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Dealing with Logs and Zeros in Regression Models

Author

Listed:
  • Christophe Bellégo

    (CREST (UMR 9194), ENSAE, Institut Polytechnique de Paris)

  • David Benatia

    (HEC Montréal, Département d'Economie Appliquée)

  • Louis-Daniel Pape

    (CREST (UMR 9194), ENSAE, Institut Polytechnique de Paris)

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.

Suggested Citation

  • Christophe Bellégo & David Benatia & Louis-Daniel Pape, 2022. "Dealing with Logs and Zeros in Regression Models," Working Papers 2022-08, Center for Research in Economics and Statistics.
  • Handle: RePEc:crs:wpaper:2022-08
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    References listed on IDEAS

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    1. Fernández-Val, Iván & Weidner, Martin, 2016. "Individual and time effects in nonlinear panel models with large N, T," Journal of Econometrics, Elsevier, vol. 192(1), pages 291-312.
    2. Davidson, Russell & MacKinnon, James G, 1981. "Several Tests for Model Specification in the Presence of Alternative Hypotheses," Econometrica, Econometric Society, vol. 49(3), pages 781-793, May.
    3. Ravallion, Martin, 2017. "A concave log-like transformation allowing non-positive values," Economics Letters, Elsevier, vol. 161(C), pages 130-132.
    4. Eaton Jonathan & Tamura Akiko, 1994. "Bilateralism and Regionalism in Japanese and U.S. Trade and Direct Foreign Investment Patterns," Journal of the Japanese and International Economies, Elsevier, vol. 8(4), pages 478-510, December.
    5. Rainer Winkelmann, 2008. "Econometric Analysis of Count Data," Springer Books, Springer, edition 0, number 978-3-540-78389-3, December.
    6. Silva João M. C. Santos & Tenreyro Silvana & Windmeijer Frank, 2015. "Testing Competing Models for Non-negative Data with Many Zeros," Journal of Econometric Methods, De Gruyter, vol. 4(1), pages 29-46, January.
    7. John Mullahy, 1997. "Instrumental-Variable Estimation Of Count Data Models: Applications To Models Of Cigarette Smoking Behavior," The Review of Economics and Statistics, MIT Press, vol. 79(4), pages 586-593, November.
    8. Dominitz, Jeff & Sherman, Robert P., 2005. "Some Convergence Theory For Iterative Estimation Procedures With An Application To Semiparametric Estimation," Econometric Theory, Cambridge University Press, vol. 21(4), pages 838-863, August.
    9. Manning, Willard G. & Mullahy, John, 2001. "Estimating log models: to transform or not to transform?," Journal of Health Economics, Elsevier, vol. 20(4), pages 461-494, July.
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    Cited by:

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    3. Glediana Zeneli (Foto) & Arsen Benga & Altin Hoti, 2024. "Analysis of Albania’s Trade Direction: Is the Open Balkan a New Center of Gravity?," Economies, MDPI, vol. 12(7), pages 1-30, July.
    4. Reda Cherif & Christoph Grimpe & Fuad Hasanov & Wolfgang Sofka, 2023. "Promoting Innovation: The Differential Impact of R&D Subsidies," Journal of Industry, Competition and Trade, Springer, vol. 23(3), pages 187-241, December.
    5. Gustave Kenedi & Louis Sirugue, 2021. "The Anatomy of Intergenerational Income Mobility in France and its Spatial Variations," PSE Working Papers halshs-03455282, HAL.
    6. Congiu, Raffaele & Sabatino, Lorien & Sapi, Geza, 2022. "The Impact of Privacy Regulation on Web Traffic: Evidence From the GDPR," Information Economics and Policy, Elsevier, vol. 61(C).
    7. Gustave Kenedi & Louis Sirugue, 2021. "The Anatomy of Intergenerational Income Mobility in France and its Spatial Variations," Working Papers halshs-03455282, HAL.
    8. Qiao Wen, 2022. "Estimating Education and Labor Market Consequences of China’s Higher Education Expansion," Sustainability, MDPI, vol. 14(13), pages 1-25, June.
    9. Mengzhen Wang & Xingong Ding & Baekryul Choi, 2023. "FDI or International-Trade-Driven Green Growth of 24 Korean Manufacturing Industries? Evidence from Heterogeneous Panel Based on Non-Causality Test," Sustainability, MDPI, vol. 15(7), pages 1-20, March.
    10. Carlos Alberto Piscarreta Pinto Ferreira, 2023. "Drivers of Sovereign Bond Demand – The Case of Japans," Working Papers REM 2023/0264, ISEG - Lisbon School of Economics and Management, REM, Universidade de Lisboa.

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    More about this item

    Keywords

    Contraction mapping; Elasticity; Gravity model; Iterative estimator; Log-linear; Selection bias;
    All these keywords.

    JEL classification:

    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C55 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Large Data Sets: Modeling and Analysis

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