Many literatures investigate the causal impact of income on economic outcomes, for example in the context of intergenerational transmission or well-being and health. Some studies have proposed to use employer wage differentials and in particular industry affiliation as an instrument for income....

Researchers frequently test identifying assumptions in regression based research designs (which include instrumental variables or difference-in-differences models) by adding additional control variables on the right hand side of the regression. If such additions do not affect the coefficient of...