*
* Example 18.4 from page 529
* There's no worked example there, so we do this with generated data. Note that
* this is not a well-behaved GMM estimation problem: the moment conditions are
* too dependent to allow safe unconstrained estimation of the weight matrix.
*
all 500
compute mu1=4.0,sig1=1.0,mu2=0.0,sig2=.50
compute p=.3
set y = %if(%ranbranch(||p,1-p||)==1,mu1+%ran(sig1),mu2+%ran(sig2))
*
stats y
compute ybar=%mean,ysq=%variance
nonlin m1 s1 m2 s2 lambda
compute m1=%mean,s1=%variance,m2=%mean+1,s2=s1,lambda=.80
dec vect[frml] mgfs(5)
dec vect tx(5)
compute tx=||-.50,-.25,.01,.25,.50||
do i=1,5
   frml mgfs(i) = exp(tx(&i)*(y-ybar)-tx(&i)**2*ysq/2)-$
     lambda*exp(tx(&i)*(m1-ybar)+tx(&i)**2*(s1-ysq)/2)-(1-lambda)*exp(tx(&i)*(m2-ybar)+tx(&i)**2*(s2-ysq)/2)
end do i
instruments constant
nlsystem(instruments,iters=500) / mgfs