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Units of Measurement and the Inverse Hyperbolic Sine Transformation

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  • Ghislain B. D. Aïhounton

    (Department of Food and Resource Economics, University of Copenhagen)

  • Arne Henningsen

    (Department of Food and Resource Economics, University of Copenhagen)

Abstract

The inverse hyperbolic sine (IHS) transformation is frequently applied in econometric studies to transform right-skewed variables that include zero or negative values. We confirm a previous study that shows that regression results can largely depend on the units of measurement of IHS-transformed variables. Hence, arbitrary choices regarding the units of measurement for these variables can have a considerable effect on recommendations for policies or business decisions. In order to address this problem, we suggest a procedure for choosing units of measurement for IHS-transformed variables. A Monte Carlo simulation assesses this procedure under various scenarios and a replication of the study by Bellemare and Wichman (2019) illustrates the relevance and applicability of our suggested procedure.

Suggested Citation

  • Ghislain B. D. Aïhounton & Arne Henningsen, 2019. "Units of Measurement and the Inverse Hyperbolic Sine Transformation," IFRO Working Paper 2019/10, University of Copenhagen, Department of Food and Resource Economics.
    • Handle: RePEc:foi:wpaper:2019_10
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    References listed on IDEAS

    as
    1. LaLonde, Robert J, 1986. "Evaluating the Econometric Evaluations of Training Programs with Experimental Data," American Economic Review, American Economic Association, vol. 76(4), pages 604-620, September.
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    3. Carboni, Oliviero A., 2012. "An empirical investigation of the determinants of R&D cooperation: An application of the inverse hyperbolic sine transformation," Research in Economics, Elsevier, vol. 66(2), pages 131-141.
    4. Ravallion, Martin, 2017. "A concave log-like transformation allowing non-positive values," Economics Letters, Elsevier, vol. 161(C), pages 130-132.
    5. Dany Bahar & Hillel Rapoport, 2018. "Migration, Knowledge Diffusion and the Comparative Advantage of Nations," Economic Journal, Royal Economic Society, vol. 128(612), pages 273-305, July.
    6. Yapo Genevier N’guessan & Allen Featherstone & Oluwarotimi Odeh & Sreedhar Upendram, 2017. "Choice of the empirical definition of zero in the translog multiproduct cost functional form," Applied Economics Letters, Taylor & Francis Journals, vol. 24(15), pages 1112-1120, September.
    7. Patrick Royston & Paul C. Lambert, 2011. "Flexible Parametric Survival Analysis Using Stata: Beyond the Cox Model," Stata Press books, StataCorp LP, number fpsaus, March.
    8. 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.
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    11. Marc F. Bellemare & Christopher B. Barrett & David R. Just, 2013. "The Welfare Impacts of Commodity Price Volatility: Evidence from Rural Ethiopia," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 95(4), pages 877-899.
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    More about this item

    Keywords

    inverse hyperbolic sine; arcsinh; unit of measurement; scale factor;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling

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