size is equal to the expected marginal cost (production loss in the two periods, part of which depends on _Eu_<sup></sup> ) on the right-hand side. Intuitively, we have a trade-off between income and risk reduction, in which the expected marginal utility and the expected demand for private transfers matter. By reducing _H_ , the household increases current income, but this increases the cost of private transfers (say, borrowing), which may decrease the expected utility if a disaster occurs. Therefore the optimal decision on _H_ depends on the likelihood of disasters and public assistance as well as risk aversion.8 Note that _H_ does not have to be narrowly defined. For example, a large household size enables agents to diversify and pool risks, which enables agents to ensure post-disaster private transfers to smooth consumption. Holding livestock is also known to increase production as well as enhance income smoothing (selling bullocks when income drops, which however decreases the next-period production). We summarize results in the proposition below.

# **Proposition 1** :

_(i) An increase in disaster probability increases the share of assets that promote post-disaster private transfers (e.g., human capital)._<sup>9</sup> _(ii) Good targeting of public assistance conditional on a disaster reduces the incentive to hold transferrable assets and increases investment in child schooling._ _(iii) Disaster decreases schooling investment unless disaster is perfectly insured._ In the next section, we will discuss the empirical strategy to test the above hypotheses.

# **3. Econometric Framework**

In this section we describe an econometric framework to clarify the hypotheses to test regarding ex-ante and ex-post actions. We use schooling progression - the number of years completed during a period to investigate how disasters affect human capital formation in the affected and unaffected areas. As discussed more carefully in the next section, the analysis utilizes data on actual natural disaster occurrences: the 1998 flood in Bangladesh, and 2001 droughts in Ethiopia and Malawi.

Strictly speaking, the use of child schooling to measure disaster impacts may be problematic since disasters may affect not only marginal utility (due to income reduction) but also the opportunity cost for schooling investment (i.e., a decrease in labor-market wage). The former decreases schooling investment in order to smooth consumption over time, but the latter increases investment since a decrease in wage reduces opportunity costs of schooling, thereby increasing the incentive to allocate more

> 8If _p_ ( _e_  _z_ ) is high and _p_ ( _x_  _z_ ) is low (i.e., disaster is likely to occur but public assistance is small), _Eu_   

> increases and _H_<sup></sup> is larger (  _r_ ( _H_ ) becomes larger). If _r_ ( _H_ ) is sufficiently large, the change in the

> right-hand side ( _Eu_<sup></sup> ) is small, and the left-hand side increases. In this case, agents will increase human capital in the initial stage. Good targeting, represented by higher _p_ ( _x_  _z_ ) , will substitute for private transfers, and therefore decreases the proportion of total assets allocated to human capital.

> 9 _Note that private transfer t_ ( _e_  _x H_ ) _is dependent on disaster occurence, public assistance and ex-ante asset allocation. In the empirical analysis, we do not directly use the information on private transfers, but rather infer the effects from how ex-ante assets alter the impact of disasters on child schooling investment._

7