Enrico Pellizzoni wrote:
> I suppose your
> standard errors are different in the 2 transformations
I am afraid not. If the lost degrees of freedoms (due to the
implicitly omitted individual dummies) are properly adjusted for the
within estimator, the coefficients and the standard errors are the
same as those from the model (1) in my previous post for which all
the dummies are estimated.
-- Eddy
Eddy wrote:
> 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.
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