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PUBLISHER ABSTRACT AB Researchers, housing program administrators, and others assume housing costs are affordable if they represent up to 30 percent of a household's income. This standard appears to be skewed against families with children. Michael Stone's "Shelter Poverty" offers a new, in some respects more precise, measure of housing affordability. Both measures were calculated to explore housing affordability among an estimated 30 million families with children, using the 1991 American Housing Survey. One-third of families had housing difficulties under either measure, but "Shelter Poverty," concentrated among lower-income families, provides a more realistic classification for families. Adopting "Shelter Poverty" would, thus, offer a more credible guide to "affordable" housing policies for America's families with children.

THE CONCEPT OF HOUSING AFFORDABILITY
       Declining availability of inexpensive housing and the concomitant effects of high housing costs on households' economic well-being have been well-documented (Stone 1990, 1993; Joint Center for Housing Studies 1991; Lazere 1991; Bratt 1986; Gilderbloom & Applebaum 1988; Linneman & Megbolugbe 1992; U.S. HUD 1991; U.S. GAO 1990; Stegman 1992; Nelson & Khadduri 1992; Khadduri & Nelson 1992). Embedded in federal policies allocating housing assistance to low-income households, and written into official bank policies guiding mortgage approvals, the "30% of Income Measure" reflects a common assumption of housing affordability. This standard, which deems housing costs affordable if they consume up to 30 percent of a household's income, appears to discriminate against families with children.
    Research examining the impact of housing costs among households suggests that families, especially poor ones, experience high housing costs more severely than other households (Nelson & Khadduri 1992: 1). Families have different housing and consumption needs than other households, which should be reflected in the conceptualization and measurement of housing affordability. This study isolates families with children as the unit of analysis to explore housing affordability measures and examine their implications for U.S. housing policy. While the "30% of Income Measure" is easily calculated as an unvarying proportion of income, its simplicity obscures real differences between households with identical incomes.
    Two hypothetical households, each with $30,000 annual incomes, illustrate the argument. Household "A" consists of a single adult, while Household "B" is a four-person family, with two parents and two children. Although both households earn the same income, their tax liabilities vary, along with consumption needs and housing requirements. A single adult could comfortably reside in a studio or one-bedroom home, whereas a family would realistically require a two-bedroom dwelling for comfort and privacy. The "30% of Income Measure" treats the housing needs of these households identically. However, if housing affordability implies that household members can both pay for decent accommodations, and afford other minimum necessities, then the varying needs of different types of households require consideration. Michael Stone's "Shelter Poverty" does just this.
    Stone defines "Shelter Poverty" as a squeeze between inadequate incomes and high housing costs (1993: 32). His "Shelter Poverty" measure is a sliding scale of income amounts, indexed to household size, composition, and need. Based on best available estimates of the type and costs of minimum necessities, Stone estimated how much income households of different sizes would need to purchase these goods, including their tax liabilities as an item. He then deducted the total value of non-shelter necessities from households' incomes to determine how much money remained after purchasing these essentials. If the amount of money left over was less than the actual costs of shelter incurred by these households, they were classified as "shelter poor." In 1991, Stone estimated that roughly one-third of all households, or 29 million, containing 85 million people, were "shelter poor" (1993: 44). The aggregate cost of supplementing the incomes of these households to enable them to meet their housing costs, and also purchase non-shelter necessities, came to $95 billion in 1989, and $105 billion in 1991 (Stone 1993: 57). The average "shelter poor" household required an additional $3,600 per year, or $300 per month, to pay for shelter and afford Stone's calculation of non-shelter necessities.

HOW HOUSING COSTS AFFECT FAMILIES WITH CHILDREN
       The rent or mortgage must be paid the first of every month. If this bill is large relative to family income, residents can devote so much of their incomes to housing that they literally cannot purchase other necessities. Often, though not always, this is out of necessity, rather than choice. Residents can move if housing costs prove to be too expensive, but the costs of finding and moving to another home may be prohibitive. Furthermore, since the 1970s, the supply of low-cost rental housing has declined, and rents have escalated faster than inflation (Lazere 1990: x-xi), while high-paying jobs for less-skilled workers have dwindled as low-paying jobs proliferate (Mishel & Bernstein 1993: 129-214). While the price of shelter affects all households, families with children represent the fastest growing subgroup of the homeless (Waxman 1991: 5; U.S. Conference of Mayors 1992; Edelman & Mihaly 1991: 92), suggesting that their housing needs are more pressing than those of other household types. If family income is siphoned off to pay high housing costs, there may be little left to purchase other necessities for children, including such essentials as nutritious food and adequate clothing.
    The United States currently has the highest child poverty rate among all industrialized nations, nearly three times the rate of its nearest competitor (U.S. House 1992: 1288). One in four children resided in families whose (pretax) incomes fell below the U.S. poverty threshold, which stood at $10,860 for a family of three, and $14,942 for a family of four, in 1991 (U.S. House 1994: 1155). The United States is both birthplace and home to internationally respected research documenting the deleterious effects of poverty on children's present and future well-being (Kamerman & Kahn 1991: 3). Growing up in poverty increases children's risks for developmental disabilities (NRC 1993: 32-33). Children living in poverty are more likely to experience health problems and academic failures (NRC 1993: 16-17). Poor teenagers are more likely to become sexually active, and, among girls, become pregnant. They have higher rates of delinquency, arrests, school drop-out, poor academic standing, and less success at moving into a job or college. They also have higher rates of health impairments, mental disorders, and depression (NRC 1993: 72-76).
    The multiplicity of stresses brought on by economic hardships reduce parents' ability to provide the necessary emotional support and stimulation required to facilitate their children's healthy development, and increase the likelihood of family disintegration (NRC 1993: 42; National Commission on Children 1991: 3). Given the state of knowledge regarding the myriad effects of economic insufficiencies on families with children, and that of the housing market, it is surprising that the links between housing affordability, high housing costs, and the economic well-being of this population have not yet been examined.
    Children have aspects of public goods: the future well-being of American society depends on how well they are raised. Children's current circumstances mainly depend on how successfully their parents are able to care for them, which is, in part, determined by parents' capacities to balance work and family obligations. Government intervention to assist families, including such programs as compulsory education, food stamps, Aid to Families with Dependent Children (AFDC), or Medicaid, illustrate society's investment to enhance children's, and thereby society's, well-being. A housing affordability measure which is skewed against families with children obscures the role of housing costs in exacerbating income shortages for families in ways which threaten children's well-being. Other industrialized nations have explicitly created policies which support parents' abilities to bear and rear children, while simultaneously working in the labor market, including housing assistance within a package of policies (Kamerman & Kahn 1978: 1-16; 1989: 89). In contrast, the United States lacks family-sensitive housing policies.

UNITED STATES HOUSING POLICY
       U.S. housing policy consists of direct cash assistance for poor households, and indirect tax expenditures (mortgage deductions) for homeowners. Direct federal expenditures to poor households has remained at or below $33 billion per year since the early 1980s (Pedone 1988: 42), while the estimated value of mortgage deductions has varied from $60 to $80 billion a year (Low Income Housing 1991: 3). Unlike other entitlement programs helping the needy, housing assistance to the poor is not an entitlement. Many households are poor enough to qualify for housing subsidies, but only a limited amount of assistance is available per year. The Section 8 federal rental housing assistance program was introduced in the 1970s to help Americans obtain "affordable housing" (Newman & Schnare 1988: 2; 1992). To ensure that it reached the neediest, only the elderly, families, and handicapped single persons were eligible (Nelson & Khadduri 1992: 3). Section 8 assistance consists mainly of project-based help and household subsidies. Recipients are required to contribute 30 percent of their income toward rent, and the government subsidizes an additional proportion up to a locally determined maximum.
    During the 1980s, the federal government focused on increasing subsidies to households rather than constructing more public housing (U.S. House 1992: 1438). However, a report about rent burdens of Section 8 recipients reveals that many spend far more than 30 percent of their limited incomes on shelter (U.S. GAO 1990: 3). Although the absolute number of poor households receiving federal rental assistance increased during the 1980s and into the 1990s, the number of poor, and likely eligible, households in need of such assistance grew at a much faster pace (Joint Center 1991: 3). A total of 7.3 million households, with 1989 incomes at or below the poverty line, were eligible for housing assistance, yet only 4.3 million received it (Joint Center 1991: 20-21). Moreover, families with children were underrepresented among households receiving assistance, but overrepresented among households in need of such help (Khadduri & Nelson 1992: 23), and overrepresented among households living in overcrowded and/or inferior housing conditions (Joint Center 1991: 4-5).
    The 1990 Cranston-Gonzalez Act, reauthorizing Section 8 funding, redefined a "family" by expanding the definition to include single persons (Nelson & Khadduri 1992: 27). This legislation impaired the usefulness of the term, and undermined the program's potential for specific housing assistance for families with children. In 1992, only 9.6 percent of all families receiving cash subsidies through AFDC resided in public housing. Another 13.8 percent of AFDC recipient families obtained either federal or state housing subsidies, while the majority (63.1%) lived in private, unsubsidized housing (U.S. House 1994: 402). The AFDC cash stipend, which has declined in value by 43 percent since the 1970s to its current median monthly value of $366 in 1994, does not raise recipient family incomes up to the federal poverty threshold in any state. Even after adding the average value of food stamps to the cash stipend, families relying on AFDC as their sole source of income are hard-pressed to pay for affordable housing, and also purchase other essentials--an important fact when two-thirds of the 11 million AFDC recipients are children (U.S. House 1994: 745).
    The role of housing costs in contributing to economic hardship among families with children may be explored by reevaluating the measure of housing affordability. If the "30% of Income Measure" fails to measure comparative need adequately, policy makers should adopt a better method of assessing housing affordability. A more precise measure of housing affordability would be useful in assessing need, as well as restructuring housing and other social policies.

THE AMERICAN HOUSING SURVEY, 1991
       Methodology and Data: The 1991 American Housing Survey (AHS), a national, stratified, random sample of 50,000 domiciled households, is conducted jointly by the U.S. Census Bureau and HUD every other year. All data refer to the 1991 calendar year. The unit of analysis, or case, is the household and all persons residing in it. The AHS describes conditions of the physical shelter itself, and provides identifying information about every person living in each unit, vis-a-vis his or her relationship to the identified head of household. Information relevant to this study includes: age, gender, marital status, wage and salary, employment, sources of income, and other socio-economic data, as well as household-level income, housing costs, utilities, and measures of housing quality. The HUD definition of housing costs--rent and/or mortgage costs and utilities--was used, omitting telephone and other expenses associated with this expenditure category.
    To examine the housing conditions and economic circumstances of families with children, the AHS was converted into a family-level file, in two steps. First, only cases with at least one child present under the age of 18 were chosen. This file had 16,903 cases, and each case represented a household with at least one child present. Second, the standard U.S. Census Bureau definition of family was used to classify families into types (that is, related through marriage, adoption, or blood), identified by the relationship of each person in the family to the head of household, taking into consideration each family member's age and marital status. Numerous cases were discarded, since they either did not fit into the family classification system, or the family had more than eight persons present. Since Stone's methodology applies only to two- to eight-person families, larger families were excluded. The final file contained 12,640 cases, which, when weighted to estimate population parameters, represented 30,033,621 families with children--24,048,851 married couple families, and 5,984,770 single parent families. Since larger families, and those whose constellations were outside the standard U.S. Census Bureau classification system, were excluded, these estimates were quite similar to those calculated by the U.S. Census Bureau in 1991 (U.S. Dept. of Commerce 1992a: 77-83).
    The impact of taxation on family incomes was calculated by modelling estimation processes used by the U.S. Census Bureau (U.S. Dept. of Commerce 1992b: C1-4). Total pretax family income of all family members, a variable on the AHS file, was used to generate after-tax family income. First, adjusted gross family income was calculated for each family. The amount of the Social Security Payroll tax (FICA), owed by each person in the family who had wages and/or salary during the past year, was calculated. The FICA tax rate was 7.65 percent of all earnings up to a maximum of $53,400 in 1991 (U.S. Dept. of Commerce 1992b: C-3). It was assumed that all married couple families filed joint tax returns, and all single parent families filed head of household returns, taking the maximum number of deductions without itemizing.
    For each family type, varying by the number of persons present, the value of standard deductions and personal exemptions were calculated and summed (U.S. House 1994: 719: Table 16-17). The resulting figure was deducted from pretax income to generate adjusted gross family income. Federal income taxes were calculated on the family's adjustable gross income, based on the 1991 tax schedule (U.S. House 1994: 719: Table 16-17). The value of the Earned Income Tax Credit (EITC) was simulated based on family income parameters and the number of children present (U.S. House 1994: 700: Table 16-11), and set to zero if the family was not eligible for it. Federal taxes owed and FICA paid were deducted from pretax income, and the value of the EITC was added. The resulting figure represented an after-tax income figure for each family.
    By assuming that every family took standard deductions and did not itemize, and therefore did not take advantage of any homeowner tax deductions, the calculation of after-tax income was biased, most likely underestimating the amount of after-tax income families had available to spend on necessities, and thus overestimating the full impact of housing costs. However, mortgage deductions have their biggest impact among upper-level households, hence their omission would have little, if any, impact on housing costs among lower-income families (Stone 1993: 331). Since the AHS did not have sufficient information to calculate state tax obligations, after-tax family income excluded the "costs" of state taxes. In 1991, 44 states had state taxes, and 65.1 percent of all households paid state taxes, at an average of $1,761 (U.S. Dept. of Commerce 1992b: C-3), implying that this omission resulted in an overestimation of the amount of after-tax income families actually had. In addition, since large families were excluded, the resulting calculations probably underestimate the full impact of housing costs on the economic status of families with children. Hence, these results should be considered preliminary estimates.

"SHELTER POVERTY" VS. "30% OF INCOME MEASURE"
       Stone used the 1981 U.S. Bureau of Labor Statistics (BLS) Lower Budgets to estimate costs of non-shelter minimum necessities for two prototypical households: Two parents with two children, and one parent with two children. Discontinued in 1981, these budgets remain the most reliable estimates of the costs of minimum necessities available to researchers. While they fall short of a socially defined or collectively agreed-upon specification of minimum necessities, they often appear in, or influence the development of, measures of economic well-being, including alternative poverty measures (Ruggles 1990; Watts 1980; Stone 1993; Renwick & Bergmann 1993).
    Stone updated the costs of necessities in the BLS budgets to 1990 for each prototypical family using the Consumer Price Index (CPI), an annual measure of the overall rise in the cost of goods (standard procedure for this type of economic analysis). He estimated the cost of taxation for one- and two-parent families with one to six children based on federal tax schedules, varying by family income, and including payroll, federal, state, and the Earned Income Tax Credit (EITC). Stone assumed that two-parent families would file joint tax returns, both worked all year, and would take all standard deductions. He also assumed that all parents in single-parent families were employed, would file as heads of households, and take the maximum number of standard deductions. Resulting tax liabilities, or "costs," varied by family size, composition, and income.
    Stone added tax "costs" to the updated BLS schedule of necessities to derive an estimate of the total costs of non-shelter necessities. He then deducted these costs from total family income to see how much income remained. This amount was each prototypical family's annual shelter maximum. Stone then calculated equivalency weights to apportion the costs of non-shelter necessities to families larger and smaller than his two prototypes. From this, he derived a schedule to estimate how much money different families (one- or two-parent families, one to six children, at varying income levels) could realistically afford to devote to housing, once other necessities were purchased and taxes paid. This amount represented an annual shelter maximum. By deducting the annual shelter maximum, or the amount which families could realistically pay for housing, from the amount they actually did pay, he determined which families were "shelter poor." Families whose shelter costs were less than Stone's annual shelter maximum amounts, then, were not "shelter poor." Stone also calculated the aggregate amount of money required to fill the "Shelter Poverty" housing gap:
    Pretax Income - Non-Shelter Necessities (Including Taxes) =
    Maximum Annual Shelter Costs (By Family Composition, Size, and Income Range)
    X = (Annual Housing Costs - Maximum Annual Shelter Costs) (Discard Cases With -X)
    Housing Gap = SigmaX
    Stone's 1990 estimates of the costs of non-shelter necessities (1993: 329) were updated to 1991 figures, using the rise in the overall cost of goods from 1990-91 as measured by the CPI-U-X1 (U.S. Dept. of Commerce 1992a: B-2), and his methodology was replicated as closely as possible in the subsequent analyses.
    To fairly compare the standard "30% of Income Measure" with Stone's "Shelter Poverty," this measure was calculated in a similar manner. After-tax family income (DI) was derived for each case by deducting the "costs" of federal and payroll taxes, and adding the value of the EITC when relevant, to family income. Thirty percent of after-tax income was calculated and deducted from each family's actual annual housing costs. If this resulted in a negative number, the family did not experience housing affordability difficulties according to this measure. If, however, the calculation resulted in a positive number, the family devoted more than 30 percent of its income to housing costs, and was considered impacted. To calculate aggregate and per family housing gap amounts, the dollar figure by which families fell short of affording shelter was summed: "30% of Income Measure":
    After-Tax Family Income = (Household Income + EITC)-(Federal + FICA Taxes) (Varying By Family Size, Composition, and Income Range)
    X = Annual Housing Costs - (.30 × DI)
    Housing Gap = SigmaX
    Methodology: The AHS was analyzed to identify and describe the number of families with children adversely affected by housing costs under two different measures of housing affordability: the "30% of Income Measure" and Stone's "Shelter Poverty." The sample was divided into four groups, based on pretax family income: 0-$11,000; $11,001-$25,000; $25,001-$64,000; and over $64,000. Estimates of the number of families classified as spending too much for housing under both measures were calculated. Statistical tests of the difference between each measure's standard error were calculated to determine if differences in family classification were statistically significant under both measures. Aggregate and per family costs of filling the "housing gap" under both measures were also calculated.
    A composite measure of inadequate housing was calculated based on the HUD definition. Prevalence of affordability difficulties was assessed under both measures for families residing in inadequate housing. A three-way cross-tabulation was calculated holding housing quality constant to estimate how many families in each income strata living in inadequate shelter experienced housing affordability difficulties under both, either, or neither measures. HUD considers housing overcrowded if more than two persons share a bedroom. Prevalence of affordability difficulties under both measures was assessed for families living in overcrowded shelter. A three-way cross-tabulation was calculated holding overcrowding constant to estimate how many families living in overcrowded shelter experienced housing affordability difficulties under both, either, or neither measures.
    Findings: Among all families with children, both the "30% of Income Measure" and "Shelter Poverty" classified similar proportions of families with housing affordability problems in 1991 (Table 1). The "30% of Income Measure" identified 35.5 percent of families with children which spent more than 30 percent of their after-tax incomes on housing in 1991, whereas 33.4 percent of families with children spent so much of their incomes on housing costs that they could not afford to purchase non-shelter minimum necessities, and were therefore categorized as "shelter poor." Each one percent of families, however, represented nearly 300,000 families, or nearly a million people, making these apparent similarities in percentages statistically significant differences in classificatory powers of the measures. This aggregate similarity also concealed substantial differences between the affordability measures within income ranges. "Shelter Poverty" and the "30% of Income Measure" classified different proportions of families within each income range as experiencing housing affordability difficulties.
    These differences were all statistically significant. While any family's likelihood of experiencing housing cost difficulties decreased as that family's income level rose, "Shelter Poverty" was more common, and more concentrated, among lower income families. No upper income families were "shelter poor." On the other hand, the "30% of Income Measure" identified housing affordability dilemmas in all four income ranges. The prevalence of housing difficulties under the "30% of Income Measure" declined as income increased, but a smaller proportion of lower income families, and a sizeable proportion of upper income families, were tagged as experiencing housing affordability difficulties.
    This differential pattern of housing affordability difficulties between both measures sheds doubt on the validity of the "30% of Income Measure," since, conceptually, a measure of affordability should realistically indicate economic hardship. It appears counter-intuitive that the wealthiest families suffered from housing affordability problems. They probably did spend more than 30 percent of their after-tax incomes on housing costs, but this most likely did not preclude them from also purchasing other non-shelter necessities. Equally, the relative preponderance of "shelter poverty" among lower income families, and its apparent absence among upper income families, suggests that "Shelter Poverty" better captures the concept of housing affordability than the "30% of Income Measure."
    Nine percent of families with children, or 2.7 million, resided in moderately or severely inadequate housing in 1991, according to HUD standards (Table 2). Table 2 illustrates the proportion of families which lived in inadequate housing in 1991, and also experienced housing affordability problems under both measures, only the "30% of Income Measure," only "Shelter Poverty," or neither measure.
    By treating the presence of housing inadequacies as another potential indicator of housing affordability problems, the pattern of housing affordability difficulty among families within each income range offers another set of findings to assess the validity of the "30% of Income Measure" vs. "Shelter Poverty." Here, as well, the results suggest that the "30% of Income Measure" may be misclassifying housing affordability difficulties, and that "Shelter Poverty" may provide a more precise quantification for this concept among families with children.
    While only 78.6 percent of the 780,000 poorest families living in inadequate housing were classified as having housing affordability difficulties under the "30% of Income Measure," all these families were categorized as "shelter poor." Since we can assume that poor families residing in inadequate shelter probably did so out of economic necessity rather than choice, it would seem logical that the preponderance of "shelter poverty" among the lower income range families omitted from the "30% of Income Measure" of housing affordability supports "Shelter Poverty's" greater applicability.
    In contrast, 174,000 families with incomes over $64,000 lived in inadequate housing in 1991, but none were "shelter poor," although 17.9 percent were categorized as having housing affordability problems by the "30% of Income Measure." Whereas inadequacies suggest affordability problems, they are not the same thing, and, given the broad definition of circumstances included in the HUD definition (Abt 1990: 66-68; Table 2, Note 1), it seems likely that wealthier households reside in what are classified as inadequate housing out of utility rather than economic necessity.
    Similar patterns occurred among the 5.9 million families residing in overcrowded housing, constituting 19.6 percent of families with children (Table 3). Table 3 illustrates the proportion of families living in overcrowded housing in 1991, and also experiencing housing affordability problems under both, either, or neither measure. By treating overcrowding as another potential additional indicator of housing affordability problems, the pattern of housing affordability difficulties among families in each income bracket also provides insight into the relevance of the "30% of Income Measure" vs. "Shelter Poverty." Here, as well, the results suggest that: the "30% of Income Measure" may be misclassifying housing affordability difficulties; whereas "Shelter Poverty" may provide a more precise quantification for this concept among families with children.
    Both measures categorized a similar proportion of families as experiencing housing affordability difficulties in 1991, but the aggregate costs of filling the respective housing gaps differed dramatically, both overall, and per family (Table 4). The "30% of Income Measure" gap came to only $31.9 billion, compared to the far larger $87.3 billion gap for "Shelter Poverty." Although it would be less expensive to fill the "30% of Income Measure" gap, this money would flow to families across the income range, rather than concentrating its effects on lower-income families, as suggested by "Shelter Poverty."

CONCLUSION
       The results suggest a number of preliminary conclusions concerning housing affordability measurement and the assessment of the impact of housing costs on families with children. By either measure, a significant number of families with children are adversely affected by housing costs. While[cont. on p.98] it appears that many children live in inadequate or overcrowded conditions, further work is necessary to explore these issues. In particular, the HUD definition of inadequacy incorporates a range of conditions, which give leaks in the basement, for example, the same weight as rodent infestation. On the other hand, the HUD definition of overcrowded housing as more than two persons sharing a bedroom ignores cultural preferences of families, or local variations in availability, rather than reflect the consequences of expensive housing alone.
    Stone's "Shelter Poverty" appears to be a better measure of the concept of housing affordability among families with children, especially if limited resources demand that policies target the neediest. The fact that the "30% of Income Measure" characterized upper income families as experiencing housing affordability problems, and "Shelter Poverty" did not, further bolsters the relevance of the latter. The pattern of housing affordability difficulties, and overcrowding and inadequate housing, despite qualifications, provides additional support for this conclusion. Most important, if the concept of housing affordability means that parents can both pay for adequate, nonluxurious housing, and also afford to buy minimum essentials for themselves and their children, "Shelter Poverty" is a more appropriate measure than the "30% of Income Measure." Yet, "Shelter Poverty" has its own methodological flaws. Since American families are heterogenous in their preferences, and given pluralistic political practices, the United States has yet to develop a socially accepted, agreed-upon list of minimum necessities, or quantify how much of each necessity is an essential.
    Charles Dechert's notion that American society ensure that no one is hungry, homeless, unemployed, or denied what is necessary to live with dignity, reflects a common moral understanding (1991: 78). Most Americans would agree in principle, but determining how to accomplish this in practice remains problematic. Unlike other social policies, U.S. housing policy has been left largely to the private market, through indirect subsidization of homeownership, and limited direct subsidization of poor rental households. For families with dependent children, the results have been less than inspiring, suggesting that new approaches to housing policy are needed which focus on America's children. Housing assistance could be reformulated within the tax system, structured similarly to the EITC to reduce stigma, and efficiently redistributed from households without, to those with, children. Even at $87 billion per year, subsidizing affordable housing for families with children would be a cost-effective method of bolstering family stability.
    Added material
    Susan D. Einbinder teaches social work at the University of Southern California, School of Social Work, Los Angeles, CA 90089.
    Table 1 Estimated Housing Affordability for Families With Children, 1991

   Annual Family     Est. Population        Measures of Housing Affordability
     Income            Parameter         30%   of Income   Shelter Poverty      St. Error
    (in U.S. $)        (in 1000s)        Percent St. E.     Percent St. E.    of Difference(FN1)
   0-11,000              4,064            79.1     (.008)     99.5      (.01)     .007*
   11,001-25,000         6,897            49.5     (.008)     70.1     (.007)     .005*
   25,001-64,000        13,952            22.9     (.004)      8.3     (.003)     .003*
   Over 64,000           5,121            16.7     (.007)       0      (n.a.)         *
   TOTAL:               30,034            35.5     (.003)     33.4     (.003)     .002*

    Source: Original Analyses, American Housing Survey, 1991.

FOOTNOTE
       1 The "Standard Error of the Differences" between both percentages was calculated according to the recommended U.S. Census Bureau formula: S[subx-y = sqrt [(S[subx)[sup2 + (S[suby)[sup2 - 2r (S[subx × S[suby)]; where r = 0.7.
    If the resulting statistic is larger than either of the individual standard errors, statistical significance can be assumed (p = .10).
    Table 2 Estimated Inadequate Housing for Families With Affordability Difficulties, 1991

   Annual Family     Est. Number of        Measures of Housing Affordability (%  )
     Income            Families(FN1)     Both      30%   of Income     Shelter Poverty Neither
    (in U.S. $)       (in 1000s)         Meas.           Only            Only              Measure
   0-11,000              780             78.6               0            21.4                 0
   11,001-25,000         284             34.3             5.6            38.7              21.3
   25,001-64,000         922              4.1            12.4             4.1              79.5
   Over 64,000           174                0            17.9               0              82.1
   TOTAL:             2,704 (9%   of families with children)

    Source: Original Analyses, American Housing Survey, 1991.

FOOTNOTE
       1 The U.S. Department of Housing and Urban Development considers shelter to be moderately inadequate for a number of difficulties such as: nonfunctioning toilet 3 or more times per year for 6 hours or more; various water leaks; hazardous steps in common stairs; incomplete or lacking plumbing; heat breakdowns more than 3 times since residents moved in; exposed wiring; inoperative public hall fixtures; et al (Abt 1990: 66-68).
    Table 3 Estimated Overcrowded Housing Among Families With Affordability Difficulties, 1991

   Annual Family     Est. Number of        Measures of Housing Affordability (%  )
     Income            Families(FN1)     Both      30%   of Income     Shelter Poverty     Neither
    (in U.S. $)       (in 1000s)         Meas.           Only             Only             Measure
   0-11,000              1,381           86.5              0              13.4              0.1
   11,001-25,000         2,209           48.3            3.3              35.9             12.6
   25,001-64,000         2,151            9.5            7.9               9.5             73.2
   Over 64,000             327              0            7.6                 0             92.4
   TOTAL:                5,888 (19.6%   of families with children)

    Source: Original Analyses, American Housing Survey, 1991.

FOOTNOTE
       1 The U.S. Department of Housing and Urban Development considers housing overcrowded if more than two persons are required to share a bedroom.
    Table 4 Estimated Costs of Filling Family Housing Affordability Gaps, 1991

   MEASURES OF HOUSING AFFORDABILITY
   Annual Family    Est. Population      Aggregate 30%          Aggregate Shelter    Average Family     Average Family
     Income           Parameter          of Income Gap            Poverty Gap        30%   of Income    Shelter Poverty
    (in U.S. $)       (in 1000s)        ($ millions) SE(FN1)    ($ millions) SE      Gap (in U.S. $)    Gap (in U.S. $)
   0-11,000             4,064           9,734   (1.383)         50,170   (3.194)        2,395             12,345
   11,001-25,000        6,897           8,490    (.812)         32,100   (1.934)        1,231              4,654
   25,001-64,000       13,952          10,350    (.590)          3,342    (.844)          741                357
   Over 64,000          5,121           3,342    (.844)              0    (.000)          653                  0
   TOTAL:              30,034          31,910    (.420)         87,250   (1.001)        1,063             2,905

    Source: Original Analyses, American Housing Survey, 1991.

FOOTNOTE
       1 The "Standard Error of the Differences," significant for each income range, was calculated as described in Table 1, Footnote 1.

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WBN: 9500102310006