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...

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....

We show that administrative hourly wage data exhibits considerable bunching at round numbers that cannot be explained by rounding of survey respondents. We consider two explanations--worker left-digit bias and employer optimization frictions. We experimentally rule out left-bunching by...