# Are There Evaluation Criteria For Instrumental Variables?

If theory points to multiple possible instruments that can be used, how can I choose which one of them is the best for 2SLS?

I read that good instrument should be significant and correlated with the endogenous variable. Does that imply that when I am preforming an auxiliary regression to see whether the instruments are good, I can compare them on the basis of their significance and $R^2$ of the auxiliary regression?

Like for example if I have two arbitrary IV variables,(lets call them $Z_1$ and $Z_2$ for the lack of better names) and in the auxiliary regression $Z_1$ has $p-value: 0.001$, and the auxiliary regression has $R^2: 0.25$ and $Z_2$ has $p-value: 0.02$, and its auxiliary regression has $R^2: 0.19$, does it mean that $Z_1$ is better instrument than $Z_2$? Or is this interpretation wrong?

Are there any other IV quality criteria to consider when picking the right IV?

You cannot simply base your choice of instrument on the $$R^2$$.