The share of household resources devoted to children is hard to identify because consumption is measured at the household level and goods can be shared. Using semiparametric restrictions on individual preferences within a collective model, we identify how total household resources are divided up among household members by observing how each family member's expenditures on a single private good like clothing vary with income and family size. Using data from Malawi we show how resources devoted to wives and children vary by family size and structure, and we find that standard poverty indices understate the incidence of child poverty. (JEL I31, I32, J12, J13, O12, O15)

Resource shares, defined as the fraction of total household spending going to each person in a household, are important for assessing individual material well-being, inequality and poverty. They are difficult to identify because consumption is measured typically at the household level, and many goods are jointly consumed, so that individual-level consumption in multi-person households is not directly observed. We consider random resource shares, which vary across observationally identical households. We provide theorems that identify the distribution of random resource shares across households, including children's shares. We also provide a new method of identifying the level of fixed or random resource shares that does not require previously needed preference similarity restrictions or marriage market assumptions. Our results can be applied to data with or without price variation. We apply our results to households in Malawi, estimating the distributions of child and female poverty across households.

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In this paper we propose a "behavioral equilibrium" definition for a class of dynamic games of perfect information. We document various experimental studies of the Centipede Game in the literature that demonstrate that players rarely follow the subgame perfect equilibrium strategies. Although some theoretical modifications have been proposed to explain the outcomes of the experiments, we offer another: players can choose whether or not to believe that their opponents use subgame perfect equilibrium strategies. We define a "behavioral equilibrium" for this game; using this equilibrium concept, we can reproduce the outcomes of those experiments.