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st: Re: xtpoisson with endogenous covariate?


From   "Rodrigo Alfaro" <ralfaro@bu.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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