Dealing with Logs and Zeros in Regression Models

Série des Documents de Travail n° 2019-13

20 Pages Posted: 5 Sep 2019 Last revised: 1 Apr 2020

See all articles by Christophe Bellégo

Christophe Bellégo

CREST (Center for Research in Economics and Statistics) - ENSAE (National School for Statistics and Economic Administration)

Louis-Daniel Pape

CREST - Institut Polytechnique de Paris

Date Written: August 28, 2019

Abstract

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.

Keywords: Log(0), Log of zero, Log-log, Bias, Elasticity, PPML

JEL Classification: C18, C51, C87

Suggested Citation

Bellégo, Christophe and Pape, Louis-Daniel, Dealing with Logs and Zeros in Regression Models (August 28, 2019). Série des Documents de Travail n° 2019-13. Available at SSRN: https://ssrn.com/abstract=3444996 or http://dx.doi.org/10.2139/ssrn.3444996

Christophe Bellégo (Contact Author)

CREST (Center for Research in Economics and Statistics) - ENSAE (National School for Statistics and Economic Administration) ( email )

Palaiseau
France

Louis-Daniel Pape

CREST - Institut Polytechnique de Paris ( email )

Route de Saclay
Palaiseau, 91120
France

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