st: re: interpretting log transformed co-efficients

[Christopher Baum <baum@bc.edu>]

<>

Ashwin said
I'm having some trouble interpretting the linear regression co- 
efficients for log transformed variables. I have outcomes (such as  
length of stay or costs) that are not normally distributed, so I'm  
including the log transformed (now normal) variables as the outcome  
measures in linear regression models. But I'm not really sure how to  
interpret the resulting co-efficients. Do they represent a % change in  
outcome for a defined change in a predictor variable? Just for  
example, suppose I'm modelling length of stay against gender (male 0  
female 1). Without log transformation, if I get a linear regression co- 
efficient of 0.6, I can say that females have a 0.6 days longer stay.  
But if I use log (length of stay) as the outcome and get a co- 
efficient 0.2 for the same linear regression model, how do I interpret  
this?

You are now calculating what economists would call a semi-elasticity  
of LOS wrt gender. Roughly, d log LOS / d Gender. So 0.2 is ~20%.
You might for comparison run the original model of LOS and then do

mfx compute, eydx

which calculates the same thing at a point in the model space (the  
point of means). In a model with a log-transformed variable, the eydx  
(or semi-elasticity) is constant throughout the model space.

Kit Baum, Boston College Economics and DIW Berlin
http://ideas.repec.org/e/pba1.html
An Introduction to Modern Econometrics Using Stata:
http://www.stata-press.com/books/imeus.html

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