Public Schools versus Private Schools: Causal Inference with Partial Compliance

An approach to handle partial compliance behavior using principal stratification is presented and applied to a subset of the longitudinal data from the New York City School Choice Scholarship Program, a randomized experiment designed to assess the effects of private schools versus public schools on academic achievement. The initial analysis suggests an interesting relationship between compliance with the offer and academic achievement, including a possible "beneficial rejected offer" effect and a possible "adjustment hardship" effect. These results seem to favor public schools in the sense they suggest that the collection of students who would attend private school when offered the scholarship but attend public school without the offer had a lower average posttest score if they attended private school than if they attended public school. This case study illustrates the strengths of principal stratification: the explicit examination of specific assumptions and directly interpretable results with possible policy implications. (Contains 9 tables and 2 figures.)