This thread developed in a very bad way, and the question by Nishant Kathuria shows that we are already harvesting the fruits of the mess we made.
The original question of the Original Poster was "which tests I need to be looking at to test the validity of the instruments." The answer to the original question of OP is not the user written -weakiv-.
The user written -weakiv- does not test the strength of instruments.
The user written -weakiv- tests whether the slope(s) of the endogenous variables are 0, using tests which are valid under weak identification, or no identification at all.
Hence no, it is not correct "to say that AR chi2(2) show that H0 is rejected at p<0.05, therefore the instrument is likely relevant and exogenous (lack of evidence that the instrument is weak)".
The null hypothesis of the AR test is that the slope(s) of the endogenous variables are 0, and this hypothesis is tested in such a way that it does not matter whether there is no identification at all, weak identification, or strong identification.
The AR tests nothing, and has nothing to say related to the strength or the validity of instruments.
The original question of the Original Poster was "which tests I need to be looking at to test the validity of the instruments." The answer to the original question of OP is not the user written -weakiv-.
The user written -weakiv- does not test the strength of instruments.
The user written -weakiv- tests whether the slope(s) of the endogenous variables are 0, using tests which are valid under weak identification, or no identification at all.
Hence no, it is not correct "to say that AR chi2(2) show that H0 is rejected at p<0.05, therefore the instrument is likely relevant and exogenous (lack of evidence that the instrument is weak)".
The null hypothesis of the AR test is that the slope(s) of the endogenous variables are 0, and this hypothesis is tested in such a way that it does not matter whether there is no identification at all, weak identification, or strong identification.
The AR tests nothing, and has nothing to say related to the strength or the validity of instruments.
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