Under what condition can the Sargan or Basmann test for overidentifying restrictions be performed in an IV/2SLS context?

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The question asks about the condition under which the Sargan or Basmann test for overidentifying restrictions can be performed in an IV/2SLS framework.
Option A: 'Only when the endogenous variable is a binary dummy variable.' This is not the criterion for applying the overidentification test. The binary nature of an endogenous regressor does not define when overidentification tests can be used.
Option B: 'Only when the number of instruments is strictly greater than the number of endogenous variables (overidentification).' This matches the fundamental requirement for these tests: there must be at least one extra instrument beyond the minimum needed to identify the model, i.e., overidentification. When there are more instruments than endogenous variables, the test checks whether the instruments are valid (uncorrelated with the error term) given their exclusion from the structural equation.
Option C: 'Only when there is exactly one instrument for one endogenous variable (exact identification).' In exact identification, there are no overidentifying restrictions, so the Sargan or Basmann test is not applicable because there are no extra instruments to test for validity.
Option D: 'Only when all instruments are perfectly uncorrelated with each other.' While instrument independence can be desirable, the key requirement for these tests is overidentification, not a condition about perfect correlation among instruments. In practice, instruments can be correlated with each other to some extent, but what matters for the test is having more instruments than endogenous variables and the exogeneity condition relative to the error term.

Under what condition can the Sargan or Basmann test for overidentifying restrictions be performed in an IV/2SLS context?

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