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I have two SEPARATE regressions (I don't know if they are "seemingly unrelated" or not):

  1. $Y_1 = b_1*X_1 + e_1 $

  2. $Y_2 = b_2*X_2 + e_2$

I create a variable $c=a*b_1 + b_2$ . How do I find the standard error for c? My guess is that $SE(c) = \sqrt{(a^2*SE(b_1) + SE(b_2) + 2aCov(b1,b2))}$ . But I don't know how to find $Cov(b_1,b_2)$ in STATA.

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It depends on the circumstances - what is being sampled how (i.e. what kind of relationships should exist between observations in the two regressions)?

If you're prepared to assume the observations in the two regressions are independent of each other it's quite straightforward -- the covariance is zero. However the formula in your question is wrong; you need to square the standard errors under the square root (and it should be made clear that the $b$'s are estimates, not population coefficients).

If at least some observations are pairwise dependent across the regressions, you're essentially in a version of a seemingly unrelated regressions style of problem (as you already anticipate).

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  • $\begingroup$ Thanks, Glen_b. The observations aren't independent. So how do I get the $Cov(b_1,b_2)$ value in STATA? An issue is that I can't use sureg because each equation uses regression-discontinuity (RD) code (using the `rd' command). $\endgroup$
    – newgrad123
    Jul 26 '15 at 15:58
  • $\begingroup$ That's a twist which I doubt anybody could have guessed from your question. There's several ways of fitting RD designs. I think you probably need a new question where you describe exactly the model you did fit and ask how to estimate the covariance term in that case. (I'm probably not the right person to answer that question, but it might depend on exactly what you did.) $\endgroup$
    – Glen_b
    Jul 26 '15 at 22:47

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