What is 0.35 log points in percentages? I have no knowledge of this subject at all. From what I've gathered, it should be Percentage change = (e^log points - 1) * 100, so 42%. Is this correct?
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1I would say it just $e^{0.35}\approx 142%$ I assume you want to transform a log scaled value. – callculus42 Jan 20 '23 at 05:26
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@callculus42 I'm not sure. The thing I'm looking at says "wages decreased by 0.35 log points after right-to-work laws were introduced." – Noah D. Jan 20 '23 at 19:55
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O.K. It increases by (e^log points - 1) * 100%. Or it increases to (e^log points ) * 100% – callculus42 Jan 20 '23 at 20:50
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The log points between $x$ and $y$ is the difference $$\log(x)-\log(y) = \log(x/y)$$
If $x$ differs from $y$ by a factor of $1+\frac{\%\Delta}{100}$ then we have $\frac{x}{y}=1+\frac{\%\Delta}{100}$,
$$\log(x)-\log(y) = \log(x/y) = \log\left(1+\frac{\%\Delta}{100}\right) $$ By exponentiation we have $$\mathrm e^{\log(x)-\text{log}(y)}=\mathrm e^{\log\left(\frac{\%\Delta}{100}+1\right)}=\frac{\%\Delta}{100}+1$$ that is $$ \%\Delta=\left(\mathrm e^{\overbrace{{\log(x)-\text{log}(y)}}^{\text{log points}}}-1\right)\cdot 100 $$
alexjo
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