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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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