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  • Help with Stochastic Frontier Analysis/Translog Cost Function in Stata 15, bc95 model

    Dear Stata users,


    I am using Stata 15 and I am quite new in using this software. I am working on a profit and cost efficiency analyses of 309 tourists firms for period 2008-2017. I have chosen to apply the Battese & Coelli(1995) model (Translog function). I have gone through the Stata journal by Belotti et al. (2013) as well. I took the ln of some of the inputs and outputs. The variables that I have chosen are: lnTotal Costs and EBIT as dependent variables, respectively for cost and profit efficiency function; independent output variable: LnSales Revenue; independent input variables: lnLabour costs, LnMaterial costs, LnPhysical Capital costs; explanatory variables of inefficiencies: 3*category, 4*category, 5*category and Tourism Specialization. Every time I try and run the model of Cost efficiency I receive these results:

    Code:
    sfpanel lTC lSR lpL lpM lpPhC Year, model(bc95) dist(tn) emean(category3 category4 category5 Tourismspecialization ) ort(o)
    These are some results.
    Code:
    initial: Log likelihood = -7224.8875
    Iteration 0: Log likelihood = -7224.8875
    Iteration 1: Log likelihood = -6065.1666 (backed up)
    Iteration 2: Log likelihood = -5868.4579 (backed up)
    Iteration 3: Log likelihood = -5714.9868 (backed up)
    Iteration 4: Log likelihood = -5693.4116 (backed up)
    Iteration 5: Log likelihood = -5635.5574 (backed up)
    Iteration 6: Log likelihood = -5627.7123 (backed up)
    Iteration 7: Log likelihood = -5576.0618 (backed up)
    Iteration 8: Log likelihood = -5492.4664 (backed up)
    Iteration 9: Log likelihood = -5170.6388 (backed up)
    Iteration 10: Log likelihood = -4820.927 (backed up)
    Iteration 11: Log likelihood = -4654.692 (backed up)
    Iteration 12: Log likelihood = -4582.0477
    Iteration 13: Log likelihood = -3682.9697
    Iteration 14: Log likelihood = -2918.4183
    Iteration 15: Log likelihood = -1668.3032
    Iteration 16: Log likelihood = -1573.0303
    Iteration 17: Log likelihood = -1407.2167
    Iteration 18: Log likelihood = -1199.2455
    Iteration 19: Log likelihood = -1111.6501
    Iteration 20: Log likelihood = -1036.1432
    Iteration 21: Log likelihood = -994.09753
    Iteration 22: Log likelihood = -961.96257
    Iteration 23: Log likelihood = -914.4405
    BFGS stepping has contracted, resetting BFGS Hessian
    Iteration 24: Log likelihood = -890.15886
    Iteration 25: Log likelihood = -890.15698 (backed up)
    Iteration 26: Log likelihood = -887.35603 (backed up)
    .................................................. ..................................
    
    Iteration 98: Log likelihood = -845.8587
    Iteration 99: Log likelihood = -841.51001
    Iteration 100: Log likelihood = -841.36681
    
    Inefficiency effects model (truncated-normal) Number of obs = 3370
    Group variable: UIC Number of groups = 348
    Time variable: Year Obs per group: min = 1
    avg = 9.7
    max = 10
    
    Prob > chi2 = 0.0000
    Log likelihood = -841.3668 Wald chi2(5) = 29977.96
    
    ---------------------------------------------------------------------------------------
    lTC | Coef. Std. Err. z P>|z| [95% Conf. Interval]
    ----------------------+----------------------------------------------------------------
    Frontier |
    lSR | .8265737 .0056998 145.02 0.000 .8154022 .8377451
    lpL | .3862649 .0144812 26.67 0.000 .3578823 .4146475
    lpM | .3463463 .0080424 43.07 0.000 .3305836 .3621091
    lpPhC | .0036081 .0061366 0.59 0.557 -.0084194 .0156357
    Year | -.0242052 .0021223 -11.41 0.000 -.0283649 -.0200455
    _cons | 49.74526 4.263296 11.67 0.000 41.38935 58.10117
    ----------------------+----------------------------------------------------------------
    Mu |
    category3 | -.0477896 .0180303 -2.65 0.008 -.0831284 -.0124509
    category4 | -.0969461 .0202058 -4.80 0.000 -.1365486 -.0573435
    category5 | -6.000944 .4847824 -12.38 0.000 -6.9511 -5.050788
    Tourismspecialization | -.1345739 .2149034 -0.63 0.531 -.5557769 .2866291
    _cons | .2507753 .0318595 7.87 0.000 .1883317 .3132188
    ----------------------+----------------------------------------------------------------
    Usigma |
    _cons | -5.155248 .2810498 -18.34 0.000 -5.706096 -4.604401
    ----------------------+----------------------------------------------------------------
    Vsigma |
    _cons | -2.400803 .0278476 -86.21 0.000 -2.455383 -2.346223
    ----------------------+----------------------------------------------------------------
    sigma_u | .0759542 .0106735 7.12 0.000 .0576683 .1000385
    sigma_v | .3010733 .0041921 71.82 0.000 .2929681 .3094028
    lambda | .2522782 .0128424 19.64 0.000 .2271076 .2774489
    ------------------------------------------------------------------------------
    Can you explain to me what this message 'BFGS stepping has contracted, resetting BFGS Hessian' means?
    Should I do some extra actions with my data or I am using wrong syntax?

    When I have trying to run the Profit Efficiency function I received this error message:

    Code:
    sfpanel EBIT lSR lpL lpM lpPhC Year, model(bc95) dist(tn) emean(category3 category4 category5 Tourismspecialization ) ort(o)
    The results are:

    Code:
    initial: Log likelihood = -3.816e+09
    Iteration 0: Log likelihood = -3.816e+09
    could not calculate numerical derivatives -- flat or discontinuous region encountered
    could not calculate numerical derivatives -- flat or discontinuous region encountered
    
    Inefficiency effects model (truncated-normal) Number of obs = 3370
    Group variable: UIC Number of groups = 348
    Time variable: Year Obs per group: min = 1
    avg = 9.7
    max = 10
    
    Prob > chi2 = .
    Log likelihood = -7.346e+05 Wald chi2(0) = .
    
    ---------------------------------------------------------------------------------------
    EBIT | Coef. Std. Err. z P>|z| [95% Conf. Interval]
    ----------------------+----------------------------------------------------------------
    Frontier |
    lSR | 1086.5 . . . . .
    lpL | -840.1726 . . . . .
    lpM | -991.0253 . . . . .
    lpPhC | -122.3459 . . . . .
    Year | 18.04479 . . . . .
    _cons | -26225.4 . . . . .
    ----------------------+----------------------------------------------------------------
    Mu |
    category3 | 1.016451 . . . . .
    category4 | 1.024072 . . . . .
    category5 | 1.004471 . . . . .
    Tourismspecialization | 1.001218 . . . . .
    _cons | 1.047579 . . . . .
    ----------------------+----------------------------------------------------------------
    Usigma |
    _cons | 22.82486 . . . . .
    ----------------------+----------------------------------------------------------------
    Vsigma |
    _cons | 434.1319 . . . . .
    ----------------------+----------------------------------------------------------------
    sigma_u | 90438.91 . . . . .
    sigma_v | 1.86e+94 . . . . .
    lambda | 4.85e-90 . . . . .
    ------------------------------------------------------------------------------
    I can not understand what this message 'could not calculate numerical derivatives -- flat or discontinuous region encountered' means.
    The dependent variables is EBIT and it can take negative value that is why I do not generate it into ln forms. Do you think that the problem is the negative values of some units or something else?

    I will be so grateful if anyone can help me.
    Thank you in advance.
    Last edited by Dora Doncheva; 29 Jul 2020, 00:42.

  • #2
    The dependent variables is EBIT and it can take negative value that is why I do not generate it into ln forms. Do you think that the problem is the negative values
    Yes.

    Perhaps this paper on "Handling Losses in Translog Profit Models" will be helpful https://www.uu.nl/sites/default/file...2007_07-17.pdf

    Comment


    • #3
      Thank you very much for your help!

      Comment


      • #4
        Hello,
        I have another problem to be solved with Profit translog function. I have generated an NPI index (as it is done in the paper "Handling Losses in Translog Profit Models") 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
        ------------------------------------------------------------------------------

        Comment

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