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

2023/11/14 by John Mullahy, Edward C. Norton · 1 voice · 5 citations
Economics, Econometrics and Finance · Mathematics · Social Sciences · #Income, Poverty, and Inequality #Monetary Policy and Economic Impact #Statistical Methods and Inference

paper · pdf · doi:10.1111/obes.12583

openalex publication_date 2023/11/14 · openalex created_date 2023/11/16 · openalex updated_date 2026/07/27

Abstract

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.

Citations

• Some Statistical Models for Limited Dependent Variables with Application to the Demand for Durable Goods
• Transforming the Dependent Variable in Regression Models
• Elasticities and the Inverse Hyperbolic Sine Transformation
• Logs with Zeros? Some Problems and Solutions
• Estimation of Limited Dependent Variable Models With Dummy Endogenous Regressors

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Discussions

• @johnmullahy.bsky.social & @nickchk.bsky.social Also have interesting & intuitive papers on transforming y and linear rescaling 1. onlinelibrary.wiley.com/doi/10.1111/... 2. arxiv.org/abs/2106.0 [bsky, 3 points, 0 comments]

Related

• Dimensional Analysis and Logarithmic Transformations in Applied Economics
• Non-Robustness in Log-Like Specifications
• Elasticities and the Inverse Hyperbolic Sine Transformation
• Transforming the Dependent Variable in Regression Models
• Reversals of Least-Squares Estimates and Model-Independent Estimation for Directions of Unique Effects