The Rule-Of-Thumb for Checking for Weak Instruments Is as Follows $F$

Short Answer

The rule-of-thumb for checking for weak instruments is as follows: for the case of a single endogenous regressor, a. a first stage $F$ must be statistically significant to indicate a strong instrument.
b. a first stage $F > 1.96$ indicates that the instruments are weak.
c. the $t$ -statistic on each of the instruments must exceed at least 1.64.
d. a first stage $F < 10$ indicates that the instruments are weak.