Why TransformY? The Pitfalls of Transformed Regressions with a Mass at Zero*

Author:

Mullahy John123ORCID,Norton Edward C.34ORCID

Affiliation:

1. Department of Population Health Sciences University of Wisconsin–Madison Madison Wisconsin USA

2. Health Economics and Policy Analysis Centre, J.E. Cairnes School of Business and Economics University of Galway Galway Ireland

3. NBER Cambridge Massachusetts USA

4. Department of Health Management and Policy and Department of Economics University of Michigan Ann Arbor Michigan USA

Abstract

AbstractApplied economists often transform a dependent variable that is non‐negative and skewed with the natural log transformation, the inverse hyperbolic sine transformation, or power function. We show that these transformations separate the zeros from the positives such that the estimated parameters are related to those from a scaled linear probability model. The retransformed marginal effects and elasticities are sensitive to changes in a shape parameter, ranging in magnitude between those of an untransformed least squares regression and those of a scaled linear probability model. Instead of transforming the dependent variable with non‐negative outcomes that includes zeros, we recommend using a non‐transformed dependent variable, such as a two‐part model, untransformed linear regression, or Poisson.

Publisher

Wiley

Subject

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

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