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

Bibliographic Data

ID21512759
AuthorsJohn Mullahy (0000-0001-8605-3899, Department of Population Health Sciences University of Wisconsin–Madison Madison Wisconsin USA), Edward C Norton (0000-0003-4555-0631, NBER Cambridge Massachusetts USA, corresponding author)
Year2024
Volume86
Issue2
Pages417-447
Publication date2024-04-01
Peer ReviewedYes
Open AccessYes
TypeARTICLE
VenueOxford Bulletin of Economics and Statistics (JOURNAL)
Journal identifiersISSN: 0305-9049 • E-ISSN: 1468-0084
PublisherWiley (PUBLISHER • GB)
DOI10.1111/obes.12583
OpenAlexW4388689099
LanguageEN
Citations received20
References cited57

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

Econometrics · Inverse · Linear regression · Mathematical analysis · Poisson distribution · Statistics · Income, Poverty, and Inequality · Mathematics · Monetary Policy and Economic Impact · Statistical Methods and Inference · Applied Mathematics

Tools

Open DOIOpen Access