On Oct 25, 2004, at 10:05 PM, Clive Nicholas wrote:
This is such a basic problem, I don't understand why I can't find the
solution, but here goes.
[snip  just the relevant equations for now]
. reg growthpc lgrowth trade lowwage fdi spend left
. predict e, resid
(70 missing values generated)
OK: by construction  by the very definition of an OLS residual  e
will be orthogonal (that is, uncorrelated) with ALL of the RHS
variables above. Stata neither knows nor cares what those RHS
variables are or mean; the vector that represents whatever is on the
RHS *will* be uncorrelated with e.
. pwcorr e lgrowth trade lowwage fdi spend left, sig
 e lgrowth trade lowwage fdi spend
left

+
e  1.0000

lgrowth  0.0000 1.0000
 1.0000

trade  0.0000 0.0787 1.0000
 1.0000 0.0553

lowwage  0.0000 0.1663 0.6208 1.0000
 1.0000 0.0000 0.0000

fdi  0.0000 0.1124 0.3373 0.2562 1.0000
 1.0000 0.0087 0.0000 0.0000

spend  0.0000 0.3736 0.5386 0.4120 0.3258 1.0000
 1.0000 0.0000 0.0000 0.0000 0.0000

left  0.0000 0.0088 0.1360 0.1353 0.0552 0.1822
1.0000
 1.0000 0.8314 0.0007 0.0008 0.1988 0.0000
And, as expected  nay, by definition  e is uncorrelated with each
of the RHS variables. Sounds like a success!
No matter how small I make the model, I keep finding that the error is
perfectly uncorrelated with the LDV (lgrowth in this case).
Sure, as long as lgrowth is contained in the list of regressors, it
*must* be uncorrelated with the residual from that regression.
Indeed, it's perfectly uncorrelated with _everything!_
Everything that is included in the regression, that is. If a variable
were excluded, that variable at least has a chance to be correlated
with the residual. (Albeit as a reflection of omitted variable bias,
possibly....)
Exactly the same happens if I: (1) restrict the model to just the
first two explanatory variables;
For the same reasons as put forth above: as long as lgrowth is one of
the regressors, OLS will return a residual series that is by
construction uncorrelated with lgrowth.
(2) estimate it with, say, areg and then predict e, resid,
Isn't areg just OLS with a bunch of dummy (i.e. categorical)
variables? Then the same explanation as above applies.
or; (3) if I change the predict, resid option to, say, rstandard
(which barely changes the values in the correlation matrix).
Sorry, couldn't find anything mentioned about rstandard in the
online help. But so long as predict is giving you OLS residuals,
then this option doesn't contradict the above explanation.
I don't know about you, but I think all this is odd.
I don't find the results odd, but I am a little uncertain what you are
trying to do in the first place. Your initial statement:
In preparing to muck around with some ivreg2 test code, I've been
running some basic laggedDV regressions in order to introduce an
instrument into an IV regression.
...is unclear to me. Perhaps I am not understanding your intentions.
How do you see these regressions helping you to "introduce an
instrument"?
 Mike
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