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On the relative well-being of the nonmetropolitan poor: an examination of alternate definitions of poverty during the 1990s.

1. Introduction

Understanding the geographic distribution of poverty is important to help target poverty-reduction policies. Throughout the 1980s and 1990s, the proportion of people living in poverty in the United States was significantly greater in nonmetropolitan than in metropolitan areas. In the 1980s the average incidence of poverty was 4.4 percentage points larger in nonmetropolitan areas than in metropolitan areas, and in the 1990s the average difference was 2.6 percentage points. (1) Although it is well documented that the incidence of poverty, also called the head count index, has been higher in nonmetropolitan areas, there is very little research that examines whether poverty is deeper or more severe in nonmetropolitan areas.

Zheng, Cushing, and Chow (1995) note that the U.S. Federal Government uses the proportion of poor as virtually the only indicator of poverty. (2) Similarly, much of the academic research on poverty is also focused on the incidence of poverty and does not examine distribution-sensitive measures of poverty. (3) For example, Hanratty and Blank (1992) compare U.S. and Canadian poverty rates from 1970 to 1986 and provide an explanation for why the Canadian poverty rate improved dramatically relative to the U.S. rate. Sawhill (1988) presents a comprehensive review of poverty measurement in the United States and proposes explanations for why there was so little change in poverty from the mid-1960s to the mid-1980s. Using a consumption-based measure of poverty, rather than the official income-based measure of poverty, Slesnick (1993) counters that there was significant progress made in reducing poverty during this time period.

In all cases, however, when the authors discuss poverty, they are referring to the incidence of poverty and never to any sort of distribution-sensitive measure. Understanding the depth and severity of poverty, in addition to the incidence, may provide information on important differences in the qualitative nature of poverty that would suggest different types of poverty-reduction policies for the different area types.

The purpose of this paper is to examine nonmetropolitan poverty relative to metropolitan and other geographic areas of the United States during the 1990s. This paper extends on the current literature in two ways. First, the analysis considers three different measures of poverty: the head count, poverty-gap, and squared poverty-gap indices. These measures belong to the Foster-Greer-Thorbecke (1984, hereafter referred to as FGT) family of poverty indices and have been widely used in the international poverty literature. (4) The head count is the standard measure used and provides a measure of the incidence of poverty. The poverty-gap index provides a measure of the depth of poverty, and the squared poverty-gap index is sensitive to the income distribution of the poor and provides a measure of the severity of poverty.

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 push the poor person over the poverty line. This transfer has no effect on the head count index, but the poor person is better off and this welfare improvement is reflected in a reduction of both the poverty-gap and squared poverty-gap indices. As another example, a transfer of income from a poor person to a poorer person will not alter either the head count or the poverty-gap index, but it improves the distribution of income of the poor, and this change is reflected by a reduction of the squared poverty-gap index. (5)

These examples point to an important reason to consider the poverty-gap and squared poverty-gap indices in addition to the commonly reported head count index. A frequently stated goal of many programs is the reduction of poverty, but the policies that are appropriate to attain tiffs goal will vary depending on which poverty measure is considered. If policy makers are focused on the head count index, then the most efficient way to reduce poverty is through assistance to the least poor. If, on the other hand, policy makers are concerned about the overall welfare of the poor and not just on reducing the number of persons living in poverty, then the appropriate measure is one that captures the depth and severity of poverty.

The second way in which this paper extends on the literature is that the statistical tests for differences in poverty are corrected for features of the sample design. (6) Most nationally representative data sets, particularly those from which poverty estimates are formed, are not based on pure random draws from the population; rather they are frequently based on stratified and multistage sample designs. As one example, the sample used for the Current Population Survey (CPS) is drawn from a census frame using a stratified, multistage design. Howes and Lanjouw (1998) present evidence that estimated standard errors for the FGT poverty indices 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, Datt, and Sharma (in press) shows that in the case of poverty indices for Egypt, falling to adjust for the characteristics of the sample design would result in an underestimate of the correct standard errors by 187-212%.

The remaining part of this paper proceeds as follows. Section 2 covers poverty measurement issues, which includes a discussion of the data, poverty line, poverty indices, and the estimates of sampling variance. Section 3 provides a discussion of the results. Examining only the incidence of poverty provides the result that poverty is worse in nonmetropolitan areas during all 10 years of the 1990s. When looking at the depth of poverty, this difference in poverty is only statistically significant in six of the 10 years; and when examining the severity of poverty, the difference is only statistically significant in three of the 10 years (at the 95% confidence level). This section also establishes that there are important nonmetro-metropolitan differences in the distribution of income of the poor and provides further geographic decompositions and some economic explanations for the differences. Section 4 provides a brief conclusion.

2. Poverty Measurement

The 1991-2000 Current Population Survey (CPS) and the U.S. Poverty Thresholds

The data used in this paper are from the 1991-2000 March Supplement to the CPS, which is conducted by the by the Bureau of the Census for the Bureau of Labor Statistics. The CPS data are the basis for the official U.S. poverty estimates and provide information on approximately 50,000 households in each year. 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 1991-2000 CPS data provide poverty estimates for 1990-1999.

The sample is representative of 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 individuals, so all individuals who are homeless at the time of the interview are excluded from the sample. Estimates of the number of homeless range from a 1990 Bureau of Census estimate of 250,000 to a 1987 Urban Institute estimate of up to 600,000 service-using homeless individuals. (7) The exclusion of homeless persons from the sample frame is noteworthy for poverty analysis, as this is a group that has a very high incidence of poverty, and it is noteworthy for a geographic analysis of poverty as homeless persons are disproportionately located in metropolitan areas. (8)

Because the homeless are disproportionately located in metropolitan areas, their exclusion from the sample biases the estimates in the direction of increasing the estimated gap between metropolitan and nonmetropolitan poverty rotes. Relative to the population of poor persons (estimated at 33.6 million in 1990), the homeless population is small, and this sample-selection bias will not significantly affect the estimated proportion of persons living in poverty. This statement is tempered, however, by noting that the homeless are most likely living in extreme poverty, and their exclusion has a greater impact on the poverty measures that are sensitive to the distribution of income. A primary finding of this paper is that distribution-sensitive measures of poverty reveal that the relative nonmetrometropolitan difference in poverty is smaller than what is indicated by comparing the incidence of nonmetropolitan and metropolitan poverty. If the homeless were included in this analysis, they would reinforce this finding.

The geographical poverty comparisons considered in this paper are primarily between metropolitan and nonmetropolitan areas. (9) Nonmetropolitan is often referred to as rural, but these terms define different geographic areas. (10) The Office of Management and Budget (2002), which issues federal standards for defining statistical areas, states that a metropolitan area is any county that contains a city with a population of at least 50,000, a county with an urbanized area as defined by the Bureau of Census, or a fringe county that is economically tied to a metropolitan area. (11) Nonmetropolitan areas are all areas outside the boundaries of metropolitan areas.

The measure of welfare used in this paper is income as it is defined for federal poverty rates. This definition includes all pretax 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 paper are the U.S. Federal Government poverty lines, which were developed in 1965 following a cost-of-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 the U.S. Department of Agriculture's (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 includes an allowance for nonfood expenditures that was twice the value of the cost of the USDA economy food plan. (12) To account for inflation, the poverty lines set in 1965 are adjusted each year using a price index. (13) The latest poverty line used in this study is from 1999, and it is set at $8,667 for an individual under 65 years of age; $11,483 for a two-person family with one child and one adult; and $19,882 for a family with two adults and three children. For a listing of 1999 poverty lines for various family sizes, see Dalaker and Proctor (2000). (14)

Poverty Measures and Standard Errors

The previous section describes the measure of welfare 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 index, I consider three measures that belong to the FGT family. The first is the head count index ([P.sub.0]), which is the percentage of the population living in families with family income less than the poverty line. The second measure is the poverty-gap index (P0, defined by the mean distance below the poverty line (expressed as a proportion of the poverty line), where the mean is formed over the entire population and counts the nonpoor as having zero poverty gap. The third measure is the squared poverty-gap index ([P.sub.2]), defined as the mean of the squared proportionate poverty gaps.

The FGT class of poverty indices, also referred to as [P.sub.[alpha]] can be represented as

(1) [P.sub.[alpha] = 1/n [summation over (i)] I ([y.sub.1] < z)[[(z - [y.sub.1]/z][.sup.[alpha]],

where n is the sample size, i subscript is the family or individual, y is the relevant measure of welfare, 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 [alpha] = 0, the resulting measure is the head count index, or [P.sub.0]. When [alpha] = 1, the FGT index results in the poverty-gap index, or [P.sub.1], and the squared poverty-gap index ([P.sub.2]) results when [alpha] = 2.

In order to answer the question of whether poverty is higher in nonmetropolitan than metropolitan areas, or more generally most any question regarding whether poverty has changed over time or varies over some geographic or demographic characteristic, estimates of the sampling variance for the indices are required. Kakwani (1993) provides two asymptotic estimates for the variance of the FGT poverty indices that are easy to calculate and frequently used. The Kakwani formula for the variance of P0, the head count index, is [P.sub.0](1 - [P.sub.0])/(n - 1), where n is the sample size. The formula for all other variance estimates of the FGT indices is ([P.sub.2[alpha]] - [P.sup.2.sub.[alpha]].)/(n - 1). The primary disadvantage of the Kakwani estimates is that they assume the sample was collected using a simple random draw from the population.

As noted in the introduction, using the Kakwani standard errors when the data were collected from a multistage sample design results in a large underestimate of the true sampling variance. The strategy used in this paper to estimate the design-corrected estimates of sampling variance is to first derive exact estimates for the poverty measures, and then to address the issue of sample design. An advantage of the FGT class of poverty indices in this context is that they are additively decomposable, a characteristic that greatly simplifies deriving exact 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.sup.(1)], ..., [y.sup.(m)]. Because P is additively decomposable with population share weights, it can be written as

(2) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where n is the sample size, [n.sub.j] 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

(3) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where i subscript is 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, the U.S. Bureau of Census (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 only provided for the head count index; there are no corrections provided for any other measures of poverty. (15)

In addition to the issue that the Census does not provide sample-design corrections for either the poverty-gap or squared poverty-gap indices, there is the additional problem that the recommended method appears to be significantly less precise for nonmetro-metropolitan comparisons. The proposed correction for all nonmetropolitan statistics provided by the U.S. Bureau of Census (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 metropolitan to nonmetropolitan 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. (16)

Given that the Census-recommended method does not provide corrections for the sampling variance of [P.sub.1] and [P.sub.2], and that the adjustment factor for nonmetropolitan areas appears to be a rough approximation, I abandoned this method. Instead, I followed an approach 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 (2001).

The first step of the synthetic design approach for this analysis of poverty is to sort the data by income. (17) 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. I select the four regions of the United States as synthetic strata to capture the geographic aspect of the CPS stratification. The Appendix provides a summary table from Jolliffe (2001) illustrating that the synthetic design approach matches the estimates provided by the Census Bureau for the head count index.

With the selection of the synthetic strata and clusters, one can then directly obtain design-corrected estimates of sampling variance based on Equation 3. Following Kish (1965) and noting from above that [P.sub.[alpha]] can be considered a sample mean, the estimated sampling variance of the FGT poverty indices from a weighted, stratified, clustered sample is given by

(4) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where the h subscripts each of the L strata, i subscripts the cluster or PSU in each stratum, and j subscripts the ultimate sampling unit (USU), so [w.sub.hij] denotes the weight for element j in PSU i and stratum h. The number of PSUs in stratum h is denoted by [n.sub.h], and the number of USUs in PSU (h, i) is denoted by [m.sub.hi]. (18)

3. Results

Nonmetro-metropolitan Poverty Comparisons

The purpose of this paper is to examine whether there is more to be learned about the difference between nonmetropolitan and metropolitan poverty than by what is revealed in an analysis of the incidence of poverty ([P.sub.0]). The incidence of poverty is insensitive to the income distribution of the poor, whereas [P.sub.1] and [P.sub.2], on the other hand, are distribution sensitive and will reflect differences in well-being. In order to anticipate what the [P.sub.[alpha]] analysis will reveal, it is useful to first examine average income and inequality of the poor to determine if there are differences in the well-being of the poor by area.

The CPS data indicate that when considering the sample of all persons, average nonmetropolitan income is approximately 25% less than metropolitan income throughout the 1990s. In contrast, Table 1 shows that when restricting the analysis to poor persons, average nonmetropolitan income is greater than average metropolitan income in eight of the 10 years. This difference in area means is not qualitatively large in any year, with the greatest difference at 5% in 1990, nor are any of the differences statistically significant. Nonetheless, this suggests that although overall, nonmetropolitan persons may be worse off, on average the nonmetropolitan poor appear to be as well off as the poor living in metropolitan areas.

Table 1 also reports the Theil measure of inequality for the nonmetropolitan and metropolitan poor. Dasgupta, Sen, and Starrett (1973) show that for a fixed total level of income, any transfer of income that reduces the level of inequality will increase social welfare if the social welfare function is Schur-or quasi-concave. This result illustrates that social welfare can be written as a function of two elements--average income (or the average level of whatever metric is used for welfare) and the distribution of income. The Theil measure of inequality can be expressed as

(5) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where Y is average income, i subscript is the individual, and n is the sample size. In general, the Theil index and the larger family of generalized Theil indices have many desirable properties that are described in Foster (1983). (19)

The inequality indices in Table 1 suggest that income of the metropolitan poor is more unequally distributed than for the nonmetropolitan poor throughout the 1990s. The nonmetro-metropolitan inequality difference of the poor ranges from a low of 11% in 1990 and 1992 to a high of 21% in 1996. Estimates of the sampling variance of the indices, based on a bootstrap method that replicates the two-stage nature of the sample design, indicate that the observed inequality differences are statistically significant in all years. (20)

The result that average income for nonmetropolitan and metropolitan poor persons is about the same, whereas the level of inequality for the metropolitan poor is worse, suggests that distribution-sensitive poverty measures will indicate a less stark nonmetro-metropolitan difference in poverty than is indicated by the head count index. Table 2 lists each of the three poverty indices ([P.sub.0], [P.sub.1], and [P.sub.2]) for metropolitan and nonmetropolitan areas. The nonmetropolitan head count index ranges from a high of 0.17 in 1993, representing 9.7 million poor people, to a low of 0.14 in 1999 (7.4 million people). The metropolitan head count index ranges from a high of 0.15 in 1993 (29.5 million people) to a low of 0.11 in 1999, or 24.8 million people living in poverty. The variation in the poverty-gap and squared poverty-gap indices is similar. Across both these measures, for metropolitan and nonmetropolitan areas alike, poverty was at its lowest level in 1999. In terms of the poverty-gap index, the year with the highest level of poverty came in 1993. The worst year, as measured by the squared poverty-gap index, came in 1997 for nonmetropolitan areas and 1993 for metropolitan areas.

One interpretation of the poverty-gap index is that it is equal to the product of the head count index and the income gap, where the income gap is the average shortfall of the poor as a fraction of the poverty line. This implies that in 1990 the average shortfall of the poor as a fraction of the poverty line is equal to 40% in nonmetropolitan areas and 44% in metropolitan areas. In 1999, the average shortfall in nonmetropolitan areas is equal to 42% of the poverty line, whereas this shortfall is 46% in metropolitan areas. During all 10 years, the average shortfall is 3 percentage points greater in metropolitan areas than in nonmetropolitan areas, which indicates that on average the metropolitan poor are worse off than the nonmetropolitan poor.

Table 2 also provides estimates of the design-corrected standard errors, which differentiates this paper from much of the U.S. poverty literature. To examine the magnitude of the adjustments, note that this table provides 60 poverty estimates ([P.sub.0], [P.sub.1], and [P.sub.2] for each year during the 1990s by metropolitan and nonmetropolitan areas). The design effect ranges from a low of 4.3 for the 1995 metropolitan estimate of [P.sub.2] to a high of 5.8 for the 1994 nonmetropolitan estimate of [P.sub.0]. For none of the estimates is the design effect 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.

Figure 1 plots the nonmetro-metropolitan percentage differences for the three poverty measures. (21) This figure readily indicates that the largest difference in poverty measurement occurs for the head count index. The incidence of poverty ([P.sub.0]) in nonmetropolitan areas ranges from 16% to 28% worse than in metropolitan areas. This nonmetro-metropolitan difference in poverty is lower when considering the depth of poverty ([P.sub.1] and diminishes even further when considering the severity of poverty ([P.sub.2]). The poverty-gap index for nonmetropolitan areas ranges from 5% to 21% greater than in metropolitan areas, and the squared poverty gap is 1-19% higher in nonmetropolitan than metropolitan areas.

[FIGURE 1 OMITTED]

Figure 1 also plots the test statistic for whether the percentage difference is statistically different from zero. The right-hand side of this figure shows that the diminishing difference between nonmetropolitan and metropolitan poverty (when considering the depth and severity of poverty) is associated with declining statistical significance of the differences, as one might expect. The incidence of poverty is greater in nonmetropolitan areas, and this difference is statistically significant during all 10 years of the 1990s. If statistical significance is based on a p-value of less than 0.05 (or the 95% confidence level), then the poverty-gap index is worse in nonmetropolitan areas in six of the 10 years, whereas the squared poverty-gap index is worse in only three of the 10 years. During most of the 1990s, there was no statistically significant difference in the severity of nonmetropolitan and metropolitan poverty.

Examining Tables 1 and 2 together can also provide useful insights into poverty changes during the 1990s. Table 1 indicates that nominal, average income of the poor increased in nonmetropolitan areas by 18% and in metropolitan areas by 21% between 1990 and 1999. During this same time, Table 2 shows that the incidence of poverty fell by 13% in nonmetropolitan and 12% in metropolitan areas. These two pieces of information seem to indicate unambiguous improvement in both metropolitan and nonmetropolitan poverty. This conclusion, however, is misleading because it ignores important changes in the distribution of income. During the 1990s, Table 1 shows that the Theil index of income inequality for the poor increased by 27% in nonmetropolitan areas and by 36% in metropolitan areas. This substantial deterioration in the income distribution of the poor worked against the gains in average income and decreases in P0. The net result is that the area-specific measures of the severity of poverty, [P.sub.2], were the same in 1990 as they were in 1999.

Further Geographic Examination of Nonmetropolitan Poverty

Figure 2 furthers the nonmetro-metropolitan poverty comparison by decomposing the metropolitan area into central cities and those metropolitan areas not in central cities (hereafter referred to as suburban). Panel A shows that the nonmetro-suburban poverty comparisons are qualitatively similar to nonmetro-metropolitan comparisons, but the differences are much larger. (22) For all three [P.sub.[alpha]] measures, nonmetropolitan poverty is significantly greater than suburban poverty. The largest difference is in the incidence of poverty, with nonmetropolitan [P.sub.0] being on average 78% greater than the suburban rate. The nonmetro-suburban difference in poverty is lower when considering the depth of poverty ([P.sub.1]) and severity of poverty ([P.sub.2]), but the magnitude of the difference is large. During the 1990s, the nonmetropolitan poverty-gap index is about 69% greater than the suburban rate, and similarly the nonmetropolitan squared poverty-gap index is approximately 60% greater.

[FIGURE 2 OMITTED]

The situation is reversed when considering nonmetropolitan poverty relative to poverty in central cities. For all three [P.sub.[alpha]], measures, nonmetropolitan poverty is significantly less than poverty in central cities, and the largest difference is in the severity of poverty. [P.sub.2] is on average 29% lower in nonmetropolitan areas, whereas [P.sub.1] is 26% and P0, 20%. Over all years, the ranking is unchanged, with the largest difference observed for [P.sub.2], followed by [P.sub.1] and the smallest difference for [P.sub.0].

Figures 1 and 2 show that when considering the relative well-being of the nonmetropolitan poor, the incidence of poverty is much larger in nonmetropolitan areas relative to metropolitan areas in general, and suburban areas in particular. An examination of distribution-sensitive poverty indices reduces this difference. In contrast, Figure 2 reveals that the incidence of poverty is lower in nonmetropolitan areas relative to central cities, and an examination of distribution-sensitive measures increases this difference.

To examine nonmetropolitan poverty at a more geographically detailed level, Table 3 provides ordinary least squares (OLS) estimates of the [P.sub.[alpha]] measures for 1999 on three sets of regressors. (23) As a baseline, panel A provides the results from regressing [P.sub.[alpha]], on just the nonmetropolitan dummy variable. The point estimates from this panel match the information provided in Table 2 and show that the nonmetro-metropolitan difference is greatest for [P.sub.0] and smallest for [P.sub.2]. Panel B interacts the nonmetropolitan dummy with indicators for the four regions of the United States. The Po estimates from this panel show that the largest nonmetro-metropolitan differences are found in the South and the West, whereas there is no significant difference in the Midwest. In the Northeast, nonmetropolitan [P.sub.0] is lower than for metropolitan areas. This panel also shows that when considering [P.sub.2], it is still the case that the nonmetropolitan South and West have higher poverty, but now both the nonmetropolitan Midwest and Northeast have lower poverty than their metropolitan areas.

For a final look at the geographic and demographic pattern of poverty, panel C provides fixed-effects estimates controlling for each of the 50 states (plus Washington, DC) and conditioning on age, race, and family structure. The estimates indicate that all measures of poverty decline with increases in age for younger persons. As the population ages, [P.sub.0] and [P.sub.1] ultimately start to increase with age. In the case of [P.sub.0], the switching point is at 59 years of age, and for [P.sub.1] it is at 87.5 years. In terms of racial characteristics, black people have much higher rates of poverty across all three measures. Finally, the estimates for family structure reveal that single mothers and single women have higher conditional rates of poverty relative to single men.

The estimates for the nonmetropolitan dummies in panel C show that the qualitative nature of the nonmetro-metropolitan [P.sub.[alpha]] differences found in the univariate analysis from panel A are robust to the inclusion of the state and demographic controls. The [P.sub.[alpha]], ordering in panel C shows that the difference in conditional poverty measures is greatest for [P.sub.0] and smallest for [P.sub.2]. Quantitatively, the nonmetropolitan point estimates are much larger in panel C than in panel A, indicating that the nonmetro-metropolitan [P.sub.[alpha]] differences are not explained away by the demographic composition of the areas.

Economic Exploration and Policy Implications

The results from above reveal that there am nonmetro-metropolitan differences in the distribution of welfare of the poor. To better understand this result and to draw out some policy implications, it is useful to examine the distribution of area-specific welfare ratios (in other words, the ratio of family income to the poverty line). (24) The advantage of welfare ratios over income is that they provide measures of well-being that control for age and family-size differences across areas. (25) This is because they are a function of the poverty thresholds, which are adjusted to reflect different levels of need for families of various size and age.

Figure 3 provides kernel density estimates of metropolitan and nonmetropolitan welfare ratios for 1990, 1993, 1996, and 1999. For all years, the nonmetropolitan welfare ratio is more peaked near the poverty line, indicating that a larger proportion of the nonmetropolitan poor subsist on greater welfare ratios and are therefore relatively better off. Similarly, the nonmetropolitan welfare ratio lies below the metropolitan distribution on the left-side of the distribution, indicating that a larger proportion of the metropolitan poor live in extreme poverty.

[FIGURE 3 OMITTED]

A candidate explanation for this difference in the relative well-being of the nonmetropolitan poor might be based on the conjecture that a larger proportion of the nonmetropolitan poor are working but employed in low-wage jobs. This hypothesis, however, appears to be rejected by the data. When considering the 1999 sample of civilian adults, the data indicate that the percentage of the metropolitan poor that are not in the labor force (58%) is the same as the nonmetropolitan proportion. Similarly, 22% of both the metropolitan and nonmetropolitan poor work full-time schedules, and the remaining 20% (again the same proportion for both metropolitan and nonmetropolitan) work part-time or are unemployed.

The results are modestly different when considering the 1999 sample of all civilians 15 years and older. In this case, 42% of the nonmetropolitan poor had done some work during 1999, whereas this was true for only 40% of the metropolitan poor. Yet of those persons who worked in the week prior to the survey, the average hours worked during the last seven days by both the metropolitan and nonmetropolitan poor was the same at 34 hours. Similarly, both the metropolitan and nonmetropolitan working poor reported working an average of 35 hours per week and over an average of 34 weeks during 1999.

Although the data do not support the hypothesis that there are significant differences in the proportion of the poor working or the hours they spend working, the data do reveal some important differences in the characteristics of the poor not in the labor force. Of the nonmetropolitan poor who did not work during 1999, 31% reported that they did not work because they were ill or disabled, and 28% reported that they were retired. These proportions for the metropolitan poor are lower, with 26% stating that they were ill or disabled, and 23% that they were retired. In contrast, 22% of the metropolitan poor reported that they did not work because they were going to school, whereas only 16% of the nonmetropolitan poor provided this as a reason.

The contrasting explanations for not working suggest that there might be differences in the nonmetro-metropolitan age composition. Figure 4 shows that the nonmetropolitan age distribution of the poor lies above the metropolitan distribution for higher ages and below for lower ages over the four years considered (1990, 1993, 1996, and 1999). (26) This indicates that the nonmetropolitan poor consist of relatively more persons between the ages of 50 and 90, whereas the metropolitan poor consist of relatively more persons between the ages of 15 and 40. (27) Not surprisingly, sources of income indicate similar nonmetro-metropolitan differences in the age composition of the poor. Twenty-two percent of the nonmetropolitan poor received Social Security payments in 1999, whereas only 16% of the metropolitan poor received Social Security. Twelve percent of the nonmetmpolitan poor received Supplemental Security Income payments, compared with 9% for the metropolitan poor.

[FIGURE 4 OMITTED]

4. Conclusion

By using measures of poverty from the Foster-Greer-Thorbecke family of poverty indices, this paper shows that the magnitude and significance of the nonmetro-metropolitan difference in poverty declines when one examines the depth and severity of poverty. Although the incidence of poverty is higher in nonmetropolitan than metropolitan areas throughout the 1990s, the poverty-gap index (depth of poverty) is only statistically significantly worse in nonmetropolitan areas during six of the 10 years, and the squared poverty-gap index (severity of poverty) is worse in only three years (at the 95% confidence level). This result suggests that the nonmetro-metropolitan differences in poverty during the 1990s (as measured by the bead count index) are not robust to considerations of distribution-sensitive poverty indices.

Further, to test for statistical significance, this paper derives sample design-corrected estimates of sampling variance for any additively decomposable poverty index, such as the [P.sub.[alpha]] indices. Design-corrected standard errors are available for the U.S. head count index in Dalaker and Proctor (2000), but I am aware of no literature on the United States that reports corrected standard errors for any other poverty measure. This paper illustrates the importance of this by noting that standard errors for all 60 reported poverty indices more than doubled in size when corrected.

By examining the ratio of the poverty-gap to the head count index, this paper establishes that the average shortfall of the poor as a fraction of the poverty line is worse in the metropolitan areas during all 10 years of the 1990s. Similarly, the distribution of the welfare ratio (income divided by the poverty line) indicates that the nonmetropolitan poor are relatively better off than the metropolitan poor.

An exploration of economic differences reveals that approximately the same proportion of the metropolitan and nonmetropolitan poor are active in the labor force and appear to work about the same number of hours per year. A comparison of the poor who are not in the labor force indicates that nonmetropolitan persons not in the labor force are more likely to be disabled and retired, whereas the nonworking, metropolitan poor are more likely to be going to school. This distinction is further supported by the data indicating that nonmetropolitan areas consist of relatively more older poor people, whereas proportionately more younger poor people reside in metropolitan areas. These differences are consistent with the supposition that nonmetropolitan areas are relatively cheaper and therefore more attractive to poor persons on fixed incomes. Attracting more jobs to these areas or providing job-training programs would presumably help many, but they will be of relatively less value to the retired and disabled.

The results on the incidence of poverty support the notion that poverty-reduction policies should include components that target nonmetropolitan areas. The distribution-sensitive poverty measures suggest that different policies may be appropriate for each area. One type of poverty-reduction strategy would be to focus on helping the young and poor get the necessary skills to enhance their opportunities in the labor market. Another type of antipoverty program would be to simply provide income assistance to help ease the burden of poverty for those who are retired or unable to work. Since many of these people live on fixed incomes, they are not the extreme poor, and a modest supplement to their income would likely increase their income to a level greater than the poverty line. The poor in both metropolitan and nonmetropolitan areas share many similarities and need both types of programs. Policies aimed at metropolitan areas, however, would be of more value if they had relatively more focus on mitigating extreme poverty, whereas nonmetropolitan areas would benefit relatively more from a somewhat greater focus on supplemental income assistance for the elderly and disabled.
Table 1. Income and Inequality of the Poor, Nonmetro-metropolitan
Comparisons

 Average Income Level of Poor Persons

Year Nonmetro Metro Difference Percent

1990 7229 6896 333 5%
 (153) (97) (181)
1991 7243 6995 248 4%
 (150) (91) (175)
1992 7316 7113 203 3%
 (153) (92) (178)
1993 7608 7428 181 2%
 (145) (105) (179)
1994 7630 7617 13 0%
 (163) (106) (194)
1995 8231 8031 200 2%
 (212) (117) (242)
1996 8104 8121 (17) 0%
 (202) (123) (237)
1997 7952 8100 149 -2%
 (187) (130) (228)
1998 8395 8104 291 4%
 (224) (123) (255)
1999 8517 8372 145 2%
 (237) (145) (278)

 Theil Index of Inequality for the Poor

Year Nonmetro Metro Difference t-statistic (a)

1990 0.221 0.247 -0.026 2.00

1991 0.218 0.252 -0.034 2.61

1992 0.233 0.260 -0.028 1.96

1993 0.226 0.278 -0.051 3.85

1994 0.237 0.271 -0.034 2.20

1995 0.232 0.278 -0.045 2.71

1996 0.226 0.285 -0.059 3.58

1997 0.272 0.314 -0.042 2.17

1998 0.270 0.332 -0.063 3.08

1999 0.281 0.336 -0.055 2.61

Income is in nominal U.S. dollars. The column headed Percent lists the
difference between nonmetropolitan and metropolitan average income,
using metropolitan as the base. Standard errors for income measures, in
parentheses, are corrected for sample design effects following the
synthetic-design approach described in Jolliffe (2001). Standard errors
for the inequality indices are bootstrap estimates based on 1000
bootstrap samples and a resampling method that replicates the two-stage
nature of the sample design. For details, see Jolliffe and
Krushelnytskyy (1999).

(a) t-statistic is for the null hypothesis that the
nonmetro-metropolitan difference in inequality index is equal to zero.

Table 2. Incidence, Depth, and Severity of Poverty,
Nonmetro-metropolitan Comparisons

 Headcount, [P.sub.0] Poverty-gap, [P.sub.1]

Year Nonmetro Metro Nonmetro Metro

1990 0.163 0.127 0.066 0.056
 (0.0042) (0.0022) (0.0021) (0.0012)
1991 0.160 0.137 0.067 0.061
 (0.0042) (0.0023) (0.0022) (0.0013)
1992 0.167 0.139 0.071 0.063
 (0.0042) (0.0023) (0.0022) (0.0013)
1993 0.171 0.146 0.072 0.067
 (0.0043) (0.0025) (0.0022) (0.0014)
1994 0.159 0.141 0.068 0.065
 (0.0043) (0.0025) (0.0023) (0.0014)
1995 0.156 0.134 0.064 0.060
 (0.0049) (0.0024) (0.0026) (0.0013)
1996 0.159 0.132 0.067 0.059
 (0.0048) (0.0023) (0.0025) (0.0013)
1997 0.158 0.126 0.070 0.058
 (0.0048) (0.0023) (0.0027) (0.0013)
1998 0.143 0.123 0.061 0.057
 (0.0046) (0.0023) (0.0024) (0.0013)
1999 0.142 0.112 0.060 0.052
 (0.0046) (0.0022) (0.0025) (0.0012)

 Squared Poverty-gap,
 [P.sub.2]

Year Nonmetro Metro

1990 0.039 0.035
 (0.0015) (0.0009)
1991 0.041 0.039
 (0.0016) (0.0010)
1992 0.044 0.040
 (0.0017) (0.0010)
1993 0.044 0.043
 (0.0017) (0.0011)
1994 0.043 0.042
 (0.0017) (0.0011)
1995 0.039 0.039
 (0.0020) (0.0010)
1996 0.041 0.038
 (0.0019) (0.0010)
1997 0.046 0.038
 (0.0021) (0.0010)
1998 0.039 0.039
 (0.0019) (0.0010)
1999 0.039 0.035
 (0.0020) (0.0010)

Poverty indices are the Foster-Greer-Thorbecke [P.sub.[alpha]] indices.
The incidence of poverty is measured by [P.sub.0], the depth by
[P.sub.1], and the severity by [P.sub.2]. Standard errors, in
parentheses, are estimated following Equation 4 using the program
described in Jolliffe and Semykina (1999).

Table 3. Regression Analysis of Poverty in 1999

 [P.sub.0]: Incidence

 Standard
 Estimate Error

Panel A: baseline
 Nonmetro Dummy 0.030 *** (0.0050)
Panel B: regional analysis
 Nonmetro Northeast -0.018 * (0.0096)
 Nonmetro Midwest 0.002 (0.0085)
 Nonmetro South 0.058 *** (0.0080)
 Nonmetro West 0.042 *** (0.0107)
Panel C: demographic analysis (a)
 Nonmetro Dummy 0.052 ** (0.0050)
 Age in years/10 -0.039 *** (0.0017)
 Age squared/1000 0.033 *** (0.0020)
 Race: black 0.081 *** (0.0070)
 Husband and wife
 family -0.118 *** (0.0053)
 Single-mother family 0.093 *** (0.0082)
 Single-father family -0.067 *** (0.0094)
 Female individual 0.057 *** (0.0067)

 [P.sub.1]: Depth

 Standard
 Estimate Error

Panel A: baseline
 Nonmetro Dummy 0.009 *** (0.0027)
Panel B: regional analysis
 Nonmetro Northeast -0.014 *** (0.0048)
 Nonmetro Midwest -0.004 (0.0042)
 Nonmetro South 0.021 *** (0.0045)
 Nonmetro West 0.015 *** (0.0058)
Panel C: demographic analysis (a)
 Nonmetro Dummy 0.019 *** (0.0027)
 Age in years/10 -0.014 *** (0.0009)
 Age squared/1000 0.008 *** (0.0011)
 Race: black 0.036 *** (0.0040)
 Husband and wife
 family -0.069 *** (0.0033)
 Single-mother family 0.040 *** (0.0051)
 Single-father family -0.045 *** (0.0052)
 Female individual 0.021 *** (0.0043)

 [P.sub.2]: Severity

 Standard
 Estimate Error

Panel A: baseline
 Nonmetro Dummy 0.004 * (0.0022)
Panel B: regional analysis
 Nonmetro Northeast -0.011 *** (0.0038)
 Nonmetro Midwest -0.005 * (0.0032)
 Nonmetro South 0.012 *** (0.0037)
 Nonmetro West 0.009 * (0.0050)
Panel C: demographic analysis (a)
 Nonmetro Dummy 0.011 *** (0.0023)
 Age in years/10 -0.008 *** (0.0008)
 Age squared/1000 0.003 *** (0.0009)
 Race: black 0.022 *** (0.0033)
 Husband and wife
 family -0.055 *** (0.0029)
 Single-mother family 0.018 *** (0.0044)
 Single-father family -0.039 *** (0.0044)
 Female individual 0.015 *** (0.0039)

Estimates are weighted ordinary least squares (OLS) and standard errors
are corrected for sample design effects as described in the paper.
Sample size is 133,710 for panels A and B and 133,380 for panel C.
Across all three panels the [R.sup.2] is less than 0.11. The intercept
is suppressed from the output for brevity.

(a) Estimates control for state fixed effects.

* P < 0.1.

** P < 0.05.

*** P < 0.01.

Appendix

Confidence Intervals from Synthetic-Design and Census-Recommended
Corrections, 1999 CPS Poverty Indices

 Estimated 90% Confidence Intervals

 Poverty Percent Reported Implied a,b
Characteristic Poor Table A by Levels Percentage

Persons, total 11.8 0.3 0.33 0.33
Persons, in families 10.2 0.3 0.34 0.34
Race, white persons 9.8 0.3 0.34 0.33
Race, black persons 23.6 1.2 1.20 1.20
Age, under 18 years 16.9 0.7 0.65 0.65
Age, 18-64 years 10.0 0.3 0.39 0.39
Age, 65 years+ 9.7 0.5 0.53 0.53
Families, total 9.3 0.3 0.33 0.28

 Estimated 90% Confidence Intervals

 Poverty a,b Match a,b Synthetic Random
Characteristic Ratio Categories Design Sample

Persons, total * yes 0.33 0.16
Persons, in families * no 0.36 0.17
Race, white persons * yes 0.31 0.16
Race, black persons * yes 1.24 0.66
Age, under 18 years 0.66 yes/no 0.64 0.37
Age, 18-64 years * no 0.30 0.20
Age, 65 years+ 0.53 yes 0.53 0.43
Families, total 0.34 yes 0.32 0.29

Edited table from Jolliffe (2001). Confidence intervals are in
percentage points, and asterisk denotes an undefined number. The first
four columns of confidence intervals are derived from Dalaker and
Proctor (2000). The bold estimate marks whether the U.S. Bureau of
Census considers the estimate a percentage or ratio. The next column
lists whether there is a direct match in characteristics between the
poverty estimates and those characteristics assigned a,b coefficients.
The estimates from the synthetic cluster approached are listed next,
followed by the confidence intervals from assuming that the data are
from a weighted, simple random sample.


I thank John Cromartie, Linda Ghelfi, Robert Gibbs. Craig Gundersen, George Hammond, Signe-Mary McKernan, Tim Parker, Caroline Ratcliffe, Laura Tiehen, Leslie Whitener, Josh Winicki, conference participants at the Southern Regional Science Association, and seminar participants at the Urban Institute and at the Society for Government Economists for comments. The views and opinions expressed in this paper do not necessarily reflect the views of the Economic Research Service of the U.S. Department of Agriculture.

(1) Nord (1997) end Jolliffe (2002) show that the incidence of poverty is greater in nonmetropolitan areas.

(2) An exception to this is the Census Bureau P-60 series (for example, Dalaker and Proctor 2000) report of the number of persons with income less than various ratios of the poverty line.

(3) There are some noteworthy exceptions. Cushing and Zheng (2000) use distribution-sensitive measures to compare regional poverty differences using 1990 Census data. Zheng, Cushing. and Chow (1995) consider several distribution-sensitive indices and test for change in poverty from 1975 to 1990; and Bishop, Formby, and Zheng (1999) examine regional differences in Sen's (1976) distribution-sensitive index from 1961 to 1996. An important methodological difference between these last two articles and the results reported in this paper is that the statistical tests considered in this paper correct for the characteristics of the sample design.

(4) The following all use these three measures: Jolliffe, Datt, and Sharma (in press) for Egypt, Dart and Ravallion (1992) cover Brazil and India, Howes and Lanjouw (1998) use examples from Pakistan and Ghana, Kakwani (1993) examines Cote d'Ivoire, and Ravallion and Bidani (1994) examine Indonesia.

(5) Unlike the Sen (1976) or Kakwani (1980) distribution-sensitive measures of poverty, the squared poverty-gap index 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).

(6) Zheng (2001) provides design-corrected 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 one half the median income level). The advantage of the estimates provided in this paper 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 paper.

(7) For a discussion of measures of homelessness and potential explanations for the rising incidence, see Quigley, Raphael, and Smolensky (2001) and Honig and Filer (1993).

(8) For a discussion of income levels and geographical distribution of homelessness, see chapter 5 and 13 of Urban Institute (1999).

(9) The analysis does also consider central cities and suburbs as a subset of metropolitan areas, as well as an examination of nonmetropolitan poverty controlling for state fixed effects.

(10) Cromartie (2000) shows that 21% of the population live in nonmetropolitan areas, 25% in rural areas, and 64% of persons living in nonmetropolitan areas also live in rural areas.

(11) For details of the definition, see Office of Management and Budget (2000).

(12) For details on the first poverty lines, see Orshansky (1965). For a history of poverty lines prior to Orshansky, see Fisher (1997). For a critical discussion of the poverty line, see Ruggles (1990).

(13) Prior to 1969, the index used was the changing cost of the USDA economy food plan, and afterward, the Consumer Price Index (CPI) for all goods and services has been used.

(14) The analysis in this paper is based on the full CPS sample, which includes all persons living alone and in families. A family is defined as a group of two or more persons residing together and related by birth, marriage, or adoption. Families also include any related subfamily members, where a subfamily is defined as a married couple with or without children, or a parent with single children under 18 years of age.

(15) Another shortcoming of the Census-recommended method is that corrections are only provided for a limited set of characteristics. For example, U.S. Bureau of Census (2000, Appendix C) provides parameter estimates to adjust the sampling variance for the head count index by several age categories. If the analysis is focused on individuals 15-24 years of age, the analyst is provided with parameter estimates. If the relevant subsample is, say, working-age adults, the Census does not provide the necessary parameters to estimate standard errors.

(16) Personal communication with the Census appears to support this assertion that the nonmetropolitan adjustment is less precise: "The factor of 1.5 has been used for nonmetropolitan 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/nonmetropolitan areas and decided that 1.5 would be a good, and somewhat conservative, estimate for most characteristics."

(17) The methodology requires sorting the data on the variable most relevant to the analysis.

(18) The poverty and sampling variance estimates are documented in more detail in Jolliffe and Semykina (1999), which also provides a program to estimate Equation 4 in the Stata software.

(19) In particular, Foster (1983) shows that an inequality index satisfies the axioms of symmetry, replication invariance, income scale independence, decomposability, and the principle of transfers only if it is a positive multiple of the Theil index.

(20) The bootstrap estimates are based on 1,000 replications. For methodology details and the program used, see Jolliffe and Krushelnytskyy (1999). Lorenz curves are art alternative way to examine inequality, and Zheng (2002) derives asymptotic covariance structure for generalized Lorenz curves when the sample is based on a complex design.

(21) The relative difference in poverty uses the metropolitan poverty level as the base and can be expressed as [([P.sub.[alpha]nonmetropolitan] - [P.sub.[alpha]metropolitan])/[P.sub.[alpha]metropolitan]].

(22) All differences listed in Figure 2 are statistically significant with p-values less than 0.01.

(23) I use OLS, rather than a censored regression model, because the zero values for each of the [P.sub.[alpha]] indices are the actual values and do not represent censored values. The estimates are weighted and design corrected.

(24) Blackorby and Donaldson (1987), using this terminology, provide an analysis of welfare ratios as an index of well-being in cost-benefit analysis.

(25) For example, in 1999 the average age of a metropolitan poor person was 28 years compared with 32 years for the nonmetropolitan poor. In terms of family size, 16% of the metropolitan poor lived in two-person families compared with 20% for the nonmetropolitan poor.

(26) The result that there are systematic differences in the metro-nonmetropolitan age distribution of the poor does not mean that the metro-nonmetropolitan poverty difference is the result of this age difference. In fact, the poverty regressions in panel C of Table 3 indicate just the opposite. If the age distribution in nonmetropolitan areas were the same as in metropolitan areas, then the metro-nonmetropolitan poverty difference would be even larger. The relevance of the area difference in age distribution is that it indicates a potential case for slight differences in how poverty alleviation policies are designed for each area.

(27) This difference in the age distribution is also partially evident in family structure characteristics. Thirty-nine percent of the metropolitan poor live in single-mother families, whereas 32% of the nonmetropolitan poor are in single-mother families.

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Dean Jolliffe, Economic Research Service, U.S. Department of Agriculture, Room S-2059, 1800 M Street NW, Washington, DC, 20036-5831; E-mail: Jolliffe@ers.usda.gov.

Received June 2002; accepted December 2002.
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