st: Re: xtpoisson with endogenous covariate?

["Rodrigo Alfaro" <ralfaro76@hotmail.com>]

Dear Alice,

Note that if Y~Poisson(lambda) then E(Y)=lambda and in MLE framework 
lambda_hat = mean(Y). When you add exogenous covariates you are adding the 
following equation to your problem lambda = exp(X*beta). 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) = X*beta. As you can see 
this is not that you want, which is E(Y) =exp(X*beta).

The "right" solution for your problem is GMM. Basically you have the 
following moment condition E{[Y-exp(beta*X)]&Z}=0, where & is outer product. 
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, using 
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
>
> _________________________________________________________________
> Is your PC infected? Get a FREE online computer virus scan from McAfee� 
> Security. http://clinic.mcafee.com/clinic/ibuy/campaign.asp?cid=3963
>
> *
> *   For searches and help try:
> *   http://www.stata.com/support/faqs/res/findit.html
> *   http://www.stata.com/support/statalist/faq
> *   http://www.ats.ucla.edu/stat/stata/
*
*   For searches and help try:
*   http://www.stata.com/support/faqs/res/findit.html
*   http://www.stata.com/support/statalist/faq
*   http://www.ats.ucla.edu/stat/stata/