st: inverse logit of gamma and xtfrontier

[Scott Merryman <scott.merryman@gmail.com>]

In the -xtfrontier- command (stochastic frontier models for panel
data), the gamma parameter is parameterized in terms of the inverse
logit of gamma and Stata reports the hypothesis test that the inverse
logit of gamma is 0.

Does this reported hypothesis test has any substantive meaning?  It
not clear to me what inferences one can draw if the inverse logit of
gamma is not statistically different from 0 (and therefore gamma is
0.50).

To test for existence of inefficiency effects, following Battese and
Coelli (1992), one would need to constrain the three parameters mu =
eta = gamma = 0 and use a likelihood ratio test:

webuse xtfrontier1
constraint 1 [eta]_cons = 0
constraint 2 [mu]_cons = 0
constraint 3 [ilgtgamma]_cons = -100 /* making gamma close to zero */
xtfrontier lnwidgets lnmachines lnworkers, tvd
est store A
xtfrontier lnwidgets lnmachines lnworkers, tvd constraints(1 2 3)
lrtest A ., stat
disp (1 - chi2(1, r(chi2)))*.5


Thank you,
Scott


Battese and Coelli. 1992 "Frontier production functions, technical
efficiency and panel data: With application to paddy farmers"  Journal
of Productivity Analysis,Volume 3, Numbers 1-2.
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