Dear Sir. Concerning your issue about he purpose of instrument orthogonality test. The Instrument Orthogonality test, also known as the C-test or Eichenbaum, Hansen and Singleton (EHS) Test, evaluates the othogonality condition of a sub-set of the instruments. This test is available for non-panel equations estimated by TSLS or GMM. The Instrument Orthogonality Test evaluates whether this condition possibly holds for a subset of the instruments but not for the remaining instruments. I think the following below links may help you in your analysis: