  School accountability systems increasingly hold schools to account for their
performances using value-added models purporting to measure the effects of
schools on student learning. The most common approach is to fit a linear
regression of student current achievement on student prior achievement, where
the school effects are the school means of the predicted residuals. In the
literature, further adjustments are usually made for student sociodemographics
and sometimes school composition and 'non-malleable' characteristics. However,
accountability systems typically make fewer adjustments: for transparency to
end users, because data is unavailable or of insufficient quality, or for
ideological reasons. There is therefore considerable interest in understanding
the extent to which simpler models give similar school effects to more
theoretically justified but complex models. We explore these issues via a case
study and empirical analysis of England's 'Progress 8' secondary school
accountability system.
