IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2106.03070.html
   My bibliography  Save this paper

Linear Rescaling to Accurately Interpret Logarithms

Author

Listed:
  • Nick Huntington-Klein

Abstract

The standard approximation of a natural logarithm in statistical analysis interprets a linear change of \(p\) in \(\ln(X)\) as a \((1+p)\) proportional change in \(X\), which is only accurate for small values of \(p\). I suggest base-\((1+p)\) logarithms, where \(p\) is chosen ahead of time. A one-unit change in \(\log_{1+p}(X)\) is exactly equivalent to a \((1+p)\) proportional change in \(X\). This avoids an approximation applied too broadly, makes exact interpretation easier and less error-prone, improves approximation quality when approximations are used, makes the change of interest a one-log-unit change like other regression variables, and reduces error from the use of \(\log(1+X)\).

Suggested Citation

  • Nick Huntington-Klein, 2021. "Linear Rescaling to Accurately Interpret Logarithms," Papers 2106.03070, arXiv.org, revised Oct 2021.
    • Handle: RePEc:arx:papers:2106.03070
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2106.03070
    File Function: Latest version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Halvorsen, Robert & Palmquist, Raymond, 1980. "The Interpretation of Dummy Variables in Semilogarithmic Equations," American Economic Review, American Economic Association, vol. 70(3), pages 474-475, June.
    Full references (including those not matched with items on IDEAS)

    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. Sharunina, A., 2016. "Where Do Public Workers Live Well? Public-Private Wage Gaps in Russia's Regions," Journal of the New Economic Association, New Economic Association, vol. 30(2), pages 105-128.
    2. Stephen Billings & Thomas Thibodeau, 2011. "Intrametropolitan Decentralization: Is Government Structure Capitalized in Residential Property Values?," The Journal of Real Estate Finance and Economics, Springer, vol. 42(4), pages 416-450, May.
    3. Nick Drydakis, 2008. "Integrated Roma Earnings: A Multivariate Analysis for the Discrimination Hypothesis in Greece," Working Papers 0829, University of Crete, Department of Economics.
    4. Allan Beltrán & David Maddison & Robert J. R. Elliott, 2018. "Assessing the Economic Benefits of Flood Defenses: A Repeat‐Sales Approach," Risk Analysis, John Wiley & Sons, vol. 38(11), pages 2340-2367, November.
    5. Tapsuwan, Sorada & Polyakov, Maksym & Bark, Rosalind & Nolan, Martin, 2015. "Valuing the Barmah–Millewa Forest and in stream river flows: A spatial heteroskedasticity and autocorrelation consistent (SHAC) approach," Ecological Economics, Elsevier, vol. 110(C), pages 98-105.
    6. Wlömert, Nils & Papies, Dominik, 2016. "On-demand streaming services and music industry revenues — Insights from Spotify's market entry," International Journal of Research in Marketing, Elsevier, vol. 33(2), pages 314-327.
    7. Wesley Nimon & John Beghin, 1999. "Are Eco-Labels Valuable? Evidence From the Apparel Industry," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 81(4), pages 801-811.
    8. Mao, Luke Lunhua & Zhang, James J. & Connaughton, Daniel P., 2015. "Sports gambling as consumption: Evidence from demand for sports lottery," Sport Management Review, Elsevier, vol. 18(3), pages 436-447.
    9. Markus Behn & Rainer Haselmann & Paul Wachtel, 2016. "Procyclical Capital Regulation and Lending," Journal of Finance, American Finance Association, vol. 71(2), pages 919-956, April.
    10. Chica-Olmo, Jorge & Cano-Guervos, Rafael, 2020. "Does my house have a premium or discount in relation to my neighbors? A regression-kriging approach," Socio-Economic Planning Sciences, Elsevier, vol. 72(C).
    11. Theodore Koutmeridis, 2013. "The Market for "Rough Diamonds": Information, Finance and Wage Inequality," CDMA Working Paper Series 201307, Centre for Dynamic Macroeconomic Analysis, revised 14 Oct 2013.
    12. Ahlfeldt, Gabriel M. & Wendlan, Nicolai, 2008. "Spatial Determinants of CBD Emergence: A Micro-level Case Study on Berlin∗," MPRA Paper 11572, University Library of Munich, Germany.
    13. Altay Mussurov & Dena Sholk & G. Reza Arabsheibani, 2019. "Informal employment in Kazakhstan: a blessing in disguise?," Eurasian Economic Review, Springer;Eurasia Business and Economics Society, vol. 9(2), pages 267-284, June.
    14. Trevon D. Logan & Manisha Shah, 2013. "Face Value: Information and Signaling in an Illegal Market," Southern Economic Journal, John Wiley & Sons, vol. 79(3), pages 529-564, January.
    15. Patrick Kampkoetter, 2012. "Determinants of Compensation in the Financial Services Industry," Cologne Graduate School Working Paper Series 03-12, Cologne Graduate School in Management, Economics and Social Sciences.
    16. Evangelista, Rui & Ramalho, Esmeralda A. & Andrade e Silva, João, 2020. "On the use of hedonic regression models to measure the effect of energy efficiency on residential property transaction prices: Evidence for Portugal and selected data issues," Energy Economics, Elsevier, vol. 86(C).
    17. Martin D. Heintzelman & Carrie M. Tuttle, 2012. "Values in the Wind: A Hedonic Analysis of Wind Power Facilities," Land Economics, University of Wisconsin Press, vol. 88(3), pages 571-588.
    18. World Bank Group, 2014. "West Bank and Gaza Investment Climate Assessment : Fragmentation and Uncertainty," World Bank Publications - Reports 20268, The World Bank Group.
    19. Brenner, Jan, 2007. "Effects of Job Entry Restrictions on Economic Integration - Evidence for Recent Ethnic German Immigrants," Ruhr Economic Papers 25, RWI - Leibniz-Institut für Wirtschaftsforschung, Ruhr-University Bochum, TU Dortmund University, University of Duisburg-Essen.
    20. Aysoy, Cevriye & Kirli, Duygu Halim & Tumen, Semih, 2015. "How does a shorter supply chain affect pricing of fresh food? Evidence from a natural experiment," Food Policy, Elsevier, vol. 57(C), pages 104-113.

    More about this item

    JEL classification:

    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C20 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - General

    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:arx:papers:2106.03070. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.