The following table presents a hypothetical panel of data:

a. Estimate the group wise heteroscedastic model of Section 11.7.2. Include an estimate of the asymptotic variance of the slope estimator. Use a two-step procedure, basing the FGLS estimator at the second step on residuals from the pooled least squares regression.

b. Carry out the Wald, Lagrange multiplier, and likelihood ratio tests of the hypothesis that the variances are all equal. For the likelihood ratio test, use the FGLS estimates.

c. Carry out a Lagrange multiplier test of the hypothesis that the disturbances are uncorrelated acrossindividuals.

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1234567690 8 10 y 30.27 35.59 17.90 44.90 37.58 23.15 30.53 39.90 20.44 36.85 i=1 X 24.31 28.47 23.74 25.44 20.80 10.55 18.40 25.40 13.57 25.60 y 38.71 29.74 11.29 26.17 5.85 29.01 30.38 36.03 37.90 33.90 i=2 x 28.35 27.38 12.74 21.08 14.02 20.43 28.13 21.78 25.65 11.66 i=3 y 37.03 43.82 37.12 24.34 26.15 26.01 29.64 30.25 25.41 26.04 21.16 26.76 22.21 19.02 18.64 18.97 21.35 21.34 15.86 13.28