Many previous studies have used sibling correlations to measure the effect of family background on earnings, income? and occupational status. This paper uses data on a sample of sisters to explore the importance of family background as a determinant of welfare program participation. The results show a strikingly high degree of sibling resemblance in welfare receipt. For example, a woman's estimated probability of having participated in welfare programs is .20 if her sister has not participated, but is -.66 if her sister has participated.

Deborah Laren

Gary Solon

Mary Corcoran

Roger H. Gordon

English

Research Papers in Economics

NBER WORKING PAPER SERIES
SIBLING AND INTERGENERATIONAL
CORRELATIONS IN WELFARE
PROGRAMPARTICIPATION
Gary Solon
Mary Corcoran
Roger Gordon
Deborah Laren
Working Paper No. 2334
NATIONAL BUREAU OF ECONOMIC RESEARCH
1050 Massachusetts Avenue
Cambridge, MA 02138
August 1987
This research was supported by a grant from the Ford Foundation to the Institute
of Public Policy Studies at The University of Michigan. The authors thank John
Bound, Charles Brown, and Greg Duncan for their comments. The research reported
here is part of the NBER's research program in Labor Studies. Any opinions expressed
are those of the authors and not those of the National Bureau of Economic Research.NBER Working Paper #2334
August 1987
Sibling and Intergenerational Correlations in Welfare Program Participation
ABSTRACT
Manyprevious studies have used sibling correlations to measure the effect of
family background on earnings, income, and occupational status. This paper uses data on
a sample of sisters to explore the importance of family background as a determinant of
welfare program participation. The results show a strikingly high degree of sibling
resemblance in welfare receipt. For example, a woman's estimated probability of having
participated in welfare programs is .20 if her sister has not participated, but is .66 if her
sister has participated.
Gary Solon
Department of Economics
The University of Michigan
Ann Arbor, MI 48109—1220
(313)763—1306
Roger Gordon
Department of Economics
The University of Michigan
Ann Arbor, MI 48109—1220
(313)764—6769
Mary Corcoran
Department of Political Science
The University of Michigan
Ann Arbor, MI 48109—1220
(313)764—9517
Deborah Laren
Institute for Social Research
The University of Michigan
Ann Arbor, MI 48109—2321
(313)936—0308Sibling and Intergenerational Correlations
in Welfare Program Participation
Both social scientists and policymakers have expressed concern about the
influence of family background on welfare program participation. According to Rein and
Rainwater (1978), for example, "One common view of the welfare 'crises,' and spiraling
welfare costs. is that the principal cause is the growth of a welfare class, which passes on
a legacy of dependency to its children." Such a view seems to underlie President Reagan's
frequent references to "the welfare culture," "the breakdown of the family," and "the
spider's web of dependency."
Many previous studies have examined the influence of family background on
earnings, income, and other measures of economic status besides welfare program
participation. Some of these studies have attempted to measure the importance of family
background by estimating sibling correlations.2 The idea is that, if family background
matters very much, siblings will show a strong resemblance in economic status; if it
matters hardly at all, they will show little more resemblance than would randomly selected
unrelated individuals. This paper similarly adopts the device of using measured sibling
resemblance to explore the importance of family background as a determinant of welfare
tSee, for example, "Transcript of President's Speech to Congress on State of Union"
(1985).
2This literature is discussed in Corcoran and Jencks (1979) and Solon, Corcoran, Gordon,
and Laren (1987).
12
program participation. The results display a startlingly high degree of sibling resemblance
in welfare receipt.
In the next section, we describe our statistical model and estimation strategy.
Then we present our results on sibling resemblance as well as related results on the
intergenerational correlation in welfare receipt. Finally, we summarize and discuss our
findings.
Statistical Model and Estimation Strategy
Our study is designed to estimate three parameters for a population of sister
pairs: p =theunconditional probability that a randomly selected woman has participated
in welfare programs, p0the conditional probability that she has participated given that
her sister has not participated, and p1 =theconditional probability that she has
participated given that her sister has participated. These parameters are related by the
identity p p I(1+p0 —pi• If family background has little effect on welfare program
participation, sisters should show little resemblance in participation status. In that case,
p0 and p1 should be close together. On the other hand, if family background is very
influential, sisters should show a large resemblance, and p1 should be much greater than
p0. In fact, p1—p0 can be shown to be exactly equivalent to the sister correlation in
welfare program participation.
One can divide a sample of N sister pairs into three groups: the N00 pairs in
which neither sister participated, the N01 + N10 pairs in which only one sister
participated, and the N11 pairs in which both sisters participated. The likelihood function
for a random sample is then
N0 N N N
L =
[(1-p)(l-p0)J°[(1-p)p0] °1[p(1-p1)] u•
Substitutingp out with the identity above, rearranging terms, and taking logarithms
produce the log likelihood function3
in L =— Nin (l+p0-p1) + (N-N00) in p0
+ N00 in (l.p0) + (N-N11) in (l-p1).
This log iikelihood function is maximized by the estimators
=
(N01+N10)/(2N00+N01+N10)
(1)
=
2N111(N01+N10+2N11).
Once derived and contemplated, these estimators become obvious. The parameter
p0, the probability of having participated if one's sister has not, is estimated by counting
up the number of women in the sample whose sisters did not participate and then
calculating the fraction of that group that did participate. Similarly, p1. the probability of
having participated if one's sister has, is estimated by the participation rate among the
sampled women whose sisters did participate.
We have applied a variant of this estimation approach to data from the Panel
Study of Income Dynamics (PS1D). Adult sister pairs can be obtained from the PSID
because the survey follows children from the original PSID families after they leave home.
Our sample consists of pairs of sisters that became heads of their own households or wives
of heads and that were between the ages of 27 and 32 at the time of the 1983 interview
(and thus between 12 and 17 at the outset of the PSID in 1968). Women that were over
the age of 17 in 1968 and entered the PSID because they were still living in their parents'
households are excluded to avoid overrepresenting women that left home at late ages. The
sample is restricted to women at least 27 in 1983 to ensure that the women have had
several years' opportunity to receive welfare. In families with more than two sisters in
the relevant age range, we use the two oldest. The resulting sample contains 137 pairs of
sisters.4
Our main measure of welfare program participation is simply whether the woman
ever reported welfare receipt between the time of leaving home and age 27. We will
focus on results based on a welfare definition that includes AFDC, general assistance, food
stamps, and SSI, but we also will mention results arising from a more restrictive
definition.
We would have applied the above-described estimation approach without
modification, except for one problem —thePSID systematically oversampled the low-
income population. As a result, sample proportions inconsistently estimate the
corresponding population proportions. An obvious example is that the sample rates of
welfare program participation will tend to be higher than the population rates. To correct
for this inconsistency, we base the estimatorsandnot on simple frequency counts as
in equations (1), but instead on counts of observations weighted by the inverse of their
probabilities of selection into the sample.4
This procedure solves the consistency problem, but complicates the estimation of
standard errors for our parameter estimators. Since the estimators are no longer derived
as maximum likelihood estimators, the conventional standard error estimators for
maximum likelihood estimators do not apply. Instead, we have used •a nonparametric
"balanced half-sample replication" procedure. This approach —describedin detail in Kish
and Frankel (1970), McCarthy (1969), and Wolter (1985) —repeatedlyapplies the
parameter estimators to a succession of strategically chosen half-samples. Each
estimator's observed variance across the half-sample replications is then used to infer an
3More precisely, the measure is whether her family (that is, the one in which she was the
head or wife) reported welfare receipt during the indicated time interval. We consider
welfare receipt reported only through age 27 (even for sample women that can be observed
until later ages) in an effort to standardize the measurement of this variable.
4This technique has been suggested in related contexts by Hausman and Wise (1981) and
Manski and Lerman (1977). For each sister pair, we use the sum of the sisters' values of
the weight described on page 459 of Survey Research Center (1985). Pages 6—19 of
Survey Research Center (1979) give a detailed explanation of the construction of the
weight.estimate of the variance of that estimator as applied to the full sample. Our
implementation of this procedure is described more fully in the Appendix.
Results
The initial results from our analysis of the PSID sister pairs are shown in the
first row of Table 1. The unconditional welfare program participation rate () is estimated
at .371. This figure may seem high at first, but is not dramatically larger than previous
estimates of population proportions ever receiving welfare over some substantial time
period.5 That it is somewhat higher should not be surprising given that our sister pairs
necessarily represent a population of women from relatively large families. If we restrict
our definition of welfare to AFDC and general assistance (excluding food stamps and SSI),
falls to .245.6
The conditional probability of participation given that one's sister did not
participate () is estimated at .199. In comparison, the estimated conditional probability
given that one's sister did participate () is .662, more than three times as large. As
shown in the last column, the difference betweenandis well over four times its
estimated standard error. Similar results appear if the welfare definition is restricted to
AFDC and general assistance. Then .163 and=.498.so that the latter remains
over three times the former.
The second row shows how these results are affected if the measure of welfare
program participation is whether the woman reported welfare receipt in at least three
different calendar years. With this longer-term measure of welfare receipt, p.216,
and 556. By this measure,is well over four times ,andthe
difference between the two is almost four times its estimated standard error. The
measured sister resemblance becomes sharper still if the welfare definition is restricted to
5See, for example, Duncan and Coe (1984).
6Almost the entire fall is accounted for by the exclusion of food stamps. Very few sample
members received SSI.6
AFDC and general assistance. Then =.151, and =.6O5. Long-term receipt
of AFDC and general assistance is estimated to be over eight times more likely if one's
sister is a long-term recipient than if she is not The evidence of a large discrepancy
between p0 and p1, no matter how they are estimated, implies that something about
sisters' shared background heavily influences the probability of welfare program
participation.
It occurred to us that race might be an especially important component of shared
background. We therefore repeated our analysis separately for nonbiacks and blacks
(using the original measure of whether the woman ever reported welfare receipt). The
results, shown in the third and fourth rows, indicate that blacks do indeed have about
twice as high an unconditional participation rate. Even within race categories, however,
the sister resemblance remains overwhelming. For nonbiacks,=.183and=.607;
for blacks, f= .355and=.801.If the welfare definition is restricted to AFDC and
general assistance, these figures become=.149and=.419for nonbiacks and =
.275and=.677for blacks. Clearly, other shared background characteristics besides
race are influential.
The strikingly large sister resemblance in welfare receipt made us curious also
about the intergenerational correlation in welfare program participation. The last two rows
show the results from an analysis broken down by whether the sisters' parents reported
receiving welfare between 1968 and the time by which both sisters had left home. The
intergenerational relationship is quite noticeable.The estimated unconditional
participation rate is .503 for those whose parents received welfare as compared to .289 for
those whose parents did not receive welfare. The difference is more than twice its
estimated standard error (.093). Again, however, the sister resemblance within categories
remains very large, indeed larger than the measured intergenerational resemblance.
Among those whose parents received welfare, .225 and=.777;among those
whose parents did not receive welfare,=.188and=.537.The corresponding7
estimates under the welfare definition restricted to AFDC and general assistance are
=.156and=.682for those whose parents received welfare and .165 afld
=.412for those whose parents did not. Evidently, daughters' welfare program
participation is influenced by other background characteristics beyond parental welfare
receipt over the time period observed in the data.
Summary and Discussion
All the results in Table 1 display a startling resemblance among sisters in their
welfare program participation. Given welfare eligibility rules in the U.S., this resemblance
in welfare program participation must reflect a resemblance in both income status and
propensity for motherhood without the father present. Indeed, in Solon, Corcoran, Gordon,
and Laren (1987), we have estimated a .5 sister correlation in a measure of permanent
income relative to needs. Also, using the same type of estimation procedure as in the
present paper, we have found a sizable sister resemblance in the probability of having a
child out of wedlock before the age of 20. These findings suggest that the probabilities
of experiencing poverty, single motherhood, and welfare receipt are greatly influenced by
background characteristics shared by sisters.
A full understanding of these results (and identification of appropriate policy
responses) would require an understanding of which background factors are crucial. Is it
that parental income status tends to be passed on to the next generation? Is it that
parents (or communities) instill sisters with common attitudes or values? To what extent
is it simply that sisters tend to live in nearby locations with similar economic conditions
and welfare program options? A few studies, including Rein and Rainwater (1978) and
Hill and Ponza (1986), have made initial attempts to sort out the influences of different
background characteristics on welfare program participation, but the combination of
7Preliminary results for this variable show =.077and 240.8
multicollinearity among the characteristics, measurement error, and omitted-variable
problems makes the achievement of reliable answers a formidable task.9
Table 1
Estimated Probabilities of Welfare Program Participation
(with Estimated Standard Errors)
io
Full sample .371 .199 .662 .463
(.032) (.040) (.071) (.105)
Full sample, .216 .122 .556 .434
three-year partici- (.028) (.033) (.089) (.117)
pation measure
Nonbiacks .318 .183 .607 .424
(.040) (.044) (.110) (.145)
Blacks .641 .355 .801 .446
(.067) (.150) (.079) (.205)
Parents received .503 .225 .777 .552
welfare (.064) (.079) (.092) (.159)
Parents did not .289 .188 .537 .349
receive welfare (.051) (.048) (.125) (.154)10
Appendix
To facilitate half-sample replications, the Survey Research Center has
characterized the PSID sample as consisting of two independent "primary selections" from
each of 32 strata. The pair of selections in the kth stratum might be, say, the PSID
samples from the Milwaukee and Minneapolis areas. The coding of these pairs is
described on pages 89—90 and 310—11 of Survey Research Center (1985). A half-sample
comprised of only one selection from each of the 32 strata more or less duplicates the
complex survey design of the PSID, but at only about half the size.
We used the 32 x32 Hadamard matrix on page 325 of Wolter (1985) to select a
set of 32 "balanced" half-samples. For any parameter ,ifdenotes the estimate from
the full sample andthe estimate from the kth half-sample, we estimate the variance of
.with
32 2
(18) Var (fl.)E (-)132.
k=1
\7Thy is this a sensible estimator of Var ()? Letdenote the estimate of from
the complement of the kth half-sample, and suppose =k+k''2'as is exactly true if
is a linear estimator and is likely to be approximately true otherwise. Then, for any
arbitrary half-sample k,
(19)E(k)2 =E[k
—
(kk1)1'2]2
=
. 2 =E(JLk,) 14
=
= 2Var
=Var()/2= Var(a).
Thus,for any particular half-sample k, the squared deviation of fromis an
approximately unbiased estimator of Var (a).Thepoint of taking 32 different half-
samples and averaging the squared deviations of the 1k from iisto improve the precision
of the variance estimator. The optimal method of choosing "balanced" half-sample
replications is discussed in detail in McCarthy (1969) and Wolter (1985).12
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Sibling and Intergenerational Correlations in Welfare Program Participation

Sibling and Intergenerational Correlations in Welfare Program Participation

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