United States

Department

of Agriculture

Economic

Research

Service

Electronic

Report

Economic

Research

Report

Number 26

September 2006

The Cost of Living and the

Geographic Distribution

of Poverty

Dean Jolliffe
www.ers.usda.gov

Want to learn more about this topic? Visit our website at 

www.ers.usda.gov.

You can also find additional information about ERS 

publications, databases, and other products at our 

website.

Visit Our Website To Learn More!

National Agricultural Library

Cataloging Record:

Cover photos: Clockwise--Courtesy of PhotoSpin; Eyewire; and Ken Hammond, USDA.

The U.S. Department of Agriculture (USDA) prohibits discrimination in all its programs and 

activities on the basis of race, color, national origin, age, disability, and where applicable,sex, 

marital status, familial status, parental status, religion, sexual orientation, genetic information, 

political beliefs, reprisal, or because all or part of an individual’s income is derived from any 

public assistance program (Not all prohibited bases apply to all programs.) Persons with 

disabilities who require alternative means for communication of program information(Braille, 

large print, audiotape, etc.) should contact USDA’s TARGET Center at (202) 720-2600 (voice 

and TDD).

To file a complaint of discrimination, write to USDA, Director, Office of Civil Rights, 1400 

Independence Avenue, S.W., Washington, D.C. 20250-9410, or call (800) 795-3272 (voice) or 

(202) 720-6382 (TDD). USDA is an equal opportunity provider and employer.

Jolliffe, Dean, 1963-

 The cost of living and the geographic distribution of poverty.

 (Economic research report (United States. Dept. of Agriculture. 

 Economic Research Service) ; no. 26)

 1. United States—Economic conditions. 2. Poverty—United States.

 3. Cost and standard of living—United States. 4. Urban poor—

 United States—Economic conditions. 5. Rural poor—United States—

 Economic conditions. 6. Public welfare—United States.

 I. United States. Dept. of Agriculture. Economic Research Service. 

 II. Title.

HV4045
United States 

Department 

of Agriculture

www.ers.usda.gov

Electronic Report from the Economic Research Service

Economic

Research

Report 

Number 26

The Cost of Living 

and the Geographic 

Distribution of Poverty

Dean Jolliffe

September 2006

Abstract

The prevalence of poverty has been greater in nonmetro areas than in metro

areas in every year since the 1960s when poverty rates were first officially

recorded. Accordingly, Federal funds for social assistance programs and

community development have favored nonmetro areas. This study suggests

that adjusting poverty measures to account for cost-of-living differences

between metro and nonmetro areas reverses that ranking. Once adjusted for

cost-of-living differences using the Fair Market Rents index, metro poverty

is greater than nonmetro poverty in terms of prevalence, depth, and severity

over the entire 1991-2002 study period. 

Keywords: Poverty, cost-of-living adjustments, Fair Market Rents data,

urban-rural comparison, sample design, Current Population Survey

Acknowledgments

The author would like to thank Kathleen Short and Erika Steinmetz, U.S.

Census Bureau, for their help in providing the Fair Market Rents index for

this analysis, and Alfred Meier, U.S. Census Bureau, for answering many

questions about Current Population Survey sample design. Thanks to Bruce

Weber, University of Oregon, for reviewing this document multiple times

and for comments. Thanks also to Elise Golan, Constance Newman, Mark

Nord, Mark Prell, Laura Tiehen, and Leslie Whitener, Economic Research

Service, and to session participants at the 2004 American Social Sciences

Association meetings and the 2004 Western Economic Association 

International conference.
Contents

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .iii

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1

Poverty Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3

The Fair Market Rents Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3

The Data: 1992-2003 CPS and U.S. Poverty Thresholds . . . . . . . . . . . . .5

The Foster-Greer-Thorbecke Poverty Measures . . . . . . . . . . . . . . . . . . . .6

Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8

Nonmetro-Metro Poverty Comparisons, 

The Unadjusted (Official) Estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . .8

Nonmetro-Metro Poverty Comparisons, 

Adjusted Using the FMR Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9

Age and the FMR-Induced Change in Nonmetro Poverty . . . . . . . . . . .11

The Cost of Housing and All Other Goods . . . . . . . . . . . . . . . . . . . . . . .13

Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .15

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .16

Appendix: Baseline Measures and Standard Errors . . . . . . . . . . . . . . .19

ii

The Cost of Living and the Geographic Distribution of Poverty/ERR-26

Economic Research Service/USDA
Summary

The prevalence of poverty has been greater in nonmetro areas than metro

areas in every year since the 1960s when poverty rates were first officially

recorded. Accordingly, Federal funds for social programs for the needy and

community development have favored nonmetro areas.

Poverty estimates figure prominently in determining the distribution of

large sums of cash and in-kind benefits from State and Federal Government

programs. For example, Federal block grants for community development

are typically linked to county-level poverty estimates. Persistently poor

rural counties benefit disproportionately from block grants, receiving more

than $1,000 per person in 1994. In 1997, per capita distribution of Federal

funds for social programs was 8 percent higher in nonmetro areas than in

metro areas.

One can argue that distribution of social assistance is well targeted because

the prevalence of poverty consistently has been greater in nonmetro areas

than in metro areas. However, how poverty is defined plays an important

role in the geographic distribution of poverty, and changes to the definition

could affect the funding for social programs.

What Is the Issue?

The official poverty measure from the U.S. Census Bureau assumes that the

cost of living is the same throughout the United States. The Federal

Government is examining experimental poverty measures, however, that

adjust poverty rates according to geographic cost-of-living differences. The

Government has developed an experimental index that uses Fair Market

Rent (FMR) data to adjust for geographic differences in the cost of living.

How does the use of an index to adjust for cost-of-living differences affect

the distribution of poverty across metro and nonmetro areas and how does it

affect the age composition of the poor?

What Did the Study Find?

Adjusting poverty rates with the FMR index completely reverses the

nonmetro-metro poverty profile. With no adjustment for cost-of-living

differences, poverty over the last 12 years is higher in nonmetro areas than

in metro areas. (The depth and severity of poverty also are higher in

nonmetro areas, but in about one-half the cases, the differences are not

statistically significant.) When the FMR index is used to adjust for cost-ofliving differences, the prevalence, depth, and severity of poverty over the

last 12 years are higher in metro areas than in nonmetro areas. In 2001, for

example, the prevalence of nonmetro poverty was 28 percent higher than in

metro areas. Once adjusted for cost-of-living differences, the rate is

reversed and the prevalence of poverty in nonmetro areas is 12 percent

lower than in metro areas.

Our analysis also examines how adjusting for cost-of-living differences affects

the age composition of the poor. The nonmetro poor consist disproportionately of the elderly, many of whom are living on fixed incomes near the

poverty line. Using the FMR index to adjust for cost-of-living differences

iii

The Cost of Living and the Geographic Distribution of Poverty/ERR-26

Economic Research Service/USDA
results in reclassifying many of the elderly poor as nonpoor. To the extent

that these elderly people are receiving Federal funds tied to poverty rates,

they have the most to lose from this reform. More generally, using the FMR

index to adjust poverty rates for cost-of-living differences could have significant adverse affects on funding for nonmetro social programs and developmental block grants.

How Was the Study Conducted?

The spatial (geographic) price index used in this analysis comes from the

Census Bureau’s research on experimental poverty measures and is based on

the FMR data collected by the U.S. Department of Housing and Urban

Development. The primary advantages of these data are that they provide

full coverage of the United States and reflect spending of lower income

households. The FMR data estimate the cost of gross rent (utilities included)

at the 40th percentile for standard-quality housing. The primary purpose of

the FMR is to determine eligibility of rental housing units for the Section 8

Housing Assistance Payments program.

The poverty estimates come from the 1992-2003 March Supplement of the

Current Population Survey (CPS), which is the data base for the official

U.S. poverty rates. The sample represents the civilian, noninstitutionalized

population and members of the Armed Forces either living off base or with

their families on base. The measure of well-being is income as it is defined

for Federal poverty rates. This definition includes all pre-tax income but

includes neither capital gains nor any noncash benefits, such as public

housing, Medicaid, or food stamps. The reference period for income-related

questions is the preceding calendar year, and therefore, the 1992-2003 CPS

data provide poverty estimates for 1991-2002.

iv

The Cost of Living and the Geographic Distribution of Poverty/ERR-26

Economic Research Service/USDA
Introduction

Poverty estimates figure prominently in the criteria that determine the

geographic distribution of large sums of cash and in-kind benefits from State

and Federal Government programs. Citro and Michael (1995, pp. 89-90)

note that, in the early 1990s, 27 different Federal assistance programs linked

their eligibility criteria in part to poverty lines or area average poverty rates.

For example, one eligibility criterion for the Food Stamp Program is that

household income must be equal to or less than 130 percent of the poverty

line. In 2003, the Food Stamp Program distributed $21 billion in program

benefits. Data from the 2003 Current Population Survey indicate that per

capita benefits were 39 percent higher in U.S. nonmetropolitan (nonmetro)

areas than in metropolitan (metro) areas.1

Another example is Federal block grants for community development,

which are typically linked to county-level poverty estimates. Reeder (1996,

p. 1) notes that persistently poor rural counties benefit disproportionately

from block grants, receiving more than $1,000 per person in 1994. Reeder

et al. (2001, p. 4) also show that, in 1997, per capita distribution of Federal

funds for social safety net programs was 8 percent higher in nonmetro than

in metro areas.

One can argue that this distribution of social assistance is well targeted

because the prevalence of poverty has been greater in nonmetro areas than

in metro areas in every year since the 1960s when poverty rates were first

officially recorded (Jolliffe, 2003b). However, how poverty is defined plays

an important role in the geographic distribution of poverty, and any changes

to the definition could affect the geographic distribution of funding for

social safety nets.

The National Academy of Sciences (NAS) Panel on Poverty and Family

Assistance has recommended several changes in how the Federal Government measures poverty, including adjustments for geographic differences in

the cost of living (Citro and Michael, 1995). While the NAS Panel recommended several changes, adjusting for cost-of-living differences is the one

aspect of reform that would most systematically change the geographic

distribution of poverty (Nord and Cook, 1995). The official Federal poverty

thresholds currently assume that the cost of living is the same throughout

the United States, but the Census Bureau has now developed experimental

poverty measures that use Fair Market Rent data to create an index for

spatial differences in the cost of living. The purpose of this report is not to

advocate for, or against, the use of this index, but rather to examine how the

use of the index to adjust for cost-of-living differences affects the distribution of poverty across metro and nonmetro areas.

An adjustment for cost-of-living differences will have the greatest effect on

a comparison of metro and nonmetro areas. The study’s focus on the two

areas is driven largely by this effect and by the strong historical difference

in poverty rates across these areas.

1

The Cost of Living and the Geographic Distribution of Poverty/ERR-26

Economic Research Service/USDA

1

Per capita benefits are averaged

over the entire population (recipients

and nonrecipients). This finding is

similar to Ghelfi (2003), who uses

data from the Bureau of Economic

Analysis and documents that per capita

food stamp benefits were 32 percent

greater in nonmetro areas than in

metro areas in 2001.
Because this study solely examines how spatial price differences affect

poverty rates, it provides information on only one of the NAS Panel’s

suggested changes, and it is important to interpret the results with this

caveat in mind. Nonetheless, an advantage to the narrow focus on spatialprice adjustments is that the findings readily highlight the sensitivity of the

relative poverty levels of nonmetro and metro areas to this change. The

results from this analysis suggest a complete reversal of all three poverty

measures considered. Specifically, once adjusted for cost-of-living differences using the Fair Market Rents index, metro poverty is greater than

nonmetro poverty in terms of prevalence, depth, and severity over the

entire 1991-2002 period considered in this analysis.

This report adds to the current literature on poverty measure reform in

primarily two ways. First, it focuses on the impact of change on relative

differences in poverty rates between metro and nonmetro areas. This focus

is important both in terms of understanding how reform could affect the

geographic distribution of benefits from Federal assistance programs and in

terms of the potential political economy issues that might develop from such

a proposed change.

Second, much of the current analysis of the experimental poverty measures

is based on how change will affect the prevalence of poverty. This study

considers three different measures of poverty-the headcount, poverty gap,

and squared poverty gap measures-that will provide more information on

the distributional effects of the proposed change. The three measures belong

to the Foster-Greer-Thorbecke (1984, hereafter referred to as FGT) family

of poverty measures and have been widely used in the international poverty

literature.2 The headcount is the standard measure used and provides a measure

of the prevalence of poverty. The poverty gap measure provides a measure

of the depth of poverty. The squared poverty gap is sensitive to the income

distribution of the poor and provides a measure of the severity of poverty.

2

The Cost of Living and the Geographic Distribution of Poverty/ERR-26

Economic Research Service/USDA

2

The following all use these three

measures: Jolliffe et al. (2004) for

Egypt, Datt and Ravallion (1992) 

for Brazil and India, Howes and

Lanjouw (1998) for Pakistan and

Ghana, Kakwani (1993) for Côte

d’Ivoire, and Ravallion and Bidani

(1993) for Indonesia.
Poverty Measurement

This section covers the Fair Market Rents index, data, poverty line, and the

FGT poverty measures.3

The Fair Market Rents Index

While the data are limited, the evidence suggests that geographic differences in the cost of living are significant. Up until 1982, the Bureau of

Labor Statistics collected data from the Family Budget Program (FBP),

which provided estimates of the relative cost of a consumption bundle for a

family of four living in different areas of the United States. The last sample

of FBP data indicates that, in 1981, the spatial variation in the cost of

purchasing the fixed bundle of goods was significant. For example, in

urban areas of the Northwest, the cost was 113 percent of the national

average, and in the nonmetro South, it was 91 percent of the national

average (Citro and Michael, 1995, p. 186).

Other sources of data on spatial differences in the cost of living are available,

but none of these include full coverage of metro and nonmetro areas. For

example, the Bureau of Labor Statistics has been working on using data

from the Consumer Price Index (CPI) to develop a spatial price index, but

these efforts have focused strictly on urban areas (Aten, 2005; Kokoski,

1991; Moulton, 1995). Perhaps the best known spatial price index is the

ACCRA index, which was developed by the American Chamber of

Commerce Researchers Association.4 The index has some shortcomings: It

provides an estimate of the cost of living in an area only if a volunteer has

reported the data, and it is intended to reflect cost-of-living differences for

households in the top quintile of income. For the purposes of poverty

analysis, this index is most likely not a useful one.

This study uses the spatial price index for 2001 developed by the Census

Bureau in their research on experimental poverty measures (Short, 2001a,

2001b) and is based on the Fair Market Rent (FMR) data collected by the

U.S. Department of Housing and Urban Development (HUD).5 The primary

advantages of the FMR data are that they provide full coverage of the

United States and reflect spending of lower income households. HUD

produces annual estimates of the FMR for 354 metro areas and 2,350

nonmetro counties. The FMR data estimate the cost of gross rent (utilities

included) at the 40th percentile for standard-quality housing.6 The purpose of

the FMR is to determine eligibility of rental housing units for the Section 8

Housing Assistance Payments program. Section 8 participants cannot rent a

unit if the rent exceeds the FMR. (FMR also serves as the payment standard

used to calculate subsidies under the Rental Voucher program.) See U.S.

Housing and Urban Development (2003) for more details.

The FMR index used in this analysis was constructed by Short (2001a,

2001b) for the Census Bureau’s experimental poverty measures and is based

on FMR data from 2001. In using this index to examine poverty differences

over many years, we are implicitly assuming that the spatial distribution of

prices has not changed significantly over the years.7 A cursory look at the

early FMR data files suggests that the results are not likely to be qualitatively

affected by this simplifying assumption. The study tests this suggestion by

3

The Cost of Living and the Geographic Distribution of Poverty/ERR-26

Economic Research Service/USDA

3

The findings in this report along

with more technical detail can also be

found in Jolliffe (2006).

4

For an ACCRA example, see

Dumond, Hirsch, and MacPherson

(1999). See Koo, Phillips, and Sigalla

(2000) for a comparison of CPI-based

and ACCRA indexes.

5

For a critique of the FMR as a 

spatial price index, see Short (2001b,

Appendix A). For an alternative 

examination of spatial price differences

based on subjective measures of food

security, see Nord (2000) and Nord

and Leibtag (2006).

6

From 1995 to 1999, the FMR is

based solely on the 40th percentile. As

of 2001, the FMR index is based on the

40th percentile except for 39 MSAs,

which are based on the 50th percentile.

Between 1983 and 1994, the index was

based on the 45th percentile.

7

While the FMR data are publicly

available, for this analysis, they need

to be merged with the CPS data using

geographic identifiers that are only

complete in the private (not for public

release) CPS files. The Census Bureau

provided the 2001 FMR index for this

research to enable participation in a

panel on “Adjusting for Geographic

Cost-of Living Differences in Federal

Statistics” held by the Society of

Government Economists.
examining the simple mean FMR for nonmetro counties and mean FMR

for Metropolitan Statistical Areas between 1991 and 2004. These estimates

will not be comparable to the means for the FMR index because they have

not been population weighted, but significant temporal variation in the

means would suggest that the findings for years other than 2001 could be

sensitive to this assumption. Over the 14 years examined, the nonmetro

mean FMR was between 68 percent and 77 percent of the metro mean

FMR, which is interpreted as evidence of some stability in the spatial

differences in prices over time.

Another caveat in interpreting the findings of this study is that about 4

percent of the counties switched from nonmetro to metro (or vice versa) in

1993, depending on the demographic changes observed in the 1990 Census.

Given the changing status of some counties in 1993 and the assumption that

the spatial distribution of prices has not changed over time, the findings for

the more recent years are viewed as somewhat more accurate. For this

reason, the core findings are presented for all years between 1991 and 2002,

but the more detailed analysis focuses on the last 2 years from the sample.

The index is constructed as a fixed-weight index consisting of two 

components—housing and all other goods and services. Following the

recommended approach of the National Academy of Sciences report (Citro

and Michael, 1995, p. 197), the index assigns a weight of 44 percent for

housing expenses and 56 percent on all other goods and services. Further, the

index assumes that variation in the FMR data reflects variation in housing

prices for the poor and that the prices of all other goods and services do not

vary. The focus on housing prices in the index is supported by Moulton (1995,

p. 181) who notes that “the cost of shelter is the single most important

component of interarea differences in the cost-of-living.” By construction then,

if the FMR data indicate that rents in a particular area are 10 percent higher

than the baseline, then the FMR index used by the Census Bureau reflects a

cost of living in this area that is 4.4 percent higher than the baseline.

The primary reason for assuming that prices for nonhousing goods and services do not vary is a lack of credible data sources for spatial price variation

in nonhousing prices. The data that do exist suggest that areas where housing

costs are high also have somewhat higher prices for other goods (housing

and nonhousing prices are positively correlated). This correlation implies

that the no-spatial-variation assumption in nonhousing prices will underestimate the magnitude spatial price differences. In other words, the estimates

are likely to be lower bound, or conservative, estimates of the effect of

adjusting poverty estimates for spatial price differences. The section “The

Cost of Housing and All Other Goods” examines the sensitivity of the core

findings to the assumption of no correlation.

Finally, the FMR index used in the Census Bureau’s experimental poverty

measures is aggregated up to 100 different price levels, one for metro areas

and one for nonmetro areas of each State and the District of Columbia.8 This

step differs from the approach followed by the National Academy of Sciences

(Citro and Michael, 1995, pp. 195-97), which used Census data and disaggregated the index by Census regions and population categories. The

National Academy of Sciences report recognizes that the use of Census data

is problematic due to the limited frequency of its availability and recommends

4

The Cost of Living and the Geographic Distribution of Poverty/ERR-26

Economic Research Service/USDA

8

New Jersey and the District of

Columbia consist of only metro areas,

hence, 100 total FMR price levels.
using an index that can be updated more frequently than once every 10 years.

They further recommend exploring the potential of using the FMR data

(Citro and Michael, 1995, p. 200), as is done in recent reports on the experimental poverty measures, including this report and Short (2001a, 2001b).

For purposes of this analysis, the FMR index is scaled to ensure that the

FMR-adjusted poverty estimates match the official U.S. Federal estimates at

the national level. With this scaling, any deviation from official estimates at

the subnational level will be strictly due to relative price differences in the

index. Table 1 lists basic descriptive statistics of the FMR index by metro and

nonmetro areas. The index shows that the average cost of living in nonmetro

areas is 79 percent of that in metro areas. It is the first indication that using

the index to adjust for cost-of-living differences is likely to significantly

affect the measurement of metro-nonmetro poverty differences.

The Data: 1992-2003 CPS and 

U.S. Poverty Thresholds

The data used in this study are from the 1992-2003 March Supplement to

the Current Population Survey (CPS) conducted by the Census Bureau for

the Bureau of Labor Statistics. The CPS data are the basis for the official

U.S. poverty estimates and provide information on about 50,000 families in

each year (80,000 in the more recent years). The March Supplement, also

called the Annual Demographic Survey of the CPS, collects information on

income and a variety of demographic characteristics. The reference period

for income-related questions is the preceding calendar year, and therefore,

the 1992-2003 CPS data provide poverty estimates for 1991 through 2002.

The sample represents the civilian, noninstitutionalized population and

members of the Armed Forces either living off base or with their families on

base. The sample frame is based on housing structures and not on individuals,

so all individuals who are homeless at the time of the interview are excluded

from the sample. Because the homeless are disproportionately located in

metro areas, their exclusion disproportionately biases the metro poverty estimates downward. A primary finding of this study is that adjusting for costof-living differences with the FMR index decreases nonmetro poverty and

increases metro poverty to the extent that the nonmetro-metro poverty rankings are completely reversed. If the homeless were included in this analysis,

they would further reinforce this finding.

The measure of well-being used in this study is income as defined for Federal

poverty rates. This definition includes all pre-tax income but does not include

capital gains or any noncash benefits, such as public housing, Medicaid, or

food stamps. The poverty thresholds used in this study are the U.S. Federal

5

The Cost of Living and the Geographic Distribution of Poverty/ERR-26

Economic Research Service/USDA

Table 1

Scaled Fair Market Rent index, nonmetro-metro comparison

Fair Market Rent index Average Median (Minimum, maximum)

National 1.00 1.00 (0.74, 1.21)

Nonmetropolitan .82 .81 (.74, 1.21)

Metropolitan 1.04 1.01 (.85, 1.19)

Note: Fair Market Rent index weighted by individual weights to match weights used for 

poverty estimation.
Government poverty lines, which were developed in 1965 following a costof-basic-needs methodology that sets the poverty line at the value of a

consumption bundle considered to be adequate for basic consumption needs.

Basic needs, in this context, represent a socially determined, normative

minimum for avoiding poverty. For more details on this methodology and

other methods of drawing poverty lines, see Ravallion (1998).

The U.S. poverty line set in 1965 was based on the cost of USDA’s

economy food plan, a low-cost diet determined to be nutritionally

adequate. In addition to the cost of this food plan, the poverty line included

an allowance for nonfood expenditures that was twice the value of the cost

of the USDA economy food plan.9 To account for inflation, the poverty

lines set in 1965 are adjusted each year using a price index.10 The latest

poverty line used in this study is from 2002, set at $9,359 for an individual

younger than 65, $12,400 for a two-person family with one child and one

adult, and $21,469 for a family with two adults and three children. For a

complete listing of 2002 poverty lines for individuals and families of

various sizes, see Proctor and Dalaker (2003, p. 4).

The Foster-Greer-Thorbecke 

Poverty Measures

The previous section describes the measure of well-being and poverty lines

used to identify who is poor. The next step is to aggregate this information

into a scalar measure of poverty. To examine the sensitivity of estimated

poverty levels to the choice of a poverty measure, we consider three measures that belong to the FGT family. The first is the headcount measure (P0

),

which is the percentage of the population that is poor. The second measure,

called the poverty gap index (P1 ), is found by first measuring the income

gap (i.e., the proportionate difference between income and the poverty line)

for all poor persons. The poverty gap index is then the average value of the

income gaps, where the average is formed over the entire population,

counting the nonpoor as having zero income gap. The third measure is the

squared poverty gap measure (P2 ) and is defined as the mean value of the

squared income gaps.

The FGT class of poverty measures, also referred to as Pa, can be 

represented as:

where n is the sample size, i subscripts the family or individual, y is the

relevant measure of well-being, z is the poverty line, and I is an indicator

function that takes the value of one if the statement is true and zero otherwise. When a=0, the resulting measure is the headcount measure, or P0

.

When a=1, the FGT measure results in the poverty gap measure, or P1

; and

the squared poverty gap measure (P2

), results when a=2.

The usefulness of these measures can be illustrated by considering a transfer

of money from a rich person to a poor person that is not large enough to

move the poor person over the poverty line. This transfer has no effect on

the headcount measure, but the poor person is better off and the improvement in well-being is reflected in a reduction of both the poverty gap and

6

The Cost of Living and the Geographic Distribution of Poverty/ERR-26

Economic Research Service/USDA

9

For details on the first poverty lines,

see Orshansky (1965). For a history of

poverty lines before Orshansky, see

Fisher (1997). For a critical discussion

of the official poverty line, see Ruggles

(1990).

10Before 1969, the index used 

was the changing cost of the USDA

economy food plan. Since 1969, the

CPI for all goods and services has

been used.

P n I y z z y z a i i i a = 1 1 / () Â ( )[( )/ ] < -
squared poverty gap. As another example, a transfer of income from a poor

person to a poorer person will not alter either the headcount or the poverty

gap measure, but it improves the distribution of income of the poor and this

change is reflected by a reduction of the squared poverty gap.11

These examples point to an important reason to consider the poverty gap

and squared poverty gap measures in addition to the commonly reported

headcount measure. A frequent goal of many programs is to reduce poverty,

but the policies appropriate to attain this goal will vary depending on which

poverty measure is considered. If policymakers are focused on the headcount measure, then the most efficient way to reduce poverty is through

assistance to the least poor. If, on the other hand, policymakers are

concerned about the overall well-being of the poor and not just on reducing

the number of people living in poverty, then the appropriate measure is one

that captures the depth and severity of poverty.

7

The Cost of Living and the Geographic Distribution of Poverty/ERR-26

Economic Research Service/USDA

11

Unlike the Sen (1976) or Kakwani

(1980) distribution-sensitive measures

of poverty, the squared poverty gap

measure also satisfies the “subgroup

consistency” property, which means

that if poverty increases in any 

subgroup and it does not decrease

elsewhere, then aggregate poverty

must also increase (Foster and

Shorrocks, 1991).
Results

Nonmetro-Metro Poverty Comparisons,

The Unadjusted (Official) Estimates

Before answering whether nonmetro-metro poverty comparisons are sensitive

to spatial price adjustments, the baseline for comparison must be established.

Appendix table 1 lists the headcount (P0

), poverty gap (P1), and squared

poverty gap (P2) measures for metro and nonmetro areas for each year

between 1991 and 2002. The appendix discusses the derivation of the

sampling variance of these estimates. The nonmetro headcount measure ranges

from a high of 0.17 in 1993, representing 9.7 million poor people, to a low

of 0.13 in 2000, 6.8 million poor people. The metro headcount measure

ranges from a high of 0.15 in 1993, 29.5 million poor people, to a low of

0.11 in 2000, 24.3 million poor people. The variation in the poverty gap and

squared poverty gap measures is similar. Across both of these measures, for

metro and nonmetro areas alike, poverty was at its lowest level in 2000. In

terms of the poverty gap measure, the year with the highest level of poverty

came in 1993. The worst year, as measured by the squared poverty gap

measure, came in 1997 for nonmetro areas and 1993 for metro areas.

Appendix table 1 also provides estimates of the design-corrected standard

errors for each of the 72 poverty estimates (P0

, P1, and P2 for each year

from 1991 to 2002 by metro and nonmetro areas). None of the estimates has

a design effect of less than 4, which means that the design-corrected standard

errors are all more than twice as large as those that would be estimated if

one (incorrectly) ignored the complex sample design.12

The poverty gap measure is equal to the product of the headcount measure

and the income gap, where the income gap is the average shortfall of the

poor as a fraction of the poverty line. The poverty gap measure implies that,

in 1991, the average shortfall of the poor as a fraction of the poverty line is

equal to 42 percent in nonmetro areas and 45 percent in metro areas. In

2002, the average shortfall in nonmetro areas is equal to 44 percent of the

poverty line and 47 percent in metro areas. During all 12 years, the average

shortfall is greater in metro areas than in nonmetro areas, which indicates

that on average the metro poor are worse off than the nonmetro poor.

This difference in the average income shortfall of the poor suggests that the

well-being of the poor could differ across areas. Figure 1 explores this issue by

graphing density estimates of the income-to-needs ratio, which is the ratio of

income to the poverty threshold. The advantage of income-to-needs ratios over

income is that they provide measures of well-being that control for demographic differences (and these demographic characteristics may differ across

areas).13 The control for demographic differences occurs because the incometo-needs ratios are a function of the poverty thresholds, which are adjusted

to reflect different levels of need for families of various sizes and ages.

Figure 1 provides kernal density estimates of metro and nonmetro incometo-needs ratios for 1992, 1995, 1998, and 2001. For all years, the nonmetro

income-to-needs ratio is more peaked near the poverty line, indicating that a

larger share of the nonmetro poor live on greater income-to-needs ratios and

are therefore relatively better off. Similarly, the nonmetro income-to-needs

8

The Cost of Living and the Geographic Distribution of Poverty/ERR-26

Economic Research Service/USDA

12The largest design effect is 6.1 for

the 2001 nonmetro P1 measure, which

means that the corrected standard errors

are almost 21⁄2 times greater than what

one would estimate if ignoring the

sample design. 

13For example, in 1999, the average

age of a metro poor person is 28 

compared with 32 for a nonmetro

poor person. In terms of family size,

16 percent of the metro poor live in

two-person families compared with 20

percent for the nonmetro poor.
ratio lies below the metro distribution on the left side of the distribution,

indicating that a larger share of the metro poor live in extreme poverty.

Another way of interpreting figure 1 is to note that, in 2001, 62 percent of the

nonmetro poor lives on income greater than one-half of the poverty line

compared with 58 percent of the metro poor. In 1998, the difference is larger;

65 percent of the nonmetro poor have income greater than one-half of the

poverty line compared with 58 percent of the metro poor. One implication

of this difference is that a small increase in income would move disproportionately more nonmetro poor than metro poor over the poverty line.

Nonmetro-Metro Poverty Comparisons,

Adjusted Using the FMR index

Table 2 compares the poverty estimates from appendix table 1 with the estimates for 2001 and 2002 using the FMR index. The unadjusted headcount

measure for 2001 shows that 14.2 percent of nonmetro residents are poor

9

The Cost of Living and the Geographic Distribution of Poverty/ERR-26

Economic Research Service/USDA

Figure 1

Income-to-needs ratios of the poor (unadjusted) by area, 1991-2001

1992

Density

1995

Welfare ratio

1998 2001

Density

Welfare ratio

Density

Welfare ratio

Notes: The density of the income-to-needs ratio is measured in terms of the reciprocal of the 

income-to-needs ratio (not measured on a probability scale) and thus can exceed 1.00. The

Epanechnikov kernal is used for all estimates with a smoothing parameter set to 0.08

1.5

1.2

0.3

0.6

0.9

0 0.25 0.50 0.75 1.00

1.5

1.2

0.3

0.6

0.9

0 0.25 0.50 0.75 1.00

Metro

Nonmetro

Metro

Nonmetro

1.5

1.2

0.3

0.6

0.9

0 0.25 0.50 0.75 1.00

Metro

Nonmetro

Welfare ratio

1.5

1.2

0.3

0.6

0.9

0 0.25 0.50 0.75 1.00

Metro

Nonmetro

Density
compared with 11.1 percent of metro residents. In other words, the nonmetro

poverty rate is 28 percent greater than the metro rate. This ranking holds for

the two other poverty measures. The 2001 poverty gap is 21 percent greater

in nonmetro than in metro areas, and similarly, the squared poverty gap is

18 percent higher in nonmetro areas. This pattern continues in 2002 (table 2).

Nonmetro poverty is higher than metro poverty across all three measures,

although the percentage difference declines as one considers the distributionsensitive measures, P1 and P2

.

The estimates listed in the FMR-adjusted columns provide the poverty estimates when each of these measures are calculated based on income levels that

have been corrected for spatial-price differences following the FMR index. In

2001, the official nonmetro poverty rate of 14.2 percent drops to 10.5 percent

when corrected for spatial-price differences. At the same time, the metro

poverty rate increases from 11.1 to 12.0 percent when adjusted using the

FMR index. The net effect is that the prevalence of nonmetro poverty is 12

percent lower than the metro poverty rate when both measures are adjusted

for cost-of-living differences (as measured by the FMR index). This reversal

of the relative ranking of nonmetro and metro poverty holds for the poverty

gap and squared poverty gap measures in 2001 and 2002 (table 2).14

10

The Cost of Living and the Geographic Distribution of Poverty/ERR-26

Economic Research Service/USDA

Table 2

Poverty measures, nonmetro-metro comparison, 2001 and 2002

Squared

Headcount Poverty gap poverty gap

FMR- FMR- FMRYear/area Actual adjusted Actual adjusted Actual adjusted

---P0 measure--- ---P1 measure--- ---P2 measure---

2001:

Nonmetro 0.142 0.105 0.063 0.050 0.043 0.036

(.004) (.003) (.002) (.002) (.002) (.002)

Metro .111 .120 .052 .055 .036 .038

(.002) (.002) (.001) (.001) (.001) (.001)

Percent

Nonmetro-metro 28 -12 21 -9 18 -5

difference (3.80) (3.01) (4.71) (3.97) (5.64) (4.97)

---P0 measure--- ---P1 measure--- ---P2 measure---

2002:

Nonmetro .142 .105 .062 .049 .041 .034

(.004) (.003) (.002) (.002) (.002) (.002)

Metro .116 .125 .055 .058 .038 .040

(.002) (.002) (.001) (.001) (.001) (.001)

Percent

Nonmetro-metro 22 -15 13 -16 8 -14

difference (3.55) (2.76) (4.06) (3.33) (4.73) (4.11)

FMR = Fair Market Rent index. Numbers in parentheses are standard errors.

Notes: Poverty measures are the Foster-Greer-Thorbecke Pa measures. FMR-adjusted

measures are poverty measures after adjusting for spatial-price variation with the Fair Market

Rent index. Nonmetro-metro differences are , both using actual 

levels and FMR-adjusted levels. Standard errors for the poverty measures are estimated 

following equation (4) and using the program described in Jolliffe and Semykina (1999).

Standard errors for the differences are second-order approximations by the delta method.

14If metro areas are separated into

central city and suburban areas, the

rankings do not reverse. Without price

adjustment, the lowest poverty rates

are in suburban areas and the highest

are in the central cities. Nonmetro

poverty rates are between the two but

significantly closer to those of inner

cities. With the price adjustment, the

rankings are the same; but nonmetro

poverty rates are significantly closer to

the suburban rates.

[( ) / ] P P P a aa nonmetro metro metro -
To understand whether the reversal of the poverty rankings is unique to

recent events, the study repeats this analysis for all years between 1991 and

2001. Appendix table 2 provides all of the FMR-adjusted poverty estimates

for these years. Panel A of figure 2 plots the nonmetro-metro percentage

differences for the three poverty measures.15 Over all years between 1991

and 2001, all three of the poverty measures indicate that nonmetro poverty

is greater than metro poverty.16 Panel B plots these same differences but for

poverty measures that have been adjusted with the FMR index. This panel

reveals that reversal of the relative rankings holds over all years considered.

The spatial-price-adjusted estimate of nonmetro poverty is lower than the

adjusted metro estimate for all measures over all years. This panel indicates

that most of the price-adjusted nonmetro poverty estimates are 10-25

percent less than the price-adjusted metro estimates.

Age and the FMR-Induced 

Change in Nonmetro Poverty

Previous research on demographic differences in area poverty rates has indicated that the nonmetro poor are more likely to be elderly and retired while

the metro poor are more likely to be younger and going to school. Figure 3

illustrates this difference by graphing the age distribution of the poor in

metro and nonmetro areas in 2001 and 2002. For both years, the nonmetro

age distribution lies below the metro distribution for younger ages and

above for older ages. Relative to the poor in metro areas, disproportionately

more of the nonmetro poor are over the age of 40 (which similarly means,

disproportionately fewer of the nonmetro poor are under 40).

While Table 2 shows that the FMR-adjusted poverty rates produce a complete

reversal of the relative rates of nonmetro and metro poverty, table 3 shows

that age is an important correlate of this readjustment. In both 2001 and 2002,

the nonmetro poor were about 2 years older than the metro poor on average.

11

The Cost of Living and the Geographic Distribution of Poverty/ERR-26

Economic Research Service/USDA

15The relative difference in poverty

uses the metro poverty level as the

base and can be expressed as 

.

16Panel A also reveals a primary

finding of Jolliffe (2003b). Namely, the

nonmetro-metro poverty differences

diminish as one considers measures

that are sensitive to the income 

distribution of the poor. In other

words, P0 indicates a much greater

nonmetro-metro difference in poverty

than does P1 and P2

.

Figure 2

Nonmetro-metro poverty differences, 1991-2002

Panel A: P differences

(no adjustment)

Percent

Panel B: P differences

(FMR-adjusted)

(Nonmetro-metro)

metro: P

(Nonmetro-metro)/

metro: P (Nonmetro-metro)/

metro: P

1991 93 95 97 99 2001

-30

-15

0

15

30

Percent

1991 93 95 97 99 2001

-30

-15

0

15

30

FMR = Fair Market Rent index.

Notes: In panel A, the P lines plot the difference between nonmetro and metro poverty as 

measured by P , P and P using metro poverty as the base, or [(P nonmetro − P metro)/P metro]. 

In panel B, the P lines are adjusted using the FMR index to correct for geographic differences

in prices.

(Nonmetro-metro)

metro: P

(Nonmetro-metro)/

metro: P

(Nonmetro-metro)/

metro: P

[( ) / ] P P P a aa nonmetro metro metro -
Adjusting for cost-of-living differences with the FMR index reduces

the average age of the nonmetro

poor by almost 2 years, eliminating the difference in average

ages. Eliminating the age difference suggests that the nonmetro

poor who are being re-classified

as nonpoor with the FMR adjustment (those with income closest

to the poverty line) are disproportionately older people.

Figure 4 explores this issue in

more detail by plotting the age

distribution of the nonmetro poor

in 2001. The nonmetro age distribution is plotted for those who are

considered poor according to the

Federal definition and by using

the FMR-adjusted rates. In both

12

The Cost of Living and the Geographic Distribution of Poverty/ERR-26

Economic Research Service/USDA

Figure 3

Age distribution of the poor (unadjusted) by area, 2001 and 2002

2001

Density

2002

Age

Density

 Nonmetro

0 10 20 30 40 50 60 70 80

0

0.1

0.025

 Metro

0 10 20 30 40 50 60 70 80

0

0.1

0.025

 Nonmetro

 Metro

Age

Notes: The Epanechnikov kernal is used with a smoothing parameter set to 1

Table 3

Average age of the poor by area

2001 2002

Item Metro Nonmetro Metro Nonmetro

Years

Poor 29.75 32.27 30.20 32.00

(.257) (.506) (.252) (.484)

FMR-adjusted poor 30.08 30.59 30.40 30.25

(.252) (.561) (.245) (.516)

Numbers in parentheses are standard errors. FMR = Fair Market Rent index.

Notes: FMR-adusted poor are those designated as poor after adjusting income with the Fair

Market Rent index. Standard errors corrected for complex design following Jolliffe (2003a).

Figure 4

Age distribution of the nonmetro 

poor: Federal poverty population 

versus FMR-adjusted poverty

population, 2001 

Density

Age

FMR = Fair Market Rent index.

Notes: The Epanechnikov kernal is used for 

both estimates with a smoothing parameter set 

to 1.2.

 Federal poverty

population

FMR-adjusted

poverty population

0 10 20 30 40 50 60 70 80

0

0.015

0.03
years, the FMR-adjusted age distribution lies below the age distribution of

the poor at ages older than 60 and above the distribution for ages younger

than about 25, confirming that the FMR adjustments reclassify disproportionately more of the nonmetro elderly as not poor. Such a reclassification

would have implications for several Federal assistance programs, including

Supplemental Security Income, Medicaid, the Child and Adult Care Food

Program, and the Commodity Supplemental Food Program.

The Cost of Housing and All Other Goods

The FMR index used by the Census Bureau implicitly assumes that the prices

of all goods other than housing costs have no spatial variation. To test the

sensitivity of the findings to the assumption, this study examines the case

where prices of housing and other goods are correlated. Kurre (2003) examines spatial price differences in all counties of Pennsylvania and finds that

prices are about 6 percent higher in urban areas for a broad basket of goods

and services. He further finds that, while housing costs are the most important component of the spatial variation in prices, prices for other categories

of goods and services are positively correlated with housing costs.

Following this line then, consider a case where the coefficient of correlation

between housing and other prices is +0.2, which implies that areas with

housing prices 10 percent higher than the baseline are also areas with prices

of other goods that are 2 percent higher. With the fixed budget weights, this

implies an FMR index that is 5.5 percent higher than the baseline (10*0.44

+ 2*0.56 = 5.5). Another way of saying this is that the assumption of positive

correlation will amplify the spatial variation by approximately 25 percent.17

For the sake of sensitivity analysis, though, also consider the case of negative correlation between prices of housing and all other goods and services.

This study examines the case where the correlation coefficient is -0.2, which

would imply a dampening of the variation in prices by 25 percent (relative

to the FMR index). If the assumption of negative correlation is justified,

then the FMR index would overstate the true spatial variation in prices.

Although the case of negative correlation in prices may seem less plausible, it

is useful to consider the extent to which the spatial variation in prices can be

dampened and still produce the reversal in rankings. Another assumption of

the FMR index is that housing costs comprise 44 percent of the budget of the

poor. If we return to the assumption of no variation in the prices of nonhousing

goods but reduce the share of the index for housing costs, this too would

dampen the price variation. Citro and Michael (1995) note that the CPI basket

uses a share of 33 percent for shelter and utilities. If the FMR index were

modified such that the weight used for housing expenses dropped from 44

percent to 33 percent, this would dampen price dispersion by 25 percent.

Considering the case of -0.2 negative correlation in prices is essentially the

same as considering an FMR index with housing assumed to only consume

33 percent of the budget (and no variation in the price of nonhousing goods).

Panel A of figure 5 presents the percentage difference between the nonmetro

and metro prevalence of poverty (P0

) under several assumptions. The single

line above zero is this difference without any adjustment for spatial price

variation. This line reflects the official Federal estimates of poverty in

13

The Cost of Living and the Geographic Distribution of Poverty/ERR-26

Economic Research Service/USDA

17In the example of housing prices

10 percent greater than the baseline, the

FMR index (with no correlation in

prices) is 4.4. When assuming +0.2

positive correlation in prices of housing

and other goods, the FMR index

increases by 25 percent to 5.5.
nonmetro and metro areas, indicating that nonmetro poverty has been

uniformly higher than metro poverty. A simple average over the 12 years

examined indicates that nonmetro poverty has been 20 percent higher than

metro poverty. The three other lines, all falling below zero, have been

adjusted using the FMR index and assuming negative, positive, and no

correlation between prices of housing and other goods. The middle line of

the three is the baseline FMR index. The most negative line assumes positive correlation, and the line closest to zero assumes correlation of -0.2.

As expected, positive correlation magnifies the primary findings. The relative

ranking of nonmetro and metro poverty, as before, is completely reversed

from the rankings based on the official poverty rates. With the coefficient of

correlation at -0.2, the findings are dampened, but the estimated level of

nonmetro poverty is still lower than metro poverty over all years examined.

Panel B shows the t-statistics for these relative differences. For the FMR

index and the FMR index with +0.2 correlation in prices, all differences are

statistically significant. With correlation of -0.2, the difference is statistically

significant (at the 5-percent confidence level) in 6 of the 12 years considered.

If the correlation in prices is negative and greater than 0.2 in magnitude, or

if the weight assigned to housing expenses drops below 33 percent, then the

primary finding of a reversal in the rankings would no longer hold.

14

The Cost of Living and the Geographic Distribution of Poverty/ERR-26

Economic Research Service/USDA

Figure 5

Nonmetro-metro poverty differences, sensitivity analysis, 1991-2001

Panel A: P differences 

Percent

 Panel B: T-stats of P differences

Percent

FMR = Fair Market Rent index.

Notes: In panel A, the P line plots the difference between nonmetro and metro poverty as 

measured by P using metro poverty as the base, or [(P nonmetro − P metro)/P metro 100. 

The three lines below all reflect the relative difference in P with COLA adjustments. The FMR 

index line uses the baseline FMR index. The line above the baseline assumes that nonrent 

prices are negatively correlated (r = -0.2) with FMR, while the bottom line assumes positive 

correlation (r = +0.2). In panel B, the lines plot t-statistics of the test for whether the nonmetrometro differences are statistically significant.

P

FMR Index

FMR with

rho = +0.2

FMR with

rho = −0.2

1991 93 95 97 99 2001

-30

-15

0

15

30

1991 93 95 97 99 2001

-8

-4

-1.96

0

1.96

4

8

P

FMR with

rho = −0.2

FMR Index

FMR with

rho = +0.2
Conclusion

The prevalence of poverty has been greater in nonmetro areas than in

metro areas in every year since the 1960s when poverty rates were first

officially recorded, and accordingly, Federal funds for social safety nets

and community development have favored nonmetro areas. The Federal

Government is examining experimental poverty measures that, among other

changes, adjust poverty rates for spatial cost-of-living differences. The

preferred experimental index is one based on the Fair Market Rent data,

which reflects spatial differences in the rental cost of low-income housing.

The purpose of this study is to examine how the use of this index to adjust

for cost-of-living differences affects the distribution of poverty across metro

and nonmetro areas.

The primary finding is that adjusting poverty rates with the FMR index

results in a complete reversal of the nonmetro-metro poverty profile. With

no adjustment for cost-of-living differences, the prevalence of poverty is

higher in nonmetro areas than in metro areas over the last 12 years. (The

depth and severity of poverty are also higher in nonmetro areas, but in

about one-half the cases, the differences are not statistically significant.)

When the FMR index is used to adjust for cost-of-living differences, the

prevalence, depth, and severity of poverty are higher in metro areas than in

nonmetro areas over the last 12 years. In 2001, for example, the prevalence

of nonmetro poverty was 28 percent higher than in metro areas. Once

adjusted for cost-of-living differences, this is reversed and the prevalence

of poverty in nonmetro areas is 12 percent lower than in metro areas.

The analysis also examines how adjusting for cost-of-living differences

affects the age composition of the poor. The nonmetro poor consist disproportionately of elderly, many of whom are living on fixed incomes near the

poverty line. Using the FMR index to adjust for cost-of-living differences

results in reclassifying many of the elderly poor as nonpoor. The average

age of the nonmetro poor drops from 32.3 years to 30.6 years when

adjusting for cost-of-living differences. To the extent that the reclassified

elderly are receiving Federal funds tied to poverty rates, they have the 

most to lose from the reform. More generally, using the FMR index to

adjust poverty rates for cost-of-living differences could have significant

adverse affects on funding for nonmetro social safety nets and developmental block grants.

15

The Cost of Living and the Geographic Distribution of Poverty/ERR-26

Economic Research Service/USDA
References

Aten, Bettina. Report on Interarea Price Levels. Bureau of Economic Analysis,

Washington, DC: National Academy Press, 2005, available at http://www.

bea.gov/bea/about/background/ PreliminaryReportonInterareaPrices.pdf,

accessed May 23, 2006.

Citro, Constance, and Robert Michael (eds.). Measuring Poverty: A New

Approach, Washington, DC: National Academy Press, 1995.

Datt, Gaurav, and Martin Ravallion. “Growth and Redistribution 

Components of Changes in Poverty Measures. A Decomposition with 

Applications to Brazil and India in the 1980s,” Journal of Development

Economics 38(2):275-95, April 1992.

Dumond, Michael, Barry Hirsch, and David MacPherson. “Wage 

Differentials across Labor Markets and Workers: Does Cost of Living

Matter?” Economic Inquiry 37(4):577-98, October 1999.

Fisher, Gordon. From Hunter to Orshansky: An Overview of (Unofficial)

Poverty Lines in the United States from 1904 to 1965. Poverty Measurement

Working Papers, U.S. Census Bureau, August 1997, available at

http://www.census.gov/hhes/poverty/povmeas/papers/ hstorsp4.html,

accessed February 19, 2002.

Foster, James, Joel Greer, and Erik Thorbecke. “A Class of Decomposable

Poverty Measures,” Econometrica 52(3):761-65, May 1984.

Foster, James, and Anthony Shorrocks. “Subgroup Consistent Poverty

Indices,” Econometrica 59(3):687-709, May 1991.

Ghelfi, Linda. “Rural Welfare.” Briefing Room on Rural Income, Poverty,

and Welfare, Economic Research Service, U.S. Department of Agriculture,

September 2003, available at http://www.ers.usda.gov /Briefing/

IncomePovertyWelfare/ruralwelfare/, accessed June 4, 2004.

Howes, Stephen, and Jean Olson Lanjouw. “Does Sample Design Matter

for Poverty Comparisons,” Review of Income and Wealth 44(1):99-109,

March 1998.

Jolliffe, Dean. “Poverty, Prices and Place: How Sensitive is the Spatial

Distribution of Poverty to Cost of Living Adjustments?” Economic Inquiry

44(2):296-310, April 2006.

Jolliffe, Dean. “Estimating Sampling Variance from the Current Population

Survey: A Synthetic Design Approach to Correcting Standard Errors,”

Journal of Economic and Social Measurement 28(4):239-261, 2003a.

Jolliffe, Dean. “On the Relative Wellbeing of the Nonmetropolitan Poor: 

An Examination of Alternate Definitions of Poverty During the 1990s.”

Southern Economic Journal 70(2):295-311, October 2003b.

16

The Cost of Living and the Geographic Distribution of Poverty/ERR-26

Economic Research Service/USDA
Jolliffe, Dean, Gaurav Datt, and Manohar Sharma. “Robust Poverty and

Inequality Measurement in Egypt: Correcting for Spatial-price Variation

and Sample Design Effects,” Review of Development Economics

8(4):557-72, 2004.

Jolliffe, Dean, and Anastassia Semykina. Robust Standard Errors for the

Foster-Greer-Thorbecke Class of Poverty Indices: SEPOV, Stata Technical

Bulletin, STB-51, September 1999.

Kakwani, Nanek. “Statistical Inference in the Measurement of Poverty,”

Review of Economics and Statistics 75(4):632-39, 1993.

Kakwani, Nanak. “On a Class of Poverty Measures,” Econometrica

48(2):437-46, March 1980.

Kish, Leslie. Survey Sampling, New York: John Wiley & Sons, 1965.

Kokoski, Mary. “New Research on Interarea Consumer Price Differences,”

Monthly Labor Review 114(7):31-34, July 1991.

Koo, Jahyeong, Keith Phillips, and Fiona Sigalla. “Measuring Regional

Cost of Living,” Journal of Business and Economic Statistics 18(1):127-36,

January 2000. 

Kurre, James A. “Is the Cost of Living Less in Rural Areas?” International

Regional Science Review 26(1):86-116, January 2003. 

Moulton, Brent. “Interarea Indexes of the Cost of Shelter Using Hedonic

Quality Adjustment Techniques,” Journal of Econometrics 68(1):181-204,

July 1995.

Nord, Mark. “Does it Cost Less to Live in Rural Areas? Evidence from

New Data on Food Security and Hunger,” Rural Sociology 65(1):104-25,

March 2000.

Nord, Mark, and Peggy Cook. Do the Proposed Revisions of the Poverty

Measure Matter for Rural America? ERS Staff Paper No. 9514, Economic

Research Service, U.S. Department of Agriculture, 1995. 

Nord, Mark, and Ephraim Leibtag. “Is the ‘Cost of Enough Food’ Lower in

Rural Areas,” Review of Regional Studies, 2006, forthcoming. 

Orshansky, Mollie. “Counting the Poor: Another Look at the Poverty

Profile,” Social Security Bulletin 28(1):3-29, January 1965.

Proctor, Bernadette, and Joseph Dalaker. Poverty in the United States: 2002,

Current Population Reports, Series P60-222, U.S. Census Bureau, 2003.

Ravallion, Martin. Poverty Lines in Theory and Practice, Living Standards

Measurement Study Working Paper No. 113, Washington, DC: World 

Bank, 1998.

Ravallion, Martin, and Benu Bidani. “How Robust Is a Poverty Profile,”

World Bank Economic Review 8(1):75-102, January 1994.

17

The Cost of Living and the Geographic Distribution of Poverty/ERR-26

Economic Research Service/USDA
Reeder, Richard, Samuel Calhoun, and Faqir Bagi. “Federal Funding in the

South: Bringing Home the Bacon, but Where’s the Beef?” Review of

Regional Studies 31(1):1-12, 2001. 

Reeder, Richard. How Would Rural Areas Fare Under Block Grants? 

Agriculture Information Bulletin No. 724-03, Economic Research Service,

U.S. Department of Agriculture, April 1996.

Ruggles, Patricia. Drawing the Line: Alternative Poverty Measures and

their Implications for Public Policy, Washington, DC: The Urban Institute

Press, 1990.

Sen, Amartya. “Poverty: an Ordinal Approach to Measurement,” 

Econometrica 44(2):219-31, March 1976.

Short, Kathleen. Where We Live: Geographic Differences in Poverty

Thresholds, Poverty Measurement Working Paper, U.S.Census Bureau,

January 2001a.

Short, Kathleen. Alternative Poverty Measures:1999, Current Population

Reports, P60-216, U.S. Census Bureau, October 2001b.

U.S. Census Bureau. “Current Population Survey: Annual Demographic

File, 2000,” Document No. 6692, Inter-university Consortium for Political

and Social Research, 2000.

U.S. Housing and Urban Development. “Fair Market Rents.” HUD User

Web Site, November 2003, available at http://www.huduser.org/datasets/

fmr.html, accessed December 5, 2003.

Zheng, Buhong. “Statistical Inference for Poverty Measures with Relative

Poverty Lines,” Journal of Econometrics 101(2):337-56, 2001.

18

The Cost of Living and the Geographic Distribution of Poverty/ERR-26

Economic Research Service/USDA
Appendix: Baseline Measures

and Standard Errors

The statistical tests used in this study for nonmetro-metro poverty differences are corrected for features of the sample design.18 The sample used for

the CPS is drawn from a census frame using a stratified, multistage design.

Howes and Lanjouw (1998) present evidence that estimated standard errors

for poverty measures can have large biases when false assumptions are

made on the nature of the sample design. In particular, they show that, if the

sample design is multistaged but standard errors are derived from the incorrect assumption of a simple random sample, then the standard errors will

significantly underestimate the true sampling variance. An example from

Jolliffe et al. (2004) shows that, in the case of poverty measures for Egypt,

failing to adjust for the characteristics of the sample design would result in

an underestimate of the correct standard errors by 187-212 percent.

The strategy followed in this study to estimate the sampling variance corrected

for design effects is to first derive exact (analytical) estimates for the poverty

measures, and then to address the issue of sample design. An advantage of

the FGT class of poverty measures in this context is that they are additively

decomposable, a characteristic that greatly simplifies deriving the analytical

estimates of the sampling variance of the poverty measures. To illustrate this,

consider any income vector y, broken down into M subgroup income vectors,

y(1) , ... , y(m). Because Pa is additively decomposable with population share

weights, it can be written as:

where n is the sample size, nj is the size of each subgroup, and z is again the

poverty line. By treating each observation as a subgroup, the estimate of

poverty is the weighted mean of the individual-specific measures of poverty

and the sampling variance of the poverty measure is the variance of this

mean, or:

where i subscripts the individual.

The next step is to incorporate the sample design information, which typically requires that the researcher has access to not only unit record data, but

also data identifying the characteristics of the sample design. In the case of

the CPS data, the sample design information that identifies the strata and

primary sampling units (PSUs) has been censored from the public-use files

to maintain respondent confidentiality. To compensate for the missing

design information, U.S. Census Bureau (2000, Appendix C) provides

detailed notes on how to approximate design-corrected standard errors for a

limited set of poverty estimates. An important shortcoming of this method is

that parameter estimates are provided for only the headcount measure; no

corrections are provided for any other poverty measures.19

19

The Cost of Living and the Geographic Distribution of Poverty/ERR-26

Economic Research Service/USDA

18Zheng (2001) provides designcorrected estimates of sampling 

variance for poverty estimates based

on relative poverty lines (i.e., the

poverty line is relative to the 

distribution of income, such as onehalf the median income level). The

advantage of the estimates provided

here is that they are based on a fixed

(or absolute) poverty line, which is

how poverty is measured in the United

States. Another advantage is that

Jolliffe and Semykina (1999) provide

a Stata program that estimates the

standard errors presented in this report.

19Another shortcoming of the

Census-recommended method is that

corrections are provided only for a

limited set of characteristics. For

example, U.S. Census Bureau (2000,

Appendix C) provides parameter 

estimates to adjust the sampling 

variance for the headcount measure by

several age categories. If the analysis

is focused on individuals ages 15-24,

the analyst is provided with parameter

estimates. If the relevant subsample is,

say, working-age adults, then Census

does not provide the necessary 

parameters to estimate standard errors.

P yz n z j j i

M

j j n P y a (;) / ) ( ;) () = ( a, =

Â 2

P nV i

i

n

i

i

n

a = =- Pa Pa a n n P Pa =

- -

=

Â , - Â , / ) ) () ( () (

1

1 1

1

2 and 1 3
In addition to the issue of Census not providing sample-design corrections

for either the poverty gap or squared poverty gap measures, another

problem is that the recommended method appears to be significantly less

precise for nonmetro-metro comparisons. The proposed correction for all

nonmetro statistics provided by the U.S. Census Bureau (2000, Appendix C)

is to multiply the design-correction coefficients by 1.5. The implication of

this correction is that, for all statistics, the ratio of the design effects for

metro to nonmetro areas is constant. Another factor likely to affect the accuracy of this correction is that it has not been updated in the last 20 years,

whereas the design-correction coefficients for all other characteristics are

frequently updated.20

Given that the Census-recommended method does not provide corrections

for the sampling variance of P1 and P2, and that the adjustment factor for

nonmetro areas appears to be a rough approximation, this method is abandoned. Instead, an approach is followed based on replicating aspects of the

CPS sample design by creating synthetic variables for the strata and clusters

that induce similar design effects. A more detailed description of the

approach and simulation results suggesting that it provides useful approximations are provided in Jolliffe (2003a).

The first step of the synthetic design approach for this analysis of poverty is

to sort the data by income.21 Then each set of four consecutive housing

units is assigned to a separate cluster. The purpose of the sorting is to induce

a high level of intracluster correlation, and the choice of four matches, on

average, the actual CPS cluster size. The four U.S. regions are selected as

synthetic strata to capture the geographic aspect of the CPS stratification.

With the selection of the synthetic strata and clusters, one can then directly

obtain design-corrected estimates of sampling variance based on (3). Following

Kish (1965) and noting earlier that Pa can be considered a sample mean, the

estimated sampling variance of the FGT poverty measures from a weighted,

stratified, clustered sample is given by:

where the h subscripts each of the L strata, i subscripts the cluster or

primary sampling unit (PSU) in each stratum, j subscripts the ultimate

sampling unit (USU), so whij denotes the weight for element j in PSU i and

stratum h. The number of PSUs in stratum h is denoted by nh

, and the

number of USUs in PSU (h,i) is denoted by mhi.

22

20

The Cost of Living and the Geographic Distribution of Poverty/ERR-26

Economic Research Service/USDA

20Personal communication with

Census appears to support the 

assertion that the nonmetro adjustment

is less precise: “The factor of 1.5 has

been used for nonmetro areas as a 

simple approximation. While the best

factor likely varies from characteristic

to characteristic, we use 1.5 for all

characteristics rather than publishing a

different factor for each estimate. Years

ago, someone looked at the data for

metro/nonmetro areas and decided

that 1.5 would be a good, and 

somewhat conservative, estimate for

most characteristics.”

21The methodology requires sorting

the data on the variable most relevant

to the analysis.

22The poverty and sampling 

variance estimates are documented in

more detail in Jolliffe and Semykina

(1999), which also provides a program

to estimate (4) in the Stata software.

V P nn P P h

h

L

h hi j

j

mh i

i

nh

hi j hi j

j

mh i

i

nh

( ) ( ) ( ) () , ,, hi j

,

, ,, ,,

,

aw a a =- - w w , ,, =

-

= = = =

Â Â Â Â Â

1

1

1 1 1 1

2 1 4
21

The Cost of Living and the Geographic Distribution of Poverty/ERR-26

Economic Research Service/USDA

Appendix table 1

Prevalence, depth, and severity of poverty (unadjusted),

nonmetro-metro comparison, 1991-2002

Squared

Headcount Poverty gap poverty gap

Year Metro Nonmetro Metro Nonmetro Metro Nonmetro

----P0 measure---- ----P1 measure---- ----P2 measure----

1991 0.137 0.160 0.061 0.067 0.039 0.041

(.002) (.004) (.001) (.002) (.001) (.002)

1992 .139 .167 .063 .071 .040 .044

(.002) (.004) (.001) (.002) (.001) (.002)

1993 .146 .171 .067 .072 .043 .044

(.002) (.004) (.001) (.002) (.001) (.002)

1994 .141 .159 .065 .068 .042 .043

(.002) (.004) (.001) (.002) (.001) (.002)

1995 .134 .156 .060 .064 .039 .039

(.002) (.005) (.001) (.003) (.001) (.002)

1996 .132 .159 .059 .067 .038 .041

(.002) (.005) (.001) (.003) (.001) (.002)

1997 .126 .158 .058 .070 .038 .046

(.002) (.005) (.001) (.003) (.001) (.002)

1998 .123 .143 .057 .061 .039 .039

(.002) (.005) (.001) (.002) (.001) (.002)

1999 .112 .142 .052 .060 .035 .039

(.002) (.005) (.001) (.003) (.001) (.002)

2000 .108 .134 .049 .057 .033 .037

(.002) (.004) (.001) (.002) (.001) (.002)

2001 .111 .142 .052 .063 .036 .043

(.002) (.004) (.001) (.002) (.001) (.002)

2002 .116 .142 .055 .062 .038 .041

(.002) (.004) (.001) (.002) (.001) (.002)

Numbers in parentheses are standard errors.

Notes: Poverty measures are the Foster-Greer-Thorbecke Pa measures. The prevalence of

poverty is measured by P0, the depth by P1, and the severity by P2. Standard errors are estimated

following equation (4) using the program described in Jolliffe and Semykina (1999).
22

The Cost of Living and the Geographic Distribution of Poverty/ERR-26

Economic Research Service/USDA

Appendix table 2

Spatial-price-adjusted poverty measures,

nonmetro-metro comparison, 1991-2002

Squared

Headcount Poverty gap poverty gap

Year Metro Nonmetro Metro Nonmetro Metro Nonmetro

----P0 measure---- ----P1 measure---- ----P2 measure----

1991 0.147 0.125 0.066 0.052 0.042 0.032

(.002) (.004) (.001) (.002) (.001) (.001)

1992 .150 .129 .068 .056 .043 .036

(.002) (.004) (.001) (.002) (.001) (.002)

1993 .157 .132 .072 .056 .046 .035

(.003) (.004) (.001) (.002) (.001) (.002)

1994 .152 .124 .069 .054 .044 .035

(.003) (.004) (.001) (.002) (.001) (.002)

1995 .143 .117 .064 .049 .041 .031

(.002) (.004) (.001) (.002) (.001) (.002)

1996 .141 .122 .063 .051 .041 .032

(.002) (.004) (.001) (.002) (.001) (.002)

1997 .135 .122 .062 .056 .041 .038

(.002) (.004) (.001) (.002) (.001) (.002)

1998 .131 .110 .060 .047 .041 .031

(.002) (.004) (.001) (.002) (.001) (.002)

1999 .121 .105 .055 .046 .037 .032

(.002) (.004) (.001) (.002) (.001) (.002)

2000 .116 .098 .052 .044 .035 .030

(.002) (.004) (.001) (.002) (.001) (.002)

2001 .120 .105 .055 .050 .038 .036

(.002) (.003) (.001) (.002) (.001) (.002)

2002 .125 .105 .058 .049 .040 .034

(.002) (.003) (.001) (.002) (.001) (.001)

Numbers in parentheses are standard errors.

Notes: Poverty measures are the Foster-Greer-Thorbecke Pa measures. The prevalence of

poverty is measured by P0, the depth by P1, and the severity by P2. Standard errors are estimated

following equation (4) using the program described in Jolliffe and Semykina (1999).