Exploring complete school effectiveness via quantile value added

Summary

In education studies value added is by and large defined in terms of a test score distribution mean. Therefore, all except a particular summary of the test score distribution is ignored. Developing a value‐added definition that incorporates the entire conditional distribution of students' scores given school effects and control variables would produce a more complete picture of a school's effectiveness and as a result provide more accurate information that could better guide policy decisions. Motivated in part by the current debate surrounding the recent proposal of eliminating co‐payment institutions as part of Chile's education reform, we provide a new definition of value added that is based on the quantiles of the conditional test score distribution. Further, we show that the quantile‐based value added can be estimated within a quantile mixed model regression framework. We apply the methodology to Chilean standardized test data and explore how information garnered facilitates school effectiveness comparisons between public schools and those that are subsidized with and without co‐payments.