Within-District School Lotteries, District Selection, and The Average Partial Effects of School Inputs

This study proposes an econometric framework to consistently estimate the average partial effects (APE) of school inputs on academic achievement when students are randomly assigned to schools within each school district but endogenously sort across school districts. We illustrate our method by estimating the APE of single-sex schooling and class size on standardized test scores using data from Seoul, Korea in the period of 2008-2009. Our APE estimates are smaller than the estimates from conventional linear regressions with school district fixed effects, which do not fully correct for endogenous district choice and thus suffer from selection bias.