# Re: st: nl command with restriction

 From "Rodolfo Coelho Prates" <[email protected]> To [email protected] Subject Re: st: nl command with restriction Date Tue, 12 Feb 2008 10:08:07 -0200 (BRST)

```Thanks Paul and Nick!

I tried implement yours sugestions, but I think my comprehention is not
correct.

I estimeted the Cobb-Doulas with three variables, like this:

program define nlces12
version 8.0
if "`1'" == "?" {
global S_1 "a b c"
global a=.15
global b=.4
global c=.3
global S_2 "Cobb-Douglas with additive error"
exit
}

replace `1' = \$a*((k^\$b)*(l^\$c)*(n^(1-\$b-\$c)))

end

This routine works well, but has that problem.

If I understood, the suggestion is:

replace `1' =
\$a*((k^(exp(\$b)/(1+exp(\$b)+exp(\$c))))*(l^(exp(\$c)/(1+exp(\$b)+exp(\$c))))*(n^(1/(1+exp(\$b)+exp(\$c)))))

Thise are the estimations with brute force:

Source |       SS       df       MS            Number of obs =       123
-------------+------------------------------         F(  2,   121) =
102.83
Model |  8.2419e+09     2  4.1209e+09         Prob > F      =
0.0000
Residual |  4.8489e+09   121  40073949.1         R-squared     =
0.6296
0.6235
Total |  1.3091e+10   123   106429266         Root MSE      =
6330.399
Res. dev.     =
2500.31
---------------------------------------------------------------------------
y |   Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+-------------------------------------------------------------
a | 2.594492  .3699407     7.01   0.000     1.862096    3.326887
b | 17.12698  .3519304    48.67   0.000     16.43025    17.82372
c | 16.97066      .        .       .            .           .
------------------------------------------------------------------------------

Works well, but the sum of coeficients are larger than one, but not
negatives. Do I need realize a transformation? Or did I made something
wrong?

Best Regards,

Rodolfo

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```