When performing IV regression, it is often taken as a sign of unbiasedness if the IV estimates are similar to the OLS estimates of the same model. My question is: If the estimates are very different, what possible explanations are there for the difference?
Say for example, with a strong instrument, that one finds that the IV estimates of some coefficient are 10 times larger than the OLS estimates. Is this most likely a sign of severe bias in the OLS estimates? Or is it just as likely that the exclusion restriction is not satisfied, and so the IV estimator is possibly even more biased than OLS?
I understand that this is an open question, but if anyone could just give me the basic range of possible explanations, and perhaps point me towards some literature on interpreting IV results when they are significantly different from OLS, that would be much appreciated?