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Re: st: XTFRONTIER: How to interpret Total Efficiency Measures


From   Scott Merryman <scott.merryman@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: XTFRONTIER: How to interpret Total Efficiency Measures
Date   Tue, 13 Apr 2010 11:27:05 -0500

On Mon, Apr 5, 2010 at 11:09 AM, Victor Waters <vvwaters@gmail.com> wrote:
> Dear StataListers,
>
> I am a little confused about the magnitude of the total efficiency
> measure. My XTFRONTIER with time varying decay model,
> runs well, almost all of the coefficients are as expected.,
>
> My total efficiency measures (for all units) are very low - between .1
> and .25. What importance should I attach to this?
> Does it mean all of the units are very inefficient?

Or the model is misspecified.

<snip>

> If eta is not 0, can I compare ti and tvd efficiency measures?

There is a significance test for eta to distinguish between the two models.

In the example below, the tvd model has efficiency estimates on that
are very low - the average less than 0.003 while the average
efficiency estimates for the ti model is about 0.50.  However, one a
time trend is added to the model (capturing technological progress),
the efficiency estimates are similar.

. webuse grunfeld,clear

. gen lninvest = ln(invest)

. gen lnmval = ln(mval)

.
. qui xtfrontier lninvest lnmval, ti nolog

. predict te_ti, te

.
. qui xtfrontier lninvest lnmval , tvd nolog

. predict te_tvd, te

.
. sum te*

    Variable |       Obs        Mean    Std. Dev.       Min        Max
-------------+--------------------------------------------------------
       te_ti |       200     .490895    .2736979   .1121026   .9170025
      te_tvd |       200    .0027195    .0019911   .0001452   .0087726

.
. qui xtfrontier lninvest lnmval time, ti nolog

. predict te2_ti, te

.
. qui xtfrontier lninvest lnmval time, tvd nolog

. predict te2_tvd, te

.
. sum te2*

    Variable |       Obs        Mean    Std. Dev.       Min        Max
-------------+--------------------------------------------------------
      te2_ti |       200    .3899374    .2795348   .0356406   .9245906
     te2_tvd |       200    .4083181    .2734767   .0326259   .9357629


Scott
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