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The inverse hyperbolic sine transformation and retransformed marginal effects

Author

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  • Edward C. Norton

    (University of Michigan)

Abstract

In this article, I show 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, when all observations are positive.

Suggested Citation

  • Edward C. Norton, 2022. "The inverse hyperbolic sine transformation and retransformed marginal effects," Stata Journal, StataCorp LP, vol. 22(3), pages 702-712, September.
    • Handle: RePEc:tsj:stataj:y:22:y:2022:i:3:p:702-712
    DOI: 10.1177/1536867X221124553
    Note: to access software from within Stata, net describe http://www.stata-journal.com/software/sj22-3/st0653/
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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. 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).
    4. 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).
    5. 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.
    6. Steven Poelhekke & Benjamin Wache, 2023. "The Impact of Venture Capital on Economic Growth," Tinbergen Institute Discussion Papers 23-050/VIII, Tinbergen Institute.

    More about this item

    Keywords

    inverse hyperbolic sine; transformation; marginal effects;
    All these keywords.

    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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