Dear Statlist members,
Good afternoon.
I am estimating a translog cost function intending to measure the efficiency of the Syrian banking sector, my sample includes 17 banks (out of a total of 20 banks) for 12 years starting from 2005 till 2016 (yielding an unbalanced panel data). I am running 3 translog cost functions (3 models) in which the first model considers only the input prices (3 input prices), 3 outputs and 2 control variables, below is the first model:
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To allow for the impact of exogenous (heterogeneity) factors on banks’ performance, we include 5 heterogeneity variables in the model for estimating cost efficiency. There are two alternative ways to account for heterogeneity influences. The first way assumes that heterogeneity factors affect costs directly through the cost frontier. Thus, the second model considers the addition of 5 heterogeneity variables which are incorporated into the cost function as regressors (model 2):

The second approach assumes that these variables influence the degree of cost inefficiency, and hence that cost efficiencies [IMG]file:///C:\Users\toshiba\AppData\Local\Temp\msohtmlclip1\0 1\clip_image006.gif[/IMG] are expressed as a function of these factors and are integrated into the stochastic frontier model (inefficiency term [IMG]file:///C:\Users\toshiba\AppData\Local\Temp\msohtmlclip1\0 1\clip_image008.gif[/IMG] is expressed as an explicit function of a vector of heterogeneity variables) (model 3)




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Where:




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 = 


when I ran model 3 in Stata I had the following message:

“could not calculate numerical derivatives -- flat or discontinuous region encountered”

I am afraid that there might be something wrong, and I fear that my dataset is too small (106 observations) to conduct this type of modeling but I can not find anything in the literature especially the paper of "Stochastic Frontier Analysis Using Stata" by Belotti, Daidone and others to support this fear, therefore could anybody help me to tackle this matter.

the codes are:

First we define our independent variables in a macro:




Code:


global xvar lntl_m lnoea_m lnnii_m lnw2_mD lnw3_mD lntl2_m lnoea2_m lnnii2_m lnw2D2_m lnw3D2_m lneq_m lnllp_m lneq2_m lnllp2_m iact1_m iact2_m iact3_m iact4_m iact5_m iact6_m iact7_m iact8_m iact9_m iact10_m iact11_m iact12_m iact13_m iact14_m iact15_m iact16_m


then we run the sfpanel command where total costs (in logarithm) is the dependent variable:




Code:


sfpanel lntc_mD $xvar cd1 cd2, cost m(bc95) dist(tnormal) emean( st si gov hhi ms)


cd1 and cd2 account for two crisis dummies variables




Code:


note: cd2 omitted because of collinearity

initial:       Log likelihood =  -64509011
Iteration 0:   Log likelihood =  -64509011  
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 =       106
Group variable: id                                Number of groups =        17
Time variable: year                             Obs per group: min =         2
                                                               avg =       6.2
                                                               max =         8

                                                     Prob > chi2   =         .
Log likelihood = -1.323e+04                          Wald chi2(0)  =         .

------------------------------------------------------------------------------
     lntc_mD |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
Frontier     |
      lntl_m |   .5286125          .        .       .            .           .
     lnoea_m |   .9039145          .        .       .            .           .
     lnnii_m |   .9639674          .        .       .            .           .
     lnw2_mD |   1.081044          .        .       .            .           .
     lnw3_mD |  -.5200749          .        .       .            .           .
     lntl2_m |  -.1191567          .        .       .            .           .
    lnoea2_m |  -.7489184          .        .       .            .           .
    lnnii2_m |  -3.099477          .        .       .            .           .
    lnw2D2_m |  -.5460163          .        .       .            .           .
    lnw3D2_m |  -.3911933          .        .       .            .           .
      lneq_m |   .0441829          .        .       .            .           .
     lnllp_m |   1.891487          .        .       .            .           .
     lneq2_m |  -.6188029          .        .       .            .           .
    lnllp2_m |  -7.986749          .        .       .            .           .
     iact1_m |  -.1328616          .        .       .            .           .
     iact2_m |   .0397784          .        .       .            .           .
     iact3_m |  -.4059629          .        .       .            .           .
     iact4_m |   .0280676          .        .       .            .           .
     iact5_m |  -.9180085          .        .       .            .           .
     iact6_m |  -.1374279          .        .       .            .           .
     iact7_m |  -.5720094          .        .       .            .           .
     iact8_m |  -.2592886          .        .       .            .           .
     iact9_m |  -1.292187          .        .       .            .           .
    iact10_m |  -.0748654          .        .       .            .           .
    iact11_m |  -.4102888          .        .       .            .           .
    iact12_m |   -.293261          .        .       .            .           .
    iact13_m |  -1.455929          .        .       .            .           .
    iact14_m |  -2.105095          .        .       .            .           .
    iact15_m |  -1.588741          .        .       .            .           .
    iact16_m |  -7.214466          .        .       .            .           .
         cd1 |  -.0582976          .        .       .            .           .
         cd2 |  -2.50e-10  (omitted)
       _cons |    -1.1243          .        .       .            .           .
-------------+----------------------------------------------------------------
Mu           |
          st |   .9289727          .        .       .            .           .
          si |   -7.01469          .        .       .            .           .
         gov |   .7239485          .        .       .            .           .
         hhi |  -974.6672          .        .       .            .           .
          ms |   .9744048          .        .       .            .           .
       _cons |   .6186555          .        .       .            .           .
-------------+----------------------------------------------------------------
Usigma       |
       _cons |   247.0814          .        .       .            .           .
-------------+----------------------------------------------------------------
Vsigma       |
       _cons |   247.0814          .        .       .            .           .
-------------+----------------------------------------------------------------
     sigma_u |   4.50e+53          .        .       .            .           .
     sigma_v |   4.50e+53          .        .       .            .           .
      lambda |          1          .        .       .            .           .
------------------------------------------------------------------------------


I appreciate any comments or help in advance and thank you all for being patient.