Stata beginner: code for stochastic production frontier model (BC92)

[Amy Thom]

*Caveat: I am a PhD student still new to Stata, and I have only a moderate level of statistics experience.

I am estimating the production frontier and firm inefficiency for a cross-sectional (agricultural) dataset with a Cobb Douglas functional form using the BC92 "tvd" model with three inputs to the frontier model and 4 exogenous inputs to the inefficiency model. According to my supervisor, the eta should be set to zero and half-normal distribution specified for the inefficiency error component.

I am quite uncertain as to which frontier command to start with: xtfrontier, sfpanel, sfmodel, sfcross? And from there, I am somewhat lost...

I would be extremely grateful if another [more experienced!] user could please share the lines of code to estimate the frontier model, the inefficiency model and predict inefficiency scores.
I have read the two existing posts regarding the BC92 model and noted their advice, but I need more comprehensive assistance. Thank you in advance!

[Scott Merryman]

Since you only have cross-sectional data you will need to use -froniter- or Federico Belotti et al -sfcross-. Something like:

frontier lnoutput lnk lnl lnm, vhet(x1 x2 x3 x4)

For example:

. clear

. webuse frontier1

. //techinical efficiency as function of firm size
. frontier lnoutput lnlabor lncapital, uhet(size)

Iteration 0:   log likelihood = -1508.3692  
Iteration 1:   log likelihood = -1505.0122  
Iteration 2:   log likelihood = -1505.0067  
Iteration 3:   log likelihood = -1505.0067  

Stoc. frontier normal/half-normal model                 Number of obs =    756
                                                        Wald chi2(2)  =   8.90
Log likelihood = -1505.0067                             Prob > chi2   = 0.0117

------------------------------------------------------------------------------
    lnoutput | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
lnoutput     |
     lnlabor |   .6709033   .2401539     2.79   0.005     .2002103    1.141596
   lncapital |   .6079313   .5638755     1.08   0.281    -.4972443    1.713107
       _cons |   .2044104   3.282278     0.06   0.950    -6.228736    6.637557
-------------+----------------------------------------------------------------
lnsig2v      |
       _cons |  -.2280262   .1953434    -1.17   0.243    -.6108922    .1548398
-------------+----------------------------------------------------------------
lnsig2u      |
        size |  -.0003938   .0001977    -1.99   0.046    -.0007812   -6.43e-06
       _cons |   2.769215   .4032404     6.87   0.000     1.978878    3.559551
-------------+----------------------------------------------------------------
     sigma_v |   .8922463   .0871472                      .7367946    1.080496
------------------------------------------------------------------------------

. //test for constant returns to scale
. test _b[lnlabor] + _b[lncapital] = 1

 ( 1)  [lnoutput]lnlabor + [lnoutput]lncapital = 1

           chi2(  1) =    0.21
         Prob > chi2 =    0.6504

. //predict technical efficiency
. predict te, te

[Amy Thom]

Thank you very much, Scott. I will come back to the post once I've run the code, if I have troubleshooting needs. I appreciate your help!

[Anushiya Thanapalan]

Hello, I'm a PhD student, and my aim is to estimate technical and allocative inefficiencies using the profit frontier model.
Profit is my dependent variable, and the independent variables are input costs ( fertiliser cost, irrigation cost, land preparation cost, seed cost). inefficiency variables are the irrigated area, crop type experience ensure the Cobb Douglas profit function, I am using log format for these variables. Cross-section data
I'm not sure how to estimate technical and allocative efficiency in STATA 16 using a one-step approach.
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