Dealing with Logs and Zeros in Regression Models
CREST - Série des Documents de Travail n° 2019-13
90 Pages Posted: 5 Sep 2019 Last revised: 3 Jun 2021
Date Written: May 28, 2021
Log-linear models are prevalent in empirical research. Yet, how to handle zeros in the dependent variable has remained obscure. This article clarifies this issue and develops a new family of estimators, called iterated Ordinary Least Squares (iOLS), which offers multiple advantages to address the "log of zero" and embeds Poisson regression as a special case. We extend it to the endogenous regressors setting (i2SLS) and address common issues like the inclusion of many fixed-effects. In addition, we develop specification tests to help researchers select between alternative estimators. Finally, our methods are illustrated through numerical simulations and replications of recent publications.
Keywords: Log(0), Log of zero, Log-log, Bias, Elasticity, PPML, Contraction mapping, Gravity model, Iterative estimator, Log-linear, Selection bias.
JEL Classification: C26, C52, C55
Suggested Citation: Suggested Citation