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
on-line 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 lagged-DV 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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