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

See all articles by Christophe Bellégo

Christophe Bellégo

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

David Benatia

CREST - ENSAE; HEC Montreal

Louis-Daniel Pape

CREST - Institut Polytechnique de Paris

Date Written: May 28, 2021

Abstract

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

Bellégo, Christophe and Benatia, David and Pape, Louis-Daniel, Dealing with Logs and Zeros in Regression Models (May 28, 2021). CREST - 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

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

Palaiseau
France

David Benatia

CREST - ENSAE ( email )

France

HEC Montreal ( email )

3000, Chemin de la Côte-Sainte-Catherine
Montreal, Quebec H2X 2L3
Canada

Louis-Daniel Pape (Contact Author)

CREST - Institut Polytechnique de Paris ( email )

Route de Saclay
Palaiseau, 91120
France

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