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st: re: Consequences of OLS with poisson distribution


From   Christopher Baum <baum@bc.edu>
To   statalist@hsphsun2.harvard.edu
Subject   st: re: Consequences of OLS with poisson distribution
Date   Tue, 21 Jul 2009 15:54:57 -0400

<>
Ronggui said
Besides the facts that prediction of ols can be less than zero which is impossible in Poisson distribution. I also know that the standard error is inconsistent. But I cannot find reference on what is the exact meaning of inconsistent. That is, is it upwards, downwards or it depends?

As any econometrics text makes clear, an estimator is consistent if its estimate converges upon the true (population) value of the parameter as sample size goes to infinity: that is, it is a large- sample property of the estimator. Thus
xtilde= sum(x)/(N-1)
is a biased but consistent estimator of sample mean, while
xttheta = 2/3 sum(x)
is not. With regard to the standard errors of estimated parameters, we cannot in general say whether an inconsistent estimate of the variance- covariance matrix (VCE) delivers s.e.'s that are too large or too small (except in contrived cases).
Kit
Kit Baum   |   Boston College Economics and DIW Berlin   |   http://ideas.repec.org/e/pba1.html
An Introduction to Stata Programming   |   http://www.stata-press.com/books/isp.html
An Introduction to Modern Econometrics Using Stata   |   http://www.stata-press.com/books/imeus.html

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