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.
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Eddy
<[email protected]> To: [email protected]
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
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