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Re: st: Why won't my LDV correlate with the model error?


From   "Michael S. Hanson" <mshanson@mac.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Why won't my LDV correlate with the model error?
Date   Mon, 25 Oct 2004 22:59:29 -0400

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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