labor-market returns from the outcomes of early-stage nutrition and health investments.<sup>7</sup> This intrahousehold issue is also important when we think about disaster impacts on child human capital because parents can endogenously control the impacts on children by adjusting resources among siblings.

The household budget constraint in the second stage is where _w_ ( _h_ 1  _D_ 2 ) is child wage, _T_ is time endowment for the child, _p_ is school fee, _b_ ( _k_  _D_ 2<sup>)</sup> is an intertemporal transfer conditional on disaster occurrence, and _y_ is exogenous household income (determined by capital stock and disaster). It is assumed 8 that child wage increases with health capital, that is, _wh_  0 . Assume that child cannot work during the pre-school stage, but can work in the labor market when he or she enters school.<sup>9</sup> Note that we treat _b_ ( _k_  _D_ 2 ) as exogenous, and the detail on this transfer will be discussed below.

Parents maximize the objective function which captures the discounted sum of expected utilities from consumption over time and the final-period returns from children. The discount factor  has an interpretation of altruism to children, who have an increasing and concave utility function _V_ . Assume that _W_ ( _h_ 1  _h_ 2 )  _R h_ 1 1  _R_ 2 _h_ 2 where _R_ 1 and _R_ 2 are financial returns to health and knowledge capital respectively. In this version, since we do not have uncertainty in the future returns to human capital, we omit the expectations operator below. If the wage function is strictly concave, parents have incentives to equalize human capital among their children.

Suppose that _b_ ( _k_  _D_ 2 ) is determined to equalize the discounted marginal utilities between the two periods. For example, agents also borrow cash from their relatives. For the sake of easing tractability, we assume that agents have to pay back in the next period     after disaster recovery. In this setting, we have   _u_ ( _c_ 2 )   _V_ ( _c_ ) where <sup></sup> is the

> 7Cunha 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 complementarity and substitutability of different inputs (e.g., early childhood and schooling stage). Children also work in the labor market where health capital has economic returns. This institutional setting creates implications that offset the health-schooling complementarity effect.

> 8It is also important to note that the income opportunity in the child wage _w_ ( _h_ 1  _D_ 2 ) is not necessarily related to labor markets. It may also capture activities such as child care and self-employment.

> 9Several reservations follow. First, we assume that income from siblings, parents, and credit are pooled in the household budget constraint and therefore are perfectly substitutable. Second, to describe the income process, the model does not assume a production function in which adult and child labor inputs are not perfectly substitutable. Third, the utility function does not include leisure, which is imperfectly substitutable between household members

> (e.g., Pitt and Rosenzweig, 1990).

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