Question: 12.7 A classmate has developed an IV regression model with one regressor, Xi, and two instruments, Z1i and Z2i. She has a strong theoretical basis

12.7 A classmate has developed an IV regression model with one regressor, Xi, and two instruments, Z1i and Z2i. She has a strong theoretical basis as to why corr1Z1i, ui2 = 0, namely that Z1i is the result of a random lottery. Preliminary work, however, showed that the first-stage F-statistic from this exactly identified model was insufficiently large for Z1i to be considered a relevant instrument set by itself. As a result she includes an additional instrument, Z2i, which is strongly relevant but is less likely to satisfy the condition of instrument exogeneity. In the instrumental variable regression model with one regressor, Xi, and two instruments, Z1i and Z2i, the value of the J-statistic is J = 7.5.

a. Does this suggest that E1ui Z1i, Z2i2 0 ? Explain.

b. Does this suggest that E1ui Z2i2 0 ? Explain.

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