How to solve a system of nonlinear equations with cross-equation correlations?

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Hi all,
I try to solve a system of nonlinear equations with STATA.
My data looks like this:
id        s                   x              e
1  .0064259    -1.008586        ?
1  .2882765        2.701381        ?
1  .1368153        2.010069        ?
where id=1,2,3,...J,


Formula: s_j=exp(x_j+e_j)/A, and A=(1+exp(x_1+e_1)+...+exp(x_j+e_j)+...+exp(x_J+e_J))
I have exactly J equations with J unknowns. I want to know e_js.

I found http://www.stata.com/support/faqs/programming/system-of-nonlinear-equations/ and http://www.stata.com/statalist/archive/2011-06/msg00674.html
but I don't know how to add "A".
I also found "nlsur", which allows me to add "A". Here is what I did.
[1] I reformatted the data as the following:
id             s1              x1                    s2                     x2              s3           x3                     s11            x11             s22                  x22               s33           x33
1        .0064259        -1.008586        .2882765        2.701381        .1368153        2.010069        .0064259        -1.008586                               
1        .0064259        -1.008586        .2882765        2.701381        .1368153        2.010069                                         .2882765        2.701381               
1        .0064259        -1.008586        .2882765        2.701381        .1368153        2.010069                                                                                .1368153        2.010069       

...

code is as the following:
nlsur (s11=exp(x11+{e1})/(1+exp(x1+{e1})+exp(x2+{e2})+...exp(xJ+{eJ}))) /*
*/     (s22=exp(x22+{e2})/(1+exp(x1+{e1})+exp(x2+{e2})+...exp(xJ+{eJ}))) /*
*/ ... (sJJ=exp(xJJ+{eJ})/(1+exp(x1+{e1})+exp(x2+{e2})+...exp(xJ+{eJ})))


STATA returns "cannot have fewer observations than parameters".

Can anyone give me some hint to proceed?

Thanks, Amy

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关键词：correlations correlation Equations Nonlinear relations matrix

Unfortunately, "nlsur" doesn't do the job.