| Summary: | Includes bibliographical references. === The thesis begins, in chapter 1, with an overview of recent debates concerning the merits of randomised programme evaluations and a detailed review of the literature on the extrapolation of treatment effects ('external validity'). Building on the insights of Cook and Campbell (1979) and a result by Hotz, Imbens, and Mortimer (2005), I then argue that the fundamental challenge to external validity may be interactive relationships between the treatment variable and other covariates. The empirical relevance of this claim is developed through two contributions to the economics of education literature, using data from the Tennessee class size experiment known as 'Project STAR'. Chapter 2 contributes to the literature on teacher quality, describing and implementing a novel method for constructing a value-added quality measure that uses a single cross-section of data in which students and teachers are randomly assigned to different-sized classes. The core insight is that constructing the value-added measure within treatment categories creates a plausible measure of quality that is simultaneously independent of treatment. The analysis of chapter 3 concerns the literature on class size effects. I argue that the effect of class size on educational achievement may be dependent on other class-level factors and that this should be considered when estimating educational production functions. Using the variable constructed in chapter 2, I estimate interaction effects between class size and teacher quality and find a number of statistically and economically significant effects. Specifically, higher quality teachers are associated with more beneficial effects of smaller classes. Those results suggest a possible unification of the class size and teacher quality literatures, with the policy problem being one of finding an optimal combination of these two factors. The broader contribution, further to the analysis of chapter 1, is to illustrate an obstacle to external validity: class size effects are unlikely to be the same across contexts where the teacher quality distribution differs. The experimental estimation of class size effects therefore serves as an empirical case study of the challenges to external validity that arise from interaction.
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