Suppose we have the model: y1 = z1*1 + 1*y2 + u1 where y2 is a scalar variable that is correlated with u1 . Define z as the vector of exogenous variables, z1 and at least one more exogenous element, z2 , and the reduced form for y2 as the linear projection: y2 = z*2 + v2 Consider the alternative to 2SLS: estimate the reduced form for y2 by OLS, and retain the estimated residuals v'2. Then estimate the following by OLS: y1 = z1*1 + 1*y2 + 1*v'2 + e - Eq (1) (a) Show that the estimates of 1 and 1 in equation (1) by OLS are equivalent to the 2SLS estimators. (b) How can one use the estimate of 1 to motivate the choice of estimator? (c) If (1) does in fact produce an equivalent estimate to 2SLS, why not just use this approach to estimate parameters when endogeneity is suspected?

Suppose we have the model where yo is a scalar variable that is correlated with u1 Define z as the vector of exogenous variables, z1 and at least one more exogenous element 22, and the reduced form for y2 as the linear projection: y2 Consider the alternative to 2SLS: estimate the reduced form for y2 by OLS, and retain the estimated residuals in. Then estimate the following by OLS (1) (a) Show that the estimates of 61 and a1 in equation (1) by OLS are equivalent to the 2SLS estimators. (b) How can one use the estimate of pl to motivate the choice of estimator? (c) If (1) does in fact produce an equivalent estimate to 2SLS, why not just use this approach to estimate parameters when endogeneity is suspected