# Re: st: SFA - variance parameter

 From smerryman@kc.rr.com To statalist@hsphsun2.harvard.edu Subject Re: st: SFA - variance parameter Date Tue, 04 May 2004 07:04:13 -0500

```I believe theta = sqrt(1/(sigma_u)^2)

Scott

----- Original Message -----
From: erik.brouwer@nl.pwc.com
Date: Tuesday, May 4, 2004 6:18 am
Subject: st: SFA - variance parameter

> 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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```