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st: Re: adjusted r square


From   Kit Baum <baum@bc.edu>
To   statalist@hsphsun2.harvard.edu
Subject   st: Re: adjusted r square
Date   Wed, 21 Feb 2007 07:02:54 -0500

This is not merely conjecture. Greene (Econometric Analysis, 5th ed.) p.565 "The Akaike information criterion retains a positive probability of leading to overfitting even as T -> \infty. In contrast, SC(p) [Schwarz or Bayes IC] has been seen to lead to underfitting in some finite sample cases."

If you do a Monte Carlo simulation in which the true DGP is an AR(p) model, and apply the AIC (pretending that you do not know the appropriate value of p) to determine the lag order, there is a positive probability that AIC will signal a lag length > p. That is what is 'widely agreed' because of that positive bias. Of course, the theory of specification error suggests that you would be better off estimating an overparameterized model than an underparameterized model.

Kit Baum, Boston College Economics
http://ideas.repec.org/e/pba1.html
An Introduction to Modern Econometrics Using Stata:
http://www.stata-press.com/books/imeus.html


On Feb 21, 2007, at 2:33 AM, Nick wrote:


 I regularly read advice such as that AIC is widely agreed
to give the wrong answer, to which the reaction has to be, How do they
know?
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