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Journal article
Poorly Measured Confounders are More Useful on the Left than on the Right
Zhuan Pei, Jörn-Steffen Pischke and Hannes Schwandt
April 2019
Paper No' :

JEL Classification: C31;C52;

Tags: balancing; hausman test; robustness checks; specification testing; variable addition;

Researchers frequently test identifying assumptions in regression based research designs (which include e.g. instrumental variables or differences-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 interest (much) a study is presumed to be reliable. We caution that such invariance may result from the fact that many observed variables are poor measures of the potential underlying confounders. In this case, a more powerful test of the identifying assumption is to put the variable on the left hand side of the candidate regression. We provide relevant derivations for the estimators and test statistics involved, as well as power calculations, which can help applied researchers to interpret their findings. We illustrate these results in the context of various strategies which have been suggested to identify the returns to schooling.