Elasticities in estimated linear models

Ever wondered how your estimation of a linear function relates to the elasticities of the estimated model? I always seem to forget, especially if I have taken the logarithm on one or both sides of the equation. Here are the four cases you can have:

The function has the following form (if you have more variables on the right hand side, this doesn’t change the story):


[math]Y=a + bX[/math]


The elasticity is given by:


[math]\epsilon= \frac{dY}{dX}\frac{X}{Y}=b\frac{X}{Y} [/math]


and the coefficient b is the change in Y from a unit increase in X.



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