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Poorly measured confounders are more useful on the left than on the right

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  • Pei, Zhuan
  • Pischke, Jorn-Steffen
  • Schwandt, Hannes

Abstract

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.

Suggested Citation

  • Pei, Zhuan & Pischke, Jorn-Steffen & Schwandt, Hannes, 2018. "Poorly measured confounders are more useful on the left than on the right," LSE Research Online Documents on Economics 88352, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:88352
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    More about this item

    Keywords

    Balancing; variable addition; robustness checks; specification testing; Hausman test;
    All these keywords.

    JEL classification:

    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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