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Employment and welfare participation among women.


The model makes a distinction between voluntary" and "involuntary" welfare receipt. The findings suggest that among female heads of households, the increase in welfare receipt that occurred between 1967 and 1979 was almost completely attributable to an increase in involuntary unemployment and an increase in the proportion of the population that was eligible for welfare (due to changes in program parameters). The passage of time, used as a proxy for changes in the stigma associated with receiving welfare, appears to be of secondary importance. The labor supply response to welfare programs is small, and possibly diminishing over time.


During the last thirty years the Aid to Families with Dependent Children (AFDC) and Food Stamp programs experienced phenomenal increases in outlays. Between 1965 and 1975 the AFDC population grew 162 percent and real government spending on benefits more than tripled. By 1980, the probability that a family was receiving AFDC was four times the probability in 1950 value. The Food Stamp program, after its introduction in the late 1960s, experienced equally dramatic increases in recipiency rates and outlays.

These striking increases in welfare costs and participation brought an emerging consensus that the AFDC and Food Stamp programs had failed. As Charles Murray writes in Losing Ground [1984, 146], "the popular wisdom is characterized by hostility toward welfare (it makes people lazy)." Historian James Patterson [1981, 179] provides an alternative, though not inconsistent explanation of the skyrocketing caseloads:

"Despite the hostility of the middle classes to increases in welfare, poor Americans refused at last to be cowed from applying for aid .... Compared to the past, when poor people-harassed and stigmatized by public authorities-were slow to claim their rights, this was a fundamental change."

Both of these explanations of the increase in welfare participation assert changes in people's response to the programs. Murray claims that program changes in the 1960s induced negative labor supply responses-increasing numbers of individuals voluntarily reduced their earned income in order to become eligible for welfare. Patterson claims that a reduction in the stigma associated with welfare led a greater percentage of those eligible to apply for welfare.

A theoretical model for evaluating the validity of these two views as descriptions of reality is presented here. The model is tested using data on women who headed households at some time between 1967 to 1979. The analysis attempts to identify changes in behavior among female heads of households, but does not model the decision to head a family-a decision which embodies both marital status and fertility choices. The implications of this limitation are discussed at the end of the paper.

The focus is on developing a tractable theoretical structure that allows for a distinction between voluntary" and "involuntary" welfare participation. The model also provides a simple test for whether reported unemployment is a constraint on choice, or rather a result of it (i.e., whether unemployment, too, is involuntary or voluntary). The empirical results enable us to dis-aggregate the changes in welfare participation into their component parts.

The findings suggest that the increase in welfare participation rates among female heads of households during the late 1960s and 1970s is attributable to both an increase in involuntary unemployment and to an increase in those eligible for welfare as a result of changes in program parameters. The passage of time, used as a proxy for a lessening of stigma, appears to be of minor importance. The labor supply response to welfare programs appears to be small, and possibly diminishing over time.

In section II a model for determining the effect of redistribution schemes on labor supply and welfare participation decisions is developed. This section also outlines an econometric specification consistent with the model. Section III describes the data used to test the model and section IV reports the empirical results. The final section summarizes the findings of the paper.


Both the AFDC and Food Stamps programs provide guaranteed levels of benefits for families with no alternative source of income. As income increases, benefits are sharply reduced, thereby generating high implicit tax rates for welfare participants.

Within the context of a labor-leisure framework, redistribution schemes create nonconvexities and kinks in the budget constraint faced by low income families. For ease of exposition, consider first the AFDC program where benefits can be characterized by equation (1):

B = [G.sub.a]- [t.sub.1]W [times]- H (1)

where B is the AFDC benefit, [G.sub.a] is the basic AFDC guarantee for families with no other income, [t.sub.1] is the implicit tax rate on benefits, W is the hourly wage rate, and H is the hours worked.

The slope along segment I of the budget constraint is W, and the slope along segment II is W(1 - [t.sub.1]). Clearly, there is an incentive for some individuals who would locate in the vicinity of point C in the absence of the program, to reduce their hours of work in response to the program and move to point D. For reasonable preferences, a comer (i.e., no-work) solution seems likely.

Juxtapositioned with this observation, Ruggles and Michel [1987] find evidence that some individuals eligible for welfare choose not to receive it and consequently settle on the interior of their budget constraint. There are several possible explanations why. It may be that individuals do not apply for welfare because they are unaware of its existence or because participation in the program involves large transactions costs. Another possibility is, as Patterson [1981] suggests, that welfare participation imposes a stigma on the recipients and thereby creates disutility. These alternative sources of non-participation by those who are eligible will not be distinguished in the model, but will be referred to simply as stigma.

The General Model

A substantial body of literature has examined the effect of welfare on the tabor supply of low-income individuals. Since the seminal work of Burtless and Hausman [1978], this work has increasingly employed a piecewise linear budget constraint. Moffitt [1983] incorporated stigma into the AFDC participation decision, and more recently, Fraker and Moffitt [1988] expanded the analysis to include a joint examination of labor supply, AFDC, and Food Stamp participation decisions.

This paper extends that of Fraker and Moffitt in two important ways. First, it examines the three decisions-labor supply, AFDC participation and Food Stamp participation-over a thirteen year period of rapid growth in the AFDC and Food Stamp Programs, thereby allowing the most important sources of growth to be identified within a consistent framework. Second, the analysis incorporates the possibility of involuntary unemployment and provides a method for estimating the extent to which reported unemployment represents a constraint on choice.

Assume that utility is a monotonic, strictly quasi-concave function of leisure and income (used to buy a Hicks composite commodity), which can be written as

U = U(l, Y) - [[phi].sub.t]P - [[alpha].sub.t]S (2)

where l is hours of leisure, and Y is income. P and S are dummy variables where P equals one for AFDC participants and zero for non-participants and S equals one for Food Stamp participants and zero otherwise. The parameters [[phi].sub.t] and [[alpha].sub.t], measure stigma in time period t. We allow differential stigma rates under the two programs since Food Stamps must be used in public and may, therefore, be more stigmatizing than AFDC. The budget constraint is

Y = W[times] H + N + B [times] P + F [times] S, (3)

where B = Ga - [t.sub.1]W [times] H - [r.sub.1]N,

F = [G.sub.f] - ([t.sub.2] - [t.sub.1][r.sub.2]P)W[times]H [r.sub.2][[G.sub.a] + (1 - [r.sub.1])N]P - [r.sub.2]N(1 - P) .

The variable W is the wage rate, H is hours of work, N is unearned (non-welfare) income, and B and F are, respectively, the dollar value of AFDC and Food Stamp benefits. [G.sub.a] and [G.sub.f] are the basic guarantees under the AFDC and Food Stamp programs, [t.sub.1] and [t.sub.2] are the implicit tax rates on earned income under each of the programs, and [r.sub.1] and [r.sub.2] are the implicit tax rates on unearned income. This formulation indicates that while AFDC benefits influence eligibility for Food Stamp benefits, the reverse is not true.

Assuming for the moment no involuntary unemployment, the maximization of equation (2) subject to the constraint expressed in (3) yields a labor supply equation of the usual form:

H = H([W.sub.*], [N.sub.*]) (4)

where [W.sub.*]=W[1-[t.sub.1]P - ([t.sub.2] - [t.sub.1][r.sub.2]P)S]

[N.sub.*]=N + ([G.sub.a] - [r.sub.1]N)P + {[G.sub.f] - [r.sub.2] [[G.sub.a] + (1 - [r.sub.1])N]P - [r.sub.2]N(1 - P)}S.

To simplify notation let [[M.sub.*].sub.1S] and [[W.sub.*].sub.OS] represent the effective wage rate when P = 1 and P = 0, respectively, for a given value of S. Similarly, [[W.sub.*].sub.p1] and [[W.sub.*].sub.p1] represent the effective wage rate when S = 1 and S = 0, respectively, for a given value of P. Identical subscripting is used for unearned income, [N.sub.*]. The AFDC participation decision is then found by determining the sign of [P.sub.*]:

[P.sub.*] = V([[W.sub.*].sub.1S], [[N.sub.*].sub.1S]) V([[W.sub.*].sub.OS], [[N.sub.*].sub.OS]) - [[phi].sub.t] (5)

where V represents the indirect utility function. If [P.sub.*] > 0, the maximum utility attainable by receiving unearned income through AFDC (and enduring high implicit tax rates and possible stigmatizing effects) is in excess of the maximum utility achievable by not receiving AFDC (and thereby enjoying lower tax rates and less stigma). Consequently, [P.sub.*] > 0 implies that the individual will choose to participate in AFDC. Similarly, the decision to be a Food Stamp recipient is determined by the sign of [S.sub.*]:

[S.sub.*] = V([[W.sub.*].sub.p1], [[N.sub.*].sub.p1]) V([[W.sub.*].sub.PO], [[N.sub.*].sub.PO]) - [[alpha].sub.t]. (6)

Specification of the Functional Form

Estimating equations (4) - (6) requires that a specific functional form be chosen for either the utility function or the indirect utility function. The log of a Cobb-Douglas utility function was chosen since it yields a tractable labor supply equation, as well as binary choices in P and S that are easy to estimate. Because income is endogenous in the model, several of the restrictive features of the more typical Cobb-Douglas utility function (where income is exogenous), do not exist.

Assuming the existence of some composite commodity X, the price of which is set equal to one, the function to be maximized is

U = alnl + blnX - [[phi].sub.t]P - [[alpha].sub.t]s, (7)

subject to the budget constraint:

X = [W.sub.*]H + [N.sub.*]. (8)

Maximization of (7) subject to (8) yields the leisure and commodity demand equations:

l = a(T [times] [W.sub.*] + [N.sub.*])/(a + b)[W.sub.*],

X = b(T [times] [W.sub.*] + [N.sub.*])/(a + b), (9)

and the labor supply equation:

H = [bT/(a+b)] - [a[N.sub.*]/(a+b)[W.sub.*]] if bT [times] [W.sub.*] [is greater than or equal to] a[N.sub.*],

H=0 otherwise (10)

where T is total time available.

Substituting (9) into (7) and collecting terms yields the indirect utility function:

V = ln [[([a.sub.a] + [b.sub.b])/[(a + b).sup.[a+b]] + (a + b)ln (T[times][W.sub.*]+ [N.sub.*]) - aln[W.sub.*] -[[phi].sub.t]P - [[alpha].sup.t]S. (11)

Using equations (5) and (11) and re-arranging terms, the decision to be an AFDC participant is determined by the sign of P*, where

[P.sub.*]+ -[[phi].sub.t] + (a+b)[ln(T[times][[W.sub.*].sub.1S] + [[N.sub.*].sub.1S]) - ln(T[times][[W.sub.*].sub.OS] + [[N.sub.*].sub.OS])] a(ln[[W.sub.*].sub.1S] - ln[[W.sub.*].sub.OS]). (12)

Similarly the decision to be a Food Stamp participant is determined by the sign of [S.sub.*], where

[S.sub.*]= [[alpha].sub.t] + (a + b)[ln(T[times][[W.sub.*].sub.p1] + [[N.sub.*].sub.p1]) -a(ln[[W.sub.*].sub.p1] - ln[[W.sub.*].sub.PO], (13)

where a > 0, b > 0, and [a/(a + b)]/[([N.sub.*]/[W.sub.*]H) + 1] is the compensated elasticity of labor supply.

The model provides a simple test of the extent to which reported unemployment is a constraint on choice, rather than the result of choice (i.e. whether unemployment is involuntary or voluntary). The labor supply equation that was generated from the maximization exercise has as its dependent variable, hours of employment plus hours of unemployment. This suggests that the labor supply equation (10) could be re-written and estimated by

E = [bT/(a + b)] - [a[N.sub.*]/(a + b)[W.sub.*] - [beta][times]Un, (14) where E is hours of employment and Un is reported hours of unemployment. If all reported unemployment is involuntary (voluntary), then the estimated coefficient should be equal to one (zero). In the participation equations, unemployment enters as a disturbance term that prevents individuals from achieving the choice that might have been made in the absence of labor market constraints.

The Econometric Specification

The decision rules implied by equations (12) and (13) select individuals onto a particular segment of their budget constraint, thereby determining their effective wage rate and level of unearned income. Ideally, the two participation equations (12) and (13) and the hours of employment equation (14) would be estimated simultaneously. This approach raises an econometric problem of substantial difficulty since the usual procedure of estimating wage rates for workers only (adjusted for selectivity bias) and using the predicted values yields inconsistent estimates.

The most reasonable procedure seems to be to estimate the two participation equations simultaneously and then to estimate the hours of employment equation separately only for those individuals who are in the labor force. 15 This exclusion of individuals eliminates the need to use a Tobit-type estimator, and enables us to apply Heckman's [1978] procedure to develop consistent estimates. All wage rates have been adjusted to account for variations in FICA tax rates across years.

A final econometric detail is that the estimated coefficients need not be equal across the two participation equations since probit coefficients are estimated only up to a factor of 1/[sigma]. Since [sigma] may well vary between the equations, so too may the estimated coefficients. However, the ratio of the first and second terms must be equal across the two equations.


The 1981 version of the Panel Study of Income Dynamics (PSID) was used to estimate the model outlined above. The PSID is an annual longitudinal survey of household heads, begun in 1968, with questions asked retrospectively for 1967. Since the AFDC program is of principal interest, the analysis is restricted to families headed by women who had children under the age of eighteen. There were originally 433 such families, but by 1979 there were 722 in the sample. Because women are often head of household for only short periods, continuous data for an extended period on any individual are very limited. Consequently, the data base is treated as a series of independent cross-section observations, rather than as a panel data base.

Two alternative approaches were used to implement the empirical work. The first approach used estimates of the actual, as opposed to the legislative, implicit AFDC tax rates. The implicit tax rates on earnings were legislatively set at 1.00 in 1967 and .67 from 1968-1981; however, the actual (estimated) tax rates on earnings vary across stateS. The estimated AFDC tax rates were developed by Fraker, Moffitt, and Wolf [1985], by state, on a bi-annual basis from 1967-1981. Since these tax rates are an important component of the analysis, the estimates of labor supply response and welfare stigma are also developed on a bi-annual basis for the years 1967-1979.

It is questionable, however, whether these implicit tax rates are the appropriate ones to use. Consequently, the empirical analysis was repeated using legislative rates, rather than estimated implicit rates. It is the latter results that are reported here.

Using the legislation tax rates requires that the final term in equations (12) and (13) be incorporated in with the time dummies. The reason is that this term reduces to ln(t). Since t is constant across states when the legislative tax rate is used, this variable is constant across observations within each year of the data. It is not constant, however, across years since the legislative tax rate was changed from 1.00 to .67 in 1968.

The 1968 change in the legislative tax rate enables us to recover its impact on participation rates through its effect on the income terms T[times][W.sub.1S]) and T[times][W.sub.1S]), since these terms are not incorporated in the time trend. That is, the effective wage rate continues to enter into the estimating equation, even though the final term of equations (12) and (13) cannot be estimated separately from the time trend.

Chosen characteristics of the sample are summarized. Over the years considered, the sample has become somewhat younger, as is the case for the broader population. The number of children in female headed households dropped dramatically from an average 3.10 in 1967 to 2.07 in 1979. Labor force participation, both in terms of hours employed as well as hours unemployed, increased among this sample of female heads, as it has among all women. Education levels also rose, although they remain quite low in comparison to the broader population of all women, reflecting the disadvantaged nature of these women heading households.


The results from the estimation of the AFDC and Food Stamp participation decisions given by equations (12) and (13). The time parameters measure changes in the intercept, relative to 1967. These parameters capture changes in information, transactions costs, and harassment, as well as changes in stigma. In addition, the effects of benefits that are associated with welfare receipt and are changing in value over time (perhaps most importantly Medicaid), are captured in these time parameters.

Evaluating these parameters at the mean values of the dummy variables associated with them indicates that the passage of time caused a monotonic increase in AFDC participation rates ranging from 0.3 percentage points in 1969 to 1.4 percentage points in 1979.

The results from the Food Stamp participation probit also show a steady increase over time, with particularly large effects between 1969 and 1971 ([delta][Time.sub.71]). In this case, the time dummies are likely to be capturing the fact that Food Stamps were not uniformly available until the early 1970s. Once again, evaluating these time parameters at the mean value of the dummy variables associated with them indicates that the passage of time caused a monotonic increase in Food Stamp participation rates ranging from 0.0 percentage points in 1969 to 8.8 percentage points in 1979.

The other results are in keeping with our expectations. When income available through welfare increases relative to that which is available when not receiving welfare, the probability of welfare receipt increases. The unemployment constraint does bind utility maximization, significantly increasing the probability of both AFDC and Food Stamp recipiency.

The implications of these results are examined further which breaks down the growth in AFDC and Food Stamp participation rates between 1967 and 1979 into their component parts. These calculations were made by first assigning to each observation in the sample during 1979, the expected value of each of the independent variables during 1967. The 1967 probability of participation was then calculated, based on these values. The calculations report the difference between this probability and the probability based on 1979 values of the independent variables.

The single most important source of growth in AFDC participation rates was a reduction in the implicit tax rate. Since this reduction resulted in an increase in the break-even level of income, holding guarantees constant, the percentage of the population that was eligible for AFDC increased. The estimate reported embodies both a mechanistic response, i.e. people merely accepting benefits for which they are eligible, and a behavioral response, i.e. people actively altering their labor supply. However, as the discussion below indicates, the behavioral response to the change was quite small.

Another source of growth in participation rates for AFDC and especially for Food Stamps among female headed households, was the passage of time. As has already been mentioned, these time parameters capture (at least in part) the increasing availability of Food Stamps.

Increases in unemployment also contributed to increases in participation rates, particularly for Food Stamps. The introduction of the earned income disregard in 1968 also increased participation slightly. Once again, the effect of this change was to increase the break-even level of income. Had it not been for the decline in AFDC guarantee levels and the increase in women's earnings capacity, participation rates would have increased even more than they did.

One final point to be noted is that while the AFDC participation equation predicted growth rates quite accurately, the Food Stamp equation seriously underpredicted the increase in Food Stamp participation rates. Since Food Stamps became available at different times in different parts of the country, the probability of Food Stamp participation was overestimated in the early years of the sample, and hence its growth rate was underestimated.

The detailed results from the estimation of the hours of work equation are not reported here to conserve space. These results are, however, very similar to those reported elsewhere in the literature: women who are white, with fewer children, older children, more education, and no health limitations, are likely to work more than other women.

Two parameters, however, from the hours equation are of particular interest. The first is the coefficient on reported hours of unemployment. For women who reported some positive hours of work and received no welfare benefits, the coefficient is -.66. In an equation estimated separately for welfare participants with some positive hours of work, the coefficient is -.47. In both cases the coefficient is significantly less than -1. But because of the method used in the PSID to construct the unemployment variable (it is set to forty times reported weeks of unemployment), it is not possible to conclude that unemployment is over-stated. We can conclude, however, that unemployment is a real constraint on labor supply since the unemployment coefficient is highly significant and negative both for welfare participants and non-participants.

The other parameter of interest in the hours equation is the coefficient -a/(a+b), on the variable [N.sub.*]/[W.sub.*]. This parameter determines the value of the compensated labor supply elasticity, and therefore, the extent of voluntary welfare participation. In 1979 the value of this coefficient for welfare women with some positive hours of work was -.0028 (with a standard error of .0015). This implies a compensated labor supply elasticity of about .03 for welfare participants. A similar calculation based on a labor supply equation estimated for working non-welfare women indicated that their labor supply elasticities are indistinguishable from zero.

These labor supply elasticities are extremely low in comparison to those estimated elsewhere in the literature. They are, however, remarkably consistent with those found in the recent work of Mroz [1987] who used specification tests to check the validity of the maintained theoretical and statistical assumptions that have been employed in previous studies of female labor supply. He was able to replicate the range of labor supply responses found in previous studies, but the specification tests indicated that most of the range should be rejected, and that the actual responses to variations in wages and non-labor income are quite small. Using a different data set and estimation strategy, Plant [1984] arrived at the same conclusion.

The implication of these low labor supply elasticities is that very few women who receive welfare benefits do so voluntarily" (i.e., as a result of a behavioral response which generates a movement around the kink point. In fact, using the compensated labor supply elasticity of .03 for 1979, the estimates indicate that not a single woman who was receiving AFDC and had income below the break-even could have earned enough to push her income above the break-even level, thereby disqualifying herself from the program. This is calculated by estimating how many additional hours each woman would work if there were no AFDC or Food Stamp benefits. This involves calculating how removing benefits would change [N.sub.*]/[W.sub.*] and then multiplying this change through by W[times][a/(a+b)]. If the resulting change in income is sufficient to push the individual across her break-even level of income, she is determined to be a voluntary" participant. Because the estimated labor supply response to the program appears to be quite small, the deadweight loss associated with the program is trivial (less than 1 percent).

The vast majority of welfare participation appears to be mechanistic; people merely accept benefits for which they are eligible. It should be noted that some recipients did, indeed, have income above the break-even level, and were consequently not included in these calculations. However, there is no reason to expect that these individuals are any more likely than others in the sample to actively alter their labor market behavior.

These findings do, however, need to be reconciled with considerable evidence that most welfare spells are of quite short duration. [1984]). Many women do seem to have the capacity to work (or marry) their way off the welfare rolls. These welfare recipients are most likely to have an annual income above the break-even level and thus were excluded from the calculations discussed above. A more detailed consideration of this point would require a monthly, rather than an annual data base.


The analysis reported here indicates that the growth in the welfare participation rates of female heads of households in the late 1960s and throughout the 1970s can be largely explained by a decrease in AFDC tax rates which automatically increased the percentage of the population that was eligible, and an increase in involuntary unemployment. The passage of time itself also "explains" a modest amount of the increase in AFDC participation. The passage of time may be capturing a reduction in "stigma" or transactions costs, or an increase in the significance of Medicaid as an unmeasured component of the welfare package. The labor supply response to the program's benefits was found to be trivial, and if anything, diminishing over time as women's earnings capacity has increased and real welfare guarantee levels have fallen.

An immediate implication of this finding is that the majority of women on welfare do not have the ability to work their way off the rolls. This could be either a temporary condition resulting from involuntary unemployment, or a more permanent condition caused by inadequate human capital. In the latter case, subsidized training might be used to assist these women in achieving economic independence. Further reductions in real benefits levels will increase economic suffering, but will have only a small effect on welfare participation rates among female heads of households.

These findings indicate that there is very little voluntary" welfare participation, i.e., that resulting from a reduction in the labor supply, among female heads of households. The decision to become a female head of household could, however, be voluntary" or endogenous. No attempt was made to model the determinants of this decision, which embodies a complex set of phenomenon including women's decisions about fertility (both in and out of marriage), whether or not to marry, remain married, or remarry should a woman become divorced or widowed. It may well be the case that while welfare has become less attractive relative to work, it has become more attractive relative to marriage for some groups of women. This appears to be a fruitful avenue for future research.


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Chamberlain, Gary. "Analysis of Covariance with Qualitative Data." Review of Economic Studies, January 1980, 225-38.

Danziger, Sheldon, Robert Haveman and Robert Plotnick. "How Income Transfers Affect Work, Savings, and Income Distribution." Journal of Economic Literature, September 1981, 975-1028.

Deaton, Angus and John Muellbauer. "Functional Forms for Labor Supply and Commodity Demands With and Without Quantity Restrictions." Econometrica, November 1981, 1521-32.

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Fraker, Thomas and Robert Moffitt. "The Effects of Food Stamps on Labor Supply: A Bivariate Selection Model." Journal of Public Economics, February 1988, 25-56.

Fraker, Thomas, Robert Moffitt, and Douglas Wolf. "Effective Tax Rates and Guarantees in the AFDC Program: 1967-1982." Journal of Human Resources, Spring 1985, 251-63.

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Heckman, James and Thomas MaCurdy. "New Methods for Estimating Labor Supply Functions: A Survey," in Research in Labor Economics, edited by Ron Ehrenberg, Vol. 4. Greenwich, Conn.: JAI Press, 1981, 65-102.

Moffitt, Robert. "An Economic Model of Welfare Stigma." American Economic Review, December 1983, 1023-35.

Mroz, Thomas. "The Sensitivity of an Empirical Model of Married Women's Hours of Work to Economic and Structural Assumptions." Econometrica, July 1987, 765-99.

Murray, Charles. Losing Ground: American Social Policy, 1950-1980. New York: Basic Books, 1984.

O'Neill, June, Douglas Wolf, Laurie Bassi and Michael Hannan. "An Analysis of Time on Welfare." Report to the Department of Health and Human Services. Washington, D.C.: The Urban Institute, 1984.

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Author:Bassi, Laurie J.
Publication:Economic Inquiry
Date:Apr 1, 1990
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