Dear all, I recently run into some seemingly unrelated regressions and did some attempts to compare them with the 'truly unrelated' regressions. From these attempts, I came up with a couple of doubts which I would like to share with you regarding how to correctly proceed:

- I read that there is no point in running the SUR, because they would be equivalent to OLS, in two cases: a) When each equation contains exactly the same set of regressors: b) when there are no cross-equation correlations between the error terms. With respect to this latter point, is there some formal test or demonstration to check the absence or presence of this cross-equation correlations (so that I can justify, eventually, the use of SUR)?

- The results that I obtain with SUR are very similar to what I obtain with OLS, except for the coefficient of the a variable that is present in three of my four model but absent in the fourth. Why may this happen? The coefficients for this variable are really unrealistic with SUR, while with OLS are ok: is there something that I should consider in interpreting the coefficient of a variable which is not present in all the models estimated with SUR?

Thanks in advance for your feedback.

Best, G.