Linear Rescaling to Accurately Interpret Logarithms

Nick Huntington-Klein

Journal of Econometric Methods, 2023, vol. 12, issue 1, 139-147

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).

Keywords: logarithms; interpretation; regression (search for similar items in EconPapers)
JEL-codes: C18 C20 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1515/jem-2021-0029

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