Jean,
Just a couple of footnotes to Steve's response:
Subject: st: RE: dmexogxt questions
Date sent: Tue, 14 Sep 2004 00:31:36 +1200
From: "Steve Stillman" <[email protected]>
To: <[email protected]>
Send reply to: [email protected]
> Hi Jean. The answers to your questions are below. Cheers, Steve
>
> -----Original Message-----
> From: [email protected]
> [mailto:[email protected]]On Behalf Of Salvati, Jean
> Sent: Saturday, September 11, 2004 8:49 AM
> To: [email protected]
> 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.
The text here can be interpreted in the same way as a Hausman test,
i.e., endogeneity/exogeneity is picked up by differences in the
coefficients between the two specifications. In effect, when you set
one or the other of x2 and x3 to be exogenous, the coeffs don't
change much compared to the benchmark case where both are
endogeneous. But when you set both to be exogenous, the coeffs
change a lot, again compared to the case of both being endogenous.
This doesn't sound very strange, at least to me.
> 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).
... and the Wu version of the test has an F-stat form in this case.
But if you're relying on asymptotics, it doesn't matter if it's an F
or chi-sq. If you want an F-stat instead of a chi-sq, you can always
get one by hand if you divide by the relevant dof.
Cheers,
Mark
> Thanks a lot.
>
> Jean Salvati
>
>
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>
Prof. Mark E. Schaffer
Director
Centre for Economic Reform and Transformation
Department of Economics
School of Management & Languages
Heriot-Watt University, Edinburgh EH14 4AS UK
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