The Two Conditions for a Valid Instrument Are A $\operatorname { corr } \left( Z _ { i } , X _ { i } \right) = 0$

Short Answer

The two conditions for a valid instrument are a. $\operatorname { corr } \left( Z _ { i } , X _ { i } \right) = 0$ and $\operatorname { corr } \left( Z _ { i } , u _ { i } \right) \neq 0$ .
b. $\operatorname { corr } \left( Z _ { i } , X _ { i } \right) = 0$ and $\operatorname { corr } \left( Z _ { i } , u _ { i } \right) = 0$ .
c. $\operatorname { corr } \left( Z _ { i } , X _ { i } \right) \neq 0$ and $\operatorname { corr } \left( Z _ { i } , u _ { i } \right) = 0$ .
d. $\operatorname { corr } \left( Z _ { i } , X _ { i } \right) \neq 0$ and $\operatorname { corr } \left( Z _ { i } , u _ { i } \right) \neq 0$ .