[Sebastian Kripfganz]

If the model without the additional instruments is correctly specified (i.e. the Hansen test excluding this group of instruments does not reject the null hypothesis), then the difference-in-Hansen test could be interpretated as a test for the validity of the additional instruments. In that regard, your understanding is correct.

As to which test results to report, it really depends. You certainly want to report the Hansen test for the full model. On top of that, it makes sense to report difference-in-Hansen tests for particular instruments if their inclusion requires particular justification. For example, if the Arellano-Bond AR(2) test does not reject the null hypothesis of no second-order serial correlation of the first-differenced errors, then you usually need not separately justify the lagged levels of the dependent variable as instruments for the first-differenced model. In contrast, the difference-in-Hansen test for the level instruments is informative because it helps to evaluate whether the Blundell-Bond mean stationarity assumption might be violated.

For example, you could report the Hansen test for the model with the instruments for the first-differenced model only, the Hansen test for the full model, and the respective difference-in-Hansen test. The Hansen test for the first-differenced model tells you something whether your model is dynamically complete (because this implies whether those instruments are valid). The difference-in-Hansen test, as mentioned before, tells you something about the mean stationarity condition needed for the validity of the level instruments. Taking these two test results at face value, the Hansen test for the full model would in principal be redundant but it is still reasonable to provide a complete picture.

[Alex Mai]

Any suggestions would be really appreciated! Many thanks.

Hope any suggestions! Thank you!

[Alex Mai]

Any suggestions would be really appreciated! Many thanks.