Output from the program FRONTIER (Version 4.1)

instruction file = eg1.ins     

data file =        eg1.dta     

Error Components Frontier (see B&C 1992)

The model is a production function

The dependent variable is logged

the ols estimates are :

                 coefficient     standard-error    t-ratio

  beta 0         0.24489834E+00  0.21360307E+00  0.11465114E+01

  beta 1         0.28049246E+00  0.48066617E-01  0.58354940E+01

  beta 2         0.53330637E+00  0.51498586E-01  0.10355748E+02

  sigma-squared  0.11398496E+00

log likelihood function =  -0.18446849E+02

the estimates after the grid search were :

  beta 0         0.58014216E+00

  beta 1         0.28049246E+00

  beta 2         0.53330637E+00

  sigma-squared  0.22067413E+00

  gamma          0.80000000E+00

  mu is restricted to be zero

  eta is restricted to be zero

iteration =     0  func evals =     19  llf = -0.17034854E+02

     0.58014216E+00 0.28049246E+00 0.53330637E+00 0.22067413E+00 0.80000000E+00

gradient step

iteration =     5  func evals =     41  llf = -0.17027230E+02

     0.56160697E+00 0.28108701E+00 0.53647803E+00 0.21694170E+00 0.79718731E+00

iteration =     7  func evals =     63  llf = -0.17027229E+02

     0.56161963E+00 0.28110205E+00 0.53647981E+00 0.21700046E+00 0.79720730E+00

the final mle estimates are :

                 coefficient     standard-error    t-ratio

  beta 0         0.56161963E+00  0.20261668E+00  0.27718331E+01

  beta 1         0.28110205E+00  0.47643365E-01  0.59001301E+01

  beta 2         0.53647981E+00  0.45251553E-01  0.11855501E+02

  sigma-squared  0.21700046E+00  0.63909106E-01  0.33954545E+01

  gamma          0.79720730E+00  0.13642399E+00  0.58436004E+01

  mu is restricted to be zero

  eta is restricted to be zero

log likelihood function =  -0.17027229E+02

LR test of the one-sided error =   0.28392402E+01

with number of restrictions = 1

[note that this statistic has a mixed chi-square distribution]

number of iterations =      7

(maximum number of iterations set at :   100)

number of cross-sections =     60

number of time periods =      1

total number of observations =     60

thus there are:      0  obsns not in the panel

covariance matrix :

  0.41053521E-01 -0.31446721E-02 -0.80030279E-02  0.40456494E-02  0.92519362E-02

-0.31446721E-02  0.22698902E-02  0.40106205E-04 -0.29528845E-04 -0.91550467E-04

-0.80030279E-02  0.40106205E-04  0.20477030E-02 -0.47190308E-04 -0.16404645E-03

  0.40456494E-02 -0.29528845E-04 -0.47190308E-04  0.40843738E-02  0.67450773E-02

  0.92519362E-02 -0.91550467E-04 -0.16404645E-03  0.67450773E-02  0.18611506E-01

technical efficiency estimates :

     firm             eff.-est.

       1           0.65068880E+00

       2           0.82889151E+00

       3           0.72642592E+00

         .

         .

         .

      58           0.66471456E+00

      59           0.85670448E+00

      60           0.70842786E+00

mean efficiency =   0.74056772E+00