Is the Quantity-Quality Trade-Off a Trade-Off for All, None, or Some?

The article provides a simple theoretical framework to motivate the distributional analysis. Most existing empirical studies focus on education as a measure of child quality and are limited to linear regression analysis. While such results are easily interpretable, at best they provide evidence of the average effect of the number of children on child-specific investments. Specifically, the impact of an exogenous increase in fertility depends on the resultant change in the shadow price of child quality. Assuming that households take into account their spouses' fertility history, this definition includes any children from previous marriages. If this is the case, then the first- and second-born children in these smaller households will be younger on average than the first- and second-born children in larger households. The second requirement for a valid instrument is independence. The instrument must be independent of potential health outcomes.