Measuring latent economic quantities from observed choices

This paper addresses two central questions in family and economic policy. First, to what extent are estimates of the cost of children derived from two-parent households applicable to single-parent families? Second, are estimated patterns of intra-household resource allocation consistent with benefit rules that condition support uniformly on family size? To address these questions, I propose a collective consumption model for one-adult households, apply it to three datasets—the Family Expenditure Survey, the Expenditures and Food Survey, and the Living Costs and Food Survey in the UK—and present two key findings. First, child cost estimates derived from two-parent households remain externally valid for single-parent families, at least for single mothers. Second, the results find no evidence of per-child resource dilution by family size once estimation uncertainty is accounted for, with differences for fathers appearing only among households at the bottom of the expenditure distribution.

We propose a method for modeling the impact of children on labor supply. Building on equivalence scales and collective models, our approach jointly considers the time and monetary costs of children. By imposing restrictions on childcare technology, we identify the total cost of children from labor supply equations with modest data inputs. We apply the model to single mothers from the 2019 PSID. Results suggest labor supply responsiveness to wages is higher for women with children, while the opposite holds for exogenous incomes. We also estimate the total cost of children and the time spent on childcare.