• 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):


    Y=a + bX


    The elasticity is given by:


    \epsilon= \frac{dY}{dX}\frac{X}{Y}=b\frac{X}{Y}


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




    log(Y)=a + bX


    and the elasticity is given
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