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?