# Standard Error for sum of two coefficients from separate regressions

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.

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).
• 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). Jul 26 '15 at 15:58