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st: RE: dmexogxt questions


From   "Steve Stillman" <stillman@motu.org.nz>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: RE: dmexogxt questions
Date   Tue, 14 Sep 2004 00:31:36 +1200

Hi Jean.  The answers to your questions are below.  Cheers, Steve

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu]On Behalf Of Salvati, Jean
Sent: Saturday, September 11, 2004 8:49 AM
To: statalist@hsphsun2.harvard.edu
Subject: st: dmexogxt questions


Hello,

I have two questions about dmexogxt:

1) The joint test clearly rejects the null hypothesis that all
regressors are exogenous, but the tests on individual regressors don't
reject the null for any of the regressors (not even close).

More precisely, let's say I estimate my model with the following
command:

xtivreg y x1 (x2 x3 = z2 z3), fe

When I do "dmexogxt", the null hypothesis that all regressors are
exogenous ism clearly rejected. However, when I do "dmexogxt x2" and
"dmexogxt x3", I definitly can't reject the null for either x2 or x3 at
the same level.

How can I interpret these results?

*** When you run the command dmexogxt x2, you are assuming that x3 is
definitely endogenous and are only testing that x2 is exogenous given
this assumption.  For whatever reason, in your example, you cannot
clearly distinguish between (x2 endog, x3 exog), (x2 exog, x3 endog), or
(both endog).  Since you do not seem to have a reason to assume either
one is definitely endogenous (thus, leading to the reduced test), my
instinct would be that you are best off treating both as being
endogenous.

2) After "xtivreg y x1 (x2 = z2 ), fe", both "dmexogxt" and "dmexogxt
x2" yield F-statistics.

*** with only one possible endogenous variable, "dmexogxt" and "dmexogxt
x2" are identical tests and thus give identical results

After "xtivreg y x1 (x2 x3 = z2 z3), fe", both "dmexogxt" still gives an
F-statistic, but "dmexogxt x2" yields a chi2(1). Why is that? Is a Wald
test used in the second case, and if so why?

*** more generally, if "dmexogxt" is only run on a subset of endogenous
variables you will end up with a chi2(number tested variables) instead
of an f-test.  This occurs because the auxiliary regression being run
for the test is now an IV regression (we still need to instrument for
the variables left out of the test) as opposed to an OLS regression (the
case when all possible endogenous variables are being tested).

Thanks a lot.

Jean Salvati


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