Principal Stratification Approach to Broken Randomized Experiments

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Abstract
The precarious state of the educational system in the inner cities of the United States, as well as its potential causes and solutions, have been popular topics of debate in recent years. Part of the difficulty in resolving this debate is the lack of solid empirical evidence regarding the true impact of educational initiatives. The efficacy of so-called “school choice” programs has been a particularly contentious issue. A current multimillion dollar program, the School Choice Scholarship Foundation Program in New York, randomized the distribution of vouchers in an attempt to shed some light on this issue. This is an important time for school choice, because on June 27, 2002 the U.S. Supreme Court upheld the constitutionality of a voucher program in Cleveland that provides scholarships both to secular and religious private schools. Although this study benefits immensely from a randomized design, it suffers from complications common to such research with human subjects: noncompliance with assigned “treatments” and missing data. Recent work has revealed threats to valid estimates of experimental effects that exist in the presence of noncompliance and missing data, even when the goal is to estimate simple intention-to-treat effects. Our goal was to create a better solution when faced with both noncompliance and missing data. This article presents a model that accommodates these complications that is based on the general framework of “principal stratification” and thus relies on more plausible assumptions than standard methodology. Our analyses revealed positive effects on math scores for children who applied to the program from certain types of schools—those with average test scores below the citywide median. Among these children, the effects are stronger for children who applied in the first grade and for African-American children.