'create a workfile
wfcreate u 10000

'set the seed
rndseed 12345

'generate simulated data series
!delta = 1
series x1 = @runif(0,1)
series x2 = @runif(0,1)
series a = @recode(@runif(0,2)<0.4,0,@recode(@runif(0,2)>1.6,2,@runif(0,2)))
!alpha=0
!beta1=1
!beta2=1
series y = @exp(!alpha+!beta1*x1+!beta2*x2)*a

'comparison of the best practice with the proposed solution
equation eqols.ls(cov=hac) log(y+!delta) c x1 x2
equation eqppml.glm(family=poisson,cov=hac) y c x1 x2
equation eqgmm.gmm(instwgt=hac, gmmiter=1, cov=hac) log(y+exp(c(2)*x1+c(3)*x2))-(c(2)*x1+c(3)*x2)-c(1) @ x1 x2

'calculating alpha
eqgmm.makeresids gmmres
!lambda = eqgmm.@coef(3)
series alphaser = log(exp(gmmres+!lambda)-1)
equation eqalpha.ls alphaser c