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How can I interpret the beta regression from regressing lny on lnx, or lny on x etc. For example in Stata I make this regression using beta function: reg lny lnx z t, beta robust

this gives me usual coefficient estimates which can be interpreted as elasticity, but it also gives standardized betas.

I know for a regression of y on x, the standardized betas are interpreted as a one standard deviation of x from its mean have a beta standard deviation change in y, for example:

reg y x z t, beta robust

But what happens if variables are lny and lnx form? How does it relate to usual elasticity interpretation in log-log regressions?

Skylar
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  • This is okay as long as x is not 0. It is common practice to add 0.5 to x when x is equal to 0. – Michael R. Chernick Mar 04 '17 at 19:39
  • @Michael I hope it's not common practice, because it's a poor general solution. See http://stats.stackexchange.com/questions/30728 for one discussion. – whuber Mar 04 '17 at 22:35
  • Skylar, this site has many threads that answer all your questions. Please see http://stats.stackexchange.com/search?q=interpret+log+regression. The duplicate is the top hit on that search when "elasticity" is also included as a keyword. – whuber Mar 04 '17 at 22:35
  • @whuber I wish you were right. I would never recommend doing it but I have seen it done all too often. – Michael R. Chernick Mar 04 '17 at 22:52
  • Thank you for the answers. I think I misworded it. I am not asking coefficient interpretation in a general regression. I want to ask standardized betas such as in Stata using beta command: reg lny lnx z t, beta robust. Then how do I interpret this beta function results? – Skylar Mar 05 '17 at 01:39
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    This doesn't make sense. If you standardize your variables first, half the values will be negative. How do you take the log of a negative value? If you add some value to all your data to shift them to all positive, you would have your data in units of SDs, then everything (interpretation, eg) is the same except w/ different units. – gung - Reinstate Monica Mar 05 '17 at 12:43

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