nlsur with cross-parameter constraints

[Stefan Wimmer]

I want to estimate the following regression in Stata 14.2:

nlsur (y = {b0} + {b1}*x1 + {b2}*x2 + {c11}*{c11}*x1x1  + {c11}*{c12}*x1x2 + ({c12}*{c12}+{c22}*{c22})*x2x2)

Unfortunately, paramters c11, c12 and c22 cannot be estimated:

-----------------------------------------------------------------------
       Equation |        Obs   Parms       RMSE      R-sq     Constant
----------------+------------------------------------------------------
 1            y |     21,619       6   885.5987    0.0108          c11
-----------------------------------------------------------------------

------------------------------------------------------------------------------
           y |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         /b0 |  -.0000846     6.0229    -0.00   1.000    -11.80475    11.80458
         /b1 |   300.1579   23.19286    12.94   0.000     254.7008    345.6151
         /b2 |   93.08839   13.34411     6.98   0.000     66.93442    119.2424
        /c11 |          0  (constrained)
        /c12 |          0  (constrained)
        /c22 |          0  (constrained)
------------------------------------------------------------------------------

I noticed that c11 and c12 can be estimated when I replace "{c11}*{c11}*x1x1" with "{c11}*x1x1".

Do you have a suggestion? Is the nlsur command the appropriate command for what I'm trying to do?

Thank you
Stefan

[Stefan Wimmer]

It seems like Stata has a problem when coefficients are in the form of

{c11}*{c11}*x

Does anyone have a hint whether the missing estimates for parameters c11, c12, and c22 are due to a convergence problem, or rather a syntax problem? The full estimation output is

Calculating NLS estimates...
Iteration 0:  Residual SS =  1.70e+10
Iteration 1:  Residual SS =  1.70e+10
Iteration 2:  Residual SS =  1.70e+10
Iteration 3:  Residual SS =  1.70e+10
Calculating FGNLS estimates...
Iteration 0:  Scaled RSS =     21619
Iteration 1:  Scaled RSS =     21619
Iteration 2:  Scaled RSS =     21619

FGNLS regression
-----------------------------------------------------------------------
       Equation |        Obs   Parms       RMSE      R-sq     Constant
----------------+------------------------------------------------------
 1            y |     21,619       6   885.5987    0.0108          c11
-----------------------------------------------------------------------

------------------------------------------------------------------------------
           y |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         /b0 |  -.0000846     6.0229    -0.00   1.000    -11.80475    11.80458
         /b1 |   300.1579   23.19286    12.94   0.000     254.7008    345.6151
         /b2 |   93.08839   13.34411     6.98   0.000     66.93442    119.2424
        /c11 |          0  (constrained)
        /c12 |          0  (constrained)
        /c22 |          0  (constrained)
------------------------------------------------------------------------------

Thank you in advance, Stefan