Can somebody explain to me why it is that “log(observation 2) – log(observation 1)” results in a percentage change measure for the variable?
In: Mathematics
The difference of two logs is the log of the ratio. That’s a mathematical identity. (proof left out for followup question)
log(observation 2) – log(observation 1) = log(observation 2 / observation 1)
The log of the ratio is not literally the ‘percentage change’ but it is along the same lines. A doubling will give you the log(2.0). A 50% increase will give you the log(1.5). A 25% increase will give you the log(1.25). Etc, etc.
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