Impact of Family Size on Education, child labor and female labor supply: The Case of Ecuador

This work is an extract from my Master thesis. I am very grateful to my thesis advisor Luis Alberto Trajtenberg and to my teachers and colleagues for the motivation and comments, especially Emanuel Agú. All errors remain under my responsibility.

asvillamila@unal.edu.co

The Demographic and Health Surveys (DHS).

Lee (2004) uses first child’s sex as instrument for family size, exploiting parent’s strong preferences for male children in South Korea, to estimate the impact over schooling investment.

Black et Al is the only reference using a dataset that covered the totality of Norwegian population aged 16 to 74 in the period 1986 - 2000.

Angrist and Evans (1998) limit the sample to mothers aged 21 to 35, given that few women younger than age 21 have two children in the U.S.

According to ILO, labor that jeopardizes the physical, mental or moral well-being of a child, either because of its nature or because of the conditions in which it is carried out, is known as “hazardous work” and affects about 115 million of children aged 5 to 17 are affected by this phenomena in diverse areas as agriculture, mining, construction, manufacturing, services, among others.

1. Results

V.1. WALD Estimates
Wald estimates offer a first approach to the family size impact, captured by the dummy “more than two children” on education, child labor and female labor supply. As shown in the first panel of table 5, bearing more than two children reduces schooling investment, measured as the probability that the oldest child attends private school, by 18.5% and early literacy by 26.4%. Both effects are significant at 5% level. There is no evidence of an impact over school attendance, probability of being held back against the cohort schooling level and positive mobility.
On the child labor side, having more than two children raise the probability of children report being working for pay in rural areas by 8.3%, while the effect in the rural areas is negative and of about 2% in urban areas, as shown in panel 2 of table 5.
Finally, panel 3 of table 5 presents the main results for mothers labor supply. On average, having more than two children reduce mother’s labor market participation by 13.2%; however, there can be wide differences in this effect once estimated for MHH vs. MNH. For the last ones, probability of being working for pay is reduced by 12%, while the impact over MHH is more than three times higher, about 28%. These results are significant at 5% level.

 

 

 

 

 

 

 

 

Table 5. Impact of Family Size on Education, Female Labor Supply and Child Labor: Wald Estimates

V.2. Instrumental Variables Estimates
V.2.a. First Stages
Two conditions are necessary for the validity of the same sex instrument: first, it has to be a good predictor for family size, usually known as relevance condition; and second, it must be uncorrelated with the error term of the structural model, which is known as exclusion restriction. In this section, the first condition is directly tested by estimating model 4.2 for the dummy more than two, including a set of covariates (Xi) to control for the sex of first two children, their ages and their mother’s, her civil status, years of education, and teenage mother condition at first birth. Controls for household geographic region and ethnic group of the unit of analysis are also included, and with the exception of first stages for child labor, all models include controls for rural condition of the dwelling. In first stages for child labor and education, a dummy for mother headed homes is included while those of female labor market participation are estimated for mothers of single and nuclear homes separately.
As shown in table 6, the parameter for same sex is highly precise and with the correct sign in all subsamples. In particular, having the first two children of the same sex rise the probability of bearing at least one more child by 2.6% to 4.7%, with a 99% confidence, a result in line with what was reported by Angrist and Evans (1998).
Intensity of correlation between the endogenous variable (N) and the instrument (Z) plays a central role in the internal validity of the strategy, an issue that can be seen through the plim equation of the IV estimator:
             (5.1)
Where y  are the standard errors of the residuals and the instrumented variable respectively. Bound et al. (1995) highlights that in finite samples IV estimates are biased in the same direction as OLS estimates, and this bias approaches to the bias of OLS estimates when the correlation between the instrument and the endogenous variable tend to zero. If this correlation is weak, a slight violation of exclusion restriction in the form of some correlation between the instrument and the error of the structural model leads to inconsistences that cannot be overcome by using a large sample.
This problem is known in the literature as “weak instruments” and has become an important issue in recent years. Bound et al. (1995) states that the first stage F statistic contains valuable information regarding the finite sample bias of the IV estimator and highlights that, after Stiger and Stock (1997), the quotient 1/F offers an approximation of the finite sample bias in terms of that of the OLS estimator. Angrist and Pishke (2009) address this issue by expressing the finite sample bias of  in terms of the first stage F statistic, the covariance between the errors of the structural model and the instrumental equation   and its error variance :
        (5.2)
As a rule of thumb, after Stiger and Stock (1997), a first stage F statistic less than 10 should be a motive of concern, under the assumption of i.i.d. errors. As shown in table 6, the first stage F statistic for each subsample oscillates between 1099.5 and 5606.3, which could be a first signal against the presence of weak instruments problems.
Table 6. First Stages

A formal definition for this problem was proposed by Stock and Yogo (2001), in terms of its consequent distortions on Wald Statistic based on inference and the bias against the OLS estimator, as shown in table 5.1. Such distortions emerge in the presence of a weak instrument problem as a result of the loss of precision of the standard errors of the IV estimator, i.e., in the presence of weak instruments, the Wald statistic allows to reject more frequently the null hypothesis of βiv=0, rising the probability of incurring in type I error. In terms of the test, an instrument is considered weak if the significance (α) level (α – level) based on IV statistics has an actual size that could exceed a tolerable threshold, 10% in this case. With the family size as the only endogenous variable and the same sex of first two children as the only instrument, the test statistic is the first stage F statistic and its critical value is 16.37, for testing the null hypothesis that the instrument does not enter the first stage, with a desired maximal size of 10%, for a 5% Wald test of β = 0. Column 6 of table 7 shows that with the exception of the first stage for the hours worked per week for children and youth aged 5 to 17, all the F statistics are higher that a critical value, so the null hypothesis that the instrument same sex is weak can be rejected.
V.2.b. The Impact of Family Size on Education, Child Labor and Female Labor Supply.
This section presents the main results of the OLS and IV estimates of the family size impact on education a labor supply.
As shown in column 3 of table 7 and in line with previous literature, OLS estimates indicate a strong and highly significant effect of family size on several measures of education, child labor and mother’s labor supply. With the exception of the effect on positive mobility, all estimators are highly significant and present the expected sign in theoretical terms, but once endogeneity is controlled using the dummy “Same_sex_1_2” as instrument, mixed effects of family size on child labor are identified and adverse effects on some indicators of education and mother’s labor market participation. In line with Báez (2008), most cases OLS models tend to underestimate the adverse effects of family size.
The potential importance of these results can be explored in the domain of a growing literature that studies the technology underlying cognitive and non-cognitive skill formation at different stages of children life cycle. Cuhna and Heckman (2008) stem that the effect of parents investment on their children, measured in a broadly sense, from the number of books in the house to the number of museum or theatre visits, over cognitive and non-cognitive skills formation is stronger at early ages, precisely from 6 to 8 years of age. Meanwhile, Cunha et al (2010) points out the importance and convenience of intervention at early ages of cognitive skills disadvantages and finds evidence supporting the existence of complementarities between parent’s investment and their children cognitive skills that get more relevant as children grow up. Given this type of complementarities and its implications on cognitive skill formation, a family size adverse impact on investment and early literacy can play a central role for policy design in this field.
On the positive mobility side, having more than two children reduces by 3.7% the probability of the oldest child overcoming the average educational level of her parents. This offers a first approach to possible long term or secular effects from family size in social mobility from a generational perspective. The importance of this result, although it is significant at a 10% level, is that quantity-quality empirical literature generally does not report evidence over this type of indicators that involves a generational component.

 

Table 7. Impact of Family Size on Education, Female Labor Supply and Child Labor: OLS and IV estimates

Unobservable interactions between private school attendance, family size and parent’s religious characteristics can underlay the wide difference observed between OLS and 2SLS estimates of the impact over private school attendance probability. Adsera (2006) stems that protestant and catholic families in developing countries usually bear a higher number of children than families from other religious beliefs.
Finally and against OLS estimates and theory predictions but in line with the findings of Cáceres-Delpiano (2006) and Angrist et al. (2010), there is no statistical evidence of an effect over school attendance and the probability of the oldest child present a lower education level compared to her cohort. Given the importance of school attendance,  Cáceres-Delpiano (2006) proposes as a possible explanation for these results the possibility that parents reallocate resources in a way that compensate the possible restrictions arising from family size on school attendance and performance of the oldest child. Conley and Glouber (2005) argue that in spite of the scarce data on religious affiliation, catholic parents are more likely to send their children to catholic schools, usually privates. Without addressing the endogeneity problems, these authors find a positive effect from family size over the probability that children attend private school, but once the endogeneity is controlled by instrumenting the number of children the effect becomes negative.
The second panel of table 7 presents the results for the family size impact over child labor. As mentioned above, given the generalized socio-economics differences between the urban and rural areas, the analysis is addressed for each one separately.
OLS estimates of family size effect on the probability of the oldest child aged 5 to 17 reports being working for pay are positive and about 4.5% for the rural areas and 2.7% for the urban ones. The effect on hours worked per week is also positive and highly significant. Once the endogeneity is addressed by instrumenting the family size, mixed results are obtained depending on the area. In rural household, having more than two children increase by 6.7% the probability of the oldest child report being working for pay, while the effect is negative and about 3% for urban ones. Both effects are significant at a 5% level.
These results suggest that besides the preponderance of the child labor phenomena in rural areas, it responds to an exogenous increase in family size in a quite different way depending on the area. For the rural ones, my estimates are in line with those reported by Báez (2008) for Colombia, notwithstanding the effect identified for urban households deserves a more detailed analysis.
Several hypothesis can explain this behavior that defies conventional wisdom and theory. First, there can be possible economies of scale as consequence not of the sex mix of first two children but associated to the presence of more siblings in the household, that can benefit the oldest one. If in urban areas, exist complementarities between siblings regarding the time allocation between school or other activities and work, the oldest child can perceive as convenient to avoid the work duties given that there are more worker prospects in the home.
Second, the theoretical models of emotionless maximizers have been seriously questioned by recent research. Mullainathan (2010) stems, for example, that beckerian model of education ignores the presence of self-control and time inconsistencies faced by individuals as decision makers and this inconsistences are more relevant under scarcity conditions and could lead to counter intuitive decisions by family members in terms of the conventional model. From this perspective, arises the possibility of an inverse relationship between family size and the working-for-pay condition of the oldest child, given that the arrival of more siblings represents not only an eventual increase in economic restrictions but in future family income as well. Accounting for the future labor market attachment of the new sibling and independently of the realization of these expectations in the future, intertemporal preferences of the oldest child can indeed been affected in such way that induce her to leave or postpone the working activities.
Third, facing a new situation in the household, such as the presence of more siblings can lead to unpredictable conducts or reactions from urban children. Bernejee and Duflo (2011, page 71) find situations where some children from poor families reported not being attending school because “they simply refused to do so,” which can be directly extended to their decision to participate in the labor market for pay. Furthermore, regarding the effects on urban child labor, school attendance and performance of the oldest child that defy the theoretical model, recent causal evidence have been reported, at least on the effect of family size on children’s education in the developing world. At the end of 1970’s decade, China government partially disarticulated the one child policy, allowing homes of certain characteristics in certain regions which only child was a girl to bear an additional one. Qian (2009) exploits this policy change as a natural experiment to estimate the impact of family size on the oldest child education, using as instrument a triple interaction between race, residence region and first child sex. The main findings indicates that an exogenous one child increase in families with three or less children with about 49% level of children’s school attendance, actually increase by a range of 14% to 16% the probability that the oldest child attends school. For families with 54% of children’s school attendance, the effect is also positive and about 12% for the oldest child. In addition to these counter-intuitive results, Angrist et al. (2010) implement a multiple natural experiment strategy to address endogeneity in the quantity-quality trade-off analysis and find no significant impact on children education. 
Finally, as shown in the third panel of table 7, the results for family size impact on labor market participation of mothers aged 18 to 40 not only confirm previous findings in this area but it also uncovers important differences depending on the monoparental condition of the household, defined in such way that captures the mother leadership of the household by her “head of the family” response at the time of census instead of the single status in marital sense. Furthermore, the analysis departs from previous literature in other way, by studying the family size impact on single mothers vs. mothers from nuclear families instead of the usual married vs. other analysis, given that in the Latin American context, mother’s leadership of the family is a powerful criteria for policy design.
The results indicate that OLS procedure underestimates the effect of family size on mother’s working-for-pay probability. The IV effect for all mothers is negative and about 9.6% with a 1% significance level. Once the sample is split into single and nuclear homes mothers, important differentiated effects arose. In particular, having more than two children reduce by 7% the probability of mothers from nuclear families reports being working for pay, while the adverse impact is more than three times higher for single mothers (25.5%.) Both results are significant at a 5% level and confirm the remarks of Arias and Palloni (1999) and Baez (2008) regarding the economic vulnerability of single mother’s households.

1. Robustness Check

VI.1. Hausman Test
Accounting for the important costs in terms of the efficiency by using the instrumental variables procedure to obtain consistent estimates, a Hausman test is implemented for the presence of endogeneity by the direct statistical comparison of IV and OLS estimators, under the null hypothesis of no endogeneity.
As shown in the last two columns of table 7 that report the test statistic and the p-value associated for each regression, the null hypothesis of no endogeneity can be rejected in the estimation of the family size impact on education investment, literacy at early ages and the probability of being working for pay for children aged 5 to 17 and mothers aged 18 to 40.
VI.2. Exclusion Restriction
One of the most important critiques to the same sex instrument strategy was first stated by Rosenweig and Zhang (2006). The main argument against the use of the children’s sex mix as instrument for family size stems that it can generate scale economies that could affect education investment through a channel other than family size, by allowing, e.g. the possibility of clothes and other sex related expenditures, to be shared or transferred among siblings, a statement that can be explored by observing the importance of clothing and related expenditures for the ecuadorian homes. If these type of expenditures represent an important proportion of the family budget, then the implicit risk of violating the exclusion restriction can be considered a motive for concern.
According to the "Encuesta de Ingresos y Gastos de Hogares Urbanos y Rurales del Ecuador" for the period 2011-2012, the expenditures on footwear and clothes for all family members represent the 8% of the total family budget. The most representative expenditures are food and transport, which represents 40% of the total family expenditure and does not depend on the sex of its members. In this sense, given the expenditures patterns in Ecuador, there is scarce evidence supporting the hypothesis of Rosenweig and Zhang (2006). Besides, Deaton (1997) remarks that consumption statistics are usually extracted from surveys that not cover the expenditure distribution among family members, so researchers face important difficulties in establishing the family members’ preferences, their tastes or sex discrimination as a possible source of expenditure patterns.
Selective abortion constitute another source of concern after Schultz (2007), meaning that if parents can decide or manipulate the sex of their births, then the sex mix of the first two as treatment should not be as good as randomly assigned, which is the core assumption of our identification strategy. The hypothesis is that "Techniques to test for the sex of the fetus early in a pregnancy (e.g. by means of ultrasound, amniocentesis, or chorionic villus sampling) allow parents who have a sufficiently strong preference for the gender of their child to abort a fetus of the unwanted sex. If this occurs, the sex composition of children may become correlated with the couples’ preferences for women to work (and other family choice outcomes), and sex of the child cease to be a valid instrument for estimating the cross-effect of fertility." Nevertheless, while abortion is legally allowed in Ecuador in some circumstances, the phenomena of selective abortion as a consequence of strong sex preferences of the couples is not common in Latin America and the statistics does not support such hypothesis. According to the population census of 2010, the proportion of men and woman among the population is almost the same, a less common fact in countries like India and other Asian, with strong preferences for one sex.

1. Conclusions

Following Angrist and Evans (1998), this paper has exploited the randomness of the sex mix of first two births and parents preferences for sex diversity among their children portfolio as a natural experiment to overcome the challenges posed by the endogeneity of family size in the estimation of its effect on the education of the oldest child, her labor market attachment and the labor market participation of her mother.
The results suggest that having more than two children has an adverse effect on some education and labor market indicators but not in all of them, as usually suggested by the theoretic models. Expected reductions of 18% and 23.4% on education investment and literacy at early ages, respectively, are identified, but there is no evidence supporting a negative impact on school attendance in general and on children’s performance at school in terms of years of education and probability of being behind her cohort average years of education. The estimates support a positive effect on child labor for rural households but a negative one for urban ones, which defies the prediction of the theoretical approaches and shed lights around the rural urban gaps that persist in Latin America. Remarkable differentiated effects were identified on the family size effect on mothers’ labor market participation depending on her household’s leader condition, an approach that departs from the broadly implemented married vs. all analysis.
The relevance of the instrument was confirmed in the first stages and formally tested with favorable results by using the Stock and Yogo (2001) approach, which is based on the inference distortions that arises as a consequence of the weak instrument problem and raises the probability of committing type I error.
Finally, the presence of endogeneity was tested and probed in most cases, especially in those where I found the most interesting results, by implementing a Hausman’s test for each regression, with the objective of weighting the need for an instrumental variables procedure given the actual costs associated in terms of efficiency loss of the estimates against the OLS approach.

 

 

 

 

 

 

 

 

 

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