Data and Econometric Specification

then be maximized in the usual way, and the first-order conditions on the remaining choice variables may be combined to determine the optimal levels of the choice variables as a function of exogenous variables. The household’s choice for the optimal number of foster children may be repre- sented as: 8 N f ⫽ N f W , M , N c , A, R, w Similarly, the household chooses the optimal level of education for its biological children and its foster children: 9 E i ⫽ E i W , M , N c , A, R, w for i ⫽ {c, f }

IV. Data and Econometric Specification

Data are available for empirical estimation of these equations from the South African Project for Statistics on Living Standards and Development PSLSD, a nationally representative data set collected by the South African Labour and Development Research Unit SALDRU of the University of Cape Town, in 1993, with funding in part from the World Bank. As is usual in this context, data were collected at the household level, with the household in mind as the unit of analysis. Clearly this sampling approach creates some challenges for the project here, where it would have been preferable to collect data directly on the extended family networks within which fostering typically takes place. Data were available on household composition and assets, community-level schooling variables such as whether a primary or secondary school was present, and children’s gender, age and school enrollment status. In addition, data were col- lected on the amount of time each household member spent collecting wood and water. Fostered-in children and households were identified as those situations in which the child did not identify any household member as his or her father or mother. No data were available on the biological families of foster children. Two distinct samples are used in the analyses that follow. A household-level sam- ple, comprising 3,320 black households with school-age children that is, aged 7– 17 for which household’s complete data were available was used to estimate the likelihood of fostering-in children and the effects of fostering on household income. A child-level sample of 8,627 children aged 7–17 with complete data was used to predict enrollment. Descriptive statistics for the household sample are presented in Tables 1 and 2, and for the child-level sample in Table 4. Ainsworth 1996 finds that fostering-in and fostering-out decisions are not sym- metric, in the sense that a linear equation predicting the fostering-in of children has different slopes and a different intercept from an equation predicting the fostering- out of children. This result is not surprising given anthropological evidence sug- gesting that fostering-in and fostering-out involve quite different kinds of decisions for example, Page 1989; Menget 1988; Goody 1982. Equation 10 expresses the net demand for foster children. Accordingly, it makes sense to estimate separate equations for the fostering-in and fostering-out decisions. Because good data to iden- Table 1 Variable Definitions and Descriptive Statistics for Black Households with School- Age Children in South Africa Standard Variable Variable Description Mean Deviation Fostering variables Fostering-in 1 if household fosters in a child 0.253 Number foster kids Number of foster children fos- 0.477 1.027 tered-in Fostering-out 1 if household fosters-out a child 0.072 Number foster-out Number of children fostered-out 0.106 0.469 Foster kids 0–6 Number of foster children aged 0.093 0.374 0–16 in the household Foster girls 7–17 Number of foster girls aged 7– 0.190 0.519 17 in the household Foster boys 7–17 Number of foster boys aged 7– 0.194 0.547 17 in the household Income and wages Log-per-cap income Log per capita permanent in- 5.417 0.712 come Expenditure Educated adult women Number of adult women in the 0.489 0.775 child’s household with ⬎7 years education Uneducated adult Number of adult women in the 1.157 0.904 women child’s household with ⱕ7 years education Educated adult men Number of adult men in the 0.355 0.667 child’s household with ⬎7 years education Uneducated adult men Number of adult men in the 0.772 0.894 child’s household with ⱕ7 years education Adults with formal job 1 for every household adult 0.664 with a formal job Adults with casual job 1 for every household adult 0.110 with a casual job Self-employed adults 1 for every self-employed 0.147 household adult Land size Hectares of cropland to which 0.473 6.660 the household has access Pension income Log of total household pension 1.791 8.841 income Demographics Biological sons 0–6 Number of biological boys 0–6 0.478 0.735 Biological sons 7–17 Number of biological boys 7–17 0.976 0.983 Table 1 continued Standard Variable Variable Description Mean Deviation Biological daughters Number of biological girls 0–6 0.452 0.726 0–6 Biological daughters Number of biological girls 7– 0.986 1.001 7–17 17 Adults over 65 Number of adults over 65 0.427 0.655 Time on wood and Person-weeks per week the 0.569 1.006 water household spends collecting fuelwood and water Human capital Full enrollment 1 if all children in household 0.946 are enrolled in school Maximum female edu- Maximum years of female edu- 4.519 3.277 cation cation in household Maximum male edu- Maximum years of male educa- 3.666 3.608 cation tion in household Primary school 1 if there is a primary school in 0.778 the community Secondary school 1 if there is a secondary school 0.548 in the community Travel time to school Minutes of travel time to school 30.724 28.303 Per-pupil cost of edu- Hundreds of Rand in total 0.426 1.176 cation monthly educational cost per pupil Cluster education av- Cluster-average of years of ed- ⫺1.079 0.651 erage ucation ⫹ 6 ⫺ age Distance to doctor Distance to nearest doctor in ki- 11.929 16.781 lometers Distance to pharmacist Distance to nearest pharmacist 21.908 26.399 in kilometers Distance to comm Distance to nearest community 11.428 23.700 health worker health worker in kms. Social attributes of the household Percent of children with Fraction of children in house- 0.366 0.300 father hold whose father is present Enough water 1 if the household reports al- 0.794 ways getting enough water Days sick Days sick of all household 0.578 1.152 member in previous week Long-term illness Number of household members 0.103 0.336 reporting a long-term illness tify fostering-out households are not available in these data, only fostering-in deci- sions are estimated here. The social norm in much of Africa when more than one child is fostered out is to try to keep siblings together where possible Page 1989; for this reason and because the number of children fostered in or out must be an integer, it is difficult for households to use the institution of fostering to achieve exactly the ideal number of foster children. Accordingly, the fostering-in equation will be estimated in a probit framework using the household-level data, in which the latent propensity to foster is represented by a linear approximation with a normally distributed error term ε i : 10 N fi ⫽ α ⫹ α 1 W ⫹ α 2 M ⫹ α 3 N c ⫹ α 4 R ⫹ α 5 w ⫹ Aβ 1 ⫹ G c β 2 ⫹ ε i , and a household is observed to foster in children iff N f ⬎ 0. As discussed above, the data are not sufficiently rich to enable estimation of a similar fostering-out equa- tion. Supply side issues play a role in whether a given household actually fosters chil- dren in—that is, whether other households will be willing to foster-out a child to a particular household. One possibility is that households will be more willing to foster a child to a particular household if they feel that household is likely to send the child to school. A good indicator of this likelihood is whether the household sends all of its own children to school. Since this decision is itself endogenous to the household’s fostering-in decision, a two-stage approach is adopted. In the first stage, a probit regression predicts the probability that a household enrolls all of its own children in school. A binary variable is then created to indicate whether there is a greater than 95 percent predicted probability that the household will enroll all of its children. This cutoff was chosen because 94.6 percent of the households in the sample enroll all of their children. Thus, the predicted variable represents whether the household is more likely than average to enroll all its children. In the second stage, this predicted enrollment indicator is included as an explanatory variable in the fostering-in regres- sion equation. 5 Variables excluded from the main, fostering-in regression that were used to predict full enrollment were the job status of the household head and community education characteristics for example, whether a primary school was nearby and the average educational-attainment level of the community. The identifying assumption of this two-stage approach is that these variables are correlated with enrollment, but uncor- related with the fostering decision, except through enrollment. This assumption seems reasonable for the community-level variables. For the job-status variables, measured at the household level, the assumption is that job status affects the opportu- nities afforded foster children, that is, those in formal-sector jobs and possibly also self-employment can offer better political and economic connections to a foster child than those in casual employment Page 1989; Goody 1982. A chi-squared test strongly rejects at the 1 percent level the null hypothesis that the coefficients on the excluded variables are jointly zero χ 2 ⫽ 45.9, 7 degrees of freedom. 5. A related, alternative specification would be to predict the average enrollment rate of the household, instead of predicting the probability of full enrollment. Presumably, however, a foster child’s chances of being enrolled are more closely proxied by the probability of the marginal child being enrolled that is, by the probability of full enrollment than by the average probability of the household’s children being enrolled. The Journal of Human Resources Table 2 Household-Level Regressions of Fostering, Enrollment, and Income among Black South African Households with School-Age Children Full Log-Per-A.E. Fostering-In Fostering-In Enrollment Income Probit Probit Probit OLS Marginal Marginal Marginal Marginal Effect |t| Effect |t| Effect |t| Effect |t| Fostering-in ⫺0.075 2.80 Educated adult women ⫺0.028 2.06 0.005 0.42 0.004 1.83 0.039 2.44 Uneducated adult women 0.011 1.17 0.009 0.90 0.001 0.10 ⫺0.143 9.96 Educated adult men ⫺0.011 0.80 0.013 0.98 0.003 1.05 0.044 2.09 Uneducated adult men 0.021 2.30 0.010 1.03 ⫺0.001 0.20 ⫺0.149 10.85 Adults with formal job ⫺0.002 0.21 ⫺0.002 0.36 0.156 6.71 Adults with casual job 0.005 0.20 0.000 0.11 ⫺0.064 2.40 Self-employed adults 0.007 0.42 ⫺0.002 0.22 0.181 7.59 Adults over 65 0.136 13.65 0.144 14.58 0.001 0.24 ⫺0.089 5.40 Land size ⫺0.001 1.04 0.000 0.46 0.002 1.19 0.003 2.63 Time on wood and water 0.018 1.71 0.011 0.95 ⫺0.001 1.32 Pension income 0.001 1.37 0.001 1.44 0.000 0.150 0.002 1.52 Distance to doctor ⫺0.001 2.06 ⫺0.001 2.03 Distance to pharmacist 0.001 1.71 0.001 1.80 Distance to community health 0.000 0.78 ⫺0.001 1.52 worker Zimmerman 569 Primary school nearby 0.001 0.04 ⫺0.002 0.78 Secondary school Nearby ⫺0.017 0.84 0.004 1.89 Per-pupil cost of education 0.001 0.13 0.027 2.07 Cluster-average education attained ⫺0.040 2.85 0.007 5.05 Enough water ⫺0.025 1.11 ⫺0.030 1.34 ⫺0.003 0.72 0.096 2.97 Days sick ⫺0.018 2.42 ⫺0.017 2.26 0.001 0.72 0.021 2.05 Long-term illnes 0.034 1.28 0.019 0.73 ⫺0.006 1.89 0.043 1.14 All children 0–6 ⫺0.001 0.65 All girls 7–17 0.012 6.42 All boys 7–17 0.010 5.58 Percent of children with father 0.005 1.60 Biological sons 0–6 0.014 1.10 ⫺0.001 0.06 ⫺0.050 3.48 Biological Sons 7–17 ⫺0.152 10.64 ⫺0.120 9.73 ⫺0.035 3.27 Biological daughters 0–6 ⫺0.015 1.20 ⫺0.023 1.91 ⫺0.038 2.47 Biological daughters 7–17 ⫺0.167 12.11 ⫺0.126 11.01 ⫺0.037 3.46 Predicted income 0.007 0.19 Predicted enrollment 0.187 10.70 Observations 3,320 3,320 3,320 3,320 Pseudo R-squared; R-squared 0.24 0.21 0.24 0.38 Chi-squared df 543.25 27 525.73 33 295.95 31 Absolute value of t-statistics in parentheses Constant, UrbanRural and Regional Dummies: Included but not reported significant at 5 percent; significant at 1 percent The Journal of Human Resources Fostering-In Fostering-In Fostering-In Fostering-In Girls Aged 0–6 Girls Aged 7–17 Boys Aged 0–6 Boys Aged 7–17 Marginal Marginal Marginal Marginal Effect |t| Effect |t| Effect |t| Effect |t| Educated adult women 0.001 0.16 ⫺0.010 1.22 0.006 1.61 ⫺0.030 3.52 Uneducated adult women 0.010 3.30 0.002 0.34 0.010 3.65 0.001 0.21 Educated adult men 0.001 0.13 ⫺0.009 1.12 0.006 1.45 ⫺0.009 0.91 Uneducated adult men 0.004 1.47 0.019 3.10 0.001 0.18 0.012 2.26 Adult over 65 0.014 4.22 0.061 9.99 0.016 4.18 0.059 8.98 Biological sons 0–6 ⫺0.003 0.61 0.009 1.14 ⫺0.007 1.59 0.017 2.26 Biological sons 7–17 ⫺0.015 3.22 ⫺0.089 9.14 ⫺0.006 1.82 ⫺0.085 9.44 Biological daughters 0–6 ⫺0.005 1.20 ⫺0.002 0.28 ⫺0.004 1.07 ⫺0.003 0.38 Biological daughters 7–17 ⫺0.012 3.40 ⫺0.096 10.34 ⫺0.010 2.40 ⫺0.101 12.40 Land size ⫺0.005 1.56 ⫺0.008 1.61 ⫺0.005 1.36 0.000 0.37 Time on wood and water 0.006 2.39 0.016 2.74 0.004 1.19 0.005 0.84 Distance to doctor 0.000 2.13 0.000 0.15 0.000 1.24 ⫺0.001 2.69 Distance to pharmacist 0.000 1.51 0.000 1.29 0.000 1.70 0.000 1.32 Distance to community health worker 0.000 0.76 0.000 0.50 0.000 0.51 ⫺0.001 2.24 Pension income 0.000 0.21 0.000 1.09 0.000 3.13 0.000 1.56 Enough water ⫺0.020 2.53 ⫺0.025 1.74 0.000 0.01 ⫺0.006 0.52 Days sick ⫺0.005 1.64 ⫺0.011 2.16 ⫺0.004 1.51 ⫺0.008 1.76 Long-term illness 0.003 0.35 0.018 1.26 0.008 1.13 0.032 2.05 Predicted enrollment 0.016 2.41 0.117 10.17 0.007 1.05 0.105 10.40 Observations 3,320 3,320 3,320 3,320 Pseudo R-squared 0.09 0.24 0.09 0.26 Chi2 df 99.25 27 381.81 27 138.03 27 437.94 27 Absolute value of t-statistics in parentheses significant at 5 percent; significant at 1 percent Constant, UrbanRural, Regional Dummies: Included but not reported A second approach uses a single fostering-in regression with these identifying variables included among the regressors. Results from both approaches are presented below. We use the child-level data to estimate a linear approximation to the optimal edu- cation levels of biological and foster children Equation 9: 11 E ij ⫽ β 1 ⫹ β 2 M 0j ⫹ β 3 A j ⫹ β 4 R j ⫹ βW 0j ⫹ β 6 N cj ⫹ G i β 7 ⫹ ε ij where E ij is the enrollment status of the ith child in the jth household. Again, a probit framework is employed, in which the child is observed as enrolled iff E ij ⬎ 0. The household exogenous variables are included in the regression, as are the child- specific characteristics. G i , which include age, gender, whether the child is a foster child, and whether the child is living with her or his biological parents in a household that has fostered-in at least one other child. Finally, we will estimate two equations related to the welfare of the foster child and the fostering-in household, which is to say, the children’s time spent in domestic tasks: 12 T zij ⫽ γ 1 ⫹ γ 2 M 0 j ⫹ γ 3 A j ⫹ γ 4 R j ⫹ γ 5 W 0j ⫹ γ 6 N cj ⫹ G i γ 7 ⫹ ε ij and a prediction of the household’s income: 13 y j ⫽ δ ⫹ δ 1 W ⫹ δ 2 M ⫹ δ 3 N c ⫹ δ 4 R ⫹ δ 5 w ⫹ Aδ 1 ⫹ G c δ 2 ⫹ ε i where y j is log per-capita income at optimal resource allocations for household j. Because the data were collected in a clustered data design, all the equations will be estimated using the Huber-White correction to the variance-covariance matrix Deaton 1997. From these estimations, we can test the following seven hypotheses, which we first enumerate and then discuss: 1. Exogenously high rates of school enrollment of biological children in a household predict a strong propensity to foster-in other children; 2. The decision to foster-in children is correlated with variables that would indicate a relatively large need for domestic labor; 3. Fostering-in children raises a household’s level of per-capita income; 4. Fostering-in children raises the enrollment rates of biological offspring; 5. Foster children are not less likely to attend school—and do not spend more time in household labor—than biological children in similar households; 6. Children tend to be fostered into households that are more likely to send them to school than the fostering-out households; and, 7. The net effect of fostering on school enrollment is positive. We will first test whether the propensity to enroll all children is positively correlated with fostering-in. Such a result would be consistent with the notion that education The Journal of Human Resources Table 4 Description of Child-Level Sample Variables for School-Age Children in Black South African Households Standard Variable Description of Variable Mean Deviation Enrollment 1 if child is currently enrolled 0.900 0.301 Fostering characteristics Foster-sibling 1 if child has a foster sibling 0.254 0.435 Present Child fostered to close kin 1 if a foster child hosted by a close relative 0.148 0.355 Child fostered to remote kin 1 if a foster child hosted by a distant- or non-relative 0.016 0.124 Fostered-in girl 1 if the child is a girl and a foster child 0.081 0.273 Child characteristics Age Age of child in years 11.666 3.176 Female 1 if a girl 0.501 0.500 Biological father present 1 if the child’s biological father is present 0.541 0.498 Household income and education characteristics Maximum female education Maximum years of female education in household 5.416 3.734 Maximum male education Maximum years of male education in household 4.198 4.003 Log per capita Log per capita permanent income expenditure 5.337 0.698 Income Pension income Exogenous pension income 1.821 6.920 Land size Hectares of cropland to which the household has access 0.465 4.587 Time on wood and water Person-weeks per week the household spends collecting 0.687 1.147 fuelwood and water Zimmerman 573 Household demographic characteristics All children 0–6 Number of children 0–6 in the child’s household 1.151 1.243 All female children 7–17 Number of girls 7–17 in the child’s household 1.563 1.180 All male children 7–17 Number of boys 7–17 in the child’s household 1.560 1.215 Adults over 65 Number of adults over 65 in the child’s household 0.451 0.665 Educated adult women Number of adult women in the child’s household with ⬎ 0.491 0.803 7 years education Uneducated adult women Number of adult women in the child’s household with 0.426 0.638 ⱕ7 years education Educated adult men Number of adult men in the child’s household with ⬎7 0.352 0.686 years education Uneducated adult men Number of adult men in the child’s household with ⱕ7 0.232 0.493 years education Days sick Day sick of all household member in previous week 0.547 1.048 Long-term illness 1 for each household member reporting a serious long- 0.115 0.360 term illness Community characteristics Primary school 1 if there is a primary school in the community 0.799 0.401 Secondary school 1 if there is a secondary school in the community 0.562 0.496 Travel time to school Minutes of travel time to school 31.297 27.768 Per-pupil cost of education 100’s of Rand in total monthly educational cost per pupil 0.441 1.146 Cluster education average Cluster-average of years of education ⫹ 6 ⫺ age ⫺1.101 0.640 Enough water 1 if the household reports always getting enough water 0.775 0.417 considerations play a major role in fostering decisions and that fostering is a useful institution for building human capital. The second hypothesis examines the extent to which fostering-in children arises out of a need for domestic labor, by testing the sign and significance of several of the coefficients. Under the domestic labor hypothesis, we would expect that the pres- ence of more men M in a household increases the demand for home-produced goods and increases the shadow value of domestic labor, thereby increasing the de- mand for foster children, and reducing the likelihood of enrolling them in school. We would expect both greater household assets A and greater exogenous income R to raise the marginal productivity of labor in home production, and therefore to increase the demand for foster children. The higher marginal productivity would tend to decrease the probability of enrollment, but greater assets or income would also generate a wealth effect tending to increase enrollment so that the net effect is ambiguous. The effect of the number of women W in the household would be stratified by their educational level. The presence of more educated women would increase the demand for domestic labor, thereby increasing the demand for foster children. The presence of more uneducated women, who in South Africa have limited income-earning capacity outside the household May 1996, would tend to lower the demand for foster children, by lowering the marginal productivity of labor in home production. For the same reason, more uneducated women would tend to in- crease the probability of enrollment. Finally, more biological children N c would tend to lower the demand for foster children. If fostering is indeed related to a demand for domestic labor, we would expect that, in response to fostering-in, households might reallocate existing labor at least in part toward greater market work. If so, fostering-in households would have higher cash income per capita as a result of the fostering decision, ceteris paribus. This hypothesis is tested via the coefficient on predicted fostering in the income regression Equation 13. For similar reasons, we might expect that fostering-in, by releasing biological offspring from domestic labor, would enhance the probability of biological children being enrolled in school. We test this hypothesis in a schooling regression, by examining the significance of the coefficient on a variable indicating whether a child lives with biological parents who have fostered-in another child. If this coeffi- cient is positive, it would suggest that fostering does respond to a need for domestic labor, although this need arises out of a desire on the part of parents to send their own children to school. In Hypothesis 5–7 we turn to the effects of fostering on the foster children’s school enrollments through three kinds of comparisons: a ‘‘Cinderella effect’’ comparison, a ‘‘migration effect’’ comparison, and a comparison of the total effect of fostering. In Hypothesis 5, we test the Cinderella effect, that is, whether foster children are less likely than biological children to be enrolled in school, controlling for other, observable child and household characteristics. A negative coefficient on foster child status will constitute at least circumstantial evidence of a Cinderella effect, and a statistically insignificant coefficient will suggest that we cannot reject the null hy- pothesis that there is no Cinderella effect. However, it is also possible that unobserv- able child characteristics are determinants both of school enrollment and of the fos- tering decision. There is very little information in the data on the cognitive ability of the children, or on their levels of discipline or potential. Indeed, the only relevant information on the children is their age and gender. Nor is there any data at all on the biological family of fostered-in children. Accordingly, it is not possible to control for such unobservable characteristics through instrumental variables. As a result, the results on the Cinderella effect must be treated with caution. For example, Silk 1987 suggests that one reason boys in particular are fostered out is to enhance their discipline, and Goody 1982 reports that ‘‘difficult and proud’’ children are likely candidates to be fostered. If bad behavior at home is indeed a reason for fostering-out, and if—as seems reasonable—it is also a determi- nant of dropping out of school, then a negative coefficient on foster status in the school enrollment equation will not be indicative of a Cinderella effect. The opposite is also possible: if fostering-out is associated with some unobservable child charac- teristic that is also associated with greater school enrollment, then a finding of no Cinderella effect might be spurious. It should be noted, however, that there is little evidence in the anthropological literature to suggest that children with high potential are systematically fostered out. The choice of child to foster corresponds to gender considerations [for example, girls are not fostered to their mother’s brothers Silk 1987], traditional norms [the second-born child is often fostered Silk 1987], and the disciplinary motives cited earlier. The second comparison of the effects of fostering on children is between the en- rollment rates of children in predicted fostering-in and fostering-out households. This comparison estimates the ‘‘migration effect,’’ that is, the contribution to a child’s enrollment probability of moving from the biological household to the foster house- hold. If fostering occurs in part to improve the human capital of children, we would expect the migration effect to be positive. Unfortunately, no data were collected on fostering-out households, that is, on biological children who live elsewhere. Data were collected, however, on the number of times each of the adult women in the household had given birth, the age of these women, and the number of children still living in the household. Using this information, it is possible to construct an indirect measure of whether the mother has fostered out children. Starting with the full sam- ple of black households, the number of living children of each woman younger than age 36 in the household is subtracted from the number of times she has given birth. If the resulting number is positive, it is assumed that she has fostered some of her children to other households. This approach, though clearly imperfect, is the best measure available in this data set, and it has been used in other studies of fostering Page 1989. The final comparison—that between enrollment rates of foster children and those of children in the families from which they come—reveals the net impact of fostering on children. Because fostering probably arises out of some combination of both demand for domestic labor considerations and a desire to invest in children’s human capital, it is not possible to sign a priori the net impact of fostering. If the Net impact is negative, and if parents are sufficiently rational or well-versed in local social norms to know this ahead of time, then the fostering-out of children may be seen as a desperation action of parents, who reduce the human capital investment in their chil- dren in the process. In this sense, a negative net impact of fostering would place the institution in a light similar to that of desperation land sales: households limiting future economic well-being out of a sense of pressing immediate need for sustenance. On the other hand, a positive net impact of fostering would suggest that the institution of fostering is a highly adaptive response to the multiple market imperfections and resource constraints of low-income areas.

V. Determinants of Fostering among South African Blacks