2.1 Generalized Least Squares The generalized least squares estimator of the slope parameters is B=(xgx)xy=(∑xx)(∑xxy As with many generalized least squares problem it is convenient to find a transform matrix 32-1/=[In 2-1/2 so that the OLS can be applied to the transformed model. Fuller and Battese(1973) suggest ITIT he transformation of yi and Xi for GLS is therefore yil -0yi y2-6 yiT -8ji and likewise for the rows of Xi. Note that the similarity of this procedure to the computation in the LsdV model, which use 0= 1. One would interpret as the effect that would remain if oe =0, because the only effect then would be u;. In this case. the fixed and the random effects model would be indistinguishable. so this results make sense 2.2 FGLs when 2 is unknown If the variance component are known, generalized least squares can be computed as shown earlier. Of course, this is unlikely, so as usual, we must first estimates the disturbance variance and then use an FGLS procedure. A heuristic approach to estimate the variance components is as follows t=a+x3+t+t;i=1,2,…,N;t=1,2,…,T2.1 Generalized Least Squares The generalized least squares estimator of the slope parameters is β˜ = (X0Ω −1X) −1X0Ω −1y = X N i=1 X0 iΣ −1Xi !−1 X N i=1 X0 iΣ −1yi) ! . As with many generalized least squares problem it is convenient to find a transform matrix Ω −1/2 = [In ⊗ Σ] −1/2 so that the OLS can be applied to the transformed model. Fuller and Battese (1973) suggest Σ −1/2 = 1 σε  IT − θ T iTi 0 T  , where θ = 1 − σε p σ 2 ε + Tσ 2 u . The transformation of yi and Xi for GLS is therefore Σ −1/2yi = 1 σε         yi1 − θy¯i yi2 − θy¯i . . . yiT − θy¯i         and likewise for the rows of Xi . Note that the similarity of this procedure to the computation in the LSDV model, which use θ = 1. One would interpret θ as the effect that would remain if σε = 0, because the only effect then would be ui . In this case, the fixed and the random effects model would be indistinguishable, so this results make sense. 2.2 FGLS when Σ is unknown If the variance component are known, generalized least squares can be computed as shown earlier. Of course, this is unlikely, so as usual, we must first estimates the disturbance variance and then use an FGLS procedure. A heuristic approach to estimate the variance components is as follows: yit = α + x 0 itβ + εit + ui , i = 1, 2, ..., N; t = 1, 2, ..., T. (4) 12