Hello,
I have a problem to be solved with Profit translog function. I am working on estimation of profit efficiency of 309 tourism firms for the period of 2008-2017. I have generated an NPI index (as it is done in the paper "Handling Losses in Translog Profit Models" https://www.uu.nl/sites/default/file...2007_07-17.pdf) but the Stata omitted the index because of collinearity. What can I do in this situation?

The steps I followed were:

1) I prepared the variables according the translog function terms. The variables that I have chosen are: Total Costs (tc) and EBIT as dependent variables, respectively for cost and profit efficiency function; independent output variable: Sales Revenue (y); independent input variables: Price of Labour (wl), Price of Material (wm), Price of Physical Capital (wk); explanatory variables of inefficiencies: z1 and z2 are dummies for 4*category, 5*category; z3 is Tourism Specialization and time trend.

2) I generated NPI index (an additional independent variable) that takes value 1 if EBIT > 0 and takes absolute value of EBIT if EBIT < 0.

3) I run the code
Code:
global xvar lny lny2 lnwlD lnwmD lnwlD2 lnwmD2 lnwlmD lnylnwlD lnylnwmD

sfpanel lnEBITD $xvar lnNPI , model(bc95) dist(tn) emean(z1 z2 z3 trend) ort(o)
4) The results were:

Code:
. sfpanel lnEBITD $xvar lnNPI, model(bc95) dist(tn) emean(z1 z2 z3 trend) ort(o)

note: lnNPI omitted because of collinearity

initial:       Log likelihood =  -3510.201
Iteration 0:   Log likelihood =  -3510.201  
Iteration 1:   Log likelihood = -3470.8279  (backed up)
Iteration 2:   Log likelihood = -3469.6762  (backed up)
Iteration 3:   Log likelihood = -3464.2091  (backed up)
Iteration 4:   Log likelihood = -3452.6898  (backed up)
Iteration 5:   Log likelihood = -3452.5744  (backed up)
Iteration 6:   Log likelihood = -3446.6273  (backed up)
Iteration 7:   Log likelihood =  -3445.044  (backed up)
Iteration 8:   Log likelihood = -3444.8962  
Iteration 9:   Log likelihood = -3441.8692  (backed up)
Iteration 10:  Log likelihood = -3436.5632  
Iteration 11:  Log likelihood = -3436.0269  (backed up)
Iteration 12:  Log likelihood = -3433.2262  
Iteration 13:  Log likelihood = -3421.8065  
Iteration 14:  Log likelihood = -3421.1973  
Iteration 15:  Log likelihood = -3421.0309  
Iteration 16:  Log likelihood = -3420.9696  
Iteration 17:  Log likelihood = -3420.9686  
Iteration 18:  Log likelihood = -3420.9685  

Inefficiency effects model (truncated-normal)        Number of obs =      2490
Group variable: id_firm                           Number of groups =       301
Time variable: Year                             Obs per group: min =         1
                                                               avg =       8.3
                                                               max =        10

                                                     Prob > chi2   =    0.0000
Log likelihood = -3420.9685                          Wald chi2(9)  =   5730.61

------------------------------------------------------------------------------
     lnEBITD |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
Frontier     |
         lny |   .7069243   .1499564     4.71   0.000     .4130152    1.000833
        lny2 |  -.0075201   .0236769    -0.32   0.751     -.053926    .0388857
       lnwlD |   1.271186   .1750752     7.26   0.000     .9280453    1.614328
       lnwmD |   .5140178   .1494781     3.44   0.001     .2210461    .8069895
      lnwlD2 |  -.2564937   .0485085    -5.29   0.000    -.3515687   -.1614188
      lnwmD2 |   .0876356   .0443475     1.98   0.048     .0007161    .1745551
      lnwlmD |   .0173517   .0400604     0.43   0.665    -.0611654    .0958687
    lnylnwlD |   .0778734   .0274736     2.83   0.005     .0240261    .1317207
    lnylnwmD |  -.0923371   .0210328    -4.39   0.000    -.1335608   -.0511135
       lnNPI |   3.12e-14          .        .       .            .           .
       _cons |  -1.323453   .6169325    -2.15   0.032    -2.532618   -.1142874
-------------+----------------------------------------------------------------
Mu           |
          z1 |  -2.958116   7.321343    -0.40   0.686    -17.30768    11.39145
          z2 |    22.1597    46.5821     0.48   0.634    -69.13955    113.4589
          z3 |  -273.8059   582.8088    -0.47   0.638     -1416.09    868.4784
       trend |    2.84031   5.998347     0.47   0.636    -8.916233    14.59685
       _cons |  -81.86916   180.4327    -0.45   0.650    -435.5107    271.7723
-------------+----------------------------------------------------------------
Usigma       |
       _cons |   4.129526    2.14995     1.92   0.055    -.0842985     8.34335
-------------+----------------------------------------------------------------
Vsigma       |
       _cons |  -1.057288   .0628779   -16.81   0.000    -1.180527     -.93405
-------------+----------------------------------------------------------------
     sigma_u |   7.883428   8.474487     0.93   0.352     .9587267    64.82393
     sigma_v |   .5894035   .0185302    31.81   0.000     .5541812    .6268644
      lambda |   13.37526   8.470531     1.58   0.114    -3.226672     29.9772
------------------------------------------------------------------------------
Thank you very much for your help in advance!