Consider the following simple regression model y=β₀+ β₁x₁+ u.Suppose z is an instrument for x.Which of the following conditions denotes instrument relevance? A)Cov(z,u) 0 B)Cov(z,u)

Question

Consider the following simple regression model y=β₀+ β₁x₁+ u.Suppose z is an instrument for x.Which of the following conditions denotes instrument relevance? A)Cov(z,u)> 0 B)Cov(z,u)< 0 C)Cov(z,x)≠ 0 D)Cov(z,x)=0

Quizplus · Accepted Answer

Instrument relevance requires that z is correlated with the endogenous variable x. Therefore, the correct condition is Cov(z,x)≠ 0. The other options (A and B) refer to the correlation between z and the error term u, which is not relevant for assessing instrument relevance. Option D (Cov(z,x)=0) implies that z is uncorrelated with x, which means that it cannot be a valid instrument.

Consider the Following Simple Regression Model Y=β0+ β1x1+ U

Consider the Following Simple Regression Model Y=β₀+ β₁x₁+ U