http://pages.stern.nyu.edu/~wgreene/Econometrics/RestrictedLeastSquares.lim
http://pages.stern.nyu.edu/~wgreene/Econometrics/farms.lpj


Restricted Least Squares Using Matrix Algebra

? Make the four input coefficients sum to 1.0
Namelist ; X = one,x1,x2,x3,x4 $
Create   ; y = yit $
Regress  ; Lhs = y ; Rhs = X ; Res = e $
? (Regress ; Lhs = y ; Rhs = X ; CLS:b(2)+b(3)+b(4)+b(5)=1$
Matrix   ; R = [0,1,1,1,1] $
Matrix   ; q = [1] $
Matrix   ; list ; m = R*b - q $
Matrix   ; A = R*<X'X>*R'
         ; C = <X'X>*R' * <A> $
Matrix   ; list ; bstar = b - C*m $
Create   ; estar = y - X'bstar $
Calc     ; list ; e'e ; estar'estar $
Matrix   ; list ; mstar = R*bstar - q $


? Make the four input coefficients sum to 1.0
? and zero out the 5 year dummy variables
Create   ; y = yit $
Namelist ; X = one,x1,x2,x3,x4,
           year93,year94,year95,year96,year97 $
Matrix   ; R = [
0,1,1,1,1,0,0,0,0,0 /
0,0,0,0,0,1,0,0,0,0 /
0,0,0,0,0,0,1,0,0,0 /
0,0,0,0,0,0,0,1,0,0 /
0,0,0,0,0,0,0,0,1,0 /
0,0,0,0,0,0,0,0,0,1 ] $
Matrix   ; q = [1/0/0/0/0/0] $
Regress  ; Lhs = y ; Rhs = X ; Res = e $
?         ; cls:b(2)+b(3)+b(4)+b(5)=1,
?           b(6)=0,b(7)=0,b(8)=0,b(9)=0,b(10)=0$
Matrix   ; list ; m = R*b - q $
Matrix   ; A = R*<X'X>*R'
         ; C = <X'X>*R' * <A> $
Matrix   ; list ; bstar = b - C*m $
Create   ; estar = y - X'bstar $
Calc     ; list ; e'e ; estar'estar $
Matrix   ; list ; mstar = R*bstar - q $
? Lagrange Multipliers
Matrix   ; list ; Lambda = <A>*m $