Hi, I'd like to estimate treatment effects on an index variable constructed using three variables.
So, I have 3 variables going into the index:
-hired labor days
-2 other variables
In the first variable I use to construct the index (i.e. hired labor days) there are several zero observations. I'd like to correct for the zeroes. So, I'd like to correct for those who never hire labor i.e. hired labor days=0 (close to half of the sample). I was thinking about applying Heckman-correction (calculating inverse Mills ratio using the selection equation and including IMR in the second stage).
heckman index3 treatment, select(hire_labor= $covariates) first mills(imr) vce(robust)
But, I am not sure if that's statistically correct. I assume that hiring labor or not (selection equation) is determined by other factors and has nothing to do with the treatment. If we apply Heckman selection, I guess we only consider the ones with non-zero values in the first stage. But my second stage outcome variable is not hired labor days but an index constructed using hired labor days with two other variables. Then I am not sure what's happening to the individuals that have zero hired labor days but non-zero values for the other two variables going into the index. Does that even make sense to try to correct for zeroes in one of the variables in an index variable? Does that make sense to use 3 variables in an index (of which 2 are continuous but scaled to range between 0-2)? What is the best way to estimate the treatment effects?
I hope someone can provide some feedback. Thank you very much in advance for your insights.
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