Dealing with Logs and Zeros in Regression Models

Log-linear and log-log regressions are one of the most used statistical models. 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. However, this method may suffer from numerical issues when the variance of the dependent variable is high. We introduce a new complementary solution that is appropriate for this situation and which consists in adding a positive value specific to each observation. We illustrate this method by revisiting a recent field experiment on the impact of consulting services on small and medium firms in Mexico