I am working on a project that has 4680 observations (18 years, 265 regions), in which one variable is endogenous. We tried various combinations of two IVs, but always end up with a significant Sargan-Hansen J Test. Recently I have found this quote:
"Testing of over-identifying assumptions is less important in longitudinal applications because realizations of time varying explanatory variables in different time periods are potential instruments, i.e., over-identifying restrictions are automatically built into models estimated using longitudinal data."
Does it mean that for panel data that contains large number of observations the Sargan-Hansen J Test is irrelevant as it almost always ends up significant?
The precondition of the test is that at least one of the IVs is a relevant IV. Should we therefore restrict ourselves to using one IV?