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

Abstract

Applied 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.