Poorly Measured Confounders are More Useful on the Left than on the Right

Zhuan Pei*, Jörn Steffen Pischke, Hannes Schwandt

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

96 Scopus citations


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 interest (much), a study is presumed to be reliable. We caution that such invariance may result from the fact that the observed variables used in such robustness checks are often 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 derivations for the estimators and test statistics involved, as well as power calculations, which can help applied researchers interpret their findings. We illustrate these results in the context of estimating the returns to schooling.

Original languageEnglish (US)
Pages (from-to)205-216
Number of pages12
JournalJournal of Business and Economic Statistics
Issue number2
StatePublished - Apr 3 2019


  • Balancing
  • C31
  • C52
  • Hausman test
  • Robustness checks
  • Specification testing
  • Variable addition

ASJC Scopus subject areas

  • Statistics and Probability
  • Social Sciences (miscellaneous)
  • Economics and Econometrics
  • Statistics, Probability and Uncertainty


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