Is there a test for how appropriate a seemingly unrelated regression (SUR) is in the presence of possible endogeneity?

Question

I have two equations which I would like to use in a SUR about innovation and investment in a specific sector:

{sector innovation proxy}=a+b1{sector specific policies}+b2{general investment policies}+b3{controls}+e

{sector specific investment}=a+b1{sector specific policies}+b2{general investment policies}+b3{controls}+e

Both equations would use the same data set, except for the dependent variable.

Now, my colleagues suggested I have to be careful not to run into endogeneity problems, but could not point to a possible source of endogeneity.

I would like to have a test showing them that a SUR is warranted and that therefore I do not need to use the two equations in some sort of simultaneous equation model or a similar solution to counter endogeneity.

I am sorry if this is a rather basic questions (I am aware that endogeneity cannot be discovered by a statistical test), but I am generally wondering if there is a statistical justification or counter-indication for SUR.

Answer 1

[...] but I am generally wondering if there is a statistical justification or counter-indication for SUR.

There is; it is a Breusch-Pagan test between the errors of the separate equations run as OLS. It is explained in this video. In short: the test shows if there is a correlation between the errors. If there is, there is a bias that could be removed by SUR.

Answer 2

first off when you run a sur model you cant use the same dependent variables in both equations because it will reduce to OLS. you should omit one dependent variable from one of the equations.