IDEAS home Printed from https://ideas.repec.org/p/crs/wpaper/2019-13.html

Dealing with the log of zero in regression models

Author

Listed:
  • Christophe BELLEGO

    (CREST; ENSAE.)

  • Louis-Daniel PAPE

    (CREST; Ecole Polytechnique.)

Abstract

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
    as

    Download full text from publisher

    File URL: http://crest.science/RePEc/wpstorage/2022-08.pdf
    File Function: CREST working paper version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. repec:boc:pcon20:13 is not listed on IDEAS
    2. 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.
    3. 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.
    4. 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.
    5. repec:spo:wpmain:info:hdl:2441/mlkvtnbqe9pg8nsvf612mcnbs is not listed on IDEAS
    6. Ravallion, Martin, 2017. "A concave log-like transformation allowing non-positive values," Economics Letters, Elsevier, vol. 161(C), pages 130-132.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. Sergio Correia & Paulo Guimarães & Tom Zylkin, 2020. "Fast Poisson estimation with high-dimensional fixed effects," Stata Journal, StataCorp LLC, vol. 20(1), pages 95-115, March.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Pedro Salas-Rojo & Juan Gabriel Rodríguez, 2022. "Inheritances and wealth inequality: a machine learning approach," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 20(1), pages 27-51, March.
    2. Francesco Decarolis & Gaétan de Rassenfosse & Leonardo M. Giuffrida & Elisabetta Iossa & Vincenzo Mollisi & Emilio Raiteri & Giancarlo Spagnolo, 2021. "Buyers' role in innovation procurement: Evidence from US military R&D contracts," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 30(4), pages 697-720, November.
    3. Brown, David P., 2022. "Socioeconomic and demographic disparities in residential battery storage adoption: Evidence from California," Energy Policy, Elsevier, vol. 164(C).
    4. Douglas L Campbell & Karsten Mau, 2021. "On “Trade Induced Technical Change: The Impact of Chinese Imports on Innovation, IT, and Productivity”," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 88(5), pages 2555-2559.
    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. Gustave Kenedi & Louis Sirugue, 2021. "The Anatomy of Intergenerational Income Mobility in France and its Spatial Variations," Working Papers halshs-03455282, HAL.
    7. Ferreira, Carolina Rodrigues Corrêa & Ferreira, Mateus Moreira de Jesus, 2021. "Sanitary and Phytosanitary Measures and Their Effects on World Agricultural Exports," 2021 Conference, August 17-31, 2021, Virtual 315137, International Association of Agricultural Economists.
    8. Piaggio, Matías, 2021. "The value of public urban green spaces: Measuring the effects of proximity to and size of urban green spaces on housing market values in San José, Costa Rica," Land Use Policy, Elsevier, vol. 109(C).
    9. Douglas L. Campbell & Karsten Mau, 2020. "Trade Induced Technological Change: Did Chinese Competition Really Increase European Innovation?," Working Papers w0262, New Economic School (NES).
    10. Khumbo Kalulu & Bernard Thole & Theresa Mkandawire & Grant Kululanga, 2021. "Resource-Efficient Characterisation of Pit Latrine Sludge for Use in Agriculture," Sustainability, MDPI, vol. 13(9), pages 1-16, April.
    11. A. Pronti & J. Berbel, 2025. "Water Demand Elasticity in Agriculture: The Case of the Central Emilia Irrigation Water District," Italian Economic Journal: A Continuation of Rivista Italiana degli Economisti and Giornale degli Economisti, Springer;Società Italiana degli Economisti (Italian Economic Association), vol. 11(3), pages 1267-1300, November.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Carter, Colin A. & Steinbach, Sandro & Zhuang, Xiting, 2022. "Global Shipping Container Disruptions and U.S. Agricultural Exports," Working Papers 320397, International Agricultural Trade Research Consortium.
    2. Breinlich, Holger & Corradi, Valentina & Rocha, Nadia & Ruta, Michele & Silva, J.M.C. Santos & Zylkin, Tom, 2021. "Machine learning in international trade research - evaluating the impact of trade agreements," LSE Research Online Documents on Economics 114379, London School of Economics and Political Science, LSE Library.
    3. Mahdi Ghodsi, 2021. "Impact of Technical Barriers to Trade on the Trade in Goods in the Information and Communications Technology Sector: Differentiating by Aim of the Regulatory Measure," wiiw Working Papers 208, The Vienna Institute for International Economic Studies, wiiw.
    4. Elina Bryngemark & Patrik Söderholm, 2022. "Green industrial policies and domestic production of biofuels: an econometric analysis of OECD countries," Environmental Economics and Policy Studies, Springer;Society for Environmental Economics and Policy Studies - SEEPS, vol. 24(2), pages 225-261, April.
    5. Agostino Capponi & Zhaonan Qu, 2025. "Handling Sparse Non-negative Data in Finance," Papers 2509.01478, arXiv.org.
    6. Bacher, Etienne & Beine, Michel & Rapoport, Hillel, 2025. "Do Anti-Immigration Attitudes Discourage Immigration? Evidence from a New Instrument," IZA Discussion Papers 18192, IZA Network @ LISER.
    7. Jordi Paniagua & Jesús Peiró-Palomino & Andrés J. Picazo-Tadeo, 2021. "Asylum Migration in OECD Countries: In Search of Lost Well-Being," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 153(3), pages 1109-1137, February.
    8. Ahn, Soojung & Kim, Dongin & Steinbach, Sandro, 2023. "Global Grain Trade Implications of the Russia-Ukraine War," 2023 Annual Meeting, July 23-25, Washington D.C. 335482, Agricultural and Applied Economics Association.
    9. Mahdi Ghodsi & Robert Stehrer, 2022. "Trade policy and global value chains: tariffs versus non-tariff measures," Review of World Economics (Weltwirtschaftliches Archiv), Springer;Institut für Weltwirtschaft (Kiel Institute for the World Economy), vol. 158(3), pages 887-916, August.
    10. Nguyen Bich Ngoc & Luu Hai Dang & Ngo Thi Tuyet Mai & Nguyen Thi Thuy Hong & Do Thi Huong & Tran Hoang Ha, 2024. "Heterogeneous trade effects of technical non‐tariff measures: Vietnamese agricultural imports," Asian-Pacific Economic Literature, The Crawford School, The Australian National University, vol. 38(1), pages 131-144, May.
    11. J. M. C. Santos Silva & Silvana Tenreyro, 2022. "The Log of Gravity at 15," Portuguese Economic Journal, Springer;Instituto Superior de Economia e Gestao, vol. 21(3), pages 423-437, September.
    12. Delgadillo Chavarria, Carlos Bruno, 2019. "El Efecto de la Mediterraneidad sobre el Flujo Comercial Internacional: Evidencia Empírica Internacional y para América del Sur (1990-2016) [The Effect of Landlocked Country Status on International Trade Flow: International and South America Empir," MPRA Paper 96294, University Library of Munich, Germany, revised 10 Sep 2019.
    13. Hendrik KRUSE & Thais NUNEZ-ROCHA & Camélia TURCU, 2019. "Infrastructure aid for resource trade? The crossroads of strategy and sustainable development," LEO Working Papers / DR LEO 2728, Orleans Economics Laboratory / Laboratoire d'Economie d'Orleans (LEO), University of Orleans.
    14. Lin, Tao & Zhang, Ling & Wan, Jun & Chen, Chien-Ming & Li, Jianglong, 2025. "Energy price uncertainty and renewable energy technological innovation: Evidence from listed Chinese firms," Renewable and Sustainable Energy Reviews, Elsevier, vol. 213(C).
    15. Mario Larch & Serge Shikher & Constantinos Syropoulos & Yoto V. Yotov, 2022. "Quantifying the impact of economic sanctions on international trade in the energy and mining sectors," Economic Inquiry, Western Economic Association International, vol. 60(3), pages 1038-1063, July.
    16. Delius, Antonia & Sterck, Olivier, 2024. "Cash transfers and micro-enterprise performance: Theory and quasi-experimental evidence from Kenya," Journal of Development Economics, Elsevier, vol. 167(C).
    17. Nicolas Apfel & Holger Breinlich & Nick Green & Dennis Novy & J. M. C. Santos Silva & Tom Zylkin, 2025. "Out-of-sample gravity predictions and trade policy counterfactuals," Papers 2509.11271, arXiv.org, revised Apr 2026.
    18. Steven Yamarik, 2026. "The effects of world heritage sites on bilateral tourism demand," Tourism Economics, , vol. 32(3), pages 570-588, May.
    19. Dongin Kim & Sandro Steinbach, 2024. "The Linder hypothesis for foreign direct investment revisited," Review of International Economics, Wiley Blackwell, vol. 32(4), pages 1901-1928, September.
    20. Adam Gorajek, 2022. "Quasilinear‐mean regression," Journal of Economic Surveys, Wiley Blackwell, vol. 36(5), pages 1288-1310, December.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:crs:wpaper:2019-13. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Secretariat General (email available below). General contact details of provider: https://edirc.repec.org/data/crestfr.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.