RE: st: Re: xtpoisson with endogenous covariate?

["ALICE DOBSON" <alice_dobson@hotmail.com>]

Thanks a lot Rodrigo! I have another question. Is there any statistical test 
to actually confirm the simultaneity of a DV and IV? Can I use the inference 
from C-Statistic or Hansen J Statistic to rule out simultaneity?
Alice




> From: "Rodrigo Alfaro" <ralfaro@bu.edu>
> Reply-To: statalist@hsphsun2.harvard.edu
> To: <statalist@hsphsun2.harvard.edu>
> Subject: st: Re: xtpoisson with endogenous covariate?
> Date: Tue, 28 Mar 2006 09:37:06 -0500
>
> Dear Alice,
>
> Note that if Y~Poisson(lambda) then E(Y)=3Dlambda and in MLE framework
> lambda_hat =3D mean(Y). When you add exogenous covariates you are adding 
> th=
> e
> following equation to your problem lambda =3D exp(X*beta). The use of exp()
> function is because lambda should be positive.
>
> On the other hand, IV process assumes that your problem is linear and
> unbounded, this means that Y is distribute over real line and the relation
> that you have E(Y) =3D X*beta. As you can see this is not that you want, 
> wh=
> ich
> is E(Y) =3Dexp(X*beta).
>
> The "right" solution for your problem is GMM. Basically you have the
> following moment condition E{[Y-exp(beta*X)]&Z}=3D0, where & is outer 
> produ=
> ct.
> In words, the errors of your expected value in the poisson process are
> orthogonal to some instruments variables (Z). Note GMM in this case is
> non-linear, but not too difficult to implement by hand using the sample
> counterpart.
>
> The lazy solution is change the dependent variable and use IV process, 
> usin=
> g
> log(Y) instead of Y. Note that this is "statistical" wrong because 
> log[E(Y)=
> ]
> is not equal to E[log(Y)]. Even worse, Y could be zero, in which case you
> have to use log(Y+a) with a>0.
>
> I hope this helps you
> Rodrigo.
>
>
> ----- Original Message -----
> From: "ALICE DOBSON" <alice_dobson@hotmail.com>
> To: <statalist@hsphsun2.harvard.edu>
> Sent: Tuesday, March 28, 2006 8:43 AM
> Subject: st: xtpoisson with endogenous covariate?
>
>
> > Hi all,
> > I use Stata 9.1. What can I do if my count dependent variable is
> > simultaneously determined with a continuous covariate in a panel data
> > setting?  In such a case my xtpoisson estimates would be biased. I have
> > good instrumental variables in the data. Should I ignore my count data
> > dependent variable and simply use xtivreg2 instead?
> > Best,
> > Alice
> >
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