The U.S. Secretary of Agriculture asks a staff economist to provide a basis for determining cattle inventories in the Midwest, Southwest, and West. Let i ¼ 1,2,3 denote the three regions. The economist hypothesizes that in each region cattle numbers at the end of the year ð Þ Cit depend on average price during the year ð Þ Pit , rainfall during the year ð Þ Rit , and cattle numbers at the end of the previous year Ci; t1

. Because growing conditions are quite different in the three regions, three separate equations are specified, one for each region:

C1t ¼ b11 þ b12P1t þ b13R1t þ b14C1; t1 þ e1t C2t ¼ b21 þ b22P2t þ b23R2t þ b24C2; t1 þ e2t C3t ¼ b31 þ b32P3t þ b33R3t þ b34C3; t1 þ e3t

(a) What signs would you expect on the various coefficients? Why?

(b) Under what assumptions about the eit should the three equations be estimated jointly as a set rather than individually?

(c) Use the data that appear in the file cattle.dat to find separate least squares estimates for each equation, and the corresponding standard errors.

(d) Test for the existence of contemporaneous correlation between the eit.

(e) Estimate the three equations jointly using the seemingly unrelated regression technique. Compare these results with those obtained in

(c) in terms of reliability and economic feasibility.