Dear statalisters,

I'm working on a Translog cost function estimation, where the dependent variables are cost-share variables for each input, and the explanatory variables are log prices of inputs. The command nlsur works fine when estimating the coefficients directly, but when I impose concavity following Ryan and Wales (2000) approach by specifying the coefficients as expressions of a triangular matrix (call it D, with elements being dij) and constant coefficiens, the nlsur returns zero estimates for the D elements. Specifically, for a three-input system the codes are:
Code:
nlsur (s1={a1}*one+(-{d11}*{d11}+{a1}-{a1}*{a1})*lnw1+(-{d11}*{d21}-{a1}*{a2})*lnw2) ///
      (s2={a2}*one+(-{d11}*{d21}-{a1}*{a2})*lnw1+({d21}*{d21}+{d22}*{d22}+{a1}-{a1}*{a1})*lnw2)
There are two equations (s1 and s2) because s1+s2+s3=1 and s3 is dropped. So the triangular matrix D contains elements d11, d12, and d22. The results are:

------------------------------------------------------------------------------
| Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
/a1 | .1300102 .0005278 246.30 0.000 .1289756 .1310447
/d11 | 0 (constrained)
/d21 | 0 (constrained)
/a2 | .2352828 .0008866 265.37 0.000 .233545 .2370205
/d22 | 0 (constrained)
------------------------------------------------------------------------------



I don't understand why this happens since d11, d12 and d22 are free parameters from what I can tell. I would greatly appreciate it if anyone has any suggestions

Many thanks in advance,
Zhenni