Observations on all the cross-section can be rewritten as X 0 0 + y or in more compact form y=XB+Da+E where y and e are NT×1, X iS NT×k,isk×1,andD=dnd2…dN]is NT XN with di is a dummy variables indicating the ith unit. This model is usually referred to as the least squares dummy variable(LSDv) model Since this model satisfy the ideal conditions, ols estimator is BLue using the familiar partitioned regression of Ch. 6, the slope estimator would B=(XMDXXMpy where MD=INT -D(DD)D Lemma M00 M D(D'D-D 0 Mo where Mo=IT-1/T(ii)is the demean-matrixObservations on all the cross-section can be rewritten as           y1 y2 . . . . yN           =           X1 X2 . . . . XN           β +           i 0 . . . 0 0 i 0 . . 0 . . . . . . . . . . . . . . . . . . . . . . . . 0 . . . 0 i                     α1 α2 . . . . αN           +           ε1 ε2 . . . . εN           , or in more compact form y = Xβ + Dα + ε, where y and ε are NT × 1, X is NT × k, β is k × 1, and D = [d1 d2 ...dN] is NT × N with di is a dummy variables indicating the ith unit. This model is usually referred to as the least squares dummy variable (LSDV) model. Since this model satisfy the ideal conditions, OLS estimator is BLUE. By using the familiar partitioned regression of Ch. 6, the slope estimator would be βˆ = (X0MDX) −1X0MDy, where MD = INT − D(D0D) −1D0 . Lemma: MD = INT − D(D0D) −1D0 =           M0 0 . . . 0 0 M0 0 . . 0 . . . . . . . . . . . . . . . . . . . . . . . . 0 . . . 0 M0           , where M0 = IT − 1/T(ii0 ) is the demean-matrix. 3