Re: st: Estimating the CES-Translog Production Function

[Nick Cox <njcoxstata@gmail.com>]

The dots (.) mean "numeric missing". There could be several reasons
why you are seeing such results, but the model did converge -- as you
stated in your first posting. The precise interpretation differs, but
the usual broad interpretation is that your model and data don't match
at all well. You should try something simpler, or otherwise different.

Gordon Hughes wrote this in a different but I think relevant thread
<http://www.hsph.harvard.edu/cgi-bin/lwgate/STATALIST/archives/statalist.1103/Date/article-1743.html>

Translog frontier models can be difficult to estimate under the best
of circumstances without trying to over-determine the frontier.  You
should start by estimating the basic log-linear Cobb-Douglas form
(dropping all of the interaction terms) and then introduce
interactions individually and very carefully.  Even then it is
unlikely that you will get any convincing results with such a small sample.

Now clearly Gordon need not agree with my borrowing -- and the
specification "frontier" does not apply here, and I see no detail on
your sample size(s) -- but the tone of caution seems appropriate.

Nick

On Fri, Apr 1, 2011 at 5:53 AM, Dawei Zhang <dz.calgary@gmail.com> wrote:

> Thanks for the advice. We tried really small steps (4e*10^-11), and also
> only imposed the constraints to make sure the log expression is valid and
> rho not equal to zero. However, we still couldn't get all the parameters to
> converge (sometimes rho, sometimes delta_Z). Actually, I am beginning the
> wonder what it means in stata if the estimation results for certain
> parameters are just "dots". Does this mean the parameters not converged? or
> the model is not identified? or singular matrix?..........

 On 27/03/2011 7:02 AM, Charles Koss wrote:

>> Two ideas come to mind:
>>
>> a) Try smaller step size between iterations.
>> b) Try different numerical optimization techniques
>>
>> Can you describe the convergence without the constraints?

On Sat, Mar 26, 2011 at 11:29 PM, Dawei Zhang <dz.calgary@gmail.com> wrote:

>> >  I am having some convergence problems when estimating the CES-Translog
>> >  production function using the "nl" command in Stata. The program has
>> >  converged in terms of reaching a minimum residual sum of squares,
>> > however
>> >  not all of the parameters converged to steady values. The estimation
>> > form is
>> >  as following:
>> >
>> >  ln(Output) = {alpha}  -(1/{rho}) * ln[ {delta_Z} * Z^{-rho} + {delta_K}
>> > *
>> >  K^{-rho} + (1 - {delta_Z} - {delta_K}) * L^{-rho} ] + {beta_ZZ} *
>> > ln(Z)^{2}
>> >  + {beta_KK} * ln(K)^{2}
>> >                       + {beta_LL} * ln(L)^{2} + {beta_ZK} * ln(Z) *
>> > ln(K) +
>> >  {beta_LZ} * ln(L) * ln(Z) + {beta_LK} * ln(L) * ln(K) + epsilon   ,
>> >
>> >  where Output, Z, K, and L are the data. We have 10 parameters to be
>> >  estimated: alpha, rho, delta_Z, delta_K, beta_KK, beta_LL, beta_ZZ,
>> > beta_ZK,
>> >  beta_LZ, and beta_LK. We use re-parameterization (mainly using tanh()
>> > and
>> >  invlogit()) to impose interval constraints on the parameters: alpha in
>> >  (-5,5), rho in (-2,2) but not equal to 0, delta_Z in (0,1), delta_K in
>> >  (0,1), 1 - delta_Z - delta_K>0 (we use multinomial logit to
>> > reparameterize
>> >  this constraint), and all the rest parameters in (-1,1).
>> >
>> >  After trying 2000 sets of starting values randomly selected from the
>> >  intervals mentioned above, we could not have all 10 parameters converge
>> > at
>> >  the same time, especially for the two parameters: delta_Z and rho. We
>> > tried
>> >  a few different datasets and this problem persists. Any suggestions on
>> > how
>> >  we can solve this problem?

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