انتقال بین نسلی و باروری: مبادله بین سرمایه انسانی و کودکان کار

This paper analyzes the relationship between demographic transition and intergenerational transfers using an overlapping generations model with endogenous fertility. In particular, this paper considers a growth model in which the young generation confronts a trade-off between an education for human capital accumulation and child labour. At low levels of human capital, both the fertility rate and income transfers from children to parents are at high levels, because the opportunity cost of child rearing is low, and the wages of child labour are important for household income with low parental labour wages. An increase in the human capital decreases the fertility rate and reverses the income transfers to the opposite direction from parents to children. Thus, we demonstrate the significant relationship between demographic transition and intergenerational transfers. We also demonstrate the possibility of multiple equilibria in the form of a poverty trap equilibrium with a low human capital level and a steady state with a high human capital level.

Many economists since Malthus (1993) have studied the very important problems associated with demographic transition and fertility rates. According to Malthus, 1993 and Kuznets, 1966, demographic transition was initially presented as the problem that population explosion causes natural resource depletion. Currently, population problem is associated with the aging of population caused by low mortality and fertility rates in developed countries. A number of theoretical approaches have been developed to explain this demographic transition. For example, Becker and Barro, 1988 and Becker et al., 1990 develop an endogenous fertility theory that explains the negative relationship between the fertility rate and the human capital level.1Galor and Weil (2000) succeed in explaining the history of the nonmonotonic relationship between economic development and the fertility rate.2 On the other hand, Caldwell, 1976 and Caldwell, 1978 reveals that intergenerational transfers play an important role for demographic transition. In Bangladesh and Nigeria, children are considered to have not only a duty to support their family, but also a role in reducing the risks of aged parents, as child wage income is important for family income.3 Based on these facts, Caldwell states that the high fertility rate is a rational parental choice because of the economic circumstances causing parents to rely on child wage income. Thus, the fertility rate is high in developing countries. In contrast, Caldwell proposes the presence in developed countries of transfers from parents to children, in the form of direct transfers like bequests and/or indirect transfers like the provision of an education. Therefore, low fertility rates occur in developed countries because parents prefer quality rather than quantity of children. We emphasize that intergenerational transfers are among important factors influencing fertility choice as pointed out by Caldwell. Blackburn and Cipriani (2005) develop a model based on the Caldwell hypothesis. They analyze the relationship between the fertility rate and intergenerational transfers expressed as gifts and bequests caused by the two-sided altruism in an overlapping generations model. In particular, Blackburn and Cipriani (2005) explain the consequences of the Caldwell hypothesis by using a dynamic analysis. 4 They explain that the fertility rate declines and intergenerational transfers turn into bequests from gifts in an endogenous growth model in which there is an externality associated with per capita labour supply. They explain the Caldwell hypothesis by considering the following situations with the technological progress. The fertility rate decreases with an increase in the opportunity cost of child rearing caused by an increase in the parental wage income. In addition, an increase in the parental wage income makes intergenerational transfers turn into bequests from gifts. In consequence, a high fertility rate and gift transfers from children to parents exist in economies with a low technological level. Technological growth decreases the fertility rate and causes intergenerational transfers to be converted into bequests from gifts.5 This paper augments Blackburn and Cipriani’s (2005) study, which is based on the Caldwell hypothesis, as we engage the problems associated with child labour and human capital.6 Child labour have a close relationship to intergenerational transfers and fertility rates because parents have to force children to work if household income crucially depends on the wages of children. In fact, the ratio of children aged between 5 and 14 at work in economic activity is 2% in developed countries, but 19% in Asia and the Pacific, 16% in Latin America and the Caribbean, 29% in Sub-Saharan Africa and 15% in the Middle East and North Africa (Statistical Information and Monitoring Programme on Child Labour (SINPOC)). By comparison, the preindustrial child-labour ratio was 36.6% in England and Wales. In addition, Rosenzweig and Evenson, 1977 and Grootaert and Kanbur, 1995 provide empirical evidence of the positive relationship between fertility and child labour. Therefore, in identifying the relationship between fertility choice and intergenerational transfers, we should consider child labour. Furthermore, the crux of the problem is that child labour impedes the ability of children to receive an education and the accumulation of the human capital. Because child labour actually imposes psychological, physical and temporal burdens, child labour has negative effects on educational achievement. For example, Jensen and Nielsen (1997) provide evidence of the trade-off between child labour and the educational level in Africa. Psacharopoulos, 1997 and Patrinos and Psacharopoulos, 1997 provide evidence for Latin America.7 In addition, parents with the high level of human capital do not engage children to work since they can afford to educate children.8 Thus, it is important to analyze the relationship between intergenerational transfers, fertility rates and child labour on the theory of human capital. This paper derives results to explain the above-mentioned empirical evidence by considering the trade-off between child labour and education and the positive relationship between education and human capital accumulation. If fertility rates and child labour are both high, the rate of human capital accumulation is slow at low educational levels, because parents depend on child labour income. If fertility rates are low and parents transfer income to children, human capital accumulation is stimulated because of low child labour and high educational level.9 Thus, this paper derives the Caldwell hypothesis that fertility rates and net transfers from children to parents decrease with economic development based on the human capital theory. In addition, the fact that educational levels increase and child labour decreases with economic development portrays a positive relationship between indirect transfers from parents to children and economic development. This relationship also explains part of the Caldwell hypothesis. Thus, the relationship between fertility rates and intergenerational transfers results in the negative relationship between child labour and economic development that is validated by the empirical evidence. 10 This paper explains the Caldwell hypothesis, pointing out a significant positive relationship between fertility and net intergenerational transfers with economic development by using a dynamic model that incorporates human capital and child labour, as follows. In an economy with a low human capital level, the following situation can be present: high net intergenerational transfers from children to parents, which we name Backward Intergenerational Transfers (BITs), are caused by low family income; a high fertility rate caused by high BITs and the low opportunity cost of child rearing; and a low educational level caused by high child labour. This regime includes a possibility of falling into a poverty trap. In an economy with a slightly higher human capital level, because the opportunity cost of child rearing increases with the human capital level, fertility rates decline, but parents choose child labour rather than education because of low family income. Therefore, economic development is still slow. In an economy with a sufficiently high human capital level, because parents can afford to invest in a child’s education because of high family incomes, child labour decreases and the educational level increases with the human capital level. The direction of intergenerational transfers switches from parents to children, which we name Forward Intergenerational Transfers (FITs). Fertility rates keep declining. Through this process, child labour vanishes eventually in a steady state with a high human capital level. We also demonstrate in this model the presence of multiple equilibria involving a poverty trap.11 As previously mentioned, the rate of human capital accumulation is slow at a low human capital level because of the low educational level caused by a high level of child labour. Conversely, the rate of human capital accumulation is faster at a high human capital level because of a high educational level caused by a low level of child labour. Thus, there are history-dependent multiple equilibria: one is a steady state with a low human capital level, and the other is a steady state with a high human capital level. This paper is organized as follows. Section 2 develops the model. Section 3 characterizes the equilibrium of intergenerational transfers, fertility rate, educational level and child labour given the human capital. Section 4 analyzes the dynamics of human capital. Section 5 provides the conclusion.

In this paper, we have investigated the Caldwell hypothesis in an overlapping generations model of endogenous fertility. This model emphasizes that intergenerational transfers play an important role in fertility. In this model, we obtain a positive relationship between the fertility rate and net transfers from children to parents. In addition, both the fertility rate and net transfers from children to parents decrease with an increase in human capital. These cases represent the demographic transition history of the real world that is explained by Caldwell. Thus, the use of intergenerational transfers as a factor in fertility choice would contribute to the demographic transition theory. In this paper, we have incorporated the issue of child labour in order to explain the relationship between demographic transition and intergenerational transfers. We observe that in poor economies, parents force children to work and parents will have more children if parents’ income crucially depends on the income of the children. Meanwhile, child labour gives rise to many specific problems.21 Child labour impedes a child’s education and economic development. In fact, there is a high level of child labour because of a low household income in developing countries. As a consequence, because the educational level remains at a low level, the economy falls into a poverty trap. We can explain this poverty trap in this model as caused by the low educational level because of poverty. Thus, this model is able to answer why child labour exists in developing countries. If the economy falls into a poverty trap as explained by Caldwell, the model provides us with policy implications, such as compulsory education or banning child labour, etc.