I'm estimating a simple bivariate fractional regression model (Stata 14). My outcome and predictor are fractions, neither include zero values. Given that the predictor is also a proportion, I believe an elasticity is the proper way to quantify the relationship. I get very different results depending on how I estimate the model. Below are the models.
From this model the elasticity is .645.
Or I can log x to get the elasticity -
The elasticity in this case is 1.94 which indicates an almost perfect 1:1 relationship between the two variables (i.e. as one doubles, the other increases by 94%).
I thought part of the difference might stem from the margins command averaging over the cases but even if I fix the margins at the means the estimate changes only slightly to .69.
Of course, another option is a varying-elasticity where I estimate the margins at different levels of X. So what gives?
Also, I'd welcome general comments on proper model specification. This is actually time series data, I'd like to put a number on how these two measures vary across time and this seemed like a reasonable way to do it. I'm also using lowess to plot them against time and against each other.
Will
Code:
fracreg logit y x, vce(robust) margins ,eyex(x)
Or I can log x to get the elasticity -
Code:
gen lnx=ln(x) fracreg logit y lnx, vce(robust) matrix b=e(b) //sets coeffs in matrix scalar lncoeff=b[1,1] //retrieves coefficient for x from matrix disp "doubling x results in " 2^(lncoeff) "change in y" // displays the elasticity
I thought part of the difference might stem from the margins command averaging over the cases but even if I fix the margins at the means the estimate changes only slightly to .69.
Of course, another option is a varying-elasticity where I estimate the margins at different levels of X. So what gives?
Also, I'd welcome general comments on proper model specification. This is actually time series data, I'd like to put a number on how these two measures vary across time and this seemed like a reasonable way to do it. I'm also using lowess to plot them against time and against each other.
Will