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What's Logs Got to do With it: On the Perils of log Dependent Variables and Difference-in-Differences

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  • Brendon McConnell

Abstract

The log transformation of the dependent variable is not innocuous when using a difference-in-differences (DD) model. With a dependent variable in logs, the DD term captures an approximation of the proportional difference in growth rates across groups. As I show with both simulations and two empirical examples, if the baseline outcome distributions are sufficiently different across groups, the DD parameter for a log-specification can be different in sign to that of a levels-specification. I provide a condition, based on (i) the aggregate time effect, and (ii) the difference in relative baseline outcome means, for when the sign-switch will occur.

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  • Brendon McConnell, 2023. "What's Logs Got to do With it: On the Perils of log Dependent Variables and Difference-in-Differences," Papers 2308.00167, arXiv.org, revised Aug 2023.
    • Handle: RePEc:arx:papers:2308.00167
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    as
    1. Emily Breza & Supreet Kaur & Yogita Shamdasani, 2018. "The Morale Effects of Pay Inequality," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 133(2), pages 611-663.
    2. Simon Jäger & Benjamin Schoefer & Jörg Heining, 2021. "Labor in the Boardroom," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 136(2), pages 669-725.
    3. Stephan Heblich & Stephen J Redding & Daniel M Sturm, 2020. "The Making of the Modern Metropolis: Evidence from London," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 135(4), pages 2059-2133.
    4. Vasco M Carvalho & Makoto Nirei & Yukiko U Saito & Alireza Tahbaz-Salehi, 2021. "Supply Chain Disruptions: Evidence from the Great East Japan Earthquake," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 136(2), pages 1255-1321.
    5. David Card & Stefano DellaVigna & Patricia Funk & Nagore Iriberri, 2020. "Are Referees and Editors in Economics Gender Neutral?," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 135(1), pages 269-327.
    6. Ufuk Akcigit & John Grigsby & Tom Nicholas & Stefanie Stantcheva, 2022. "Taxation and Innovation in the Twentieth Century," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 137(1), pages 329-385.
    7. Davide Cantoni & Jeremiah Dittmar & Noam Yuchtman, 2018. "Religious Competition and Reallocation: the Political Economy of Secularization in the Protestant Reformation," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 133(4), pages 2037-2096.
    8. Stephen Hansen & Michael McMahon & Andrea Prat, 2018. "Transparency and Deliberation Within the FOMC: A Computational Linguistics Approach," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 133(2), pages 801-870.
    9. Lisa Cameron & Jennifer Seager & Manisha Shah, 2021. "Crimes Against Morality: Unintended Consequences of Criminalizing Sex Work," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 136(1), pages 427-469.
    10. Katrine Jakobsen & Kristian Jakobsen & Henrik Kleven & Gabriel Zucman, 2020. "Wealth Taxation and Wealth Accumulation: Theory and Evidence From Denmark," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 135(1), pages 329-388.
    11. Barbara Biasi & Heather Sarsons, 2022. "Flexible Wages, Bargaining, and the Gender Gap," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 137(1), pages 215-266.
    12. Sarah Miller & Norman Johnson & Laura R Wherry, 2021. "Medicaid and Mortality: New Evidence From Linked Survey and Administrative Data," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 136(3), pages 1783-1829.
    13. Paula Bustos & Gabriel Garber & Jacopo Ponticelli, 2020. "Capital Accumulation and Structural Transformation [“Capital Deepening and Nonbalanced Economic Growth”]," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 135(2), pages 1037-1094.
    14. Joshua D. Angrist & Jörn-Steffen Pischke, 2009. "Mostly Harmless Econometrics: An Empiricist's Companion," Economics Books, Princeton University Press, edition 1, number 8769.
    15. Marcella Alsan & Marianne Wanamaker, 2018. "Tuskegee and the Health of Black Men," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 133(1), pages 407-455.
    16. Alonso Alfaro-Ureña & Isabela Manelici & Jose P Vasquez, 2022. "The Effects of Joining Multinational Supply Chains: New Evidence from Firm-to-Firm Linkages," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 137(3), pages 1495-1552.
    17. Nicolai V. Kuminoff & Jaren C. Pope, 2014. "Do “Capitalization Effects” For Public Goods Reveal The Public'S Willingness To Pay?," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 55(4), pages 1227-1250, November.
    18. David A Keiser & Joseph S Shapiro, 2019. "Consequences of the Clean Water Act and the Demand for Water Quality," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 134(1), pages 349-396.
    19. Simon Jäger & Benjamin Schoefer & Samuel Young & Josef Zweimüller, 2020. "Wages and the Value of Nonemployment," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 135(4), pages 1905-1963.
    20. Guojun He & Shaoda Wang & Bing Zhang, 2020. "Watering Down Environmental Regulation in China," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 135(4), pages 2135-2185.
    21. Bradley Setzler & Felix Tintelnot, 2021. "The Effects of Foreign Multinationals on Workers and Firms in the United States," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 136(3), pages 1943-1991.
    22. Emily Breza & Cynthia Kinnan, 2021. "Measuring the Equilibrium Impacts of Credit: Evidence from the Indian Microfinance Crisis," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 136(3), pages 1447-1497.
    23. H. Spencer Banzhaf, 2021. "Difference-in-Differences Hedonics," Journal of Political Economy, University of Chicago Press, vol. 129(8), pages 2385-2414.
    24. Park, Sujeong & Powell, David, 2021. "Is the rise in illicit opioids affecting labor supply and disability claiming rates?," Journal of Health Economics, Elsevier, vol. 76(C).
    25. Fernando Alvarez & David Argente, 2022. "On the Effects of the Availability of Means of Payments: The Case of Uber," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 137(3), pages 1737-1789.
    26. Paul J Eliason & Benjamin Heebsh & Ryan C McDevitt & James W Roberts, 2020. "How Acquisitions Affect Firm Behavior and Performance: Evidence from the Dialysis Industry," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 135(1), pages 221-267.
    27. Meredith Fowlie & Michael Greenstone & Catherine Wolfram, 2018. "Do Energy Efficiency Investments Deliver? Evidence from the Weatherization Assistance Program," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 133(3), pages 1597-1644.
    28. Meyer, Bruce D, 1995. "Natural and Quasi-experiments in Economics," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(2), pages 151-161, April.
    29. Amanda Agan & Sonja Starr, 2018. "Ban the Box, Criminal Records, and Racial Discrimination: A Field Experiment," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 133(1), pages 191-235.
    30. Ciani Emanuele & Fisher Paul, 2019. "Dif-in-Dif Estimators of Multiplicative Treatment Effects," Journal of Econometric Methods, De Gruyter, vol. 8(1), pages 1-10, January.
    31. Alessandro Iaria & Carlo Schwarz & Fabian Waldinger, 2018. "Frontier Knowledge and Scientific Production: Evidence from the Collapse of International Science," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 133(2), pages 927-991.
    32. Powell, Lisa M. & Leider, Julien, 2020. "The impact of Seattle’s Sweetened Beverage Tax on beverage prices and volume sold," Economics & Human Biology, Elsevier, vol. 37(C).
    33. Oriana Bandiera & Michael Carlos Best & Adnan Qadir Khan & Andrea Prat, 2021. "The Allocation of Authority in Organizations: A Field Experiment with Bureaucrats," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 136(4), pages 2195-2242.
    34. Jason J Sandvik & Richard E Saouma & Nathan T Seegert & Christopher T Stanton, 2020. "Workplace Knowledge Flows," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 135(3), pages 1635-1680.
    35. Clare Balboni & Oriana Bandiera & Robin Burgess & Maitreesh Ghatak & Anton Heil, 2022. "Why Do People Stay Poor? [“Exploring Poverty Traps and Social Exclusion in South Africa Using Qualitative and Quantitative Data,”]," The Quarterly Journal of Economics, Oxford University Press, vol. 137(2), pages 785-844.
    36. Martin Beraja & Andreas Fuster & Erik Hurst & Joseph Vavra, 2019. "Regional Heterogeneity and the Refinancing Channel of Monetary Policy," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 134(1), pages 109-183.
    37. Goodman-Bacon, Andrew, 2021. "Difference-in-differences with variation in treatment timing," Journal of Econometrics, Elsevier, vol. 225(2), pages 254-277.
    38. Matthew Smith & Danny Yagan & Owen Zidar & Eric Zwick, 2019. "Capitalists in the Twenty-First Century," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 134(4), pages 1675-1745.
    39. Doruk Cengiz & Arindrajit Dube & Attila Lindner & Ben Zipperer, 2019. "The Effect of Minimum Wages on Low-Wage Jobs," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 134(3), pages 1405-1454.
    40. Abby Alpert & William N Evans & Ethan M J Lieber & David Powell, 2022. "Origins of the Opioid Crisis and its Enduring Impacts [Synthetic Control Methods for Comparative Case Studies: Estimating the Effect of California's Tobacco Control Program]," The Quarterly Journal of Economics, Oxford University Press, vol. 137(2), pages 1139-1179.
    41. Ariella Kahn-Lang & Kevin Lang, 2020. "The Promise and Pitfalls of Differences-in-Differences: Reflections on 16 and Pregnant and Other Applications," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 38(3), pages 613-620, July.
    42. Ellora Derenoncourt & Claire Montialoux, 2021. "Minimum Wages and Racial Inequality," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 136(1), pages 169-228.
    43. Evan K Rose, 2021. "Who Gets a Second Chance? Effectiveness and Equity in Supervision of Criminal Offenders," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 136(2), pages 1199-1253.
    44. Patrick Kline & Neviana Petkova & Heidi Williams & Owen Zidar, 2019. "Who Profits from Patents? Rent-Sharing at Innovative Firms," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 134(3), pages 1343-1404.
    45. Joppe de Ree & Karthik Muralidharan & Menno Pradhan & Halsey Rogers, 2018. "Double for Nothing? Experimental Evidence on an Unconditional Teacher Salary Increase in Indonesia," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 133(2), pages 993-1039.
    46. Desmond Ang, 2021. "The Effects of Police Violence on Inner-City Students," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 136(1), pages 115-168.
    47. Jonathan Roth & Pedro H. C. Sant'Anna, 2023. "When Is Parallel Trends Sensitive to Functional Form?," Econometrica, Econometric Society, vol. 91(2), pages 737-747, March.
    48. Christian Dustmann & Attila Lindner & Uta Schönberg & Matthias Umkehrer & Philipp vom Berge, 2022. "Reallocation Effects of the Minimum Wage," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 137(1), pages 267-328.
    49. Abhay Aneja & Guo Xu, 2022. "The Costs of Employment Segregation: Evidence from the Federal Government Under Woodrow Wilson [“The Effects of the 1930s HOLC ‘Redlining’ Maps,”]," The Quarterly Journal of Economics, Oxford University Press, vol. 137(2), pages 911-958.
    50. Jing Cai & Shing-Yi Wang, 2022. "Improving Management Through Worker Evaluations: Evidence from Auto Manufacturing [“Expectations, Wage Hikes, and Worker Voice,”]," The Quarterly Journal of Economics, Oxford University Press, vol. 137(4), pages 2459-2497.
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    2. Jarosław M. Nazarczuk & Marlena Cicha-Nazarczuk, 2024. "Sustainable Employment Creation through the Polish Investment Zone in Lagging Regions," Sustainability, MDPI, vol. 16(12), pages 1-14, June.

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