120 APPENDIX At the second stage, knowledge capital kj accumulates with schooling in-


vestments sj. The knowledge production function is given as kj = g(sj, hj, x) + εj2,


tarity between schooling and health investments is captured by ——— > 0. An ∂s∂h


where investment g(sj2, hj, x) has health capital as its argument. Complemen- ∂2g


implication of such complementarity (or substitutability) is that parents want to observe the outcome of health capital among their children in order to optimally decide schooling investments in the children. Owing to the sequen- tial nature of human capital investment, parents can learn about the total outcomes of child human capital and their labor-market returns from the out- comes of early-stage nutrition and health investments.7 The household budget constraint in the second stage is


c2 + pΣsj = y + j Σw(hj)[T – sj] + b, j


where w(hj) is the opportunity cost of schooling (returns to health capital), T is the time endowment for the child, p is the school fee, b is savings and


loans, and y is exogenous household income. It is assumed that the opportu- nity costs increase with health capital, that is, w′(h) ≥ 0.8 Assume that the child cannot work at the pre-primary-school stage, and can work in the labor market only when he or she enters school.9


7 Cunha et al. (2004) summarize some key concepts in the sequential development of child human capital. They focus on cognitive and noncognitive development. Their analysis does not directly include health and nutritional status as part of human capital in child development. The exclusion of health capital from the analysis results in a framework in which they can focus on human capital production function and the complementarity and substitutability of different inputs (for example, at the early-childhood and schooling stages). In this appendix, children are also considered as working in the labor market or participating in other activities where health capital has economic returns. This institutional setting creates implications that offset the


health-schooling complementarity effect. 8 It is also important to note that the income opportunity in the child wage w(h) is not necessarily


related to labor markets. It may also capture activities such as child care and self-employment. 9 Several qualifications follow. First, I assume that income from siblings, parents, and credit is pooled in the household budget constraint and is therefore perfectly substitutable. Second, to describe the income process, the model does not assume a production function in which adult and child members supply labor inputs that are not perfectly substitutable. This assumption is suitable in our empirical setting of South Africa, where wage employment (including formal and informal jobs) is a major source of income. Third, the utility function does not include leisure, which is imperfectly substitutable between household members (for example, Pitt and Rosenzweig 1990).


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