Before revision: 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 .
After revision: This paper presents 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 .