Children's Working Hours and School Enrollment

Introduction

Child labour is thought to be harmful in many ways to children's welfare. It interferes with human capital accumulation and may affect the present and future health of the child. The determinants of child labour supply have been recently analysed in the literature (see Basu (1999), Rosati-Tzannatos (2003), Cigno-Rosati-Tzannatos (2001), Cigno -Rosati (2002), and the literature therein cited for the discussion of theoretical models and empirical results). The attention of the literature has mainly focused on the determinants of the categorical decision of the household on the activity of the child: whether to send a child to school, to work or allow him to perform both activities 1 . Almost no attention has been paid to the amount of time that children devote to work (either when this is their only activity or when they combine it with school attendance). An exception is Ray (2000), which, however, treats labour supply separately from the household decision of sending a child to school.

The number of hours spent working is not only important in itself as a measure of child welfare (it is a measure of forgone leisure, etc.), but is also an essential ingredient to evaluate the cost of work in terms of health and human capital accumulation.

In this paper we analyse the hours of work supplied by children. As mentioned above, the literature on child labour has mainly focused on the participation decision of the children. Almost no attention has been paid to the hours supplied. This paper innovates on the existing literature by focusing on the simultaneous decision relative to school attendance and to the amount of work supplied. On the basis of a simple theoretical model, we estimate a simultaneous two equations system. This model allows us not only us to take into proper consideration the joint decisions about work and schooling, but also to calculate marginal effects conditioning on the "latent" propensity of the child to attend school and/or to work. These marginal effects are in some cases rather different across the "latent" states of the child and this has interesting analytical and policy implication.

A theoretical outline

To outline our theoretical model we consider an altruistic set up, where parents care about the present and future consumption and current leisure of their children 2 . The number of children is taken as given and for simplicity of exposition is normalized to 1 3 . We also assume that human capital accumulation is the only way to transfer resources for children's future consumption 4 . Human capital is accumulated by sending children to school 5 . The time a child has to spend at school is fixed at h S . Normally school hours are not flexible and school attendance requires a minimum fixed amount of time devoted to school. Some of the children that work and attend school might miss classes and thus make their school hours more "flexible". However, the degree of "flexibility" that can be achieved in this way is rather limited, as skipping school often results in dropping out and is normally not tolerated by school authorities 6 . Hence we treat school hours as fixed. School attendance does not rule out child labour. However, we assume that working hours have a negative influence on human capital accumulation. Hours spent at work reduce time available for study, tire the child and reduce her learning productivity, etc. Given the nature of the work that children perform, mainly unskilled and mostly at their family farm or business, we can safely consider the hours spent at work, h L, as flexible and treat them as a continuous choice variable.

The human capital production function takes the form:

(1)

2 -As discussed in Rosati-Tzannatos (2003), similar results will be obtained if a non-altruistic model were used. 3 -Endogenous fertility does make a difference to child labour analysis (See Rosati-Tzannatos 2003), but for the present analysis nothing of substance is changed by treating fertility as exogenous. 4 -If capital market were present the efficient level of human capital investment will equalize returns to human capital investment to the market interest rate. Allowing for the presence of capital markets will complicate the exposition without bringing additional insights. For a discussion of the role of capital markets in determining child labour supply see Rosati-Tzannatos (2000). 5 -Child labour could also contribute to human capital accumulation by, for example, on the job training. We do not consider this case in our discussion for two reasons. Firstly, there is no evidence to substantiate the statement on the role of child labor as a means to accumulate human capital. Secondly, formal education plays an empowerment role that goes beyond that of increasing the productivity of working time. This effect is captured in our model by introducing human capital as such as an argument of the utility function. 6 -There are programs that try to make school hours more flexible to accommodate child labour activities, but their coverage is marginal and, in any case, such programs are not present in Pakistan.

Parents maximize a utility function defined over the current consumption of the household members, the current leisure and the future consumption of the children.

Current household consumption C 1 is given by:

if parents send their children to school.

Where y is the (exogenous) income of the parents, w is the wage rate (marginal product) of child labour, h L are the hours of work supplied by children and q is the direct cost of education.

Future children's consumption, C 2S , is given by K+H where K is the exogenous endowment of human capital and H is defined in (1). Parents also attach value to the (current) leisure enjoyed by the children, L= 1 -h S -h L (having normalised total available time to 1).

If parents do not send their children to school, present consumption is given by C 1L = y + w h L , future consumption by C 2L = K and current leisure by L= 1-h L .

In both cases the choice variable is h L (the time spent at work), but the money and time budget constraints are different according to whether the child is sent to school or not.

As the amount of time required by school attendance is fixed, the parent's choice of h L is given by

and M represents a vector of household characteristics like education of the parents, locality of residence, etc. In other words, parents compare the maximized utility under the two regimes and select the one that yields the highest welfare.

The optimal decision regarding school enrolment, s, is given by: s>0, if * U S > * U L and vice versa.

(6).

The system (3) -(6) generates two behavioural equations in s and h L , that can be expressed in reduced form as function of the set of exogenous variables discussed above.

The comparative statics properties of the model show that an increase in parent's income increases the probability that a child attends school and reduces the numbers of hours worked. An increase in the cost of schooling reduces human capital accumulation. These results, however, depend on the simplifying assumption of exogenous fertility and absence of capital markets. Relaxing such assumptions would not change the results relevant to the focus of the present paper, but it will make a difference for the discussion of child labour policies. A detailed analysis of these issues can be found in Rosati-Tzannatos (2003). Note that child labour supply is expected, other things being equal, to be lower when children are attending school, because of the negative effect on human capital accumulation and the higher marginal value of leisure.

Also observe that corner solutions are possible in both regimes for h L .

The econometric model

As illustrated in the Section 2, the decision of schooling and working are simultaneous.

In particular we observe that a child is enrolled in school if Us* -U L *>0 0 * > ⇒ s and that the hours of work supplied by the children depend also on their enrolment status.

We model hours worked and enrolment status using the following reduced form 7 :

h* are the hours worked, s* is the enrolment status of the child, ε and u are the disturbance terms following a bivariate normal distribution with zero means and variance co-variance matrix (Σ) as follows:

We allow the two equations to be correlated via their error terms. One possible source of correlation is the unobservable (by the researcher) ability of the child. If children with higher abilities are more likely to go to school and work fewer hours, we expect a negative correlation between the two error components.

Both the enrolment rate and the hours worked are latent variables. Enrolment is observed as a dichotomous variable according to the following structure:

As it is not possible to buy time, the hours worked are censored at zero. We assume that observed hours worked are described by the following Tobit model:

The joint decision of working and studying is described by a simultaneous equation model that combines a Tobit and a probit model with correlated disturbances.

More specifically, each observation belongs to one of the four possible regimes:

We estimate this model by maximum likelihood. The log likelihood function (L) for estimation of the parameters b, ρ and σ is given by: 7 We drop the subscript L as no confusion can arise 8 The probability associated to each of the regimes can be written as follows:

The data sets

are respectively the univariate density function, univariate cumulative function, and the bivariate cumulative function.

We have employed two different data sets in the estimates: one survey conducted in Pakistan and the other survey in Nicaragua. It is interesting to test the determinants of hours of works and school enrolment with data relative to largely different economies and social structures. Moreover, the structure of children's employment in the two countries is different as in Pakistan a relatively larger number of children is working for a wage. This allows us to be more confident on the generality of the results obtained.

Moreover, the structure of children's employment in the two countries is different as in Pakistan a relatively larger number of children is working for a wage.

Pakistan

The survey was carried out in 1996 and contains information on working children by age, sex, location, occupation and industry; on the working conditions of the children, In describing the data set utilized for the estimates, however, we refer to the statistics derived from the sample. The figures discussed, therefore, refer to the sample of households with at least a working child and not to the whole Pakistani population.

Children aged between 5 and 14 amount to 30,772 in the sample. Table 1 shows the fraction of children who work and are enrolled in school programmes and also the fraction of full-time students and part-time workers among total children. The overall enrolment rate is about 40%, and there is a very large gender differential in enrolment rate at any age group. A large fraction of children cannot be classified in any of the three activities: "working only", "studying only", "working and studying". We define them as children with "no activity". Girls are more likely than boys to belong to the latter group: this is likely due to the fact that household chores are not classified, according to the questionnaire, as working activity.

Nicaragua

The Nicaragua survey refers to year 1998 and is part of the LSMS (Living Standards Measurement Study) survey 10 . There are 6,084 children aged 5 to 14 in the sample, representing the 28.8% of the total Nicaraguan sample.

The majority of children, about 73 per cent, attend school. The school attendance rate is higher for females than males at all ages. Most of the children study only (67 per cent of boys and 76 per cent of girls). Girls are less likely than boys to belong to the work.

About 20 per cent of the children are apparently involved in no activity. Among them girls are the majority, this is perhaps due to the fact they are involved in household chores more than boys.

The tables 4-6 summarises the activities performed by children in the age group 6 to 14 in Nicaragua.

. Table 8 and 9, respectively 11 . The coefficient of correlation ρ is negative in both estimates indicating that it would be inappropriate to estimate the two equations separately. This is confirmed also by the results of estimates from independent Probit and Tobit regressions shown in the Appendix (Tables A1 and A2 regressors has been used for Nicaragua. However, for Nicaragua, given the different characteristics of the sample, the education of the parents is represented by two dummies. The first dummy takes the value of one if the father/mother has completed the primary school (Eduf/Edum prim), the second takes the value of one if the father/mother has completed the secondary school (Eduf/Edum secon). Moreover, the data for Nicaragua did not allow separate adult from children's income, we then used total expenditures as a proxy of total household available resources.

Given the structure of the model we can compute the marginal effects conditioning on the latent status of children: enrolled or not, working or not. This will give information on the effects of exogenous variables differentiated by "latent" group of children. As we shall see, not negligible differences emerge among the various groups, indicating that policy effects of interventions might be differentiated according to the target selected.

Columns (a) and (b) of tables 8 and 9 report (respectively for Pakistan and Nicaragua) the marginal effects conditioned on the "latent" index of working hours being positive or not. Some of the explanatory variables have quite different effects on the two groups.

The standard errors of the marginal effects are reported in the Appendix (Tables A3 and A4) in order to help to assess the extent to which they are statistically different. School enrolment is a non-linear function of age. Income has a positive effect on enrolment.

However, the effect is much smaller for children with a high propensity to work with respect to the other group. The household composition effects are well determined. As we control for income these effects should mainly reflect the marginal productivity of children's time in the various activities. Again the marginal effects are differentiated across latent groups. Household size has a negative and small effect on the probability of attending school for the potentially working children, while it has a strong and significant positive effect on the other group. As we control for income, this is likely to be a marginal productivity effect. In households that are not likely to send their children to work, substitutability between adult and child work appears to be stronger than in the other group. An additional child aged 6-14 in the household negatively affects the enrolment rate for the non working children in both countries. The presence of preschool age children reduces the enrolment probability for those children who are not likely to work, while is has the opposite effect for those children who are likely to work. This effect is more pronounced for the girls, even though in Nicaragua it is only significant at 10% level. Children living in rural areas are also less likely to be enrolled in school. The presence of a significant gender differential in enrolment is confirmed by the estimates in both countries, albeit in opposite directions. Girls are less likely to be at whom wage data are not available. We obtained the total adult income by netting out the predicted child earnings from the household income.

Table 1 : Children enrolled in school. Pakistan.

Table 2 :

Table 3 :

Table 4 :

Table 5 : Children working only and working and studying.

Table 6

Table 7 . Descriptive statistics

Table 8 . ML estimates of enrolment and hours worked. Pakistan

Table 9 . ML estimates of enrolment and hours worked. Nicaragua

Table A3 . Standard errors and confidence interval for marginal effects. PakistanTable A4 . Standard errors and confidence interval for marginal effects. Nicaragua