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Interpreting coefficient in a log-log model

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Hi everyone,

I am currently working with a log log model specification. To my understanding, the correct interpretation of the coefficients is 1% increase in x is associated with a ß1% increase in y
The issue that I am having is, my explanatory variable is in percentage (0.01-0.99), how does the interpretation change in this case?

I checked this in the Wooldridge book but so far, couldn't clarify my doubt.
My guess so far is:

1 percentage point increase in x leads to a ß1% increase in y, is this correct?
I have seen some people using the means to interpret this kind of relationships, could I leave it in a simple way, or is it always necessary to calculate this at the mean, or any specific value?


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