Doubts about interpretation of the estimated coefficients using a stochastic frontier model

[Rene Zacker]

In my thesis, I´m estiming a stochastic frontier model (SFM). The first equation estimates the production frontier model and the second equation estimates the inefficiency distribution, which is used in the production frontier function. For that purpose I used the sfpanel command in STATA.

However, the coefficients of the inefficiency distribution cannot really be interpreted in a easy way. Now, I'm trying to estimate the marginal effects of my model after running a two-equation regression.

However, I still cannot find the way to calculate these marginal effects for the variables that explain the term inefficiency.

Someone will have a suggestion

[Phil Bromiley]

You'll increase your chances of a useful answer by following the FAQ on asking questions - provide Stata code in code delimiters, readable Stata output and sample data using dataex. We don't even know exactly what you ran.

sfpanel postestimation has a bunch of things it will predict including inefficiency. I don't use frontier models so I'm not even sure what marginal effects means. In general, I find working with predicted values (often varying one variable and holding the other variables at their means) helps interpretation. For Stata procedures, the margins command does this, but with user written commands, there is no guaranteed they work with margins. With a user-written procedure, getting help depends on someone active on the list happening to use the procedure.

[Rene Zacker]

Phil, thanks for your comment.

I estimated a stochastic frontier model (SFM) for a sample of firms belonging to the same sector. The structure of my data is a panel of two periods. For the estimation I follow Battese & Coelli (1995).

Battese & Coelli (1995). A model for technical inefficiency effects in a stochastic frontier production function for panel data.
Empirical Economics 20: 325-332.

In the SFM estimate, I used the logarithm of the production value (lpv) as the dependent variable, as independent variables I considered the logarithm of the number of blue collar employees (lbe) and the logarithm of the capital of the firm (lcf). In the estimation of inefficiency term (U) I considered a dummy variable which takes the value of one if the firm has a quality control department (qc) and zero in any other case; I also considered a variable that measures the percentage of trained personnel (per_tp) a year before.

. xi: sfpanel lpv lbe lcf, model(bc95) u( por_tp i.qc) robust
i.qc              _Iqc_0-1            (naturally coded; _Iqc_0 omitted)


initial:       Log pseudolikelihood = -5387.7015
Iteration 0:   Log pseudolikelihood = -5387.7015  
Iteration 1:   Log pseudolikelihood = -5379.6189  
Iteration 2:   Log pseudolikelihood = -5358.7663  
Iteration 3:   Log pseudolikelihood = -5355.3939  
Iteration 4:   Log pseudolikelihood = -5349.3455  
Iteration 5:   Log pseudolikelihood = -5345.5249  
Iteration 6:   Log pseudolikelihood = -5343.6951  
Iteration 7:   Log pseudolikelihood =  -5341.704  
Iteration 8:   Log pseudolikelihood = -5338.9792  
Iteration 9:   Log pseudolikelihood = -5338.6383  
Iteration 10:  Log pseudolikelihood = -5338.4574  
Iteration 11:  Log pseudolikelihood = -5338.4068  
Iteration 12:  Log pseudolikelihood = -5338.3876  
Iteration 13:  Log pseudolikelihood = -5338.3859  
Iteration 14:  Log pseudolikelihood = -5338.3856  
Iteration 15:  Log pseudolikelihood = -5338.3856  

Inefficiency effects model (truncated-normal)        Number of obs =      3129
Group variable: mun2                              Number of groups =      1796
Time variable: year                             Obs per group: min =         1
                                                               avg =       1.7
                                                               max =         2

                                                     Prob > chi2   =    0.0000
Log pseudolikelihood = -5338.3856                    Wald chi2(2)  =   2540.23

                                (Std. Err. adjusted for 1796 clusters in mun2)
------------------------------------------------------------------------------
             |               Robust
         lpv |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
Frontier     |
         lbe |   .8672515   .0303076    28.61   0.000     .8078496    .9266534
         lcf |   .3172884   .0177705    17.85   0.000     .2824589    .3521179
       _cons |   13.29697   .0703137   189.11   0.000     13.15916    13.43478
-------------+----------------------------------------------------------------
Mu           |
       _cons |  -3.154241   .8404152    -3.75   0.000    -4.801425   -1.507057
-------------+----------------------------------------------------------------
Usigma       |
      por_tp |   3.185112   .3166099    10.06   0.000     2.564568    3.805656
      _Iqc_1 |   .8901654   .0973669     9.14   0.000     .6993298    1.081001
       _cons |   .0336813   .2881557     0.12   0.907    -.5310934    .5984561
-------------+----------------------------------------------------------------
Vsigma       |
       _cons |  -.1034471   .0852968    -1.21   0.225    -.2706258    .0637316
-------------+----------------------------------------------------------------
  E(sigma_u) |    2.59848                                 2.557942    2.639019
     sigma_v |   .9495914   .0404986    23.45   0.000     .8734426    1.032379
------------------------------------------------------------------------------

Of the results that I got. I have doubts in the interpretation of the coefficients obtained in the estimation of the term of inefficiency.

Someone will have a suggestion.

[Anushiya Thanapalan]

------------------------------------------------------------------------------
lnprofit | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
lnprofit |
lnseed | .1747188 .0470893 3.71 0.000 .0824254 .2670123
lnirri | .8454282 .1673978 5.05 0.000 .5173346 1.173522
lnlab | .650646 .2488486 2.61 0.009 .1629118 1.13838
lnfer | .2176773 .1079339 2.02 0.044 .0061307 .4292238
lnche | -.0870072 .1172303 -0.74 0.458 -.3167743 .1427599
lnNPI | -.9598595 .036801 -26.08 0.000 -1.031988 -.8877308
oth | -.0269979 .1684612 -0.16 0.873 -.3571758 .3031799
_cons | -4.085947 .6209705 -6.58 0.000 -5.303027 -2.868868
-------------+----------------------------------------------------------------
mu |
rf | .8357975 .2739999 3.05 0.002 .2987675 1.372827
sup | .4475144 .2900098 1.54 0.123 -.1208944 1.015923
qual | -.0186924 .2169382 -0.09 0.931 -.4438835 .4064987
hig_mo_wa | .4418592 .3458635 1.28 0.201 -.2360209 1.119739
over | -.0177333 .2444538 -0.07 0.942 -.496854 .4613874
deci | -.0282881 .2166438 -0.13 0.896 -.4529021 .3963258
totare | .0002899 .004471 0.06 0.948 -.008473 .0090528
farmcate | .4197956 .2117045 1.98 0.047 .0048624 .8347289
soilquality | -.1422485 .2035687 -0.70 0.485 -.5412359 .2567389
_cons | .2950845 .6834696 0.43 0.666 -1.044491 1.63466
-------------+----------------------------------------------------------------
/lnsigma2 | .0583253 .2293172 0.25 0.799 -.3911282 .5077787
/lgtgamma | 1.313763 1.40526 0.93 0.350 -1.440497 4.068023
-------------+----------------------------------------------------------------
sigma2 | 1.06006 .2430899 .6762935 1.661596
gamma | .7881421 .2346422 .1914683 .9831767
sigma_u2 | .8354777 .3936817 .0638757 1.60708
sigma_v2 | .224582 .2221664 -.2108561 .6600202
------------------------------------------------------------------------------

. predict te_tn, te
(30 missing values generated)

. summarize te_tn

Variable | Obs Mean Std. Dev. Min Max
-------------+---------------------------------------------------------
te_tn | 185 .2784945 .198747 .0135758 .8463281

. predict marginal

[Akbar Muhammad]

Greetings Rene,

Recently im estimating using same method like you do. Would you like to share your paper/article?

Thanks