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Linear Rescaling to Accurately Interpret Logarithms

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  • Huntington-Klein Nick

    (Economics, Seattle University, Seattle, 98122-4340, USA)

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 log1 + 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

  • Huntington-Klein Nick, 2023. "Linear Rescaling to Accurately Interpret Logarithms," Journal of Econometric Methods, De Gruyter, vol. 12(1), pages 139-147, January.
    • Handle: RePEc:bpj:jecome:v:12:y:2023:i:1:p:139-147:n:5
    DOI: 10.1515/jem-2021-0029
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    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.
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    More about this item

    Keywords

    logarithms; interpretation; regression;
    All these keywords.

    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

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