Dear all,

I do a research using instrumental variables, the main problem is that we are not sure which result should be chosen . We found the instruments are weak, so we decided to use CLR test, K test and AR test to get the weak-identification-robust inferences. The null hypothesis of these tests is that if estimate of beita is equal to zero. Our estimate of ß is around 0.06.
BUT we found that If we add some control variables, we will accept the null hypothesis, however, if we drop these two control variables, we will reject the null hypothesis.
We found that the two control variables are not related with the explanatory variables, so if we can say that it is because these control variables dilute the strength of estimate of ß which is very small ? Or there are other explanations we can use for this case.

Thank you.

Result of not adding two unrelated control variables
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Result of adding two unrelated control variables
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