Before revision:  I use these conditions to construct a valid control function . The key identifying requirements on the observable "shifter" variables are likely to hold in settings where a rich array of individual characteristics are observed. The identification strategy is constructive and leads to a semiparametric, regression-based estimator of group-level causal effects, which I show to be consistent and asymptotically normal. A simulation study indicates good finite-sample properties of this estimator. I use my results to re-analyze the effects of school/neighborhood characteristics on student outcomes, following the work of Altonji and Mansfield (2018) .
After revision:  I use these conditions to construct a valid control function , where the definition of a proxy variable is the same as in the measurement error literature. The identifying assumptions are distinct from existing methods, in particular instrumental variables and selection on observables approaches, and I provide an alternative identification strategy in settings where existing approaches are not applicable. Building on the identification result, I consider three estimation approaches, ranging from nonparametric to flexible parametric methods, and characterize asymptotic properties of the proposed estimators .