Beyond LATE with a Discrete Instrument
展示了如何利用离散工具变量识别边际处理效应，允许个体存在异质性和自选择，并应用于分析子女数量与质量之间的权衡，发现家庭规模效应的大小甚至符号会变化。
We show how a discrete instrument can be used to identify the marginal treatment effects under a functional structure that allows for treatment heterogeneity among individuals with the same observed characteristics and self-selection based on the unobserved gain from treatment. Guided by this identification result, we perform a marginal treatment effect analysis of the interaction between the quantity and quality of children. Our estimates reveal that the family size effects vary in magnitude and even sign and that families act as if they possess some knowledge of the idiosyncratic effects in the fertility decision.