Consider the following three equations simultaneous model y1 = 1 + 2y2 + 1X1 + u1 (1) y2 = 2 + 1y1 + 3y3 +

Consider the following three equations simultaneous model y1 = α1 + β2y2 + γ1X1 + u1 (1)

y2 = α2 + β1y1 + β3y3 + γ2X2 + u2 (2)

y3 = α3 + γ3X3 + γ4X4 + γ5X5 + u3 (3)

where the X’s are exogenous and the y’s are endogenous.

(a) Examine the identifiability of this system using the order and rank conditions.

(b) How would you estimate equation (2) by 2SLS? Describe your procedure step by step.

(c) Suppose that equation (1) was estimated by running y2 on a constant X2 and X3 and the resulting predicted ˆy2 was substituted in (1), and OLS performed on the resulting model.

Would this estimating procedure yield consistent estimates of α1, β2 and γ1? Explain your answer.

(d) How would you test for the over-identification restrictions in equation (1)?