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Dealing with the log of zero in regression models


  • Christophe BELLEGO


  • Louis-Daniel PAPE

    (CREST; Ecole Polytechnique.)


Log-linear and log-log regressions are one of the most used statistical model. 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. We then introduce a new complementary solution to deal with zeros consisting in adding a positive value specific to each observation that avoids some numerical issues faced by the former.

Suggested Citation

  • Christophe BELLEGO & Louis-Daniel PAPE, 2019. "Dealing with the log of zero in regression models," Working Papers 2019-13, Center for Research in Economics and Statistics.
  • Handle: RePEc:crs:wpaper:2019-13

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    References listed on IDEAS

    1. Keith Head & Thierry Mayer, 2019. "Brands in Motion: How Frictions Shape Multinational Production," American Economic Review, American Economic Association, vol. 109(9), pages 3073-3124, September.
    2. David McKenzie, 2017. "Identifying and Spurring High-Growth Entrepreneurship: Experimental Evidence from a Business Plan Competition," American Economic Review, American Economic Association, vol. 107(8), pages 2278-2307, August.
    3. Ravallion, Martin, 2017. "A concave log-like transformation allowing non-positive values," Economics Letters, Elsevier, vol. 161(C), pages 130-132.
    4. Rogowski, Jeannette A. & Newhouse, Joseph P., 1992. "Estimating the indirect costs of teaching," Journal of Health Economics, Elsevier, vol. 11(2), pages 153-171, August.
    5. S. R. Johnson & Gordon C. Rausser, 1971. "Effects of Misspecifications of Log-Linear Functions When Sample Values are Zero or Negative," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 53(1), pages 120-124.
    6. Chiara Criscuolo & Ralf Martin & Henry G. Overman & John Van Reenen, 2019. "Some Causal Effects of an Industrial Policy," American Economic Review, American Economic Association, vol. 109(1), pages 48-85, January.
    7. Marc F. Bellemare & Casey J. Wichman, 2020. "Elasticities and the Inverse Hyperbolic Sine Transformation," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 82(1), pages 50-61, February.
    8. J. M. C. Santos Silva & Silvana Tenreyro, 2006. "The Log of Gravity," The Review of Economics and Statistics, MIT Press, vol. 88(4), pages 641-658, November.
    9. Sergio Correia & Paulo Guimarães & Tom Zylkin, 2020. "Fast Poisson estimation with high-dimensional fixed effects," Stata Journal, StataCorp LP, vol. 20(1), pages 95-115, March.
    10. repec:hal:spmain:info:hdl:2441/mlkvtnbqe9pg8nsvf612mcnbs is not listed on IDEAS
    11. Gourieroux, Christian & Monfort, Alain & Trognon, Alain, 1984. "Pseudo Maximum Likelihood Methods: Applications to Poisson Models," Econometrica, Econometric Society, vol. 52(3), pages 701-720, May.
    12. David Card & Stefano DellaVigna, 2017. "What do Editors Maximize? Evidence from Four Leading Economics Journals," NBER Working Papers 23282, National Bureau of Economic Research, Inc.
    13. MaCurdy, Thomas E & Pencavel, John H, 1986. "Testing between Competing Models of Wage and Employment Determination in Unionized Markets," Journal of Political Economy, University of Chicago Press, vol. 94(3), pages 3-39, June.
    14. S. R. Johnson & Gordon C. Rausser, 1971. "Effects of Misspecifications of Log-Linear Functions When Sample Values Are Zero or Negative: Reply," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 53(4), pages 673-674.
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    More about this item


    Log(0); Log of zero; Log-log; Bias; Elasticity; PPML;
    All these keywords.

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