All of the following conditions are necessary for an instrumental variable Z to be a valid instrument for X in the regression: Y_i = β₀ + β₁X_i + U_i except for which condition? A) Cov(X_i, Z_i) ≠ 0 B) Cov(Z_i, U_i) = 0 C) Cov(X_i, Y_i) ≠ 0 D) None of these choices are correct.

Question

Quizplus · Accepted Answer

Condition C, Cov(X, Y) ≠ 0, is not necessary for Z to be a valid instrument for X. The validity of an instrumental variable requires it to be correlated with the independent variable X (A) and not correlated with the error term U (B), but it does not require X and Y to be correlated once we control for the instrument.

All of the Following Conditions Are Necessary for an Instrumental