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The Inverse Hyperbolic Sine Transformation and Retransformed Marginal Effects

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  • Edward C. Norton

Abstract

This paper shows how to calculate consistent marginal effects on the original scale of the outcome variable in Stata after estimating a linear regression with a dependent variable that has been transformed by the inverse hyperbolic sine function. The method uses a nonparametric retransformation of the error term and accounts for any scaling of the dependent variable. The inverse hyperbolic sine function is not invariant to scaling, which is known to shift marginal effects between those from an untransformed dependent variable to those of a log-transformed dependent variable.

Suggested Citation

  • Edward C. Norton, 2022. "The Inverse Hyperbolic Sine Transformation and Retransformed Marginal Effects," NBER Working Papers 29998, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberwo:29998
    Note: EH TWP
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    Cited by:

    1. D M Zimmer, 2023. "The effect of food stamps on fibre intake," Economic Issues Journal Articles, Economic Issues, vol. 28(2), pages 71-86, September.
    2. Yu Na Lee & Laura Stortz & Mike von Massow & Christopher Kimmerer, 2023. "Impact of ‘‘high in” front‐of‐package nutrition labeling on food choices: Evidence from a grocery shopping experiment," Canadian Journal of Agricultural Economics/Revue canadienne d'agroeconomie, Canadian Agricultural Economics Society/Societe canadienne d'agroeconomie, vol. 71(3-4), pages 277-301, September.
    3. Crossley, Thomas F. & Levell, Peter & Low, Hamish, 2024. "House price rises and borrowing to invest," Journal of Economic Behavior & Organization, Elsevier, vol. 223(C), pages 86-105.
    4. John Mullahy & Edward C. Norton, 2024. "Why Transform Y? The Pitfalls of Transformed Regressions with a Mass at Zero," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 86(2), pages 417-447, April.
    5. Benatti, Nicola & Groiss, Martin & Kelly, Petra & Lopez-Garcia, Paloma, 2024. "The impact of environmental regulation on clean innovation: are there crowding out effects?," Working Paper Series 2946, European Central Bank.
    6. Garz, Marcel & Schneider, Andrea, 2023. "Data sharing and tax enforcement: Evidence from short-term rentals in Denmark," Regional Science and Urban Economics, Elsevier, vol. 101(C).
    7. Buchot, Tom & Couttenier, Mathieu & Laugerette, Lucile & Mougin, Elisa & Verlet, Alexandre, 2024. "A Comment on Bai, Jia &, Yang (2023) Web of Power: How Elite Networks Shaped War and Politics in China," I4R Discussion Paper Series 115, The Institute for Replication (I4R).
    8. Aatishya Mohanty & Nattavudh Powdthavee & Cheng Keat Tang & Andrew J. Oswald, 2024. "Temperature Variability and Natural Disasters," Papers 2409.14936, arXiv.org.
    9. Goncalves, Judite & Merenda, Roxanne & Pereira dos Santos, João, 2023. "Not So Sweet: Impacts of a Soda Tax on Producers," IZA Discussion Papers 15968, Institute of Labor Economics (IZA).
    10. Johannes Gessner & Wolfgang Habla & Ulrich J. Wagner, 2023. "Can Social Comparisons and Moral Appeals Induce a Modal Shift Towards Low-Emission Transport Modes?," CRC TR 224 Discussion Paper Series crctr224_2023_451, University of Bonn and University of Mannheim, Germany.
    11. Steven Poelhekke & Benjamin Wache, 2023. "The Impact of Venture Capital on Economic Growth," Tinbergen Institute Discussion Papers 23-050/VIII, Tinbergen Institute.
    12. Judite Gonçalves & Roxanne Merenda & João Pereira dos Santos, 2024. "Not so sweet: impacts of a soda tax on producers," International Tax and Public Finance, Springer;International Institute of Public Finance, vol. 31(5), pages 1388-1412, October.

    More about this item

    JEL classification:

    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
    • I1 - Health, Education, and Welfare - - Health

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