Dealing with logs and zeros in regression models

Prevalence of the Log of Zero in the AER (2016-2020)


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.

Working Paper (New version soon)
David Benatia
David Benatia
Assistant Professor of Economics