nlsur nonlinear parameter constraints

[Jules Duberga]

I want to estimate a system of equations, imposing that one
coefficient of the first equation equal the inverse of a coefficient of the
second equation.

nlsur (y1 = {b0}+{b1}*x1+{b2}*x2+{b3}*x3+{b4}*x4) (y2 ={d0}+{d1}*x5+{d2}*x6) (y3= {g0}+{g1}*x7)

and want to impose b1=1/d2. How would you do that? Is the lnsur command the appropriate command for what I'm trying to do?

Many thanks,

Jules.

[Scott Merryman]

Replace {b1} with 1/{d2} in equation 1. For example

webuse petridish,clear
//unconstrained
nlsur (p1 = {b1}*{b2}^t) (p2 = {g1}*{g2}^t)
//constrained
nlsur (p1 = {b1=1}*{b2}^t) (p2 = (1/{b1=1})*{g2}^t)

[Joro Kolev]

And with your type of constraint it is crucial to specify a starting value for the parameter different from 0. Apparently Stata -nlsur- by default initialises the parameters at 0, and this causes a problem with your type of constraint 1/b:

. webuse petridish,clear

. nlsur (p1 = {b1}*{b2}^t) (p2 = (1/{b1})*{g2}^t)
(obs = 25)

Calculating NLS estimates...
could not evaluate equation 2
starting values invalid or some RHS variables have missing values
r(480);

. nlsur (p1 = {b1=1}*{b2}^t) (p2 = (1/{b1=1})*{g2}^t), nolog
(obs = 25)
Calculating NLS estimates...
Calculating FGNLS estimates...

FGNLS regression 
-----------------------------------------------------------------------
       Equation |        Obs   Parms       RMSE      R-sq     Constant
----------------+------------------------------------------------------
 1           p1 |         25       2   .7212319    0.9264*      (none)
 2           p2 |         25       2    .642312    0.9353*      (none)
-----------------------------------------------------------------------
* Uncentered R-sq

------------------------------------------------------------------------------
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         /b1 |   .9395144   .0558379    16.83   0.000      .830074    1.048955
         /b2 |   1.072133   .0043015   249.25   0.000     1.063702    1.080564
         /g2 |   1.062249   .0043854   242.23   0.000     1.053654    1.070844
------------------------------------------------------------------------------

.

[Jules Duberga]

Works perfectly now. I did not set initial values at first.

Thanks a lot to both!