122 APPENDIX β ——— ∂2g ∂sj∂hj
—— RkV′(cj) + βV″(cj)Rk —— Rk —— + Rh ∂sj
∂g
≥ < w′(hj)u′(c2
{ ∂g
*) + {w(hj) + p} ————— . ∂hj
∂hj ∂u′(c2
*)
There are four effects in this condition. First, the complementarity effect is summarized in the first term on the left-hand side, which increases school- ing investment. Second, the concavity of the child utility function (that is, V″(cj) < 0) creates incentives to equalize the human capital outcomes and the future returns, which decreases schooling investment for children with greater health capital (the second term on the left-hand side). Parents are averse to sibling inequality. Third, an increase in health capital augments income opportunity outside school, which increases the opportunity cost of school- ing investment (the first term on the right-hand side). Fourth, an increase in health capital also relaxes the household budget constraint, which weakens the necessity to work outside and increases schooling investment (the second term on the right-hand side). Whether or not health capital increases school- ing investment depends on the magnitudes of these factors. It is easy to see the effect of other siblings’ health capital on schooling. In this case, we only have the budget-relaxing effect, and an increase of other siblings’ health capital always relaxes the household budget constraint, which increases schooling investment.10 Interestingly, however, the effect of other siblings’ health capital on schooling investment exists only when the financial market is imperfect. An exogenous improvement in other siblings’ health relaxes the budget constraint, which reduces the marginal utility λ*. If liquidity constraint is more likely to bind as the household income drops, the sibling effect is more likely to hold among poor households. This does not happen when the loan market is perfect.
We have two other conjectures. First, in the case of the convex return
function Rk, for which the second-order condition does not always hold, we expect some corner solutions. Parents can maximize welfare by investing in
some children while ignoring others. When health capital is complementary to schooling investment, parents concentrate schooling investments in well- endowed children, if the labor market wage is constant. However, greater health capital also raises opportunity costs, which decreases schooling invest-
10 See Parrish and Willis (1993) for related evidence. See also Black, Devereux, and Salvanes (2005) for birth-order effects on child education.
}
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