Dear Statalisters,
My question is fairly simple but I have struggled to
find a good answer. I am estimating a stochastic
production frontier and I want to properly test
whether technical inefficiency is present (and thus
whether frontier estimation is appropriate). The
stata routine does this for you when the default
half-normal model is used, but I am using the
truncated normal model with explanatory variables for
inefficiency (u = d*Z + w) through the cm(variables)
option.
If I want to do a likelihood ratio test of
H_o: sigma_u = 0
With a test statistic of LR = -2*(L(H_o)-L(H_a),
what is the appropriate value for L(H_o)?
Is it the e(ll_c) value saved in the frontier results
(in which case e(chi2_c) is my test statistic) or is
it the implied log-likelihood from an OLS version of
the production function (assuming normal errors),
including Z directly as a set of controls on the
right hand side?
I thought they would be numerically equivalent (if
sigma_u = 0, the frontier collapses to a simple
linear regression - and the likelihoods for normal
errors should be the same). In my data, e(ll) from
the OLS and e(ll_c) from the frontier are only the
same when Z is empty (no cm(variables) option
specified). Does anyone know why they are not
generally equivalent and which one is correct to use
when Z is included? What is this "ll_c" value stata
is calculating?
Thank you!
Ben Gilbert
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