Hello,

In the last few weeks I have compared the performance of the -nl and -gmm commands since I am working with nonlinear functional forms. I have been dealing with one issue for a couple of days now and cannot get around it. I would appreciate your help.

The example I use is based on the manual entry on the use of the -gmm command for exponential regression model with panel data and exogenous regressors. It considers multiplicative fixed effects so the equation to be estimated is:

y_it = exp(x_it' b + n_i) + err_it

where x_it is a vector of k explanatory variables and n_i are the individual fixed effects. The manual provides the program to estimate the model by GMM. I tried to write a program to estimate the same model using NLS. Setting k=3, the two programs are:

*GMM program - from manual:
program gmm_poi
version 11
syntax varlist if, at(name)
tempvar mu mubar ybar
qui gen double `mu' = exp(x1*`at'[1,1] + x2*`at'[1,2] + x3*`at'[1,3]) `if'
qui egen double `mubar' = mean(`mu') `if', by(id)
qui egen double `ybar' = mean(y) `if', by(id)
replace `varlist' = y - `mu'*`ybar'/`mubar' `if'
end


*NLS program:
program nlpoi
version 11
syntax varlist(min=1 max=1) if, at(name)
local depvar `varlist'
tempvar mu mubar ybar
qui gen double `mu' = exp(x1*`at'[1,1] + x2*`at'[1,2] + x3*`at'[1,3]) `if'
egen double `mubar' = mean(`mu') `if', by(id)
egen double `ybar' = mean(`depvar') `if', by(id)
replace `depvar' = `mu'*`ybar'/`mubar' `if'
end


However, when I run the code, I get an error message for NLS (while GMM does work). In the command line:

*data:
use http://www.stata-press.com/data/r11/poisson1 , clear

*gmm - FE:
gmm gmm_poi, nequations(1) parameters(b1 b2 b3) instruments(x1 x2 x3, noconstant) onestep

*NLS -FE:
nl poi @ y , parameters(b1 b2 b3)


I cannot figure out why this is a problem for NLS. When I simplify the NLS code to take out the fixed effects, the program runs well.

Best wishes,

Paulo