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.
Best Answer
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.