The TSLS estimator is A)(X'X)^-¹ X'Y B)(X'Z(Z'Z)^-¹Z'X)^-¹ X'Z(Z'Z)^-¹Z' Y C)(XΩ^-¹^X)^-¹(XΩ^-¹^Y) D)(X'P_z)^-¹^P_zY

Question

Quizplus · Accepted Answer

The TSLS estimator involves multiplying the original regression equation by two projection matrices, one based on the instruments and one based on the original explanatory variables. The correct formula is B = (X'Z(Z'Z)^(-1)Z'X)^(-1)X'Z(Z'Z)^(-1)Z'Y. This is equivalent to choice B once it is rearranged using the results of the first stage regression. The other choices include incorrect or incomplete formulas.

The TSLS Estimator Is