Bayesian Modeling of School Effects UsingHierarchical Models with Smoothing Priors

We describe a new and flexible framework for modeling school effects. Like previouswork in this area, we introduce an empirical model that evaluates school performance onthe basis of student level test-score gains. Unlike previous work, however, we introducea flexible model that relates follow-up student test scores to baseline student test scoresand explore for possible nonlinearities in these relationships.Using data from High School and Beyond (HSB) and adapting the methodologydescribed in Koop and Poirier (2004a), we test and reject the use of specifications thathave been frequently used in research and as a basis for policy. We find that nonlinear-ities are important in the relationship between intake and follow-up achievement, thatrankings of schools are sensitive to the model employed, and importantly, that com-monly used specifications can give different and potentially misleading assessments ofschool performance. When estimating our preferred semiparametric specification, wefind small but \significant" impacts of some school quality proxies (such as district-levelexpenditure per pupil) in the production of student achievement.[...]