**************************************************************************
* Estimation of a CES production function by the Gauss-Newton algorithm
* Section 12.2.3b of Judge, Hill et al. [1988, p.514-5]
**************************************************************************
SAMPLE 1 30
READ  L K Q
      0.228      0.802      0.256918
      0.258      0.249      0.183599
      0.821      0.771      1.212883
      0.767      0.511      0.522568
      0.495      0.758      0.847894
      0.487      0.425      0.763379
      0.678      0.452      0.623130
      0.748      0.817      1.031485
      0.727      0.845      0.569498
      0.695      0.958      0.882497
      0.458      0.084      0.108827
      0.981      0.021      0.026437
      0.002      0.295      0.003750
      0.429      0.277      0.461626
      0.231      0.546      0.268474
      0.664      0.129      0.186747
      0.631      0.017      0.020671
      0.059      0.906      0.100159
      0.811      0.223      0.252334
      0.758      0.145      0.103312
      0.050      0.161      0.078945
      0.823      0.006      0.005799
      0.483      0.836      0.723250
      0.682      0.521      0.776468
      0.116      0.930      0.216536
      0.440      0.495      0.541182
      0.456      0.185      0.316320
      0.342      0.092      0.123811
      0.358      0.485      0.386354
      0.162      0.934      0.279431
* Number of coefficients to estimate
NCOEF: 4
* Starting values
* The parameters must be named B1, B2, .... 
GEN1 B1=0.5
GEN1 B2=0.5
GEN1 B3=-1 
GEN1 B4=-1  
* Maximum number of iterations
NITER: 50
* Convergence criteria - the algorithm stops when the
* gradient sum of squares is less than the value specified.
DELTA: .0001
* Equation specification - A CES production function
* The left-hand side of the equation
Y: LOG(Q) 
* The right-hand side of the equation
EQRHS: (B1 + B4 * LOG ( B2*L**B3 + (1-B2)*K**B3))
* Estimation by the Gauss-Newton algorithm
FILE PROC gauss.prc 
EXEC GAUSS
* ----------------------------------------------------------------------
* Now try the NL command to do the estimation by a different algorithm
* Use the same starting values as above - model does not converge
GENR LNQ=LOG(Q)
NL 1 / NCOEF=4 
EQ LNQ=C1 + C4 * LOG ( C2*L**C3 + (1-C2)*K**C3)
COEF C1 0.5 C2 .5 C3 -1 C4 -1 
END
* Now try different starting values
NL 1 / NCOEF=4 
EQ LNQ=C1 + C4 * LOG ( C2*L**C3 + (1-C2)*K**C3)
COEF C1 0.5 C2 .3 C3 -3 C4 -1 
END
STOP