| Summary: | This dissertation addresses statistical methods for understanding treatment effect variation in randomized experiments, both in terms of variation across pre-treatment covariates and variation across post-randomization intermediate outcomes. These methods are then applied to data from the National Head Start Impact Study (HSIS), a large-scale randomized evaluation of the Federally funded preschool program, which has become an important part of the policy debate in early childhood education.
Chapter 2 proposes a randomization-based approach for testing for the presence of treatment effect variation not explained by observed covariates. The key challenge in using this approach is the fact that the average treatment effect, generally the object of interest in randomized experiments, actually acts as a nuisance parameter in this setting. We explore potential solutions and advocate for a method that guarantees valid tests in finite samples despite this nuisance. We also show how this method readily extends to testing for heterogeneity beyond a given model, which can be useful for assessing the sufficiency of a given scientific theory. We finally apply this method to the HSIS and find that there is indeed significant unexplained treatment effect variation.
Chapter 3 leverages model-based principal stratification to assess treatment effect variation across an intermediate outcome in the HSIS. In particular, we estimate differential impacts of Head Start by alternative care setting, the care that children would receive in the absence of the offer to enroll in Head Start. We find strong, positive short-term effects of Head Start on receptive vocabulary for those Compliers who would otherwise be in home-based care. By contrast, we find no meaningful impact of Head Start on vocabulary for those Compliers who would otherwise be in other center-based care. Our findings suggest that alternative care type is a potentially important source of variation in Head Start.
Chapter 4 reviews the literature on the use of principal score methods, which rely on predictive covariates rather than outcomes for estimating principal causal effects. We clarify the role of the Principal Ignorability assumption in this approach and show that there are in fact two versions: Strong and Weak Principal Ignorability. We then explore several proposed in the literature and assess their finite sample properties via simulation. Finally, we propose some extensions to the case of two-sided noncompliance and apply these ideas to the HSIS, finding mixed results. === Statistics
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