I am trying to estimate following two simultaneous equations using 3SLS:
y1 = x1 x2
y2 = y1 y1*x1 x1 x3 (where y1*x1 is an interaction term; it is the variable of interest)
My problem is 1st stage results for the 1st equation, because it estimates y1 on x1 x2 x3 andy1*x1 (it takes all RHS vars from both equations). This of course totally messes up the results of the first stage (as the interaction term, of course, absorbs much of the variance in the dependent variable), and destroys second stage results.
As check, I try to run instead:
y1 = x1 x2
y2 = y1 x1 x3
And here the results are good (y1 enters the way I expect). But my model focuses on the interaction term in that second regression, so this is not good enough. I also get good results if I runt the regression above as 2SLS (because the 1st equation becomes the 1st stage equation, and is not augmented with additional variables from the second one). But, again, I have good reason to believe that y2 and affects y1, so 2SLS not good enough.
Questions: how can I run the 3SLS above, without having the interaction term y1*x1 entering the 1st equation? Or can I replicate the 3SLS by somehow doing all the steps "manually" (presumably with residuals from simple OLS regressions) and having full control over 1st stage?
y1 = x1 x2
y2 = y1 y1*x1 x1 x3 (where y1*x1 is an interaction term; it is the variable of interest)
My problem is 1st stage results for the 1st equation, because it estimates y1 on x1 x2 x3 andy1*x1 (it takes all RHS vars from both equations). This of course totally messes up the results of the first stage (as the interaction term, of course, absorbs much of the variance in the dependent variable), and destroys second stage results.
As check, I try to run instead:
y1 = x1 x2
y2 = y1 x1 x3
And here the results are good (y1 enters the way I expect). But my model focuses on the interaction term in that second regression, so this is not good enough. I also get good results if I runt the regression above as 2SLS (because the 1st equation becomes the 1st stage equation, and is not augmented with additional variables from the second one). But, again, I have good reason to believe that y2 and affects y1, so 2SLS not good enough.
Questions: how can I run the 3SLS above, without having the interaction term y1*x1 entering the 1st equation? Or can I replicate the 3SLS by somehow doing all the steps "manually" (presumably with residuals from simple OLS regressions) and having full control over 1st stage?
