Dealing with Logs and Zeros in Regression Models

CREST - Série des Documents de Travail n° 2019-13

71 Pages Posted: 5 Sep 2019 Last revised: 5 Apr 2022

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

HEC Montreal; CREST - ENSAE

Louis-Daniel Pape

CREST - Institut Polytechnique de Paris

Date Written: March 22, 2022

Abstract

Log-linear models are prevalent in empirical research. Yet, how to handle zeros in the dependent variable remains an unsettled issue. This article clarifies it and addresses the ``log of zero'' by developing a new family of estimators called iterated Ordinary Least Squares (iOLS). This family nests standard approaches such as log-linear and Poisson regressions, offers several computational advantages, and corresponds to the correct way to perform the popular log(Y+1) transformation. We extend it to the endogenous regressor setting (i2SLS) and overcome other common issues with Poisson models, such as controlling for many fixed-effects. We also develop specification tests to help researchers select between alternative estimators. Finally, our methods are illustrated through numerical simulations and replications of landmark 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 Benatia, David and Pape, Louis-Daniel, Dealing with Logs and Zeros in Regression Models (March 22, 2022). 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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