Linear Rescaling to Accurately Interpret Logarithms

2021/06/06 by Huntington-Klein, Nick · 1 citation
#Econometrics (econ.EM) #FOS: Economics and business

paper · doi:10.48550/arxiv.2106.03070

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 \(log(1+X)\).

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