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Cautions when normalizing the dependent variable in a regression as a z‐score

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  • Jeffrey Penney

Abstract

It is common in empirical analysis to facilitate inference by transforming the dependent variable to follow a standard normal distribution. In this paper, I show that using this transformation results in the estimated treatment effects being systematically attenuated toward zero and bounded in magnitude. The level of attenuation can be empirically relevant. I propose an alternative normalization wherein the dependent variable is divided by the square root of its within variation, which corrects these issues. I show that, in a simple linear regression, the method produces an estimated treatment effect that is numerically identical to Cohen's d.

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  • Jeffrey Penney, 2023. "Cautions when normalizing the dependent variable in a regression as a z‐score," Economic Inquiry, Western Economic Association International, vol. 61(2), pages 402-412, April.
    • Handle: RePEc:bla:ecinqu:v:61:y:2023:i:2:p:402-412
    DOI: 10.1111/ecin.13127
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    References listed on IDEAS

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