This paper presents a new identification result for causal effects of group-level variables when agents select into groups. The model allows for group selection to be based on individual unobserved heterogeneity. This feature leads to correlation between group-level covariates and unobserved individual heterogeneity. Whereas many of the existing identification strategies rely on instrumental variables for group selection, I introduce alternative identifying conditions which involve individual-level covariates that "shift" the distribution of unobserved heterogeneity . 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) .
I develop a new identification approach for partial effects in nonseparable models with endogeneity. I use a proxy variable for the unobserved heterogeneity correlated with the endogenous variable 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 .
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This paper presents
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result for causal effects of group-level variables when agents select into groups. The model allows for group selection to be based on individual unobserved heterogeneity. This feature leads to correlation between group-level covariates and unobserved individual heterogeneity. Whereas many of the existing identification strategies rely on instrumental variables for group selection, I introduce alternative identifying conditions which involve individual-level covariates that "shift" the distribution of unobserved heterogeneity . I use these conditions
approach for partial effects in nonseparable models with endogeneity. I use a proxy variable for the unobserved heterogeneity correlated with the endogenous variable
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. 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)
, 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