options crt;
?
?  Estimating a Poisson model using Patents-R&D data.
?  The model is
?         lambda(i) = exp(Xb)
?  with y distributed as a Poisson r.v. with expected value lambda(i).
?
smpl 1 385 ;
read (file='tdir:patdata.dat') cusip patents logr0-logr5 year logk scisect ;
msd patents logr0-logr5 year logk scisect ;
?
?     The likelihood function for a Poisson model is
?          L = exp(-lambda(i)) lambda(i)**y(i) / y(i)!
?
frml lambeq lambi=exp(alpha+b0*logr0+b6*logk) ;
frml fisheq logl = -lambi+y*log(lambi) ;
eqsub fisheq lambeq ;
param alpha .1 b0 .6 b6 .2 ;
y = patents ;
ml fisheq ;
?
?  Now estimate a negative binomial model using the same data.
?
frml nbeq logl = lgamfn(lambi+y) - lgamfn(lambi) + lambi*log(delta)
               - (lambi+y)*log(1+delta) ;
eqsub nbeq lambeq ;
param delta .04992 alpha -1.9916 b0 .51239 b6 .25896 ;
ml(print,gradchec) nbeq ;
ml nbeq ;
ml(hiter=n,hcov=nb) nbeq ;