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Kin availability and the living arrangements of older women
SOCIAL
SCIENCE
RESEARCH
13, 72-89 (1984)
Kin Availability and the Living Arrangements of Older Women DOUGLAS A. WOLF The Urban Institute This paper models the distribution of older women across household types, taking account of variations in the availability of kin, as well as other explanatory variables such as income and race. Household types are distinguished by the presence or absence in the household of siblings, parents, children, or others, including unrelated individuals. A modified multinomial logit model is used to represent the simultaneous effects of kin availability and other variables on the probability of living in each household type. The results indicate that while income is related to the propensity to live alone, the relationship appears to operate solely through the effect of income upon the propensity to share a household with close relatives. Older black women are shown to be more likely to live in extended-family households, holding constant both income and the availabihty of kin.
In recent decades there has been a dramatic increase in the propensity of older people, and especially of older unmarried women, to establish independent living arrangements. For example, while in 1940 13.3% of women aged 65 and older were classified as “primary individuals”persons either living alone or heading a household containing only nonrelatives-by 1970 the corresponding figure was 33.4% (Kobrin, 1976b). Attempts to explain this trend have focused upon two major factors. The first is a demographic trend relating to kin availability. Kobrin (1976a) demonstrates, using aggregate time-series data, a downward trend in the ratio of “daughters” (women aged 35 to 44) per “mother” (divorced or widowed women aged 55 and over) which mirrors the increased prevalence of older female primary individuals. Others have emphasized the role of economic factors as determinants of living arrangements, pointing to the This research has been funded in part with federal funds from the Department of Health and Human Services under contract NOl-HD-12183. The contents of this paper do not necessarily reflect the views or policies of the U.S. government or of The Urban Institute or its sponsors. Thanks are due to Robert Avery, Robin Barnes, William Birdsall, Tom Burch, Julia Ericksen, Tom Espenshade. Terri Murray, and members of the Labor and Household Behavior Workshop at the University of Pennsylvania for their contributions to this work. Requests for reprints should be sent to Douglas A. Wolf, The Urban Institute, 2100 M Street, N.W., Washington, DC 20037. 72 0049-089X/84 $3 .OO Copyright All rights
0 1984 by Academic Pres\. Inc. of reproduction in any form reserved.
LIVING
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WOMEN
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rising income levels enjoyed by society in general (Beresford and Rivlin, 1966) and by the elderly in particular (Michael, Fuchs, and Scott, 1980). Michael et al. are able to explain nearly all of the increase during 19501976 in the propensity of older widows to live alone, using a single income variable: average constant-dollar Social Security benefits. Elsewhere in the existing literature, several studies have attempted to quantify the benefits received by those older people who do live with their relatives. Moon (1977) examines the flows of net cash and in-kind transfer income within family units containing one or more elderly members. She finds that, while a larger share of the elderly are recipients than are contributors of income to relatives with whom they live (16 versus 12%), the average of such intrafamily resource flows is negative, indicating that those elderly who live with kin are net contributors of resources to their younger relatives. Morgan (1978) has also calculated intrafamily transfers, broadening the income concept to include the value of time spent on housework and child care. Morgan’s results, like Moon’s, indicate that older women are net providers of transfers to other family members. Morgan’s results, however, are not presented separately for women who do and do not live with relatives other than a spouse. Taken together, these previous studies suggest that kin availability, financial resources, and the distribution of older people by household type are interrelated. Yet, few existing studies have attempted to encompass all three phenomena, and it is this gap that the present paper seeks to fill. This study examines the determinants of the distribution of older unmarried women among several categories of living arrangementsliving alone, living with relatives, and living with others-while controlling for kin availability as well as other explanatory variables. The need to take account of the variation across individuals in the existence of kin, and hence the variation in opportunities to adopt certain living arrangements, poses a methodological problem which, as is shown below, can be readily solved using existing analytic techniques, The paper is organized as follows. In the next section the relevant literature is reviewed. This is followed by a discussion of the methodology of the present study. A final section describes the data used, and presents and discusses the findings. PREVIOUS
RESEARCH
Several previous studies have analyzed factors which influence the living patterns of the elderly, including, in addition to those studies cited in the first paragraph, the work of Soldo and her associates (Soldo, 1977; Soldo and Lauriat, 1976; Soldo and Myers, undated; Soldo, Sharma, and Campbell, 1983), Chevan and Korson (1972), Tissue and McCoy (198I), and Schwartz, Danziger, and Smolensky (1983). These analyses have established associations between living arrangements and income, health status, and race. However, most studies of the living arrangements of
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A. WOLF
the elderly have not controlled for variations in kin availability. Notable exceptions include the work of Shanas and her associates (Shanas, Townsend, Wedderburn, Friis, Milhoj, and Stehouwer, 1968; Shanas, 1978) and Bachrach (1980). Surveys of the U.S. elderly conducted by Shanas in 1957, 1962, and 1975 obtained information on the existence and number of living relatives in various categories. Shanas et al. (1968) present findings based upon the 1962 data which illustrate the role of available kin in determining household structure. For example, among those elderly of both sexes who were never-married, widowed, divorced, or separated (hereafter, “unmarried”), 26% of those with one living son (and no other children) lived with their child, while 46% of those with one daughter lived with her; 44% of those with two or more children lived with a child (Shanas et al., 1968, Table VI-18a). The corresponding figures from the 1975 survey show sharp declines in all three measures: 17% of unmarried individuals with one son only, 19% of those with one daughter only, and 26% of those with two or more living children lived with a child (Shanas, 1978, Table 6-8A). Shanas’s data also reveal differences in the distribution of the elderly among other household types, such as living with siblings, living with other relatives, and living with nonrelatives, according to the number and sex of living children, and the sex and marital status of the respondent. Bachrach’s (1980) study focuses upon the relationship between number of living children and living arrangements in a sample of 1328 individuals aged 65 or older in 1974. Bachrach employs two alternative measures of living arrangements, a binary-coded variable (living alone versus living with others) and a multiple-coded variable (living alone, living with offspring only, living with other relatives only, living with offspring and other relatives, living with friends, living with others of unknown relationship). Both measures of living arrangements are revealed by tabular analyses to vary according to the number of living children. Bachrach also analyzes the binary-coded living arrangements variable using a regression equation which controls for several social, demographic, and current resource variables in addition to number of living children. All of the regression coefficients representing the effects of number of living children upon the probability of living alone are statistically significant. Bachrach includes one other measure of available kin-the number of living siblings-which proves to be insignificantly related to the probability of living alone in her sample. Bachrach’s multivariate analysis also reveals a greater probability of living alone among older women than among older men. Also relevant to the present study are several analyses of racial differentials in the formation of extended-family households. Black-white differentials in the incidence of extended-family households have been well documented [see, for example, the review article by Lee (198O)l
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and shown in some studies to persist when income levels are held constant (Allen, 1979; Hays and Mindel, 1973). Recent studies have extended this result, demonstrating significant net-of-income household-composition differentials among blacks, non-Hispanic whites, and several subgroups of Hispanics distinguished by country of origin (Angel and Tienda, 1982; Tienda and Angel, 1982). While the studies cited in this paragraph bear only indirectly upon the elderly population, they nevertheless suggest that race may be an important determinant of the living arrangements of older women. However, like most other previous work, these studies have failed to control for the availability of kin. METHODOLOGY As mentioned in the introduction, this study employs a multichotomous representation of household composition, distinguishing among the categories living alone, living with relatives, and living with others. With such a dependent variable, we wish to characterize the probability of being observed in each category, conditional upon the values of a set of explanatory variables, including kin availability. The special feature of the present problem is the fact that for certain patterns of kin availability, one or more of the categories of household composition may be ruled out (i.e., have a probability of zero). Therefore, we require an analytic technique which permits explanatory variables to be related to the propensity to live in each of several household types, while simultaneously providing for variation, within a sample of older women, in the set of household types that are feasible. Although alternative techniques are possible, this study uses-partly for reasons of computational convenience-a modified multinomial logit specification. In order to make the following discussion more concrete, the model is specified in terms of the variables actually used in the subsequent empirical analysis. Other potential applications of the general technique are noted in the summary. In this study, which focuses upon unmarried women aged 65 to 69, kin availability is measured by the two variables SP, which equals one if the woman has living siblings and/or parent(s) (family-of-origin kin), and zero otherwise; and C, which equals one if the woman has any living children (family-of-procreation kin), and zero otherwise. Thus, there are as many as five mutually exclusive household types among which a sample woman might be observed: (1) living alone; (2) living with others, but not with siblings, parents, or children; (3) living with siblings and/ or parents (but not children); (4) living with children (but not siblings or parents); and (5) living with siblings and/or parents as well as children.’ ’ Note that these household types do not reflect the concept of household headship, but merely the relationships among individuals sharing a dwelling unit; the notion of dependency is not addressed in this study.
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DOUGLAS
A. WOLF
Categories (1) and (2) are assumed to be universally feasible, while the feasibility of (3) through (5) is conditioned by the availability pattern of living kin. The distinct configurations of kin availability and the relationship between kin availability and potential household types is summarized in panel A of Table 1. It bears emphasis at this point that the concept of kin “availability,” as used in this analysis, refers only to the existence of certain relatives, and not to any of their other attributes, such as the proximity, income, or household structure of each individual in the available-kin pool. Proximity to kin, in particular, has been shown by previous research to be an important aspect of the living-arrangement decisions of older women. In a cross-sectional study such as this one, however, proximity to kin is an aspect of the dependent variable-a decision to live in the same dwelling as a relative is, equivalently, a decision to make “distance to nearest relative” equal to zero. To incorporate proximity to kin into the present study, whether measured using a continuous or interval-valued variable, would greatly complicate the estimation: for this reason, the issue is not pursued further.
Relationships
TABLE 1 between Kin Availability and Potential Household Type Available kin configurations
Values of kinavailability variables:
A
B
C
D
SP
0
c
0
1 0
0 1
I 1
X
X
X
X
X
X
A. Basic specification Potential household types (HHTYPE): x Living alone” (1) Living with “others” only (2) X Living with siblings/parents (3) Living with children (4) Living with siblings/parents and children (5) B . Expanded specification Category designations of potential household types: Living alone Living with “others” only Living with siblings/parents Living with children Living with siblings/parents and children a x indicates configuration.
the feasibility
of a particular
household
X
X X
X X
lB 28 38
lC 2c 4=
lD 2O 3D 4D SD
type, given an available-kin
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Jn order to specify the model, we need the following additional notation. First, let HHTYPE represent the five-category dependent variable, with HHTYPE = 1,. . .,5 as indicated in the previous paragraph (and Table 1). Then, define five “feasibility” indicators, &, such that fj = 1 if category j of HHTYPE is a feasible household type for observation i. That is, ifSPi = 1andC; = 0, .ti = :, otherwise; and so on (see Table 1); as mentioned before, fir, = fi2 = 1 for all i. Then, the probabilities that i will be observed in each of the five categories of HHTYPE, conditional upon an n-vector, Xi, of explanatory variables, are of the form Pi(k) = Pr(HHTYPE;
5Ak exP(Zik 1 , k = 1,. . .,5;
= k) =
(1)
klE, J;.k ew(zik) where the Zik'S are logistic “index functions” of the fOrIn Zik = ak + PlkJil + * * * + Pupin, Or (Yk + B~i.* Within a given configuration of available kin (columns A to D in Table l), Eq. (1) is a straightforward multinomial logit model.3 Because the parameters of the household-type probabilities (the (Yk’s and @k’s) are independent of kin availability, Eq. (1) represents the most restrictive model of the relationship between the full X-vector and the householdtype probabilities4 Equation (1) is a restrictive model in the sense that some possible interaction effects of the kin-availability variables are ruled out. To see this, consider the probability of living with “others” for (a) someone with no living kin (that is, SPi = 0 and Cj = 0), which (with zI normalized to 0) is 1
ew(z2
1 + ev(zi2) and (b) someone with living children only (SPi = 0) and Ci = l), which is exPtZi2) 1 +
While the probabilities
exP(Zd
+
exP(Zi4)
are different, the log-odds of living with “others”
2 In this study the normalization rule a, = PI - 0, required in order to identify a unique set of logit coefficients, is imposed. 3 Available-kin configuration A-with SP = 0 and C = O-generates a binary logit model. 4 More restrictive specifications than (1) are, of course, possible, if a priori information is used to constrain the values of some of the ok’s and pk’s.
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DOUGLAS
A. WOLF
versus living alone, which equals za in both cases, is independent of kin availability. The appropriateness of such an independence assumption is a matter for both theoretical and empirical investigation. As we show below, more general specifications are possible. At the other extreme of model generality (within the basic framework under consideration) is a specification in which a separate set of parameters is assumed for each distinct available-kin configuration. That is, we associate with each category of household type, and with each corresponding parameter vector, an additional index denoting the distinct available-kin configuration within which that category is feasible. This more general, “stratification,” model is equivalent to the specification of four separate multinomial logit models, one for each of the sample strata, or distinct available-kin configurations implied by the variables SP and C. However, the general model can also be formulated as a single, modified multinomial logit model, using the feasibility-indicator approach described earlier. To see this, consider the expanded dependent variable HHTYPE”, with 14 categories, shown as lA, lB,. . ., 2*, 2’,. . ., 4O, 5D in panel B of Table 1. Now, the category designation of the dependent variable indicates not only the household type in which the older woman is observed to live, but the other household types in which she could be observed as well. In choice-theoretic language, the label attached to each potential outcome indicates not only which outcome was chosen, but which outcomes were rejected as well. However, since we must impose the normalization zy = 0 (or an equivalent normalization) for each m, the distinctions between categories lA, lB, I’, and lD vanish, leaving us with a lo-category model, in which HHTYPE = 1 is a universally feasible category. As before, we define 10 feasibility indicators fl,j = 1 3. . *,5., m = A,. . .,D, and adopt a modified multinomial logit specification for the expanded outcome set, with probabilities defined by the equation (2)
The model specified by Eq. (2) represents a complex alternative hypothesis against which the more parsimonious, and more readily interpreted, ’ Yet another specification, mathematically equivalent to (2), can be obtained by retaining the original five-category HHTYPE variable, but defining the interaction variables X, * SP,, Xi * Ci, and X, * SP, * C,, and expanding the zj’s of (1) to include all of these interaction terms as explanatory variables. This approach necessitates numerous exclusion restrictions in the parameter vectors, due to the implicit information regarding the values of SP, and C, that is conveyed by the HHTYPE-category designations.
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model embodied in Eq. (1) can be tested.6 Intermediate levels of model complexity can also be tested, and are specified by imposing equality constraints upon the parameters implicit in Eq. (2). One particularly simple such intermediate model, estimates for which are presented in the following section, permits only the intercepts of each subgroup of the 10 zz’s to differ (and, hence, to reflect interactions or “cross-effects” among the available-kin indicators). This intermediate-level model is obtained by imposing equality constraints of the form g = @ = B; = Bf, Bf = Bf, and so on. Equivalently (see footnote 5), such a model can be estimated by appropriate additions of the available-kin indicators to Eq. (I), as zi2 = (YZ~+ a**SPi + (~23Ci + a24SP; * C; + B&i, Zn
=
a31
Zi4
=
(Y41
Zi5
=
as1
+ +
a33ci
ff4*SPi
+
B&iv
+
Bkxi,
(3)
and + BSi.
The number of parameters to be estimated in (3) is 9 + 4n. Since the basic model presented in (l), the full-interaction model (2), and intermediate models, of which (3) is an example, are nested models, they can be tested against each other using likelihood-ratio techniques. We now turn to an application of these models to data on the living arrangements of older unmarried women. EMPIRICAL
ANALYSIS
Source of Data The data used in this study are taken from the Retirement History Survey (RHS), a multiyear survey sponsored by the Social Security Administration. The RHS provides data on a sample of 11,153 noninstitutionalized persons born between 1905 and 1911, and aged 58 to 63 in 1%9. Respondents were first interviewed in 1%9, and were reinterviewed semiannually through 1979. In 1971 and subsequent years, interviews were attempted with the surviving spouses of deceased previous respondents. Sample attrition due to death, failure to relocate respondents, or other reasons had reduced the original sample to approximately 8700 by 1975. The RHS is an unusually rich source of information on both household structure and the existence and characteristics of kin living elsewhere. ’ With n explanatory variables and an intercept appearing in each z~, and with cy, and p, set to zero, Eq. (1) has 4 (1 +n) unknown parameters; in contrast, Eq. (2) specifies a model with 9 (1 +n) unknowns.
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A. WOLF
For each household member, the data include age, sex, detailed relationship to respondent (distinguishing, for example, among children, grandchildren, parents, stepparents, in-laws, and siblings), and marital status. Moreover, one can construct fairly detailed measures of the number and types of a respondent’s living kin. Unfortunately, several important characteristics of individual kinship members, such as their age and economic status, are not measured. Finally, in addition to information on available kin and living arrangements, extensive background information on topics such as labor market behavior, job characteristics, retirement, health, and income are available.7 Sample Selection and Variable Definition The analysis presented in this paper is restricted to unmarried women aged 65 to 69 in 1975. The household-type (HHTYPE) and kin-availability (SP and C) variables were defined in the previous section.8 Parents and siblings are combined into a single family-of-origin category of available kin, spanning two generations, because so few of the women in this age group have one or more living parents. In fact, 93% of those coded as having living siblings and/or parents in this sample have living siblings only. The independent variables used in this analysis consist of measures of disability status, race, home ownership, marital status, age, and income. A dummy variable (DISABLED) is used to indicate affirmative responses to the question, “Do you have any health condition, physical handicap, or disability that limits how well you get around?” Additional dummy variables indicate home ownership (OWNHOME), blacks (BLACK), women whose current marital status is separated or divorced (DIVORCED), and women aged 68 or 69 (AGE). Income is measured as the sum of income received from the following sources: rent, dividends, interest, pensions, disability or workmen’s compensation programs, and social security. These sources of income are “portable” across different living arrangements, in the sense that they are independent of the actual category of living arrangements in which a woman appears. Other sources of income, including earnings, Supplemental Security Income and other welfare payments, and contributions from relatives living elsewhere, are excluded in order to guard against possible simultaneity biases, since the level of income from such sources itself depends upon living arrangements. Descriptive statistics for this sample are shown in Table 2. The sample of unmarried women was further divided into never-married and ever’ For further information on the RHS, see lrelan and Schwab (1981). * It should be noted that HHTYPE is coded hierarchically, with the presence of relatives taking priority over the presence of “others”; thus, for example, a woman living with children (but not siblings/parents) is coded as HHTYPE = 4 whether or not “others” are also present in the household.
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OF OLDER WOMEN
TABLE 2 Mean Values of Variables Used in Analysis Ever-married women (n = 1515) Distribution of dependent variable (HHTYPE) (1) Living alone (2) Living with others (3) Living with siblings/parents (only) (4) Living with children (only) (5) Living with siblings/parents and children Mean values of available-kin variables Has living siblings/parents (SP= 1) Has living children (C= 1) Has living siblings/parents and children (SP=l and C=l) Mean values of independent variables” DISABLED OWNHOME BLACK DIVORCED AGE INCOME a All variables except INCOME
Never-married women (n = 275)
.66 .08 .06 .20 .Ol
.56 .09 .36 -
.86 .81
.89 -
.71 .40 .50 .15 .18 .43 $2834
.29 .44 .06 .38 $3798
are dummy variables; for variable definitions see text.
married women. Six never-married women who reported that they had living children (either living with them or elsewhere) are excluded from the present analysis. As a result, living arrangement categories which include children (HHTYPE = 4 or 5) are ruled out for the never-married women. The figures in Table 2 show that ever-married women are more likely to live alone than are never-married women (66 versus 56%), and less likely to live with relatives than are never-married women (27 versus 36%). The proportions living with “others” were about equal for both marital-status groups. Turning to the available-kin variables in Table 2, we see that 89% of the never-married women had living siblings and/or parents; thus, for the never-married women, three categories of the living arrangements variable-living alone, living with siblings/parents, and living with othersare feasible for 89% of the sample, while only two categories-living alone and living with others-are feasible for the remaining 11%. Among ever-married women, 86% had living siblings and/or parents, while 71% had siblings/parents and living children; therefore 15% (86 minus 71) had living siblings/parents but not children. A similar calculation reveals that 10% had living children but not siblings/parents. Five percent of the evermarried women had no living siblings, parents, or children; for these
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DOUGLAS
A. WOLF
TABLE 3 Summary Statistics and Likelihood-Ratio Tests for Alternative Models, Ever-Married Women Value of likelihood function at maximum
Specification (number of parameters) A. Models estimated Basic model (28) Basic model plus: (a) Intercept shifts (33) (b) Intercept shifts plus race interactions (38) (c) Intercept shifts plus income interactions (38) Full-interaction model (63)
(1) (II)
(III)
B. Likelihood-ratio
IIa IIb IIc III
versus versus versus versus
- 1356.01 - 1357.46 - 1344.88 Chi square statistic (degrees of freedom)
I IIa IIa IIa
29.06 6.36 3.46 28.62
women, only two categories of the living arrangements alone and living with others-are feasible. Results I: Ever-Married
- 1359.19
tests
Models compared (1) (2) (3) (4)
- 1313.72
(5) (5) (5) (30)
variable-living
Women
For the sample of ever-married women, several alternative models, varying in their degree of generality-that is, in the extent to which available-kin interactions are permitted-were estimated, and the results of these alternative specifications are summarized in Table 3 .9 In addition to the basic model [using the specification of Eq. (l), shown as model I in Table 31 and the full-interaction model [based on Eq. (2) and shown as model III in Table 31, three intermediate-level models were estimated: model IIa, in which the slopes, but not the intercepts, of the z functions pertaining to a given household type were equalized across available-kin configurations [that is, the model shown earlier as Eq. (3)]; model IIb, in which, in addition, race effects were permitted to vary by availablekin configuration; and model IIc, in which income effects (but not race effects) were permitted to vary by available-kin configuration. Based upon the likelihood-ratio test statistics shown in part B of Table 3, model IIa provides a significant improvement over the basic model 0, < .005), 9 The models were estimated using a slightly modified version of the CRAWTRAN computer program (Avery, 1980).
LIVING
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while none of the more complicated models tested led to significant improvements over model IIa in terms of overall fit. The acceptance of model IIa, against more complicated alternative hypotheses, is a pleasing result in that model IIa is a considerably more parsimonious model than its full-interaction alternative. The estimated parameters of model IIa are shown in Table 4. These parameters are to be interpreted as the effect of a change in an independent variable upon the relative probabilities of living in the indicated household type (the column headings of the table) and living alone (the reference category), given the feasibility of the household type in question. Several interesting findings appear in Table 4. Income, which has been shown TABLE 4 Parameters of Logit Model for Ever-Married
Women (Model Ha)
Category of HHTYPE
(2)
“Others”
(3)
(4)
Siblings/ parents only
Children only
(5) Siblings/ parents and children
(.391)*** (2.79)*** - .623 (4.34)*** ,539 (2.69)*** - .449 (2.34)** - .245 (1.73)* - .082 (2.36)** - ,632 (2.52)***
(.033)*** (.05) ,573 (.82) 1.78 (2.59)*** ,687 (.93) ,335 t.511 -.I34 (.65) -4.95 (5.37)***
,106 (.50)
-
-
-
-
-
Independent variables” DISABLED OWNHOME BLACK DIVORCED AGE INCOME
(1000s)
Intercept Intercept-shifts SP
c SP * c
a * ** ***
(.180)***
(.066)***
C.88)
t.28)
- .343 (1.68)* 1.25 (5.34)*** -.143 (.55) .016 (.W - .027
- .239 (1.05) - ,018 (.05) ,187
(.W -2.20 (4.39)*** - .225 (.45) .267 (.53) - .063 (.lI)
(.68) - .298 (1.31) - Jo5 (.15) -1.20 (4.18)***
- 1.186 (5.18)***
-
Absolute values of t statistics in parentheses. Significant at .lO level. Significant at .05 level. Significant at .Ol level.
84
DOUGLAS
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in numerous previous studies to be a significant predictor of household composition-usually, based upon a binary living alone/not living alone measure of household composition-is shown here to be related (negatively) only to the relative probability of living with children. Thus, we would conclude, on the basis of these results, that among unmarried women without living children, parents, or siblings (women for whom only the first column of parameters are relevant), income is unrelated to household composition. Income is also, apparently, unrelated to decisions regarding coresidence with living siblings and/or parents. The results in Table 4 imply an income elasticity of the propensity to live alone, calculated as the weighted sum of the income elasticities in each available-kin configuration, evaluated at the appropriate subsample means, of only .053. This elasticity is far below that calculated by Michael et al. (1980)1.0”based upon state-level aggregate data for widows aged 65 and over. At least part of the reason for this difference is the fact that the present analysis takes more careful account of kin availability.‘” Most of the significant parameters shown in Table 4 are found in the “living with children” column, although this may in part be due to the lower sample frequencies of the other three categories of the dependent variable. It is interesting to note that in category 5, the only significant parameter indicates the greater propensity of black women to adopt this household type. Black women are also found to be more prone to live with “others,” controlling for kin availability.” Since this mode1 controls both for income and kin availability, these findings lend further support to those studies that have demonstrated persistent net racial differentials in the formation of extended-family households. One might conjecture that the race effects shown in Table 4 reflect differential opportunities to share households, rather than an unmeasured race-specific effect, if blacks with living siblings (children) have more siblings (children), on average, than do whites with living siblings (children). Yet the mean number of living siblings among blacks with living siblings is 2.8, somewhat lower than the corresponding mean of 3.1 for whites. The mean number of living children, among those with any living children, is larger for blacks than for whites: 3.4 versus 3.0. However, while black women have, on average, 13% more children than white women, they are 46% more likely to live with a child, given the feasibility of doing so. There are other candidates for the omitted variable or variables which ‘” When the sample of ever-married women is used to estimate a binary living-alone/ not-living-alone model, disregarding kin availability but otherwise identical to model Ha. the resulting income elasticity of the propensity to live alone is .12, more than twice that obtained from the more complex model. ” Recall that in model IIb, we found no significant interaction effects between race and the available-kin variables, within either the “living with others.” “living with parents/ siblings,” or “living with children” parameter vectors.
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85
would, if included, eliminate the significant race differences in household behavior shown in Table 4. Among these variables are attributes of the available kin such as their age, health status, marital status, and income. Given the limitations of data currently available, these issues must be addressed in future research. The intercept-shift parameters shown at the bottom of Table 4 represent the “interactive” effects of kin availability. These effects are shown as differences between the intercept reported in each column and the corresponding intercept of an expanded, available-kin configuration-specific model. Thus, for example, the constant in zz--the living-with-others index for available-kin configuration A (SP = 0 and C = O)-is - 2.20, while the constant in zj-the living-with-others index for available-kin configuration B (SP = 1 and C = 0) is -2.20 - .225 = -2.425. Shown as differences, the available-kin intercept shifts indicate more readily the effect of variations in kin availability upon the household-type distribution. Also, the t statistics shown for these shift parameters pertain to the differences between intercepts. The results indicate that the relative probabilities of living with “others” and living alone are independent of the kin-availability variables (judged by the t statistics for the intercept shifts in the first column of Table 4). However, the relative probabilities of living with siblings/parents and living alone are significantly reduced by the existence of living children. This reduction presumably reflects both the competing obligations for providing support, and the expanded opportunities for receiving support, associated with having children. Thus, we find evidence of interactions among the variables measuring kin availability, but these interaction effects are confined to the relative probabilities of living with relatives and living alone. Results II: Never-Married
Women
Due both to the smaller sample size and reduced variability in availablekin configurations among never-married women, only the basic model was estimated for this subgroup. The logit parameters for this model are presented in Table 5. The only available-kin variable defined for the never-married women is SP, indicating the existence or nonexistence of siblings and/or parents. Hence, only categories 1 (living alone), 2 (living with others), and 3 (living with siblings/parents) of the dependent variable HHTYPE are relevant in this sample. Also, the DIVORCED variable is not used in this sample, being irrelevant to never-married women. Some of the parameters shown in Table 5 reveal similarities in the behavior of ever-married and never-married women. First, with both groups of women the previously established positive relationship between income and the propensity to live alone appear to hold only when living
86
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TABLE 5 Parameters of Logit Model for Never-Married
Women
Category of HHTYPE
(2) Others
(3) Siblings/parents
Independent variable” ( - .337)*** DISABLED
t.63) -.154 (.33) 1.85 (2.53)** .855 (1.86)** .052
OWNHOME BLACK AGE INCOME Intercept a * ** ***
(1000s)
t.87) -2.46 (5.11)***
(- .olo)** (.032) ,548 (1.91)* - .026 (.04) .613 (2.15)** -.I17 (2.59)** - .328 (1.23)
Absolute values of r statistics in parentheses. Significant at .lO level. Significant at .05 level. Significant at .Ol level.
with nuclear-family relatives is compared to living alone; income bears no relationship to the propensity to live with other than nuclear-family kin in this sample. Second, black women have relatively strong propensities to live with relatives other than siblings, parents, or children, and with unrelated people, as well as with available kin. This implies that if older black women with no living kin were compared to older women of other races, also with no living kin, the blacks would be more likely to be living in shared households, other variables held constant. However, there are some contrasts revealed by Tables 4 and 5 as well. Notably, home ownership is unrelated to the propensity to live with siblings/parents among ever-married women, but strongly positively related to living with siblings/parents among never-married women. In the case of never-married women, home ownership may be associated with greater residential stability (both retrospectively and prospectively) and thus a more likely setting for the care of an elderly parent or dependent sibling. Summary
This paper has examined factors influencing the distribution of older unmarried women across household types, with the household types distinguished by the presence or absence of selected kinds of relatives. This approach to the study of household structure necessitates an analytic
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methodology whereby differences across individuals in the array of living kin are taken into account. The models discussed in this paper, while formulated narrowly in terms of this substantive focus, are potentially useful for the analysis of other demographic, sociological, or economic phenomena as well. For example, spells of unemployment may be ended in one of three ways-by the start of a new job, by exit from the labor force, or by recall to the previous job-but the third such outcome is impossible for those whose unemployment spell is due to a plant closing. The results presented here include some findings which confirm those of earlier studies and include some which are new. These results indicate that black women have a greater propensity to form extended-family households than do women of other races, holding constant their financial resources (both income flows and wealth, represented by home ownership). However, we have also shown that black women have a greater relative propensity to live with “others” as well-holding constant their opportunities for living with relatives.]* Kin availability itself affects living arrangements both directly and indirectly, in the model used here. It is mechanically (and trivially) true that the probability of living with kin is higher when kin are available, since the corresponding probability when kin are unavailable is zero. It is more illuminating to calculate the effects of kin availability upon the probability of living alone; this probability (at the sample mean, in the ever-married sample) is .86 for those with neither living children nor siblings/parents, dropping to .74 if siblings/ parents only are living, .66 if children only are living, and .63 if kin in both categories are living. We also found some evidence of direct interactive effects of kin availability upon the probabilities of living in shared households: the findings indicate that the existence of children significantly reduced the odds of living with siblings/parents only (given the existence of siblings and/or parents), other factors held constant. The indirect effects of kin availability upon living arrangements arise because the effects upon the probabilities of each feasible household-type category of all other explanatory variables in the model are conditional upon the full set of available-kin indicators. As an illustration of these indirect effects, the calculated slope of the relationship between income and the probability of living alone is .0033 for ever-married women with neither children or siblings/parents, .0023 for those with siblings/parents but no ‘* It should be remembered that the “living with others” category of HHTYPE includes women living with relatives other than parents, siblings, or children4.g.. aunts, uncles, grandchildren-as well as those living with nonrelatives. For ever-married women, the “living with others” differential for blacks may in fact reflect primarily households in which grandchildren are present; this phenomenon is, however, much less likely for the essentially childless never-married women, among whom the same “living with others” differential for blacks was found.
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children, and .0147 for those with children (whether or not they also have living siblings/parents). I3 Finally, the results presented here confirm earlier findings regarding the inverse relationship between income and the sharing of a household, but only in selected instances: for ever-manied women, the effect emerges only for the living-with-children parameter, and for never-married women, the effect appears only for the living-with-siblings/parents parameter. Overall, the findings of this study suggest that the process by which the elderly sort themselves among the array of household types available to them is a complex one, albeit one that can be modeled in a reasonably parsimonious way. A major further advance in our understanding of the process could be gained if data were available which provided measures not only of the financial and health circumstances of the elderly, and of the pattern of living relatives available to them, but of the financial and health circumstances of these available kin as well. REFERENCES Allen, W. R. (1979), “Class, culture, and family organization: The effects of class and race on family sturcture in urban America,” Journal of Comparative Family Studies 19(Autumn), 310-313. Angel, R., and Tienda, M. (1982), “Determinants of extended household structure: Cultural pattern or economic need?” American Journal of Sociology 87(May), 1360-1383. Avery, R. B. (1980), Qualitative Dependent Variable Program CRAWTRAN, unpublished manuscript, Carnegie-Mellon University. Bachrach, C. A. (1980), “Childlessness and social isolation among the elderly,” Journal of Marriage and the Family 42(August), 627-636. Beresford, J. C., and Rivlin. A. M. (1966), “Privacy, poverty, and old age,” Demography 3(August), 247-258. Chevan, A., and Korson, J. H. (1972), “The widowed who live alone: An examination of social and demographic factors,” Social Forces 51(September), 45-54. Hays, W. C., and Mindel C. H. (1973), “Extended kinship relations in black and white families,” Journal of Marriage and the Family 35(February), 51-57. Irelan, L. M., and Schwab, K. (1981), “The Social Security Administration’s Retirement History Study,” Research on Aging 3(December). 381-386. Kobrin, F. E. (1976), “The fall in household size and the rise of the primary individual in the United States,” Demography 31(February), 127-138. (a) Kobrin, F. E. (1976), “The primary individual and the family: Changes in living arrangements in the United States since 1940,” Journal of Marriage and the Family S(May), 233238. (b) Lee, G. R. (1980), “Kinship in the seventies: A decade review of research and theory,” Journal of Marriage and the Family 42(November), 923-934. Michael, R. T., Fuchs, V. R., and Scott, S. R. (1980), “Changes in the propensity to live alone: 1950-1976,” Demography 17(February), 39-56. ” These slopes are calculated by differentiating Eq. (1) with respect to a particular explanatory variable. The resulting expression depends upon the values of all the explanatory variables in the model; for the examples given, the expression has been evaluated at the sample mean of the explanatory variables.
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Moon, M. (1977), The Measurement of Economic Welfare: Its Application to the Aged Poor, Academic Press, New York. Morgan, J. N. (1978), “Intra-family transfers revisited: The support of dependents inside the family,” in Five Thousand American Families-Patterns of Economic Progress (Duncan and Morgan, Eds.), Vol. 1, Survey Research Center, The University of Michigan, Ann Arbor. Schwartz, S., Danziger, S., and Smolensky, E. (1983), The Choice of Living Arrangements by the Elderly, Brookings Institution, Washington, DC. Shanas, E. (1978), A National Survey of the Aged, Final report to the Administration on Aging, U.S. Department of Health, Education, and Welfare. Shanas, E., Townsend, P., Wedderbum, D., Friis, H., Milhej, P., and Stehouwer, J. (1968) Old People in Three Industrial Societies, Atherton Press, New York. Soldo, B. J. (1977), The Role of Demographic Composition in Accounting for Changes in the Distribution of Living Arrangements among the Elderly: 1960-1970, presented at the annual meeting of the Population Association of America. Soldo, B., and Lauriat, P. (1976), “Living arrangements among the elderly in the United States: A loglinear approach,” Journal of Comparative Family Studies 7(Summer). 351-366. Soldo, B. J., and Myers, G. C. (undated), Structural Profiles of Living Arrangements among the Elderly: 1970, Center for Demographic Studies Working Paper 1, Duke University. Soldo, B. J., Sharma, M., and Campbell, R. T. (1983), The Effects of Functional Health Status and Demographic Characteristics on the Living Arrangements of Older Unmarried Women, presented at the 1981 annual meeting of the Population Association of America (revised). Tienda, M., and Angel, R. (1982), “Headship and household composition amongblacks, Hispanics, and other whites,” Social Forces Bl(December), 508-531. Tissue, T., and McCoy, J. L. (1981), “Income and living arrangements among ,poor aged singles,” Social Security Bulletin 44(April), 3-13.
SCIENCE
RESEARCH
13, 72-89 (1984)
Kin Availability and the Living Arrangements of Older Women DOUGLAS A. WOLF The Urban Institute This paper models the distribution of older women across household types, taking account of variations in the availability of kin, as well as other explanatory variables such as income and race. Household types are distinguished by the presence or absence in the household of siblings, parents, children, or others, including unrelated individuals. A modified multinomial logit model is used to represent the simultaneous effects of kin availability and other variables on the probability of living in each household type. The results indicate that while income is related to the propensity to live alone, the relationship appears to operate solely through the effect of income upon the propensity to share a household with close relatives. Older black women are shown to be more likely to live in extended-family households, holding constant both income and the availabihty of kin.
In recent decades there has been a dramatic increase in the propensity of older people, and especially of older unmarried women, to establish independent living arrangements. For example, while in 1940 13.3% of women aged 65 and older were classified as “primary individuals”persons either living alone or heading a household containing only nonrelatives-by 1970 the corresponding figure was 33.4% (Kobrin, 1976b). Attempts to explain this trend have focused upon two major factors. The first is a demographic trend relating to kin availability. Kobrin (1976a) demonstrates, using aggregate time-series data, a downward trend in the ratio of “daughters” (women aged 35 to 44) per “mother” (divorced or widowed women aged 55 and over) which mirrors the increased prevalence of older female primary individuals. Others have emphasized the role of economic factors as determinants of living arrangements, pointing to the This research has been funded in part with federal funds from the Department of Health and Human Services under contract NOl-HD-12183. The contents of this paper do not necessarily reflect the views or policies of the U.S. government or of The Urban Institute or its sponsors. Thanks are due to Robert Avery, Robin Barnes, William Birdsall, Tom Burch, Julia Ericksen, Tom Espenshade. Terri Murray, and members of the Labor and Household Behavior Workshop at the University of Pennsylvania for their contributions to this work. Requests for reprints should be sent to Douglas A. Wolf, The Urban Institute, 2100 M Street, N.W., Washington, DC 20037. 72 0049-089X/84 $3 .OO Copyright All rights
0 1984 by Academic Pres\. Inc. of reproduction in any form reserved.
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OLDER
WOMEN
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rising income levels enjoyed by society in general (Beresford and Rivlin, 1966) and by the elderly in particular (Michael, Fuchs, and Scott, 1980). Michael et al. are able to explain nearly all of the increase during 19501976 in the propensity of older widows to live alone, using a single income variable: average constant-dollar Social Security benefits. Elsewhere in the existing literature, several studies have attempted to quantify the benefits received by those older people who do live with their relatives. Moon (1977) examines the flows of net cash and in-kind transfer income within family units containing one or more elderly members. She finds that, while a larger share of the elderly are recipients than are contributors of income to relatives with whom they live (16 versus 12%), the average of such intrafamily resource flows is negative, indicating that those elderly who live with kin are net contributors of resources to their younger relatives. Morgan (1978) has also calculated intrafamily transfers, broadening the income concept to include the value of time spent on housework and child care. Morgan’s results, like Moon’s, indicate that older women are net providers of transfers to other family members. Morgan’s results, however, are not presented separately for women who do and do not live with relatives other than a spouse. Taken together, these previous studies suggest that kin availability, financial resources, and the distribution of older people by household type are interrelated. Yet, few existing studies have attempted to encompass all three phenomena, and it is this gap that the present paper seeks to fill. This study examines the determinants of the distribution of older unmarried women among several categories of living arrangementsliving alone, living with relatives, and living with others-while controlling for kin availability as well as other explanatory variables. The need to take account of the variation across individuals in the existence of kin, and hence the variation in opportunities to adopt certain living arrangements, poses a methodological problem which, as is shown below, can be readily solved using existing analytic techniques, The paper is organized as follows. In the next section the relevant literature is reviewed. This is followed by a discussion of the methodology of the present study. A final section describes the data used, and presents and discusses the findings. PREVIOUS
RESEARCH
Several previous studies have analyzed factors which influence the living patterns of the elderly, including, in addition to those studies cited in the first paragraph, the work of Soldo and her associates (Soldo, 1977; Soldo and Lauriat, 1976; Soldo and Myers, undated; Soldo, Sharma, and Campbell, 1983), Chevan and Korson (1972), Tissue and McCoy (198I), and Schwartz, Danziger, and Smolensky (1983). These analyses have established associations between living arrangements and income, health status, and race. However, most studies of the living arrangements of
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the elderly have not controlled for variations in kin availability. Notable exceptions include the work of Shanas and her associates (Shanas, Townsend, Wedderburn, Friis, Milhoj, and Stehouwer, 1968; Shanas, 1978) and Bachrach (1980). Surveys of the U.S. elderly conducted by Shanas in 1957, 1962, and 1975 obtained information on the existence and number of living relatives in various categories. Shanas et al. (1968) present findings based upon the 1962 data which illustrate the role of available kin in determining household structure. For example, among those elderly of both sexes who were never-married, widowed, divorced, or separated (hereafter, “unmarried”), 26% of those with one living son (and no other children) lived with their child, while 46% of those with one daughter lived with her; 44% of those with two or more children lived with a child (Shanas et al., 1968, Table VI-18a). The corresponding figures from the 1975 survey show sharp declines in all three measures: 17% of unmarried individuals with one son only, 19% of those with one daughter only, and 26% of those with two or more living children lived with a child (Shanas, 1978, Table 6-8A). Shanas’s data also reveal differences in the distribution of the elderly among other household types, such as living with siblings, living with other relatives, and living with nonrelatives, according to the number and sex of living children, and the sex and marital status of the respondent. Bachrach’s (1980) study focuses upon the relationship between number of living children and living arrangements in a sample of 1328 individuals aged 65 or older in 1974. Bachrach employs two alternative measures of living arrangements, a binary-coded variable (living alone versus living with others) and a multiple-coded variable (living alone, living with offspring only, living with other relatives only, living with offspring and other relatives, living with friends, living with others of unknown relationship). Both measures of living arrangements are revealed by tabular analyses to vary according to the number of living children. Bachrach also analyzes the binary-coded living arrangements variable using a regression equation which controls for several social, demographic, and current resource variables in addition to number of living children. All of the regression coefficients representing the effects of number of living children upon the probability of living alone are statistically significant. Bachrach includes one other measure of available kin-the number of living siblings-which proves to be insignificantly related to the probability of living alone in her sample. Bachrach’s multivariate analysis also reveals a greater probability of living alone among older women than among older men. Also relevant to the present study are several analyses of racial differentials in the formation of extended-family households. Black-white differentials in the incidence of extended-family households have been well documented [see, for example, the review article by Lee (198O)l
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and shown in some studies to persist when income levels are held constant (Allen, 1979; Hays and Mindel, 1973). Recent studies have extended this result, demonstrating significant net-of-income household-composition differentials among blacks, non-Hispanic whites, and several subgroups of Hispanics distinguished by country of origin (Angel and Tienda, 1982; Tienda and Angel, 1982). While the studies cited in this paragraph bear only indirectly upon the elderly population, they nevertheless suggest that race may be an important determinant of the living arrangements of older women. However, like most other previous work, these studies have failed to control for the availability of kin. METHODOLOGY As mentioned in the introduction, this study employs a multichotomous representation of household composition, distinguishing among the categories living alone, living with relatives, and living with others. With such a dependent variable, we wish to characterize the probability of being observed in each category, conditional upon the values of a set of explanatory variables, including kin availability. The special feature of the present problem is the fact that for certain patterns of kin availability, one or more of the categories of household composition may be ruled out (i.e., have a probability of zero). Therefore, we require an analytic technique which permits explanatory variables to be related to the propensity to live in each of several household types, while simultaneously providing for variation, within a sample of older women, in the set of household types that are feasible. Although alternative techniques are possible, this study uses-partly for reasons of computational convenience-a modified multinomial logit specification. In order to make the following discussion more concrete, the model is specified in terms of the variables actually used in the subsequent empirical analysis. Other potential applications of the general technique are noted in the summary. In this study, which focuses upon unmarried women aged 65 to 69, kin availability is measured by the two variables SP, which equals one if the woman has living siblings and/or parent(s) (family-of-origin kin), and zero otherwise; and C, which equals one if the woman has any living children (family-of-procreation kin), and zero otherwise. Thus, there are as many as five mutually exclusive household types among which a sample woman might be observed: (1) living alone; (2) living with others, but not with siblings, parents, or children; (3) living with siblings and/ or parents (but not children); (4) living with children (but not siblings or parents); and (5) living with siblings and/or parents as well as children.’ ’ Note that these household types do not reflect the concept of household headship, but merely the relationships among individuals sharing a dwelling unit; the notion of dependency is not addressed in this study.
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Categories (1) and (2) are assumed to be universally feasible, while the feasibility of (3) through (5) is conditioned by the availability pattern of living kin. The distinct configurations of kin availability and the relationship between kin availability and potential household types is summarized in panel A of Table 1. It bears emphasis at this point that the concept of kin “availability,” as used in this analysis, refers only to the existence of certain relatives, and not to any of their other attributes, such as the proximity, income, or household structure of each individual in the available-kin pool. Proximity to kin, in particular, has been shown by previous research to be an important aspect of the living-arrangement decisions of older women. In a cross-sectional study such as this one, however, proximity to kin is an aspect of the dependent variable-a decision to live in the same dwelling as a relative is, equivalently, a decision to make “distance to nearest relative” equal to zero. To incorporate proximity to kin into the present study, whether measured using a continuous or interval-valued variable, would greatly complicate the estimation: for this reason, the issue is not pursued further.
Relationships
TABLE 1 between Kin Availability and Potential Household Type Available kin configurations
Values of kinavailability variables:
A
B
C
D
SP
0
c
0
1 0
0 1
I 1
X
X
X
X
X
X
A. Basic specification Potential household types (HHTYPE): x Living alone” (1) Living with “others” only (2) X Living with siblings/parents (3) Living with children (4) Living with siblings/parents and children (5) B . Expanded specification Category designations of potential household types: Living alone Living with “others” only Living with siblings/parents Living with children Living with siblings/parents and children a x indicates configuration.
the feasibility
of a particular
household
X
X X
X X
lB 28 38
lC 2c 4=
lD 2O 3D 4D SD
type, given an available-kin
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Jn order to specify the model, we need the following additional notation. First, let HHTYPE represent the five-category dependent variable, with HHTYPE = 1,. . .,5 as indicated in the previous paragraph (and Table 1). Then, define five “feasibility” indicators, &, such that fj = 1 if category j of HHTYPE is a feasible household type for observation i. That is, ifSPi = 1andC; = 0, .ti = :, otherwise; and so on (see Table 1); as mentioned before, fir, = fi2 = 1 for all i. Then, the probabilities that i will be observed in each of the five categories of HHTYPE, conditional upon an n-vector, Xi, of explanatory variables, are of the form Pi(k) = Pr(HHTYPE;
5Ak exP(Zik 1 , k = 1,. . .,5;
= k) =
(1)
klE, J;.k ew(zik) where the Zik'S are logistic “index functions” of the fOrIn Zik = ak + PlkJil + * * * + Pupin, Or (Yk + B~i.* Within a given configuration of available kin (columns A to D in Table l), Eq. (1) is a straightforward multinomial logit model.3 Because the parameters of the household-type probabilities (the (Yk’s and @k’s) are independent of kin availability, Eq. (1) represents the most restrictive model of the relationship between the full X-vector and the householdtype probabilities4 Equation (1) is a restrictive model in the sense that some possible interaction effects of the kin-availability variables are ruled out. To see this, consider the probability of living with “others” for (a) someone with no living kin (that is, SPi = 0 and Cj = 0), which (with zI normalized to 0) is 1
ew(z2
1 + ev(zi2) and (b) someone with living children only (SPi = 0) and Ci = l), which is exPtZi2) 1 +
While the probabilities
exP(Zd
+
exP(Zi4)
are different, the log-odds of living with “others”
2 In this study the normalization rule a, = PI - 0, required in order to identify a unique set of logit coefficients, is imposed. 3 Available-kin configuration A-with SP = 0 and C = O-generates a binary logit model. 4 More restrictive specifications than (1) are, of course, possible, if a priori information is used to constrain the values of some of the ok’s and pk’s.
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versus living alone, which equals za in both cases, is independent of kin availability. The appropriateness of such an independence assumption is a matter for both theoretical and empirical investigation. As we show below, more general specifications are possible. At the other extreme of model generality (within the basic framework under consideration) is a specification in which a separate set of parameters is assumed for each distinct available-kin configuration. That is, we associate with each category of household type, and with each corresponding parameter vector, an additional index denoting the distinct available-kin configuration within which that category is feasible. This more general, “stratification,” model is equivalent to the specification of four separate multinomial logit models, one for each of the sample strata, or distinct available-kin configurations implied by the variables SP and C. However, the general model can also be formulated as a single, modified multinomial logit model, using the feasibility-indicator approach described earlier. To see this, consider the expanded dependent variable HHTYPE”, with 14 categories, shown as lA, lB,. . ., 2*, 2’,. . ., 4O, 5D in panel B of Table 1. Now, the category designation of the dependent variable indicates not only the household type in which the older woman is observed to live, but the other household types in which she could be observed as well. In choice-theoretic language, the label attached to each potential outcome indicates not only which outcome was chosen, but which outcomes were rejected as well. However, since we must impose the normalization zy = 0 (or an equivalent normalization) for each m, the distinctions between categories lA, lB, I’, and lD vanish, leaving us with a lo-category model, in which HHTYPE = 1 is a universally feasible category. As before, we define 10 feasibility indicators fl,j = 1 3. . *,5., m = A,. . .,D, and adopt a modified multinomial logit specification for the expanded outcome set, with probabilities defined by the equation (2)
The model specified by Eq. (2) represents a complex alternative hypothesis against which the more parsimonious, and more readily interpreted, ’ Yet another specification, mathematically equivalent to (2), can be obtained by retaining the original five-category HHTYPE variable, but defining the interaction variables X, * SP,, Xi * Ci, and X, * SP, * C,, and expanding the zj’s of (1) to include all of these interaction terms as explanatory variables. This approach necessitates numerous exclusion restrictions in the parameter vectors, due to the implicit information regarding the values of SP, and C, that is conveyed by the HHTYPE-category designations.
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model embodied in Eq. (1) can be tested.6 Intermediate levels of model complexity can also be tested, and are specified by imposing equality constraints upon the parameters implicit in Eq. (2). One particularly simple such intermediate model, estimates for which are presented in the following section, permits only the intercepts of each subgroup of the 10 zz’s to differ (and, hence, to reflect interactions or “cross-effects” among the available-kin indicators). This intermediate-level model is obtained by imposing equality constraints of the form g = @ = B; = Bf, Bf = Bf, and so on. Equivalently (see footnote 5), such a model can be estimated by appropriate additions of the available-kin indicators to Eq. (I), as zi2 = (YZ~+ a**SPi + (~23Ci + a24SP; * C; + B&i, Zn
=
a31
Zi4
=
(Y41
Zi5
=
as1
+ +
a33ci
ff4*SPi
+
B&iv
+
Bkxi,
(3)
and + BSi.
The number of parameters to be estimated in (3) is 9 + 4n. Since the basic model presented in (l), the full-interaction model (2), and intermediate models, of which (3) is an example, are nested models, they can be tested against each other using likelihood-ratio techniques. We now turn to an application of these models to data on the living arrangements of older unmarried women. EMPIRICAL
ANALYSIS
Source of Data The data used in this study are taken from the Retirement History Survey (RHS), a multiyear survey sponsored by the Social Security Administration. The RHS provides data on a sample of 11,153 noninstitutionalized persons born between 1905 and 1911, and aged 58 to 63 in 1%9. Respondents were first interviewed in 1%9, and were reinterviewed semiannually through 1979. In 1971 and subsequent years, interviews were attempted with the surviving spouses of deceased previous respondents. Sample attrition due to death, failure to relocate respondents, or other reasons had reduced the original sample to approximately 8700 by 1975. The RHS is an unusually rich source of information on both household structure and the existence and characteristics of kin living elsewhere. ’ With n explanatory variables and an intercept appearing in each z~, and with cy, and p, set to zero, Eq. (1) has 4 (1 +n) unknown parameters; in contrast, Eq. (2) specifies a model with 9 (1 +n) unknowns.
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For each household member, the data include age, sex, detailed relationship to respondent (distinguishing, for example, among children, grandchildren, parents, stepparents, in-laws, and siblings), and marital status. Moreover, one can construct fairly detailed measures of the number and types of a respondent’s living kin. Unfortunately, several important characteristics of individual kinship members, such as their age and economic status, are not measured. Finally, in addition to information on available kin and living arrangements, extensive background information on topics such as labor market behavior, job characteristics, retirement, health, and income are available.7 Sample Selection and Variable Definition The analysis presented in this paper is restricted to unmarried women aged 65 to 69 in 1975. The household-type (HHTYPE) and kin-availability (SP and C) variables were defined in the previous section.8 Parents and siblings are combined into a single family-of-origin category of available kin, spanning two generations, because so few of the women in this age group have one or more living parents. In fact, 93% of those coded as having living siblings and/or parents in this sample have living siblings only. The independent variables used in this analysis consist of measures of disability status, race, home ownership, marital status, age, and income. A dummy variable (DISABLED) is used to indicate affirmative responses to the question, “Do you have any health condition, physical handicap, or disability that limits how well you get around?” Additional dummy variables indicate home ownership (OWNHOME), blacks (BLACK), women whose current marital status is separated or divorced (DIVORCED), and women aged 68 or 69 (AGE). Income is measured as the sum of income received from the following sources: rent, dividends, interest, pensions, disability or workmen’s compensation programs, and social security. These sources of income are “portable” across different living arrangements, in the sense that they are independent of the actual category of living arrangements in which a woman appears. Other sources of income, including earnings, Supplemental Security Income and other welfare payments, and contributions from relatives living elsewhere, are excluded in order to guard against possible simultaneity biases, since the level of income from such sources itself depends upon living arrangements. Descriptive statistics for this sample are shown in Table 2. The sample of unmarried women was further divided into never-married and ever’ For further information on the RHS, see lrelan and Schwab (1981). * It should be noted that HHTYPE is coded hierarchically, with the presence of relatives taking priority over the presence of “others”; thus, for example, a woman living with children (but not siblings/parents) is coded as HHTYPE = 4 whether or not “others” are also present in the household.
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TABLE 2 Mean Values of Variables Used in Analysis Ever-married women (n = 1515) Distribution of dependent variable (HHTYPE) (1) Living alone (2) Living with others (3) Living with siblings/parents (only) (4) Living with children (only) (5) Living with siblings/parents and children Mean values of available-kin variables Has living siblings/parents (SP= 1) Has living children (C= 1) Has living siblings/parents and children (SP=l and C=l) Mean values of independent variables” DISABLED OWNHOME BLACK DIVORCED AGE INCOME a All variables except INCOME
Never-married women (n = 275)
.66 .08 .06 .20 .Ol
.56 .09 .36 -
.86 .81
.89 -
.71 .40 .50 .15 .18 .43 $2834
.29 .44 .06 .38 $3798
are dummy variables; for variable definitions see text.
married women. Six never-married women who reported that they had living children (either living with them or elsewhere) are excluded from the present analysis. As a result, living arrangement categories which include children (HHTYPE = 4 or 5) are ruled out for the never-married women. The figures in Table 2 show that ever-married women are more likely to live alone than are never-married women (66 versus 56%), and less likely to live with relatives than are never-married women (27 versus 36%). The proportions living with “others” were about equal for both marital-status groups. Turning to the available-kin variables in Table 2, we see that 89% of the never-married women had living siblings and/or parents; thus, for the never-married women, three categories of the living arrangements variable-living alone, living with siblings/parents, and living with othersare feasible for 89% of the sample, while only two categories-living alone and living with others-are feasible for the remaining 11%. Among ever-married women, 86% had living siblings and/or parents, while 71% had siblings/parents and living children; therefore 15% (86 minus 71) had living siblings/parents but not children. A similar calculation reveals that 10% had living children but not siblings/parents. Five percent of the evermarried women had no living siblings, parents, or children; for these
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TABLE 3 Summary Statistics and Likelihood-Ratio Tests for Alternative Models, Ever-Married Women Value of likelihood function at maximum
Specification (number of parameters) A. Models estimated Basic model (28) Basic model plus: (a) Intercept shifts (33) (b) Intercept shifts plus race interactions (38) (c) Intercept shifts plus income interactions (38) Full-interaction model (63)
(1) (II)
(III)
B. Likelihood-ratio
IIa IIb IIc III
versus versus versus versus
- 1356.01 - 1357.46 - 1344.88 Chi square statistic (degrees of freedom)
I IIa IIa IIa
29.06 6.36 3.46 28.62
women, only two categories of the living arrangements alone and living with others-are feasible. Results I: Ever-Married
- 1359.19
tests
Models compared (1) (2) (3) (4)
- 1313.72
(5) (5) (5) (30)
variable-living
Women
For the sample of ever-married women, several alternative models, varying in their degree of generality-that is, in the extent to which available-kin interactions are permitted-were estimated, and the results of these alternative specifications are summarized in Table 3 .9 In addition to the basic model [using the specification of Eq. (l), shown as model I in Table 31 and the full-interaction model [based on Eq. (2) and shown as model III in Table 31, three intermediate-level models were estimated: model IIa, in which the slopes, but not the intercepts, of the z functions pertaining to a given household type were equalized across available-kin configurations [that is, the model shown earlier as Eq. (3)]; model IIb, in which, in addition, race effects were permitted to vary by availablekin configuration; and model IIc, in which income effects (but not race effects) were permitted to vary by available-kin configuration. Based upon the likelihood-ratio test statistics shown in part B of Table 3, model IIa provides a significant improvement over the basic model 0, < .005), 9 The models were estimated using a slightly modified version of the CRAWTRAN computer program (Avery, 1980).
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while none of the more complicated models tested led to significant improvements over model IIa in terms of overall fit. The acceptance of model IIa, against more complicated alternative hypotheses, is a pleasing result in that model IIa is a considerably more parsimonious model than its full-interaction alternative. The estimated parameters of model IIa are shown in Table 4. These parameters are to be interpreted as the effect of a change in an independent variable upon the relative probabilities of living in the indicated household type (the column headings of the table) and living alone (the reference category), given the feasibility of the household type in question. Several interesting findings appear in Table 4. Income, which has been shown TABLE 4 Parameters of Logit Model for Ever-Married
Women (Model Ha)
Category of HHTYPE
(2)
“Others”
(3)
(4)
Siblings/ parents only
Children only
(5) Siblings/ parents and children
(.391)*** (2.79)*** - .623 (4.34)*** ,539 (2.69)*** - .449 (2.34)** - .245 (1.73)* - .082 (2.36)** - ,632 (2.52)***
(.033)*** (.05) ,573 (.82) 1.78 (2.59)*** ,687 (.93) ,335 t.511 -.I34 (.65) -4.95 (5.37)***
,106 (.50)
-
-
-
-
-
Independent variables” DISABLED OWNHOME BLACK DIVORCED AGE INCOME
(1000s)
Intercept Intercept-shifts SP
c SP * c
a * ** ***
(.180)***
(.066)***
C.88)
t.28)
- .343 (1.68)* 1.25 (5.34)*** -.143 (.55) .016 (.W - .027
- .239 (1.05) - ,018 (.05) ,187
(.W -2.20 (4.39)*** - .225 (.45) .267 (.53) - .063 (.lI)
(.68) - .298 (1.31) - Jo5 (.15) -1.20 (4.18)***
- 1.186 (5.18)***
-
Absolute values of t statistics in parentheses. Significant at .lO level. Significant at .05 level. Significant at .Ol level.
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in numerous previous studies to be a significant predictor of household composition-usually, based upon a binary living alone/not living alone measure of household composition-is shown here to be related (negatively) only to the relative probability of living with children. Thus, we would conclude, on the basis of these results, that among unmarried women without living children, parents, or siblings (women for whom only the first column of parameters are relevant), income is unrelated to household composition. Income is also, apparently, unrelated to decisions regarding coresidence with living siblings and/or parents. The results in Table 4 imply an income elasticity of the propensity to live alone, calculated as the weighted sum of the income elasticities in each available-kin configuration, evaluated at the appropriate subsample means, of only .053. This elasticity is far below that calculated by Michael et al. (1980)1.0”based upon state-level aggregate data for widows aged 65 and over. At least part of the reason for this difference is the fact that the present analysis takes more careful account of kin availability.‘” Most of the significant parameters shown in Table 4 are found in the “living with children” column, although this may in part be due to the lower sample frequencies of the other three categories of the dependent variable. It is interesting to note that in category 5, the only significant parameter indicates the greater propensity of black women to adopt this household type. Black women are also found to be more prone to live with “others,” controlling for kin availability.” Since this mode1 controls both for income and kin availability, these findings lend further support to those studies that have demonstrated persistent net racial differentials in the formation of extended-family households. One might conjecture that the race effects shown in Table 4 reflect differential opportunities to share households, rather than an unmeasured race-specific effect, if blacks with living siblings (children) have more siblings (children), on average, than do whites with living siblings (children). Yet the mean number of living siblings among blacks with living siblings is 2.8, somewhat lower than the corresponding mean of 3.1 for whites. The mean number of living children, among those with any living children, is larger for blacks than for whites: 3.4 versus 3.0. However, while black women have, on average, 13% more children than white women, they are 46% more likely to live with a child, given the feasibility of doing so. There are other candidates for the omitted variable or variables which ‘” When the sample of ever-married women is used to estimate a binary living-alone/ not-living-alone model, disregarding kin availability but otherwise identical to model Ha. the resulting income elasticity of the propensity to live alone is .12, more than twice that obtained from the more complex model. ” Recall that in model IIb, we found no significant interaction effects between race and the available-kin variables, within either the “living with others.” “living with parents/ siblings,” or “living with children” parameter vectors.
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would, if included, eliminate the significant race differences in household behavior shown in Table 4. Among these variables are attributes of the available kin such as their age, health status, marital status, and income. Given the limitations of data currently available, these issues must be addressed in future research. The intercept-shift parameters shown at the bottom of Table 4 represent the “interactive” effects of kin availability. These effects are shown as differences between the intercept reported in each column and the corresponding intercept of an expanded, available-kin configuration-specific model. Thus, for example, the constant in zz--the living-with-others index for available-kin configuration A (SP = 0 and C = O)-is - 2.20, while the constant in zj-the living-with-others index for available-kin configuration B (SP = 1 and C = 0) is -2.20 - .225 = -2.425. Shown as differences, the available-kin intercept shifts indicate more readily the effect of variations in kin availability upon the household-type distribution. Also, the t statistics shown for these shift parameters pertain to the differences between intercepts. The results indicate that the relative probabilities of living with “others” and living alone are independent of the kin-availability variables (judged by the t statistics for the intercept shifts in the first column of Table 4). However, the relative probabilities of living with siblings/parents and living alone are significantly reduced by the existence of living children. This reduction presumably reflects both the competing obligations for providing support, and the expanded opportunities for receiving support, associated with having children. Thus, we find evidence of interactions among the variables measuring kin availability, but these interaction effects are confined to the relative probabilities of living with relatives and living alone. Results II: Never-Married
Women
Due both to the smaller sample size and reduced variability in availablekin configurations among never-married women, only the basic model was estimated for this subgroup. The logit parameters for this model are presented in Table 5. The only available-kin variable defined for the never-married women is SP, indicating the existence or nonexistence of siblings and/or parents. Hence, only categories 1 (living alone), 2 (living with others), and 3 (living with siblings/parents) of the dependent variable HHTYPE are relevant in this sample. Also, the DIVORCED variable is not used in this sample, being irrelevant to never-married women. Some of the parameters shown in Table 5 reveal similarities in the behavior of ever-married and never-married women. First, with both groups of women the previously established positive relationship between income and the propensity to live alone appear to hold only when living
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DOUGLAS
A. WOLF
TABLE 5 Parameters of Logit Model for Never-Married
Women
Category of HHTYPE
(2) Others
(3) Siblings/parents
Independent variable” ( - .337)*** DISABLED
t.63) -.154 (.33) 1.85 (2.53)** .855 (1.86)** .052
OWNHOME BLACK AGE INCOME Intercept a * ** ***
(1000s)
t.87) -2.46 (5.11)***
(- .olo)** (.032) ,548 (1.91)* - .026 (.04) .613 (2.15)** -.I17 (2.59)** - .328 (1.23)
Absolute values of r statistics in parentheses. Significant at .lO level. Significant at .05 level. Significant at .Ol level.
with nuclear-family relatives is compared to living alone; income bears no relationship to the propensity to live with other than nuclear-family kin in this sample. Second, black women have relatively strong propensities to live with relatives other than siblings, parents, or children, and with unrelated people, as well as with available kin. This implies that if older black women with no living kin were compared to older women of other races, also with no living kin, the blacks would be more likely to be living in shared households, other variables held constant. However, there are some contrasts revealed by Tables 4 and 5 as well. Notably, home ownership is unrelated to the propensity to live with siblings/parents among ever-married women, but strongly positively related to living with siblings/parents among never-married women. In the case of never-married women, home ownership may be associated with greater residential stability (both retrospectively and prospectively) and thus a more likely setting for the care of an elderly parent or dependent sibling. Summary
This paper has examined factors influencing the distribution of older unmarried women across household types, with the household types distinguished by the presence or absence of selected kinds of relatives. This approach to the study of household structure necessitates an analytic
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methodology whereby differences across individuals in the array of living kin are taken into account. The models discussed in this paper, while formulated narrowly in terms of this substantive focus, are potentially useful for the analysis of other demographic, sociological, or economic phenomena as well. For example, spells of unemployment may be ended in one of three ways-by the start of a new job, by exit from the labor force, or by recall to the previous job-but the third such outcome is impossible for those whose unemployment spell is due to a plant closing. The results presented here include some findings which confirm those of earlier studies and include some which are new. These results indicate that black women have a greater propensity to form extended-family households than do women of other races, holding constant their financial resources (both income flows and wealth, represented by home ownership). However, we have also shown that black women have a greater relative propensity to live with “others” as well-holding constant their opportunities for living with relatives.]* Kin availability itself affects living arrangements both directly and indirectly, in the model used here. It is mechanically (and trivially) true that the probability of living with kin is higher when kin are available, since the corresponding probability when kin are unavailable is zero. It is more illuminating to calculate the effects of kin availability upon the probability of living alone; this probability (at the sample mean, in the ever-married sample) is .86 for those with neither living children nor siblings/parents, dropping to .74 if siblings/ parents only are living, .66 if children only are living, and .63 if kin in both categories are living. We also found some evidence of direct interactive effects of kin availability upon the probabilities of living in shared households: the findings indicate that the existence of children significantly reduced the odds of living with siblings/parents only (given the existence of siblings and/or parents), other factors held constant. The indirect effects of kin availability upon living arrangements arise because the effects upon the probabilities of each feasible household-type category of all other explanatory variables in the model are conditional upon the full set of available-kin indicators. As an illustration of these indirect effects, the calculated slope of the relationship between income and the probability of living alone is .0033 for ever-married women with neither children or siblings/parents, .0023 for those with siblings/parents but no ‘* It should be remembered that the “living with others” category of HHTYPE includes women living with relatives other than parents, siblings, or children4.g.. aunts, uncles, grandchildren-as well as those living with nonrelatives. For ever-married women, the “living with others” differential for blacks may in fact reflect primarily households in which grandchildren are present; this phenomenon is, however, much less likely for the essentially childless never-married women, among whom the same “living with others” differential for blacks was found.
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children, and .0147 for those with children (whether or not they also have living siblings/parents). I3 Finally, the results presented here confirm earlier findings regarding the inverse relationship between income and the sharing of a household, but only in selected instances: for ever-manied women, the effect emerges only for the living-with-children parameter, and for never-married women, the effect appears only for the living-with-siblings/parents parameter. Overall, the findings of this study suggest that the process by which the elderly sort themselves among the array of household types available to them is a complex one, albeit one that can be modeled in a reasonably parsimonious way. A major further advance in our understanding of the process could be gained if data were available which provided measures not only of the financial and health circumstances of the elderly, and of the pattern of living relatives available to them, but of the financial and health circumstances of these available kin as well. REFERENCES Allen, W. R. (1979), “Class, culture, and family organization: The effects of class and race on family sturcture in urban America,” Journal of Comparative Family Studies 19(Autumn), 310-313. Angel, R., and Tienda, M. (1982), “Determinants of extended household structure: Cultural pattern or economic need?” American Journal of Sociology 87(May), 1360-1383. Avery, R. B. (1980), Qualitative Dependent Variable Program CRAWTRAN, unpublished manuscript, Carnegie-Mellon University. Bachrach, C. A. (1980), “Childlessness and social isolation among the elderly,” Journal of Marriage and the Family 42(August), 627-636. Beresford, J. C., and Rivlin. A. M. (1966), “Privacy, poverty, and old age,” Demography 3(August), 247-258. Chevan, A., and Korson, J. H. (1972), “The widowed who live alone: An examination of social and demographic factors,” Social Forces 51(September), 45-54. Hays, W. C., and Mindel C. H. (1973), “Extended kinship relations in black and white families,” Journal of Marriage and the Family 35(February), 51-57. Irelan, L. M., and Schwab, K. (1981), “The Social Security Administration’s Retirement History Study,” Research on Aging 3(December). 381-386. Kobrin, F. E. (1976), “The fall in household size and the rise of the primary individual in the United States,” Demography 31(February), 127-138. (a) Kobrin, F. E. (1976), “The primary individual and the family: Changes in living arrangements in the United States since 1940,” Journal of Marriage and the Family S(May), 233238. (b) Lee, G. R. (1980), “Kinship in the seventies: A decade review of research and theory,” Journal of Marriage and the Family 42(November), 923-934. Michael, R. T., Fuchs, V. R., and Scott, S. R. (1980), “Changes in the propensity to live alone: 1950-1976,” Demography 17(February), 39-56. ” These slopes are calculated by differentiating Eq. (1) with respect to a particular explanatory variable. The resulting expression depends upon the values of all the explanatory variables in the model; for the examples given, the expression has been evaluated at the sample mean of the explanatory variables.
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Moon, M. (1977), The Measurement of Economic Welfare: Its Application to the Aged Poor, Academic Press, New York. Morgan, J. N. (1978), “Intra-family transfers revisited: The support of dependents inside the family,” in Five Thousand American Families-Patterns of Economic Progress (Duncan and Morgan, Eds.), Vol. 1, Survey Research Center, The University of Michigan, Ann Arbor. Schwartz, S., Danziger, S., and Smolensky, E. (1983), The Choice of Living Arrangements by the Elderly, Brookings Institution, Washington, DC. Shanas, E. (1978), A National Survey of the Aged, Final report to the Administration on Aging, U.S. Department of Health, Education, and Welfare. Shanas, E., Townsend, P., Wedderbum, D., Friis, H., Milhej, P., and Stehouwer, J. (1968) Old People in Three Industrial Societies, Atherton Press, New York. Soldo, B. J. (1977), The Role of Demographic Composition in Accounting for Changes in the Distribution of Living Arrangements among the Elderly: 1960-1970, presented at the annual meeting of the Population Association of America. Soldo, B., and Lauriat, P. (1976), “Living arrangements among the elderly in the United States: A loglinear approach,” Journal of Comparative Family Studies 7(Summer). 351-366. Soldo, B. J., and Myers, G. C. (undated), Structural Profiles of Living Arrangements among the Elderly: 1970, Center for Demographic Studies Working Paper 1, Duke University. Soldo, B. J., Sharma, M., and Campbell, R. T. (1983), The Effects of Functional Health Status and Demographic Characteristics on the Living Arrangements of Older Unmarried Women, presented at the 1981 annual meeting of the Population Association of America (revised). Tienda, M., and Angel, R. (1982), “Headship and household composition amongblacks, Hispanics, and other whites,” Social Forces Bl(December), 508-531. Tissue, T., and McCoy, J. L. (1981), “Income and living arrangements among ,poor aged singles,” Social Security Bulletin 44(April), 3-13.