Consider the three demand equations ln Q1t b11 b12 ln P1t b13 ln Yt e1t ln Q2t b21

Consider the three demand equations lnð Þ¼ Q1t b11 þ b12 lnð Þþ P1t b13 lnð Þþ Yt e1t lnð Þ Q2t ¼ b21 þ b22 lnð Þ P2t þ b23 lnð Þ Yt þ e2t lnð Þ¼ Q3t b31 þ b32 lnð Þþ P3t b33 lnð Þþ Yt e3t where Qit is the quantity consumed of the ith commodity, i = 1,2,3, in the tth time period, t ¼ 1,2,...,30, Pit is the price of the ith commodity in time t, and Yt is disposable income in period t. The commodities are meat (i =1), fruits and vegetables

(i ¼ 2), and cereals and bakery products (i ¼ 3). Prices and income are in real terms, and all data are in index form. They can be found in the file demand.dat.

(a) Estimate each equation by least squares and test whether the equation errors for each household are correlated. Report the estimates and their standard errors.

Do the elasticities have the expected signs?

(b) Estimate the system jointly using the SUR estimator. Report the estimates and their standard errors. Do they differ much from your results in part (a)?

(c) Test the null hypothesis that all income elasticities are equal to unity. (Consult your software to see how such a test is implemented.)