Weak instruments test in ivreg2h

[Dario Maimone Ansaldo Patti]

Dear All,

I am using ivreg2h command to carry out an IV estimation. After the first stage I checked the waek instruments tests and I got the following:

Weak-instrument-robust inference
Tests of joint significance of endogenous regressors B1 in main equation
Ho: B1=0 and orthogonality conditions are valid
Anderson-Rubin Wald test           F(26,70)=       3.80     P-val=0.0000
Anderson-Rubin Wald test           Chi-sq(26)=   142.66     P-val=0.0000
Stock-Wright LM S statistic        Chi-sq(26)=    32.87     P-val=0.1658

The two tests should have the same null hypothesis, but they provide different evidence. If I am correct and look at the AR test, I should reject the validity of my instruments. Instead the SW test indicates the opposite. How could I interpret such a result?

Thanks in advance

Dario