Question: please write all your steps on the paper. 4. Consider the three-equation structural model y1i=12y2i+13y3i+11z1i+13z3i+14z4i+u1iy2i=21y1i+21z1i+u2iy3i=31z1i+32z2i+33z3i+34z4i+u3i where z1=1,E[ugi]=0, and cov[zki,ugi]=0 for all k and g=1,2,3. In

please write all your steps on the paper. 4. Consider the

please write all your steps on the paper.

4. Consider the three-equation structural model y1i=12y2i+13y3i+11z1i+13z3i+14z4i+u1iy2i=21y1i+21z1i+u2iy3i=31z1i+32z2i+33z3i+34z4i+u3i where z1=1,E[ugi]=0, and cov[zki,ugi]=0 for all k and g=1,2,3. In addition to the exclusion restrictions that have already been imposed, assume that 13+14=1. (a) Using the order and rank conditions, what must hold for the structural parameters of Equation 1 to be identified? (b) How would you estimate Equation 1 using a single-equation method? 5. Consider the two-equation structural model y1i=10+12y2i+13y2iz1i+11z1i+12z2i+u1iy2i=20+21y1i+21z1i+23z3i+u2i where E[u1izi]=E[u2izi]=0. Note that the nonlinear regressor y2z1 appears in Equation 1. (a) Solve for E[y1izi] and E[y2izi] using the reduced forms of y1 and y2. What instruments would be appropriate for each equation? (b) Suppose that 23=0. Is Equation 1 identified? Is it possible to perform a hypothesis test of H0:13=0 ? Why or why not

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