# Econometrics

• ## 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:

Linear:
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-linear