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

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

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