 &CARD1
 NOBS    =        1000,
 NC      =           1,
 NF      =        1000,
 NFP     =        1000,
 NOBEL   =           1,
 NM      =           0,
 NSTEP   =         500,
 EPSI    =  1.000000000000000E-007,
 WGHT    =   1.00000000000000     
 /
 &CARD2
 NB      =           3,
 NRO     =           0,
 NSL     =           0,
 NGF     =           0,
 MAXF    =           0,
 NGV     =           3,
 MAXV    =           1,
 NLY     =           1,
 NDM     =          -1,
 NLE     =           0,
 ND      =           0
 /
 &CARD3
 NCOR    =           0,
 NRES    =           0,
 NPW     =           0,
 NGUVW   =           0,
 NPDQL   =           0,
 NCOV    =           0,
 NEY     =           0,
 VARNAME = BC4      ,
 NVARIANT        =          10
 /



Working space used : 18305 out of 500000


 group           1 (estimated lambda(x))
 initial value:  0.500000000000000     
 variable no.
   1


 group           2 (estimated lambda(x))
 initial value:  0.500000000000000     
 variable no.
   2


 group           3 (estimated lambda(x))
 initial value:  0.500000000000000     
 variable no.
   3


 lambda(y) initial value:   1.00000000000000     
 upper limit for y   0.000000000000000E+000



no.  variable       minimum        mean         maximum    null obs.

     Tij          0.58995D+04   0.25740D+08   0.34194D+09        0
  1  Ti           0.15809D+05   0.18607D+06   0.35135D+06        0
  2  Tj           0.69620D+04   0.18512D+06   0.43378D+06        0
  3  Util_BC4     0.38681D-07   0.73462D-03   0.13996D-01        0
  4  constant     0.10000D+01   0.10000D+01   0.10000D+01        0


INITIAL ESTIMATES
                                                                                       E L A S T I C I T Y   E L A S T I C I T Y
    VARIABLE     LAMBDA(X)    COEFFICIENT      MEAN(X)       STD-ERROR    STUDENT-T    y(sample)  E(y)       y(sample)  E(y)
                                                                                                  SIGMA(y)              SIGMA(y)
                                                                                                  GAMMA(y)              GAMMA(y)
                type  group                                                            -first obs       1    -first obs    1000
                                                                                       -last obs     1000    -last obs     1000
  1 Ti           EL     1    0.1137649D+05  0.1860662D+06  0.5558245D+04     2.0468      0.1907     0.1107     0.0660     0.0548
                                                                                                    0.0300                0.0004
                                                                                                   -0.1922               -0.5461
  2 Tj           EL     2    0.2467735D+05  0.1851223D+06  0.4911284D+04     5.0246      0.4125     0.2396     0.0792     0.0657
                                                                                                    0.0649                0.0005
                                                                                                   -0.4158               -0.6550
  3 Util_BC4     EL     3    0.5153756D+09  0.7346229D-03  0.2576602D+08    20.0021      0.5427     0.3152     0.5891     0.4887
                                                                                                    0.0854                0.0036
                                                                                                   -0.5470               -4.8731
  4 constant     NL     0    0.1008067D+10  0.1000000D+01  0.4980307D+08    20.2411     39.1640    22.7485    11.7036     9.7093
                                                                                                    6.1610                0.0718
                                                                                                  -39.4766              -96.8106

LAMBDA TYPE SYMBOL:
 NL = NO LAMBDA
 FL = FIXED LAMBDA
 EL = ESTIMATED LAMBDA



Derivatives of y(sample), E(y), SIGMA(y) and GAMMA(y)
with respect to the Independent Variables at the sample means

    Variable    Der.y(sample)  Der.E(y)       Der.SIGMA(y)   Der.GAMMA(y)

  1 Ti          0.2637392D+02  0.2286342D+02  0.4662347D+01 -0.5230058D-06

  2 Tj          0.5735472D+02  0.4972052D+02  0.1013909D+02 -0.1137368D-05

  3 Util_BC4    0.1901479D+11  0.1648383D+11  0.3361411D+10 -0.3770713D+03

  4 constant    0.1008067D+10  0.8738883D+09  0.1782048D+09 -0.1999039D+02

MRS between two moments (E(y), SIGMA(y), GAMMA(y))
at the sample means
===============================================

row / col    E(y)        SIGMA(y)    GAMMA(y)  
===============================================

E(y)         0.1000D+01  0.4904D+01 -0.4372D+08

SIGMA(y)     0.2039D+00  0.1000D+01 -0.8915D+07

GAMMA(y)    -0.2288D-07 -0.1122D-06  0.1000D+01


Elasticity of substitution between two moments
(E(y), SIGMA(y), GAMMA(y)) at the sample means
===============================================

row / col    E(y)        SIGMA(y)    GAMMA(y)  
===============================================

E(y)         0.1000D+01  0.3692D+01 -0.5763D+00

SIGMA(y)     0.2708D+00  0.1000D+01 -0.1561D+00

GAMMA(y)    -0.1735D+01 -0.6407D+01  0.1000D+01


MRS of X(l) with respect to X(k) at the sample means
===================================================================================================================================
        X(k) Ti          Tj          Util_BC4    constant  
X(l)
===================================================================================================================================

Ti           0.1000D+01  0.2175D+01  0.7210D+09  0.3822D+08

Tj           0.4598D+00  0.1000D+01  0.3315D+09  0.1758D+08

Util_BC4     0.1387D-08  0.3016D-08  0.1000D+01  0.5301D-01

constant     0.2616D-07  0.5690D-07  0.1886D+02  0.1000D+01


Mean probability of y to be at the lower (upper) limit
if lambda(y) is positive (negative) = 0.2536

Estimation Sample   :       1    1000

             OBSERVED Y     FITTED E(Y)
MEAN         0.2573965D+08  0.3109813D+08
STD.ERROR    0.3864076D+08  0.1806627D+08
SKEWNESS         3.4428570      2.4525615

E(y) at the means   :  0.3841520D+08

Sig(y) at the means :  0.2892461D+08

C.o.V. at the means :      0.7529470

Gam(y) at the means :      0.5063862

Pearson-R2          :      0.2721886

Pearson-R2 bar      :      0.2699964

Pseudo-(l)-R2       :      0.2880923

Pseudo-(l)-R2 bar   :      0.2859480

Error Variance      :  0.1061892D+16

Log-likelihood      : -0.1871835D+05


initialization cards for control routine follow - - id card - no. parameters , no. steps , step size 
minimization tolerance - starting values of parameters - relative uncertainties of parameters (error estimates) - 
and starting direction (relative parameter increments for 1st step)

                                                                              
         4       500   0.1D+01   0.1D-06
  0.50000D+00  0.50000D+00  0.50000D+00  0.10000D+01
  0.10000D+01  0.10000D+01  0.10000D+01  0.10000D+01
  0.00000D+00  0.00000D+00  0.00000D+00  0.00000D+00

first entry to fcn , parameters of current step follow - - f,x(i)
   0.2976721891D+03  0.50000D+00  0.50000D+00  0.50000D+00  0.10000D+01

new absolute minimum , parameters for fcn entry     5  follow - - f,x(i)
  -0.7785298588D+03  0.49963D+00  0.50122D+00  0.43494D+00  0.11586D+00

new absolute minimum , parameters for fcn entry    10  follow - - f,x(i)
  -0.9502614268D+03  0.49595D+00  0.50398D+00 -0.89866D-02  0.56206D-01

new absolute minimum , parameters for fcn entry    16  follow - - f,x(i)
  -0.9584005664D+03 -0.15412D-01  0.15626D+01 -0.38192D-01  0.52847D-01

new absolute minimum , parameters for fcn entry    19  follow - - f,x(i)
  -0.9600218978D+03 -0.48928D+00  0.15478D+01 -0.32109D-01  0.54484D-01

new absolute minimum , parameters for fcn entry    22  follow - - f,x(i)
  -0.9605933295D+03 -0.40343D+00  0.16223D+01 -0.17297D-01  0.60320D-01

new absolute minimum , parameters for fcn entry    24  follow - - f,x(i)
  -0.9607025421D+03 -0.41461D+00  0.15669D+01 -0.17035D-01  0.66823D-01

new absolute minimum , parameters for fcn entry    26  follow - - f,x(i)
  -0.9607183650D+03 -0.42280D+00  0.15139D+01 -0.15942D-01  0.65961D-01

new absolute minimum , parameters for fcn entry    28  follow - - f,x(i)
  -0.9607184915D+03 -0.41879D+00  0.15132D+01 -0.15953D-01  0.65920D-01

new absolute minimum , parameters for fcn entry    29  follow - - f,x(i)
  -0.9607184917D+03 -0.41878D+00  0.15133D+01 -0.15948D-01  0.65916D-01

new absolute minimum , parameters for fcn entry    30  follow - - f,x(i)
  -0.9607184917D+03 -0.41878D+00  0.15133D+01 -0.15947D-01  0.65915D-01

new absolute minimum , parameters for fcn entry    31  follow - - f,x(i)
  -0.9607184917D+03 -0.41878D+00  0.15133D+01 -0.15947D-01  0.65915D-01

new absolute minimum , parameters for fcn entry    32  follow - - f,x(i)
  -0.9607184917D+03 -0.41878D+00  0.15133D+01 -0.15947D-01  0.65915D-01


the function (fcn) has not improved by    0.10000D-06 after 3 steps which include a minimum - - -


therefore the run has been terminated
  -0.9607184917D+03 -0.41878D+00  0.15133D+01 -0.15947D-01  0.65915D-01

all numbers of last entry refer to final pt. of run

the lowest value of the function (fcn) was  -0.9607184917D+03 for entry   32 - - x(i) follows
 -0.41878D+00  0.15133D+01 -0.15947D-01  0.65915D-01



run statistics follow - -

nfcn=   32 nst=   12


Mean probability of y to be at the lower (upper) limit
if lambda(y) is positive (negative) = 0.0000

Estimation Sample   :       1    1000

             OBSERVED Y     FITTED E(Y)
MEAN         0.2573965D+08  0.2802745D+08
STD.ERROR    0.3864076D+08  0.3201173D+08
SKEWNESS         3.4428570      2.3275355

E(y) at the means   :  0.4566249D+08

Sig(y) at the means :  0.5335503D+08

C.o.V. at the means :      1.1684652

Gam(y) at the means :      4.1263222

Pearson-R2          :      0.2958613

Pearson-R2 bar      :      0.2908926

Pseudo-(l)-R2       :      0.5891062

Pseudo-(l)-R2 bar   :      0.5862067

Error Variance      :  0.9812630D+01

Log-likelihood      : -0.1745996D+05


FINAL ESTIMATES
                                                                                       E L A S T I C I T Y   E L A S T I C I T Y
    VARIABLE     LAMBDA(X)    COEFFICIENT     GRADIENT       STD-ERROR    STUDENT-T    y(sample)  E(y)       y(sample)  E(y)
                                                                                                  SIGMA(y)              SIGMA(y)
                                                                                                  GAMMA(y)              GAMMA(y)
                type  group                                                            -first obs       1    -first obs    1000
                                                                                       -last obs     1000    -last obs     1000
  1 Ti           EL     1    0.1797463D+03 -0.5556250D-06  0.6038239D+03     0.2977      0.3625     0.3394     0.2959     0.2829
                                                           0.2064250D+02     8.7076                 0.3093                0.2585
                                                                                                   -0.0404               -0.0320
  2 Tj           EL     2    0.2703144D-07 -0.1574103D+02  0.1112843D-06     0.2429      0.8212     0.7689     0.1987     0.1899
                                                           0.2635716D-08    10.2558                 0.7007                0.1736
                                                                                                   -0.0915               -0.0215
  3 Util_BC4     EL     3    0.1449012D+01  0.2336512D-05  0.4672253D+00     3.1013      0.5279     0.4943     0.4679     0.4472
                                                           0.3854856D-01    37.5893                 0.4505                0.4087
                                                                                                   -0.0588               -0.0506
  4 constant     NL     0   -0.3852050D+03 -0.2351118D-06  0.1142945D+04    -0.3370   -125.0894  -117.1160  -115.5164  -110.4228
                                                           0.4889496D+02    -7.8782              -106.7325             -100.9127
                                                                                                   13.9432               12.4987
    Box-cox on (x)

  5 lambda(x) 1             -0.4187819D+00 -0.2271758D-03  0.2943889D+00    -1.4225
                                                                            -4.8194

  6 lambda(x) 2              0.1513264D+01 -0.4634101D-05  0.3382285D+00     4.4741
                                                                             1.5175

  7 lambda(x) 3             -0.1594710D-01 -0.6063505D-05  0.1561613D-01    -1.0212
                                                                           -65.0576

    Box-cox on (y)

  8 lambda(y)                0.6591521D-01  0.5158532D-04  0.1559442D-01     4.2268
                                                                           -59.8986

    Residual (w)

  9 error variance           0.9812630D+01  0.4737183D-13  0.4913189D+01     1.9972
                                                           0.4194147D+00    23.3960


LAMBDA TYPE SYMBOL:
 NL = NO LAMBDA
 FL = FIXED LAMBDA
 EL = ESTIMATED LAMBDA



Derivatives of y(sample), E(y), SIGMA(y) and GAMMA(y)
with respect to the Independent Variables at the sample means

    Variable    Der.y(sample)  Der.E(y)       Der.SIGMA(y)   Der.GAMMA(y)

  1 Ti          0.5015128D+02  0.8329800D+02  0.8870151D+02 -0.8961589D-06

  2 Tj          0.1141822D+03  0.1896492D+03  0.2019517D+03 -0.2040335D-05

  3 Util_BC4    0.1849762D+11  0.3072333D+11  0.3271634D+11 -0.3305360D+03

  4 constant   -0.3219758D+10 -0.5347807D+10 -0.5694717D+10  0.5753421D+02

MRS between two moments (E(y), SIGMA(y), GAMMA(y))
at the sample means
===============================================

row / col    E(y)        SIGMA(y)    GAMMA(y)  
===============================================

E(y)         0.1000D+01  0.9391D+00 -0.9295D+08

SIGMA(y)     0.1065D+01  0.1000D+01 -0.9898D+08

GAMMA(y)    -0.1076D-07 -0.1010D-07  0.1000D+01


Elasticity of substitution between two moments
(E(y), SIGMA(y), GAMMA(y)) at the sample means
===============================================

row / col    E(y)        SIGMA(y)    GAMMA(y)  
===============================================

E(y)         0.1000D+01  0.1097D+01 -0.8399D+01

SIGMA(y)     0.9113D+00  0.1000D+01 -0.7655D+01

GAMMA(y)    -0.1191D+00 -0.1306D+00  0.1000D+01


MRS of X(l) with respect to X(k) at the sample means
===================================================================================================================================
        X(k) Ti          Tj          Util_BC4    constant  
X(l)
===================================================================================================================================

Ti           0.1000D+01  0.2277D+01  0.3688D+09 -0.6420D+08

Tj           0.4392D+00  0.1000D+01  0.1620D+09 -0.2820D+08

Util_BC4     0.2711D-08  0.6173D-08  0.1000D+01 -0.1741D+00

constant    -0.1558D-07 -0.3546D-07 -0.5745D+01  0.1000D+01


Log-likelihood

    - initial value :    -18718.3529

    - final value   :    -17459.9623

    - ratio test    :      2516.7814


  Pearson-r2     :            0.2959

  Pearson-r2 bar :            0.2909

  Pseudo-(l)-r2     :         0.5891

  Pseudo-(l)-r2 bar :         0.5862

  Std-error of (w)  :         3.1325



  Number of observations    first-last obs.no.

    - sample     :   1000           1 -    1000

    - estimation :   1000           1 -    1000



CPU TIME:      0.28 sec
