Income Uncertainty & Schooling: A Portfolio Model

The existing literature predominantly links low primary school enrollment in developing nations to poverty and liquidity constraints. This perspective, often grounded in Ben-Porath's intertemporal human capital investment model, emphasizes the inability of impoverished parents to finance their children's education due to a lack of access to credit. The inability to borrow against a child's future increased earnings to cover current schooling costs is cited as a primary reason for children leaving school and entering the workforce. This focus on the cost side of the human capital investment decision and on child labor as an ex-post risk-coping mechanism constitutes the core explanation for low enrollment and widespread child labor. While acknowledging the validity of these explanations, the paper argues that they may not be the complete picture and other factors influencing low school enrollment rates require investigation.

Empirical studies have explored the relationship between poverty, credit constraints, and schooling. While some find the expected negative correlations, establishing clear causal links remains challenging. Some research shows negative correlations between credit constraints, poverty, and schooling, but these findings are largely suggestive and consistent with the theoretical frameworks. Other studies present mixed results, revealing no significant or even positive correlations between income/wealth and child labor, highlighting the complexity of the issue. This ambiguity is further underscored by the identification of a ‘wealth paradox’ where imperfections in land and labor markets force households to utilize their children's labor, even when wealthier, to meet labor demands. The relationship between poverty and child labor exhibits non-monotonic patterns across different income levels, revealing the limitations of simplistic cause-and-effect interpretations. Further complicating the issue, the fact that parents often cannot borrow against future child income stems from incomplete credit markets and problems of agency, where parents cannot fully enforce repayment of educational expenses later in life. This agency problem stems from imperfect altruism between parents and children, affecting intergenerational transfers.

A third stream of research examines the impact of transitory income shocks on child labor and schooling. Studies analyzing effects of exogenous income variations (e.g., due to weather or crop loss) reveal self-insurance strategies where households reduce human capital investment and increase child labor during income shortfalls. This highlights the lack of ex-post consumption-smoothing mechanisms. However, existing literature frequently neglects other crucial aspects. Several studies acknowledge the influence of future income uncertainty and incomplete insurance on schooling decisions. These emphasize that a high mortality rate among adult children can influence parental human capital investment decisions. Other research focuses on explaining sibling differences in educational attainment, pointing to factors such as heterogeneity in children’s abilities and increasing returns to human capital investment (like sheepskin effects). The role of sibling rivalry and the complexities of interactions between siblings within the household are further considered. Even the inherent educational element within child work participation in traditional settings is understudied. The paper argues that existing models too narrowly focus on child work as a mere additional current income source, failing to appreciate its potential educational component and the role of specific versus general human capital.

The literature on fertility highlights the importance of children as security assets for parents, especially in high-risk environments with incomplete credit and insurance markets. Children often serve as a form of old-age security, with intergenerational transfers from children to parents widely documented, even in the presence of potential agency problems. Empirical evidence shows these transfers exist and contribute to informal old-age support systems. The introduction of public social security schemes has been observed to partially crowd out private transfers from children, further validating the prevalence of this intergenerational reliance. Several recent theoretical papers explore the link between intergenerational transfers, child labor, and schooling decisions. These studies show that the relationship between parental income and child labor may not be monotonically decreasing, and that life expectancy positively influences human capital investment since parents need to live long enough to benefit. The role of altruism and reciprocity in determining parental investment is also acknowledged, underscoring the complexity of this dynamic.

This paper challenges the existing literature by highlighting the significant impact of future income uncertainty on household decisions regarding children's education. The core argument is that rural parents, facing considerable uncertainty about their children's future earnings, may employ a strategic risk diversification strategy. This involves sending some children to school, thereby acquiring general human capital suited for urban employment, while others remain at home to learn traditional agricultural practices, gaining specific human capital. This deliberate diversification of human capital investments is presented as an ex-ante risk management strategy, intended to mitigate potential income shocks and ensure old-age security for the parents. The paper emphasizes that this strategic approach is not simply a reaction to immediate economic pressures but a proactive measure to balance future returns and risk exposure within the family. This perspective stands in contrast to previous models which typically focus solely on the cost side of the educational investment decision and on child labor as an ex-post response to economic hardship.

A key innovation of this paper is the explicit consideration of sibling dependence and the joint human capital investment decision within a household. The model departs from traditional single-child frameworks by acknowledging that parents don't consider each child's education independently. Instead, they optimize the overall portfolio of human capital investments across all their children. This joint decision-making process highlights the intricate interplay between siblings' educational choices and the parents' need to manage risk and secure their future income. The parents' decision is driven by the desire to balance the potential high returns of formal education (general human capital) with the reduced risk of diversifying into traditional agricultural education (specific human capital) for at least some of their children. This approach significantly alters the analysis, as the outcome for one child directly impacts the decisions regarding other siblings.

The paper suggests that the need for income smoothing and old-age security, coupled with the uncertainty surrounding future returns to education, leads to less than full school enrollment within a household. This holds true even in a scenario of perfect credit markets, where the financial constraints often highlighted in the literature are absent. The paper’s findings provide an alternative explanation for why it may be optimal for parents not to send all their children to school – a decision often misinterpreted as stemming solely from poverty or lack of access to credit. Instead, it proposes that the strategic diversification of human capital investments and the pursuit of ex-ante risk management significantly influence household choices concerning education. This fundamentally reframes the child labor debate, moving beyond the traditional emphasis on ex-post consumption smoothing within liquidity-constrained households. The implication is that policies aimed solely at reducing the cost of schooling might prove insufficient to achieve full enrollment, and interventions focusing on managing the return side of the investment decision may be necessary.

The paper introduces a novel human capital portfolio model to analyze the impact of future income uncertainty on household decisions regarding children's education. Unlike most existing models in the child labor literature, this model incorporates four key features: (1) uncertainty about future returns to education, (2) parental reliance on children's future income for old-age support, (3) a multi-child framework allowing for sibling dependence in the human capital investment decision, and (4) an explicit consideration of the trade-off between general and specific human capital acquisition through formal schooling and traditional agricultural practices. By abstracting from liquidity constraints and child labor in the initial model formulation, the study isolates the pure effect of income uncertainty on schooling decisions. The purpose is not to refute the influence of poverty and credit constraints but to offer a complementary explanation from a risk management perspective focusing on joint sibling decisions and ex-ante risk diversification. The model is explicitly designed for rural households where children participate in family-based farming; child labor in this context is seen solely as work participation in family agriculture.

The model is calibrated using data from the 1994 Human Resource and Development Survey (HRDS) in Tanzania. This nationally representative survey of 5000 households provides detailed information on household members, their educational status, economic activity, assets, and expenditures. For the calibration, the analysis focuses on a subset of 1982 rural households with school-aged children. The data provides direct information on the educational expenditure (e_b) associated with formal schooling but lacks direct information for traditional agricultural education (e_a). Consequently, e_a is proxied using half the cost of formal schooling, suggesting a trade-off between cost and profitability of each type of education. The calibration explores how the optimal proportion of children sent to school (φ) responds to variations in income uncertainty (σ), considering both perfect risk correlation and no risk correlation among siblings in urban labor market outcomes. The goal is to determine if existing levels of urban income dispersion are sufficient to explain less-than-full school enrollment even in a context of perfect credit markets.

The model is calibrated using three different preference structures: quadratic, cubic, and constant relative risk aversion (CRRA). The calibration results consistently show a negative relationship between income uncertainty and the optimal proportion of children sent to school. For the average Tanzanian household in the sample, a moderate level of urban income uncertainty, based on the observed income spread, is enough to cause less-than-full school enrollment. The findings are shown to be robust to the choice of preference structure, even under perfect credit markets. The introduction of liquidity constraints, where households can save but not borrow, has a negligible impact on the results unless coupled with immediate returns to child labor. The impact of uncertainty on the optimal human capital portfolio allocation is substantial even when the financial constraints frequently discussed in the literature are absent. This suggests that even with sufficient resources, risk aversion caused by income uncertainty is a driving force behind educational choices in rural settings.

The core model, initially presented without liquidity constraints or child labor, is extended to incorporate these crucial factors often cited in the existing literature as primary drivers of low school enrollment. This extension allows for a more comprehensive assessment of their influence in conjunction with income uncertainty. The introduction of liquidity constraints restricts households' ability to borrow, permitting only saving. This modification aims to capture the real-world limitations faced by many families in developing countries. The inclusion of child labor allows the model to account for the potential income generated through children's work, which may influence the educational choices made by parents. By integrating these constraints into the model, the paper directly addresses the existing literature's predominant explanations for low school attendance while simultaneously analyzing the distinct contributions of income uncertainty.

The calibrated model allows for a comparison between the independent effects of income uncertainty and the combined effects of liquidity constraints and child labor on school enrollment. This comparative analysis is crucial for determining the relative importance of each factor. The results reveal that while both liquidity constraints and child labor can negatively impact the optimal proportion of children sent to school, the effect is markedly amplified when uncertainty is also present. Moreover, the influence of uncertainty is surprisingly large even under perfect credit markets. Interestingly, the introduction of a simple liquidity constraint (no borrowing) with no immediate returns to child labor has a minimal effect on the optimal school enrollment rate in the average household. Only when immediate returns to child labor are high enough to cover a sibling’s schooling costs (e_a = e_b) does the liquidity constraint produce a noticeable negative effect. This clearly suggests that while poverty and credit constraints play a role, they are not the sole determinants of school attendance decisions and that income uncertainty plays a significant independent role.

The calibration results underscore the significant influence of income uncertainty on educational decisions, even when considering liquidity constraints and child labor. The findings highlight the importance of modelling multiple children rather than focusing on individual cases. The model shows that uncertainty has a negative effect on educational choices across all children, while liquidity constraints and child labor effects mainly dominate in households with more children than average. This emphasizes the need to model sibling interdependence for a clearer understanding of household dynamics. This is further reinforced by the finding that, even without uncertainty, the optimal decision for a single child might not extend to all children in a larger household. Therefore, the model's predictions about the optimal proportion of children in school are notably altered when considering the impact of both uncertainty and the number of children in the family. This analysis suggests that educational policies which solely address the cost side of human capital investment—by tackling poverty and liquidity constraints—may prove insufficient for achieving full school enrollment. Supplementing these policies with strategies designed to address future income uncertainty and its impact on risk diversification within rural households is seen as crucial for effectively enhancing school enrollment rates.