Treatment Effect Heterogeneity in Theory and Practice

Instrumental Variables (IV) methods identify internally valid causal effects for individuals whose treatment status is manipulable by the instrument at hand. Inference for other populations inevitably requires some sort of homogeneity assumption. I develop a simple theoretical framework that nests all possible homogeneity assumptions for a causal treatment-effects model with a binary instrument. This framework suggests a new specification test for selection bias and simple strategies for using IV to estimate average treatment effects. These ideas are illustrated in an application using sibling-sex composition to estimate the effect of child-bearing on marital status, poverty status, and welfare receipt for the population of mothers with two or more children. The application is motivated by American welfare reform, which penalizes further childbearing by welfare mothers on the grounds that additional childbearing makes continued poverty and welfare receipt more likely. The results generally support this conjecture, though the ability to make sharp distinctions between alternative average effects is limited by the imprecision of IV estimates.