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From |
"Enrico Pellizzoni" <Enrico.Pellizzoni@borsaitalia.it> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: panel within transformation cause serial correlation? |

Date |
Fri, 12 Dec 2003 16:01:13 +0100 |

I remember within estimator is surely serially correlated. Anyway, this estimator is still consistent, even if it is not efficient. That's why the coefficient estimated with your transofrmation 1 and 2 are numerically identical, but I suppose your standard errors are different in the 2 transformations Enrico. ______________________________ Enrico Pellizzoni Borsa Italiana Spa Research & Development Piazza Affari, 6 - 20123 Milano Tel: 02 72426 304 Fax: 02 86464323 E-mail: enrico.pellizzoni@borsaitalia.it Eddy <eddy_05831@yahoo.com> To: statalist@hsphsun2.harvard.edu Sent by: cc: owner-statalist@hsphsun2. Subject: st: panel within transformation cause serial correlation? harvard.edu 12/12/2003 15.53 Please respond to statalist Dear listers, In a typical panel data model with individual fixed effect, we have y_{it} = a_i + B*X + e_{it}, --- (1) where a_i is individual effect. Assume e_{it} is iid distributed for i and t. A standard estimation procedure is to first do the "within" transformation to get rid of the potentially large number of the a_i dummies. The transformation essentially subtracts the group means from the variables: y_{it} -y_{i.} = B*(X_{it}-X_{i.}) + (e_{it}-e_{i.}), -- (2) where e_{i.} = (1/T) *(e_{i1} + e_{i2} + ... + e_{iT}). It can be shown numerically that OLS estimations on models (1) and (2) give you exactly the same results. My question is: In model (2), the transformed error term (e_{it}-e_{i.}) seems to be serially correlated within any given individual (i.e., for any i), but the OLS estimation assumes no correlation. Thus, how come the serial correlation can be ignored in estimating (2), and the results are still the same as (1)? To be more clear, consider the transformed error terms of individual i in period t and t-1. They are (e_{it}-e{i.}) = e_{it} - (1/T) *(e_{i1} + e_{i2} + ... + e_{iT}) (e_{it-1}-e{i.}) = e_{it-1} - (1/T) *(e_{i1} + e_{i2} + ... + e_{iT}) . I think they are correlated because of the common term on the RHS of the expressions. Any insight will be appreciated. --Eddy __________________________________ Do you Yahoo!? New Yahoo! Photos - easier uploading and sharing. http://photos.yahoo.com/ * * 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/ ---------------------------------------------------------------------------- L'utilizzo non autorizzato del presente messaggio è vietato e potrebbe costituire reato. Se il presente messaggio non e' a Lei indirizzato, Le saremmo grati se, via e-mail, ne comunicasse l'errata ricezione. Il contenuto del presente messaggio non deve essere considerato come trasmesso o autorizzato da Borsa Italiana. Borsa Italiana non si assume alcuna responsabilità per eventuali intercettazioni, modifiche o danneggiamenti del presente messaggio e-mail. The unauthorized use of this e-mail is prohibited and could constitute an offence. Please notify Borsa Italiana immediately by reply e-mail if you are not the intended recepient. The contents of this message shall be understood as neither given nor endorsed by Borsa Italiana. Borsa Italiana does not accept liability for corruption, interception or amendment, if any, or the consequences thereof. ---------------------------------------------------------------------------- (Embedded image moved to file: pic22279.pcx)

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