log(y) = b* log(x) b represents the percentage change in y that
is associated with a 1% change in x. But this transformation is
not always a good idea. I frequently see papers that examine the
effect of temperature (or control for it because they care about
some other factor) and use log(temperature) as an independent
variable. This is a bad idea because a 1% change in temperature
is an ambiguous value. Imagine an author estimates log(Y) =
b*log(temperature) and obtains the estimate b = 1. The author
reports that a 1% change in temperature leads to a 1% change in
Y. I have seen this done many times. Now an American reader
wants to apply this estimate to some hypothetical scenario where
the temperature changes from 75 Fahrenheit (F) to 80 F. She
computes the change in the independent variable D: DAmerican =
log(80)-log(75) = 0.065 and concludes that because temperature
is changing 6.5%, then Y also changes 6.5% (since 0.065*b =
0.065*1 = 0.065). But now imagine that a Canadian reader wants
to do the same thing