The model satisfies the Group Wise heteroscedastic regression model of Section 11.7.2. All variables have zero means. The following sample second-moment matrix is obtained from a sample of 20 observations:

?a. Compute the two separate OLS estimates of β, their sampling variances the estimates of σ21 and σ22, and the R2??s in the two regressions.

b. Carry out the Lagrange multiplier test of the hypothesis that σ21 = σ22.

c. Compute the two-step FGLS estimate of β and an estimate of its sampling variance. Test the hypothesis that β equals 1.

d. Carry out the Wald test of equal disturbance variances.

e. Compute the maximum likelihood estimates of β, σ21, and σ22 by iterating the FGLS estimates to convergence.

f. Carry out a likelihood ratio test of equal disturbance variances.

g. Compute the two-step FGLS estimate of β, assuming that the model in (14-7) applies. (That is, allow for cross-sectional correlation.) Compare your results with those of part c.

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