Suppose we have a regression model of Y = ßo + ß1X + U, where E(XU) ≠ 0. Suppose Z is a varible that is highly correlated with X and no correlation with U.
a. Do an OLS estimate of the ß1 coefficient and analyze the statistical properties of the estimated coefficient.
b. Do an IV estimate of the ß1 coefficient and analyze the statistical properties of the estimated coefficient.