Strategies to address normal distribution assumption concerns can quickly lead to the log transformation of variables. However, what to do with "zeros" in a variable requiring log transformation persists as an under-studied issue. And one well-known example, punitive damage awards, makes clear that such "zeros problems" are not uncommon in many empirical legal research projects.
In Dealing With the Log of Zero in Regression Models, the authors, Christophe Bellego (Center for Research in Economics and Statistics) and Louis-Danile Pape (Center for Research in Economics and Statistics), engage with this nettlesome issue head-on. The brief (15 pp.) paper's abstract follows.
"Log-linear and log-log regressions are one of the most used statistical model. However, handling zeros in the dependent and independent variable has remained obscure despite the prevalence of the situation. In this paper, we discuss how to deal with this issue. We show that using Pseudo-Poisson Maximum Likelihood (PPML) is a good practice compared to other approximate solutions. We then introduce a new complementary solution to deal with zeros consisting in adding a positive value specific to each observation that avoids some numerical issues faced by the former."
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