Dear Statalist,
I'm interested in simultaneously estimating two equations where one outcome of interest is continuous and another is categorical with three response values (0 1 2). My naive approach to the problem was to estimate a "forbidden" regression by calculating the predicted probabilities from the multinomial logit and then to use them in the equation for the continuous outcome. I have researched the problem and found two paths to follow: Wooldridge's control function approach, but I am unsure of how to apply this given that my first equation is multinomial; and a -cmp- approach. I first decided to try -cmp- (in Stata 14.2):
cmp (y1 = Y2 x1 X) (Y2 = x1 Z), ind($cmp_cont $cmp_mprobit) cluster(id)
where Y2 takes the 0 1 2 values, x1 is my primary determinants of interest, and X and Z are sets of control variables that differ between equations. Stata returned an error message "equation Y2 not found."
I then used a different syntax:
cmp (y1 = Y2 x1 X) (Y2 = x1 Z) (Y3 = x1 Z), ind($cmp_cont $cmp_mprobit $cmp_mprobit) cluster(id)
where Y2 and Y3 are binary indicators for responses.
The model converged, but with "." in place of the standard errors/z-scores etc for the full model. I re-specified
cmp (y1 = Y2 x1 X) (Y2 = x1 Z) (Y3 = x1 Z), ind($cmp_cont $cmp_probit $cmp_probit) cluster(id)
This "worked" in the sense that Stata provided estimates and test statistics.
My questions are:
1) Why did Stata return the "equation not found" error message? Based on my reading of Roodman's work, I would guess that what I specified is not logically possible, but I do not understand why.
2) Does this appear to be a reasonable strategy if I am interested in the effect of x1 on the y1 and the responses in y2?
3) Would the control function approach be a reasonable alternative? I've read Wooldridge (2015) "Control Function Methods in Applied Econometrics" in the Journal of Human Resources, but I am unsure of how to implement this procedure with the multinomial "first stage."
I appreciate any help list members can offer.
Michael Tyburski
I'm interested in simultaneously estimating two equations where one outcome of interest is continuous and another is categorical with three response values (0 1 2). My naive approach to the problem was to estimate a "forbidden" regression by calculating the predicted probabilities from the multinomial logit and then to use them in the equation for the continuous outcome. I have researched the problem and found two paths to follow: Wooldridge's control function approach, but I am unsure of how to apply this given that my first equation is multinomial; and a -cmp- approach. I first decided to try -cmp- (in Stata 14.2):
cmp (y1 = Y2 x1 X) (Y2 = x1 Z), ind($cmp_cont $cmp_mprobit) cluster(id)
where Y2 takes the 0 1 2 values, x1 is my primary determinants of interest, and X and Z are sets of control variables that differ between equations. Stata returned an error message "equation Y2 not found."
I then used a different syntax:
cmp (y1 = Y2 x1 X) (Y2 = x1 Z) (Y3 = x1 Z), ind($cmp_cont $cmp_mprobit $cmp_mprobit) cluster(id)
where Y2 and Y3 are binary indicators for responses.
The model converged, but with "." in place of the standard errors/z-scores etc for the full model. I re-specified
cmp (y1 = Y2 x1 X) (Y2 = x1 Z) (Y3 = x1 Z), ind($cmp_cont $cmp_probit $cmp_probit) cluster(id)
This "worked" in the sense that Stata provided estimates and test statistics.
My questions are:
1) Why did Stata return the "equation not found" error message? Based on my reading of Roodman's work, I would guess that what I specified is not logically possible, but I do not understand why.
2) Does this appear to be a reasonable strategy if I am interested in the effect of x1 on the y1 and the responses in y2?
3) Would the control function approach be a reasonable alternative? I've read Wooldridge (2015) "Control Function Methods in Applied Econometrics" in the Journal of Human Resources, but I am unsure of how to implement this procedure with the multinomial "first stage."
I appreciate any help list members can offer.
Michael Tyburski
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