Leecht -
NO. 1 is the true log likelihood. The second is ok to use for a "log
likelihood" for purposes of maximimization with respect to beta since
log(sigma) is just an additive constant. But when estimating beta AND
sigma,you need the other term.
Al FEiveson
-----Original Message-----
From: leechtcn [mailto:[email protected]]
Sent: Thursday, October 30, 2003 5:43 AM
To: [email protected]
Subject: st: Log Likelihood for Linear Regression Models
Dear Listers,
I have asked this question before. I am posting it a
second time in case you guys have not received it.
I am sorry for the all convinence caused!
I have a question concerning William Gould and William
Sribney's "MAximium Likelihood Estimation" (1st
edition):
In its 29th page, the author write the the following
lines:
For instance, most people would write the log
likelihood for the linear regression model as:
LnL = SUM(Ln(Normden((yi-xi*beta)/sigma)))-ln(sigma)
(1)
But in most econometrics textbooks, such as William
Green, the log likelihood for a linear regression is
only:
LnL = SUM(Ln(Normden((yi-xi*beta)/sigma)))
(2)
that is, the last item is dropped
I have also tried to use (2) in stata, it will give
"no concave" error message. In my Monte Carlo
experiments, (1) always gives reasonable results.
Can somebody tell me why there is a difference between
stata's log likelihood and those of the other
textbooks?
thanks a lot
Leecht
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