st: Poisson MLE in Microeconometrics using Stata

[Beatrice Crozza <beatrice.crozza@gmail.com>]

Dear All,

I want to estimate parameters of my model using a MLE, but assuming a
Poisson distribution.

I have the book "Microeconometrics using stata" and there is a chapter
for the count models and the Poisson, but they are related to a
regression. Now, I am little bit confused. For my MLE I want to know
the values of parameters that I cannot directly observe from my data.

How can I perform my MLE?

Following is my MLE without assuming Poisson for r,s and t:

program define mle
version 10.0
args lnf a d b n g

tempvar ma md mb  mn mg

quietly gen double `ma'=1-`a'
quietly gen double `md'=1-`d'
quietly gen double `mb'=1-`b'
quietly gen double `mn'=1-`n'
quietly gen double `mg'=1-`g'

quietly replace
`lnf'=ln((`a')*(`d')*((((`b')*(`md')*(`g')+(`b')*(`mg')*(`g')*(`n'))^r)*(((`mb')*(`mo')*(`g')+(`mb')*(`mn)*(`ma')*(`n'))^s)*(((`b')*(`md')*(`mg')*(`mn'))^t)*(((`mb')*(`mn')*(`ma')*(`g'))^s)*(((`b')*(`mg')*(`md')+(`mb')*(`b')*(`n'))^t)))

end

Now, to assume a Poisson distribution for r, s and t, I need only to
rewrite my code in a way that they follow a Poisson or I have also to
specify something in the mle?

Moreover, if I observe overdispersion in the book is suggested to use
the option VCE to obtain a robust estimate of the variance-covariance
matrix. How can I reach the same result in my mle program?

Could you please help me?

Thank you very much.

Bast,
Bea
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