On Jul 30, 2004, at 12:18 AM, Clive Nicholas wrote:
All of the X's from the regression show zero-correlations with E,
including (puzzlingly) the LDV (LEDCONPC), which ought to be
correlated with E.
I may not be understanding correctly what procedures you have
undertaken. However, as I read your message, this seems to be exactly
what one would expect, provided all the variables being correlated with
E were included as regressors in the estimation that produced E. (Or
they are linear combinations of the regressors.) By construction, the
OLS residuals are uncorrelated with all the regressors -- this includes
the lagged dependent variable (LDV). While an OLS regression may be
statistically invalid because of endogenous regressors (what you are
trying to test, IIUC), mathematically the OLS residuals will be
uncorrelated with any and all X variables included as regressors in
estimation. In other words, while the LDV theoretically may be
correlated with the _error_, econometrically it will be uncorrelated
with the _residual_.
Following Wooldridge (2003: 507), I've also run a 'reduced test' of
endogeneity: i.e., -regress- the LDV on the other variables, save the
residuals and then -pwcorr if e(sample)- as above. This also produces
the
same results: every X-var shows a zero-correlation with E.
I don't have my copy of Wooldridge handy, so I'm not certain what is
meant by a "reduced test." Perhaps a "reduced form test"? The
procedure you describe doesn't seem likely to produce a different
result than above: assuming the LDV is regressed on the same X's as
were used to construct E, the residual of this regression is just the
part of the LDV that is not correlated with (or "explained by") the
other X's. However, since E is already orthogonal to the LDV (by the
above regression procedure), it is still orthogonal to the portion of
the LDV that is not explained by the other regressors.
What I think you may be missing is a set of Z's to serve as
instruments for the LDV. With these Z's -- which are correlated with
the LDV and which are not regressors in the original specification --
you could undertake 2SLS estimation of the dependent variable.
(Actually, off-hand I'm not entirely certain how having a LDV as
opposed to some other potentially endogenous regressor changes the
appropriateness of this approach. Presumably your data are
stationary.... Do any of your other regressors vary over time?) If
the candidate endogenous regressor is truly exogenous (or, in the case
of a LDV, predetermined with respect to the error term), then 2SLS is
inefficient (higher variance of your estimates) -- but if this variable
is endogenous, then OLS is inconsistent. Hence you'll need some
instruments -- some exogenous variables that are not regressors -- to
investigate this question, for example via a Hausman test. There may
be an alternative "reduced form" test, but it almost certainly has to
involve some instruments -- likely in the second regression for the
LDV. It comes down to whether the "other variables" in this regression
are in any way distinct from "every X-var" in the first regression or
not. If not, then I would not be surprised by your results.
Hope that helps. I could be way off base; it might help to see the
specification of the regressions (at least the two you mention).
-- Mike
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