter and utilities). The implication of this 

assumption is that the implicit economies of scale for housing are the same as those for the 

thresholds as a whole. If, on the other hand, one assumes that housing expenditures are subject 

to greater economies of scale than the food and clothing parts of the thresholds, it would be 

reasonable to use a larger percent to identify the housing portion of the thresholds for smaller 

families. This would have two consequences for SPM poverty statistics. First, the portion of the 

SPM thresholds subject to the geographic adjustment would be larger for smaller families ---

increasing thresholds for those who live in areas with housing costs greater than the national 

median and decreasing thresholds for those who live in areas with lower housing costs Second, 

since the values of housing subsidies in SPM resources are capped at the housing portion of the 

thresholds, this would increase the value of housing subsidies for some smaller consumer units 

and could reduce their poverty rates. In this paper we investigate the impact of varying the 

housing share of the SPM poverty thresholds directly by changing housing directly first and then 

indirectly by applying differing equivalence scales by consumer unit size. American Community 

Survey (ACS) and U.S. Consumer Expenditure Interview Survey (CE) data are used to explore 

how housing expenditures as a share of income and expenditures on food, clothing shelter and 

utilities (FCSU), respectively, vary by consumer unit size. Data from the CE are also used to 

estimate equivalence scales; these scales result in indirect adjustment to the housing shares. The 

Current Population Survey Annual Social and Economic Supplement data are used to analyze the 

impact of allowing the housing share of the thresholds to vary on SPM poverty rates. Results 

suggest that choice of the housing shares (and equivalence scales) has very little impact on either 

overall poverty rates or the impact of housing assistance on poverty.
2

Introduction

In late December 2009, the Office of Management and Budget’s Chief Statistician 

formed an Interagency Technical Working Group (ITWG) on Developing a Supplemental 

Poverty Measure. That group included representatives from the U.S. Census Bureau, Bureau of 

Labor Statistics (BLS), Economics and Statistics Administration, Council of Economic Advisers, 

U.S. Department of Health and Human Services, and Office of Management and Budget. In 

March 2010 the Interagency Working Group issued a series of suggestions to the Census Bureau 

and BLS on how to develop, and continue research on improvements, a new Supplemental 

Poverty Measure (Observations from the Interagency Technical Working Group on Developing a 

Supplemental Poverty Measure); recommendations for funding this work were also included.

1

The ITWG’s suggestions drew on the recommendations of the 1995 report of National Academy 

of Sciences (NAS) Panel on Poverty and Family Assistance and the extensive research on 

poverty measurement conducted over the past 15 years, at the Census Bureau and elsewhere. 

Thresholds for the Supplemental Poverty Measures (SPM) are produced at the BLS as a 

research project within the Division of Price and Index Number Research.2 They use five years 

of quarterly data from the U.S. Consumer Expenditure Interview Survey (CE). These thresholds 

are based on out-of-pocket spending on for food, clothing, shelter, utilities and other basic goods 

and services (this bundle of commodities is referred to as “FCSU”). Once the two adults with 

two children thresholds are produced at the BLS, they are sent to the Census Bureau for two 

further adjustments. First, the three-parameter equivalence scale is again used to adjust for 

consumer/resource units with differing numbers of adults and children. And second, an 

adjustment is applied to the thresholds to account for differences in spending on housing across 

geographic areas. 

In addition to the SPM thresholds, the BLS routinely reports the share of the thresholds 

that are devoted to out-of-pocket housing expenditures for each tenure type for the reference 

resource unit. For example, for the reference unit composed of two adults with two children, 

housing accounted for 50.5 percent of the 2015 SPM threshold for owners with mortgages, 41.1 

percent of the owners without mortgages’ threshold, and 49.8 percent of the renters’ threshold.3

These “shares” are used in two ways in the SPM estimates. First, they are used to determine the 

portion of the SPM thresholds subject to the adjustment for geographic differences in the cost of 

housing. Second, they are used to establish the cap for the value of rental housing assistance 

added to the SPM resources before determining poverty status.4 The same share is used for all 

SPM resource units, independent of size and composition.

 

1 Funding for the Census Bureau has been granted but none has been forthcoming for the BLS.

2 As the product of a research project, the SPM thresholds are not produced using BLS production quality standards. 

For more information see: http://stats.bls.gov/pir/spmhome.htm . 

3 See web link in previous footnote for shares for this and other years.

4 Housing subsidies help families pay their rent and as such are added to resources for the SPM measure. However, 

there is general agreement that, while the value of a housing subsidy can free up a family’s income to purchase food 

and other basic items, it will only do so to the extent that it meets the need for housing. Thus, the values for housing 

(rental subsidies in particular) subsidies added to other income are limited to the proportions of the threshold that are 

allocated to housing costs.4
3

This paper explores the implications of the practice of using for same housing share for 

all SPM resource units, independent of size and composition. CE and American Community 

Survey (ACS) data are used to explore how housing as a share of income varies by resource unit 

size.5 CE data are used to estimate size equivalence scales that recognize that not all components 

of the thresholds are subject to the same economies of scale. Data from the 2016 CPS ASEC data 

are used to analyze the impact of allowing the housing share of the thresholds to vary on SPM 

poverty rates for 2015. Size equivalence scales are derived from analysis of 2008Q2-2013Q1 

U.S. Consumer Expenditures Interview Survey data.

Supplemental Poverty Measure Thresholds

SPM thresholds use five years of quarterly data from the CE. These thresholds are based 

on out-of-pocket spending on for food, clothing, shelter, utilities and other basic goods and 

services. Food expenditures in the CE Survey are defined to include the implicit value of 

Supplemental Nutrition Assistance Program (SNAP) benefits in the measure of spending on 

food. Rents expenditures do not include the value of rental subsidies or the market value of 

public housing. Thresholds for “reference” consumer units composed of two adults and two 

children are derived using data from all consumers units with two children, the “estimation” 

sample. A three-parameter scale, recommended by the ITWG, is applied to the CE estimation 

sample expenditures to convert them to reference consumer unit expenditures. The threeparameter scale accounts for differences in adults and children, with a separate adjustment for 

single parents, plus a separate economies of scale parameter. The thresholds are produced at the 

BLS as a research project within the Division of Price and Index Number Research.

6

The ITWG also recommended that separate thresholds be produced for owners with 

mortgages, owners without mortgages, and renters. Research conducted in the early days of the 

ITWG meetings revealed that consumer units representing each of these housing groups 

exhibited housing expenditures that differed in important ways based on previously made

housing choices. The use of housing expenditures for consumer units without a distinction for 

housing type could result in an overestimate of poverty. For example, owners without mortgages 

report substantially lower housing expenditures, on average, than do renters or owners with 

mortgages. Not accounting for this difference could result in an overestimate of owners without 

mortgages being poor.

Once the two adults with two children thresholds are produced at the BLS, they are sent 

to the Census Bureau for two further adjustments. First, the three-parameter equivalence scale is

again used to adjust for consumer/resource units with differing numbers of adults and children. 

And second, an adjustment is applied to the thresholds to account for differences in spending on 

 

5 For information on sampling and estimation methods, confidentiality protection, and sampling and nonsampling 

errors ,please see the “American Community Survey Multiyear Accuracy of the Data ( 5-year 2010-2014)” available 

at http://www2.census.gov/programs-surveys/acs/tech_docs/accuracy/MultiyearACSAccuracyofData2014.pdf.

6 As the product of a research project, the SPM thresholds are not produced using BLS production quality standards. 

For more information see: http://stats.bls.gov/pir/spmhome.htm . 
4

housing across geographic areas. The American Community Survey (ACS) data on rents paid 

(including utilities) are used for this geographic adjustment.

The three-parameter equivalence scale is applied to the two-adults-two-children 

thresholds to derive the SPM thresholds for resources units of differing numbers of adults and 

children. Of course this means that the dollar values of the thresholds change with composition 

and size and the dollar values of the constant housing shares will change. However, accounting 

for differing needs of adults and children are not expected to fully account for differences in 

economies of scale, particularly for housing. If there are additional economies of scale for 

housing, the economies of scale parameter would be expected to change with size; a result is that

the housing shares of the thresholds would also change. Yet, in the derivation of the current SPM 

thresholds, the economies of scale parameter remains constant.

Given that housing is expected to exhibit greater economies of scale than food and 

clothing, it seems reasonable to examine the impact of using smaller or larger portions of the 

thresholds to account for differences in economies of scale for housing. As noted earlier, this 

would have two consequences for SPM rates. First, the portion of the SPM thresholds subject to 

the geographic adjustment would be larger for smaller families --- increasing thresholds for those 

who live in areas with housing costs greater than the national median and decreasing thresholds 

for those who live in areas with lower housing costs Second, since the values of housing 

subsidies are capped at the housing portion of the thresholds, this would increase the value of 

housing subsidies for some smaller families and could reduce their poverty rates. 

During the ITWG meetings held in 2010, there was much ongoing research, examining 

the impact of various assumptions being considered for the production of the SPM thresholds, 

among these, economies of scale. Instead of allowing for differing economies of scale for 

housing, the group decided to keep the economies of scale parameter constant while allowing for 

differences in housing expenditures to be accounted for through the production of separate 

housing type thresholds and by making adjustment for the number of adults and children. Test 

SPM thresholds were first presented to academic community during the November 2010 

Southern Economics Association Annual Meetings (Garner, 2010). As a discussant of the paper, 

John Bishop (2010) was rather critical of holding the economies of scale parameter constant.

Not until Renwick and Mitchell (2015) looked at the results of replacing the current 

percentage of the threshold assigned to housing for one and two person families was the 

assumption of constant economies of scale for housing tested. This exercise used 70 percent for 

one-person families and 60 percent for two-person families.7 Using this method the poverty rate 

for persons reporting housing assistance fell from 34.7 percent to 31.8 percent. This reduced the 

percent of SPM units reporting assistance with zero subsidies from 17.6 percent to 13.6 percent 

and the percent capped from 50.5 percent to 29.9 percent. The aggregate amount of subsidies 

increased from 21.6 billion with the current method to 26.0 billion

 

7 These percentages were derived from a rough estimate of an alternative housing share that assumed small

economies of scale for food (based on USDA factors associated with their cost of food at home estimates) and no 

economies of scale for clothing and miscellaneous. This left residual housing percentages of the threshold of 70 

percent and 60 percent for one and two person resource units.
5

The objective of this paper is to further investigate whether or not the housing share of 

the SPM poverty thresholds should vary directly by changing the shares or through application of 

an equivalence scale for housing (and for food plus clothing) that varies by a consumer unit size. 

CE and ACS data are used to explore how housing as a share of income varies by resource unit 

size. CE data are used to estimate size equivalence scales that recognize that not all components 

of the thresholds are subject to the same economies of scale. Data from the 2016 CPS ASEC data 

are used to analyze the impact of allowing the housing share of the thresholds to vary on SPM 

poverty rates for 2015. Size equivalence scales are derived from analysis of 2008Q2-2013Q1 

U.S. Consumer Expenditures Interview Survey data.

Estimating Housing Shares

This paper explores two sources of data on shelter and housing expenditures that could be 

used to calculate the housing shares: the CE and the ACS. From the ACS we can get a measure 

of housing costs as a percent of income, not as a percent of total expenditures. The advantage of 

the ACS is that the data is readily available from AmericanFactFinder. However, the ACS 

definition of housing costs includes items that are not included in the estimation of the SPM 

thresholds. For example, ACS calculations of total owners’ costs include payments on home 

equity loans, payments that are not included in the estimation of the SPM thresholds using CE 

data. On the other hand, the CE calculations include expenditures for owner and renter 

maintenance and repairs including parking, landscaping, rent as pay for renters, and telephone 

service and phone cards but these payments are not included in the ACS estimate. See Appendix 

1 for a more detailed definition of housing costs in the ACS. The following graph shows the 

pattern of owners and rental costs as a percent of income by household size from the ACS. 

Comparable figures are shown in Appendix 2 based on data form the CE data: housing 

expenditure shares as percentages of income before taxes and as shares of total expenditures as 

defined by the BLS.

A problem with using the entire ACS sample (or the CE sample) to estimate these income 

shares is that the share of income devoted to housing may vary depending on the household’s 

0%

10%

20%

30%

40%

50%

60%

70%

80%

1 2 3 4 5 6 7+

Household Size

Figure 1. Total Population Housing Costs as a Percent of Income

Gross Rent as a Percentage of

Household Income

Selected Monthly Owners Costs as a

Percentage of Household Income -

Mortgage

Selected Monthly Owners Costs as a

Percentage of Household Income -

No Mortgage

Source: 2014 American Community Survey Five Year Data. For more information, 

see census.gov/acs.
6

relative location in the income distribution. Specifically, lower income households may devote 

more of their annual income to housing than higher income households. To address these 

concerns, we use ACS data to look at these rental/owner costs as a percent of income for the 

bottom part of the income distribution. The following figure looks at the relationship between 

housing costs as a percent of income and household size for households with income below 200 

percent of the official poverty threshold.

Using data from the CE, we can look at housing expenditures as a percent of expenditures 

on the bundle of goods and services covered by the SPM thresholds – food, clothing, shelter, 

utilities (FCSU) plus 20 percent for other basic needs. Since the definition of housing is 

consistent in such shares, the CE could be a better source for housing share estimates for all 

consumer units even through the estimated housing shares would not be based on the SPM 

threshold estimation sample expenditures. The following graph shows these relationship using all 

consumer unit quarterly data from 2008Q2-2013Q1 from the CE by consumer unit size for each 

housing tenure group. 

0%

10%

20%

30%

40%

50%

60%

70%

80%

1 2 3 4 5 6 7+

Household Size

Figure 2. Housing Costs as a Percent of Income - Households with 

Income Less than 200 percent of Official Poverty

Gross Rent as a Percentage of

Household Income

Selected Monthly Owners Costs as

a Percentage of Household Income

- Mortgage

Selected Monthly Owners Costs as

a Percentage of Household Income

- No Mortgage

Source: 2014 American Community Survey Five Year Data. For more information, 

see census.gov/acs.
7

Unlike the ACS results, the housing shares of owners with mortgages relative to total FCSU*1.2 

is higher for owners with mortgages, followed by renters. Not surprisingly, all of the housing 

expenditures shares are higher than for the ACS which are related to total gross income. No 

statistical testing has been done comparing the shares across surveys, housing tenure types, or 

consumer unit size. 

Despite the conceptual and definitional differences in the ACS and CE, for renters and 

owners without a mortgage the relationship between housing shares and household/consumer 

unit size are similar. There is a divergence in the relationship for owners with a mortgage, with 

the ACS estimates more sensitive to changes in household size.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

1 2 3 4 5 6 7+

Consumer Unit Size

Figure 3. Housing Expenditures as a Percent of the Sum of Food, Clothing, 

Shelter, Utilities (FCSU), and Other Basic Needs (20%) Expenditures

Renters

Owners with Mortgage

Owners without a Mortgage

Source: Quarterly Consumer Expenditure Survey, all consumer units participating in 2008Q2-2013Q1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

1 2 3 4 5 6 7+

Household/Consumer Unit Size

Figure 4. Housing Shares for Renters

CE

ACS

Sources: American Community Survey and Consumer Expenditiures Survey as defined earlier. For more information, 

see census.gov/acs.
8

Equivalence Scales

In this section of the paper we describe two types of equivalence scales which we use to 

examine the impact on SPM poverty rates. The first is the equivalence scale recommended by 

the Interagency Technical Working Group (ITWG, 2010), and the second set is based on the 

relationship between housing expenditures and consumer unit size.

Interagency Technical Working Group Scale

The Interagency Technical Working Group (2010) recommended a 3-parameter 

equivalence scale to adjust the SPM thresholds for consumer units with different numbers of 

adults and children and to account for their differing needs. The scale, first proposed by Betson 

(1996), has been used by the BLS and Census Bureau since the SPM was first produced. A 

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

1 2 3 4 5 6 7+

Household/Consumer Unit Size

Figure 5. Housing Shares for Owners without a Mortgage

CE

ACS

Sources: American Community Survey and Consumer Expenditiures Survey as defined earlier. For more 

information, see census.gov/acs.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

1 2 3 4 5 6 7+

Household/Consumer Unit Size

Figure 6. Housing Shares for Owners with a Mortgage

CE

ACS

Sources: American Community Survey and Consumer Expenditiures Survey as defined earlier. For more information, 

see census.gov/acs.
9

distinguishing feature of the three-parameter equivalence scale is the adjustment for single 

parents; no adjustment for single parents is included in the two-parameter scale proposed by the 

National Academy of Sciences (NAS) Panel (Citro and Michael, 1995). The three-parameter 

scale is shown below:

One and two adults = (A) f (1)

Single adults with children scale = (1 + a + ß(K-1))f (2)

Multiple adults with children scale = (A + ßK)f (3)

where

a = parameter to account for the needs of the first child, 

ß = parameter to account for the needs of additional children, 

f = parameter to account for economies of scale within the consumer unit, 

A = number of adults within the consumer unit, and 

K = number of children within the consumer unit.

The parameters a, ß, and f were estimated by Betson to fit the cost of children literature. For 

consumer units with one or two adults, neither with children, f is set to 0.5. For consumer units 

with children, the parameters are set to 0.8, 0.5, and 0.7, respectively.8

The Census Bureau uses the three-parameter scale to derive the SPM thresholds for 

resource units with varying numbers of adults and children but starts with the reference SPM 

threshold for two adults and two children. As noted earlier, the reference threshold is produced 

by the BLS using FCSU out-of-pocket expenditures for consumer units with two children. The 

same three-parameter scale (but not for CUs with adults only) is used to equivalize expenditures 

across all consumer units with varying numbers of adults but two children only. Once these 

expenditures are equivalized and converted to two-adult two child expenditures, the SPM 

thresholds are derived based on the mean of the 30-36th percentile of FCSU expenditures and the 

housing shares of expenditures for owners with mortgages, owners without mortgages, and 

renters, plus the 20 percent multiplier to account for other basic goods and services such as nonwork transportation and personal care products (BLS, 2016; Garner, 2011). 

Regression-Based Equivalence Scales

One of the oldest methods for estimating equivalence scales is attributable to Engel, who 

argued that the budget share devoted to food falls as standard of living rises. According to Engel, 

poorer families, or larger ones with the same income, spend a greater share of income on food.

Here we assume that the proportion of income spent on necessities, not just food, is indicative of 

material well-being (i.e., households that devote the same share to necessities are equally welloff, all else constant), and thereby use an Engel approach to estimate consumer unit size 

equivalence scales. This method has been used in previous research to produce equivalence 

scales for the U.S. and for Canada using household expenditure survey data and different bundles 

of necessities (Phipps and Garner, 1994; Daley et al., 2014; Daley et al., 2015), and by Statistics 

 

8 The NAS Panel recommended a range of 0.65 to 0.75. Bishop (2010) commented that the equivalence scale factor 

is too large and should be reduced given the shares of the threshold for shelter and utilities, commodity groups with 

large economies of scale. 
10

Canada to estimate differences in income needs by family size for the production of Low income 

Cut-Offs (see Daley et al., 2015). 

In this study, we identify housing expenditures as one necessity and food plus clothing as 

a second. In this way we apply a separate equivalence scale to housing as opposed to the other 

goods and services (food and clothing) that are represented by the SPM thresholds. For each 

necessity, we use a single-parameter approximation to estimate equivalence scales. We restrict 

this analysis to consumer units with four quarters of expenditures such that their reported annual 

income refers to the same time period as their expenditures over the same 12 months. We pool 

five years of CE data from 2008 quarter 2 to 2013 quarter 1 for the analysis. Five years of data 

are used for the production of the SPM thresholds, although for those, all quarterly data are used

not just those representing four reports. We produce two sets of single-parameter equivalence 

scales. One based on an analysis of expenditure data for all consumer units, not distinguished by 

housing type, and another set with consumer unit size equivalence scales estimated for each 

housing type (i.e., owners with mortgages, owners without mortgages, and renters) separately. 

All expenditures and income are converted to constant dollars using the All Urban Consumer 

Units, All-Items CPI (not seasonally adjusted) before the regression models are estimated. The 

models are estimated with consumer unit population weights; these weights are created such that 

the resulting sample has the same distribution in terms of size as does the total population in each 

year.

The basic model is defined as in equation 4 below:

lnExp = β0 + β1lnY − β2lnN + ⋯ + ε (4)

Exp refers to housing or food plus clothing expenditures and Y is before tax income that includes 

the value of SNAP benefits. N denotes consumer unit size. We control for rural/urban status, 

region (Northeast, South, Midwest, and West) and time (2008, 2009, 2010, 2011, 2012) using the 

pooled data. βj are parameter estimates.. ε is the error term.

Rearranging predicted values yields an expression for log income share devoted to housing, for 

example. 

lnSHARE = β0 + (β1 − 1) ln Y − β2lnN + ⋯ (5)

All else constant, a consumer unit with YN will be equally well-off as a single person with Y1 if:

β0 + (β1 − 1) ln Y1 + ⋯ = β0 + (β1 − 1) ln YN − β2lnN + ⋯ (6)

Cancelling and rearranging terms yields the single-parameter approximation as presented in 

equation 7 below.

YN

Y1

= N

β2

β1−1 (7)
11

Suppose β2

β1−1

= 0.3. This would imply that a consumer units of household of two people requires 

1.23 (i.e., two raised to the power of 0.3) times the income as an otherwise similar single person 

to have the same material standard of living; a consumer unit of three people requires 39 percent 

more income, a consumer unit of four requires 52 percent more, and so on. Figure 7 includes the 

single parameter equivalence scales based on housing expenditures separately from food plus 

clothing expenditures, consumer unit size, and before tax income as defined by the BLS for CE 

data release. As expected, the equivalence scale consumer unit size parameters for housing are 

less than that for food plus clothing for both estimations. The scales diverge, with greater 

economies of scale for housing and to fewer economies of scale for food and clothing, when the 

parameters are based on separate housing tenure group regression models. Standard errors have 

not been produced and thus it is not possible for us to indicate whether the differences are 

statistically significantly different across the parameters. The food plus clothing parameters are 

in the relative range of those presented by Daley et al., (2014) for the U.S. In that study, using 

data from 2005Q2-2013Q1, the equivalence scale parameter for total food was 0.561, and for 

food, clothing, and housing it was 0.421. Separate scales for housing were not produced. 

Source: Bureau of Labor Statistics, Garner’s analysis of internal CE Interview data from 2008Q2 through 2013Q1, four quarters 

of data for each consumer unit. Three parameter scale based on 1 person=1adult, 2 people=1 adult+1 child, 3 people=2 adults+1 

child, 4 people=2 adults+2 children, 5 people=2 adults+3 children, and 6 people=3 adults+3 children.

The differences in economies of scale for owners versus for renters is most interesting. 

Research is needed to explore why the scale parameter is more than twice that for renters. Is it 

because of differences in the number of bedrooms in renter units versus owner units? Or is it 

related to something else entirely? 

Greater economies of scale for housing imply greater shares of income being allocated to 

housing by smaller consumer units versus larger ones. We can examine how this comes through 

in estimated SPM thresholds for consumer units of varying sizes. Using the equivalence scale 

parameters presented in Figure 7, we produce thresholds for consumer units with differing 

consumer unit sizes. We start with the SPM thresholds for two adults and two children, 

published by the BLS. These are reproduced below in Table 1.

0.569

0.316

0.589

0.118

0.571

0.120

0.665

0.286

0.582

0.000

0.100

0.200

0.300

0.400

0.500

0.600

0.700

0.800

0.900

1.000

3-Parameter

Scale

Housing Food+Clothing Housing Food+Clothing Housing Food+Clothing Housing Food+Clothing

All Housing Types Together Owners with Mortgages Owners without Mortgages Renters

Figure 7. Consumer Unit Size Equivalence Scale Parameters
12

Table 1. Official and Research Experimental Supplemental Poverty Measure (SPM) Thresholds 

for Two Adults and Two Children, 2015

Threshold amount

SPM Owners with mortgages $25,930 

SPM Owners without mortgages $21,806 

SPM Renters $25,583 

http://www.bls.gov/pir/spm/spm_chart1_2015data.htm

The three-parameter and estimated equivalence scale parameters are applied to the 

reference consumer unit thresholds for 2015. The results are show in Figure 8. Thresholds are 

plotted for renters, owners with mortgages, and owners without mortgages using each set of 

equivalence scale parameters. All SPM thresholds are based on FCSU with the 20 percent 

multiplier. The first panel includes thresholds produced for seven consumer unit types, varied by 

the number of adults and children, with the largest for three adults with three children, or six 

people. The other two panels represent the thresholds for consumer units with one to six people, 

with no distinction for adults and children. Thresholds for consumer units with one person, the 

only comparable thresholds across the three panels, suggest that the three-parameter equivalence 

scale results in SPM thresholds that are lower than those based on single parameter estimations. 

Thus, based on these results, the three-parameter scale does not sufficiently account for the 

housing expenditures for single person consumer units relative to those with more members. 

The second two panels suggest that economies of scale for renters differ from that of owners, as 

surmised from the bar charts presented in Figure 7. Each of the equivalence scales results in 

differing housing shares as a percentage of gross income. These results are shown and presented 

in Figure 9.
13

Figure 8. 2015 SPM Thresholds Based on Different Equivalence Scales: Three- Parameter versus Single Consumer Unit Size Parameter

Source: Bureau of Labor Statistics, Garner’s analysis of internal CE Interview data from 2008Q2 through 2013Q1, four quarters of data for each consumer unit.

$10,000

$15,000

$20,000

$25,000

$30,000

$35,000

Three-Parameter Scale 

Owner With Mortgage

Owner Without Mortgage

Renter

$10,000

$15,000

$20,000

$25,000

$30,000

$35,000

1 2 3 4 5 6

Single Parameter for All CUs

Owner With Mortgage

Owner Without Mortgage

Renter

$10,000

$15,000

$20,000

$25,000

$30,000

$35,000

1 2 3 4 5 6

Single Parameter for Housing 

Type Separately

Owner With Mortgage

Owner Without Mortgage

Renter
14
15

Impact of Changing Housing Share on SPM Estimates

How do changing housing shares, either directly or indirectly through the use of 

estimated equivalence scales, impact SPM poverty estimates? In order to assess the impact of 

changing shares we estimated SPM poverty rates using housing shares that varied by number 

of persons in the SPM resource unit. These adjustments change two elements of the SPM 

calculation: the share of the threshold subject to the geographic cost-of-living adjustments and 

the cap used for housing assistance.

The reference unit for the published SPM thresholds is composed of two adults and two 

children, or four people. In this section we compare the impact of changing the housing shares 

relative to the shares for this reference unit. The shares for units of other scales are scaled 

proportionate with the CE and ACS results. For example, as shown in Figure 9, the housing

(shelter plus utilities) portion of the thresholds for renters for the published SPM estimates is

0.498. Using the ACS housing to income shares, the percentage for single-person renter 

resource units increase to 0.593 while using the CE housing to FCSU+1.2 share is 0.528. The 

shares for renter units with six members decreases to 0.458 using the ACS estimates and to 

0.483 using the CE estimates. 

Direct Adjustment of Housing Shares

Table 2 includes the results of modifying the housing shares and their impacts on overall 

SPM poverty rates.9 The rates vary little. However, changes for the SPM estimates for resource 

units with housing subsidies are relatively larger. 

 

9 The estimates in this paper are from the 2016 Annual Social and Economic Supplement (ASEC) to the Current 

Population Survey (CPS). The estimates in this paper (which may be shown in text, figures, and tables) are based 

on responses from a sample of the population and may differ from actual values because of sampling variability or 

other factors. As a result, apparent differences between the estimates for two or more groups may not be 

statistically significant. All comparative statements have undergone statistical testing and are significant at the 90 

1 2 3 4 5 6

SPM 49.8% 49.8% 49.8% 49.8% 49.8% 49.8%

ACS 59.3% 52.8% 52.8% 49.8% 47.3% 45.8%

CE 53.3% 51.8% 50.3% 49.8% 48.3% 47.8%

SP for All Units 59.2% 54.5% 51.8% 49.8% 48.3% 47.0%

SP by Housing Type 59.9% 54.9% 51.9% 49.8% 48.1% 46.8%

40.0%

45.0%

50.0%

55.0%

60.0%

Unit Size

Figure 9. Housing Share of SPM Thresholds by Methodology
16

 Using the ACS-share adjustment, SPM poverty rates for units with housing subsidies 

fall from 31.5 to 29.8 percent. Using the CE-share adjustment, SPM rates for these 

units fall from 31.5 to 30.7 

 The percent of units reporting assistance, but assigned a $0 subsidy, falls from 24.5 

percent with the current methodology to 21.7 percent and 23.3 percent with the 

alternative shares. 

 The number of SPM units with capped housing subsidies falls from 44.7 percent to 36.8 

percent and 43.0 percent.

 There is a small increase in the aggregate value of housing subsidies, from $20.4 billion 

to $22.7 billion using the ACS-based shares. Using the CE-based shares the total is

$21.3 billion, not statistically different than the aggregate value with the current 

method. (The difference between the ACS-based aggregate and the CE-based 

aggregate is not statistically significant.)

 The impact of housing subsidies on the SPM rates of those reporting housing assistance 

increases from 21.1 percentage points to 22.6 percentage points and 21.9 percentage 

points.

Implicit Adjustment of Housing Shares via Equivalence Scales

Also shown in Table 2 are the results when the housing shares are implicitly adjusted 

through the use of estimated equivalence scale parameters.

 Overall SPM poverty rates increase from 14.3 percent to 14.6 percent with the 

application of the housing and food plus clothing equivalence scale parameters 

estimated for all housing units together. Estimating the alternative equivalence scale by 

housing type increases the SPM rate to 15.1 percent. 

 SPM rates for individuals in units with housing assistance increase from 31.5 percent to 

34.7 percent and 35.4 percent.

 The percent of units reporting assistance but assigned a $0 subsidy fall from 24.5 

percent with the current methodology to 19.7 percent and 19.6 percent with the 

alternative equivalence scales. (The difference between the percent with zeros with the 

two alternative methods is not statistically significant.

 The number of SPM units with capped housing subsidies falls from 44.7 percent to 26.2 

percent and 24.0 percent.

 There was an increase in the aggregate value of housing subsidies, from $20.4 billion to 

$24.6 billion and $25.0 billion. (The difference between the aggregates using the two 

alternative approaches is not statistically significant.)

 The impacts of housing subsidies on the SPM rates of those reporting housing 

assistance were 21.1 percentage points (current method), 21.0 percentage points (Single 

Parameter for All Units) and 20.9 percentage points (Single Parameter by Housing 

Type). The differences across the three methods were not statistically significant. 

 

percent confidence level unless otherwise noted. Standard errors were calculated using replicate weights. Further 

information about the source and accuracy of the estimates is available 

http://www2.census.gov/library/publications/2016/demo/256/p60-256sa.pdf
17

Conclusion

While conceptually the estimated equivalence scales that recognize the different 

economies of scales for housing separately from food plus clothing, this exercise has shown 

that empirically these differences do not matter. One of the major advantages of the SPM is its 

ability to gauge the impact of government programs on poverty rates. We have shown in this 

paper that the choice of housing share or the choice of equivalence scale (as estimated) has 

very little impact on the measure of the impact of housing assistance on overall poverty rates. 

Even the impact on the poverty rates of those reporting housing assistance is relatively small. 

Therefore, this does not seem to be a refinement of the SPM methodology worth pursing at this 

time.

Future research might investigate the impact of these alternative methodologies on 

other subgroups of the population, e.g. the individuals aged 65 and older, one-person SPM 

resource units, and renters. 

Works Cited

Betson, David, “Is Everything Relative? The Role of Equivalence Scales in Poverty 

Measurement,” University of Notre Dame, Poverty Measurement Working Paper, 

U.S. Census Bureau, 1996.

Bishop, John, Discussant of “Supplemental Poverty Measure Thresholds: Estimates for 2008,” 

presentation by Thesia I. Garner at the Society of Government Economists Annual Meeting, 

Washington, DC, November 15, 2010. 

Bureau of Labor Statistics (BLS), Division of Price and Index Number Research, PINR 

Experimental Poverty Measures, http://stats.bls.gov/pir/spmhome.htm , 2016.

Citro, Connie F. and Robert T. Michael (ed.). Measuring Poverty: A New Approach, 

Washington, DC, National Academy Press, 1995.

Daley, Angela, Peter Burton, and Shelley Phipps, "Measuring Poverty and Inequality in 

Northern Canada," 2015, Journal of Children and Poverty,21:2, pp. 87-107.

Daley, Angela, Thesia I. Garner, Shelley Phipps, Eva Sierminska, and Patricia Ruggles, 

“Cross-National Comparisons of Changes in Expenditure Patterns over Time,” presented at the 

2014 IARIW conference, Rotterdam, The Netherlands, 2014.

Garner, Thesia I. SEA November 2010. http://stats.bls.gov/pir/spm/spm_pp_rsch_thres10.pdf

(an earlier version of paper below presented at ASSA 2011.

Garner, Thesia I., “Supplemental Poverty Measure Thresholds: Laying the Foundation,” paper 

prepared for the ASSA Annual Meetings, Chicago, IL, January 2011; available at: 

http://www.bls.gov/pir/spm/spm_pap_thres_foundations10.pdf
18

Interagency Technical Working Group on Developing a Supplemental Poverty Measures. 

2010. “Observations from the Interagency Technical Working Group on Developing a 

Supplemental Poverty Measure. 

http://www.census.gov/hhes/www/poverty/SPM_TWGObservations.pdf

Phipps, Shelley and Thesia I. Garner, "Are Equivalence Scales the Same for Canada and the 

US?" 1994, The Review of Income and Wealth, 40:1, 1-17.

Renwick, Trudi and Joshua Mitchell. Estimating the Value of Federal Housing Assistance for 

the Supplemental Poverty Measure, SEHSD Working Paper, 2015. 

Short, Kathleen. 2015. The Research Supplemental Poverty Measure: 2014, U.S. Census 

Bureau, Current Population Reports, P60-254. Washington, DC.

Renwick, Trudi and Joshua Mitchell. Estimating the Value of Federal Housing Assistance for 

the Supplemental Poverty Measure, SEHSD Working Paper, 2015. 

Short, Kathleen. 2015. The Research Supplemental Poverty Measure: 2014, U.S. Census 

Bureau, Current Population Reports, P60-254. Washington, DC.
19

Appendices

Appendix 1: American Community Survey Housing Cost Variables

The data on gross rent were obtained from answers to Housing Questions 11a-d and 

15a in the American Community Survey. Gross rent is the contract rent plus the estimated 

average monthly cost of utilities (electricity, gas, and water and sewer) and fuels (oil, coal, 

kerosene, wood, etc.) if these are paid by the renter (or paid for the renter by someone else). 

Gross rent is intended to eliminate differentials that result from varying practices with respect 

to the inclusion of utilities and fuels as part of the rental payment. The estimated costs of water 

and sewer, and fuels are reported on a 12-month basis but are converted to monthly figures for 

the tabulations. Renter units occupied without payment of rent are shown separately as “No 

rent paid” in the tabulations.

The data on selected monthly owner costs were obtained from Housing Questions 11ad and Question 13 and Questions 17 through 21 in the American Community Survey. The data 

were obtained for owner-occupied units. Selected monthly owner costs are the sum of 

payments for mortgages, deeds of trust, contracts to purchase, or similar debts on the property 

(including payments for the first mortgage, second mortgages, home equity loans, and other 

junior mortgages); real estate taxes; fire, hazard, and flood insurance on the property; utilities 

(electricity, gas, and water and sewer); and fuels (oil, coal, kerosene, wood, etc.). It also 

includes, where appropriate, the monthly condominium fee for condominiums (Question 13) 

and mobile home costs (Question 21) (installment loan payments, personal property taxes, site 

rent, registration fees, and license fees). Selected monthly owner costs were tabulated for all 

owner-occupied units, and usually are shown separately for units “with a mortgage” and for 

units “not mortgaged.”
20

Appendix 2

Source: U.S. Consumer Expenditure Interview Survey, population weighted sample of all consumer 

units participating in survey from 23008Q2-2013Q1.

Source: U.S. Consumer Expenditure Interview Survey, population weighted sample of all consumer 

units participating in survey from 23008Q2-2013Q1.

0.0%

5.0%

10.0%

15.0%

20.0%

25.0%

30.0%

35.0%

40.0%

45.0%

50.0%

1 2 3 4 5 6 7+

Appendix Figure 1. Average Shares of Annual Housing 

Expenditurea as Percent of Before Tax Income by CU Size

owners with mortgages

renters

owners without

mortgages

0.0%

5.0%

10.0%

15.0%

20.0%

25.0%

30.0%

35.0%

40.0%

45.0%

50.0%

1 2 3 4 5 6 7+

Appendix Figure 2. Average Shares of Annual Housing 

Expenditures as Percent of Total Expenditures by CU Size

owners with mortgages

renters

owners without

mortgages
21

Appendix 3.

Weighted Consumer Unit Distributions by Housing Types and Number of Members (Size)

Source: Bureau of Labor Statistics, Garner’s analysis of internal CE Interview data from 2008Q2-2013Q1, four 

quarters of data for each cons unit; Statistics for equivalence scale regression samples.

46.4%

30.0%

23.6%

0.0

10.0

20.0

30.0

40.0

50.0

60.0

70.0

Owners with Mortgages Owners without Mortgages Renters

Percent

Distribution of Consumer Units by Housing Type

0.0

10.0

20.0

30.0

40.0

50.0

60.0

70.0

1 person 2 people 3 people 4 people 5 people 6 people 7 or more

Percent

Distribution of Consumer Units by Housing Group into Sizes

Owners with Mortgages Owners without Mortgages Renters

0.0

10.0

20.0

30.0

40.0

50.0

60.0

70.0

1 person 2 people 3 people 4 people 5 people 6 people 7 or more

Percent

Distribution of Consumer Units by Size into Housing Groups

Owners with Mortgages Owners without Mortgages Renters