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st: SFA - variance parameter


From   erik.brouwer@nl.pwc.com
To   statalist@hsphsun2.harvard.edu
Subject   st: SFA - variance parameter
Date   Tue, 4 May 2004 13:18:29 +0200

Dear Stata-users,

Currently I am doing a Stochastic Frontier Analysis in Stata, as opposed to
Limdep which I used in the past. The problem which arises with this
transition to Stata is that I am not able to derive in what way the
parameter 'theta' (one of the variance parameters) is calculated by the
Limdep package.

As this parameter is used in the formula by which the percentage of the
error term assigned to inefficiency can be calculated, I would like to know
how I can derive this term from the results of SFA by means of Stata.


Limdep results:
Variances:     Sigma-squared(v)=       .01407
                 Sigma-squared(u)=       .01068
Stochastic Cost Frontier, e=v+u.
+---------+--------------+----------------+--------+---------+----------+
|Variable | Coefficient  | Standard Error |b/St.Er.|P[|Z|>z] | Mean of X|
+---------+--------------+----------------+--------+---------+----------+
          Primary Index Equation for Model
 Constant    -2.398824811       .42999158   -5.579   .0000
 LNLOCSW      .4676510927       .10859080    4.307   .0000     16.842014
 LNNOLINE     .4787993242       .11729499    4.082   .0000     14.355184
 LNDUCT   -.6791673073E-01  .36352854E-01   -1.868   .0617    -5.5786894
          Variance parameters for compound error
 Theta        9.676302022       5.3867624    1.796   .0724
 Sigmav       .1186164475   .32301046E-01    3.672   .0002

Stata results:
------------------------------------------------------------------------------
     lnb1hca |      Coef.   Std. Err.      z    P>|z|     [95% Conf.
Interval]
-------------+----------------------------------------------------------------
     lnlocsw |   .4676511   .0813805     5.75   0.000     .3081482
.627154
   lnnolines |   .4787993   .0855751     5.60   0.000     .3110753
.6465234
      lnduct |  -.0679167   .0279463    -2.43   0.015    -.1226904
-.0131429
       _cons |  -2.398824   .3871222    -6.20   0.000     -3.15757
-1.640079
-------------+----------------------------------------------------------------
    /lnsig2v |  -4.263715   .5266097    -8.10   0.000    -5.295852
-3.231579
    /lnsig2u |  -4.539367    .944926    -4.80   0.000    -6.391388
-2.687346
-------------+----------------------------------------------------------------
     sigma_v |   .1186167   .0312324                      .0707979
.1987337
     sigma_u |   .1033449   .0488266                      .0409381
.2608857
      sigma2 |   .0247501   .0061499                      .0126966
.0368036
      lambda |   .8712505   .0760584                      .7221787
1.020322
------------------------------------------------------------------------------
Likelihood-ratio test of sigma_u=0: chibar2(01) = 1.06   Prob>=chibar2 =
0.152



Thanks and regards,

Erik Brouwer

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