Interpreting log in regression

sarahgi

New member
Joined
Jun 12, 2019
Messages
1
Good morning,
I am new to this forum and would like some help with the interpretation of the following regression. I hope I am in the right place.

logWaste = -1.85(logGDP) +0.1(logGDP)^2

Now I am trying to give an interpretation of what would happen to Waste if GDP increases by x%.
I usually report the elasticity easily but I am not sure how to work with this since I have two different values of GDP that I should take into account when differentiating. I hope this makes sense and someone can give me a hand.

Many thanks to all!
 

ksdhart2

Senior Member
Joined
Mar 25, 2016
Messages
1,253
Letting \(w\) denote the Waste and \(g\) denote GDP, and assuming that we're using the natural log, then the problem can be restated as:

\(\displaystyle \ln(w) = -1.85 \ln(g) + 0.1 \ln^2(g)\)

If we raise \(e\) to both sides, to counteract the natural log, we get:

\(\displaystyle e^{\ln(w)} = e^{-1.85 \ln(g) + 0.1 \ln^2(g)}\)

\(\displaystyle w = e^{-1.85 \ln(g) + 0.1 \ln^2(g)}\)

By continuing to simplify this down into a "nicer" form, you can get to the point where taking the derivative to find \(\displaystyle \frac{dw}{dg}\) will be a matter of applying the quotient rule, which shouldn't be that bad.
 
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