Consider the following simple regression model: y = ₀ + ₁x₁ + u. Suppose z is an instrument for x. Which of the following conditions denotes instrument exogeneity? A)Cov(z,u) 0 B)Cov(z,x) 0 C)Cov(z,u) = 0 D)Cov(z,x) = 0

Question

Consider the following simple regression model: y = ₀ + ₁x₁ + u. Suppose z is an instrument for x. Which of the following conditions denotes instrument exogeneity? A)Cov(z,u) > 0 B)Cov(z,x) > 0 C)Cov(z,u) = 0 D)Cov(z,x) = 0

Quizplus · Accepted Answer

Instrument exogeneity requires that the instrument, z, is not correlated with the error term, u. Therefore, Cov(z,u) = 0 is the condition that denotes instrument exogeneity. Choice A is incorrect as a positive covariance between the instrument and the error term indicates that the instrument is not exogenous. Choice B is incorrect as a positive covariance between the instrument and x suggests that the instrument is endogenous. Choice D is incorrect as a zero covariance between the instrument and x does not necessarily indicate that the instrument is exogenous, as it could be correlated with the error term.

Consider the Following Simple Regression Model: Y = 0

Consider the Following Simple Regression Model: Y = ₀