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Re: st: RE: xtivreg2 testing for regressor endogeneity


From   Costas Lambrinoudakis <costas.lambrinoudakis@gmail.com>
To   Statalist <statalist@hsphsun2.harvard.edu>
Subject   Re: st: RE: xtivreg2 testing for regressor endogeneity
Date   Wed, 24 Apr 2013 18:33:33 +0300

Many thanks!

On 23 April 2013 23:17, Schaffer, Mark E <M.E.Schaffer@hw.ac.uk> wrote:
> Costas,
>
> See my comments interspersed below.
>
>> -----Original Message-----
>> From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-
>> statalist@hsphsun2.harvard.edu] On Behalf Of Costas Lambrinoudakis
>> Sent: 23 April 2013 15:40
>> To: Statalist
>> Subject: st: xtivreg2 testing for regressor endogeneity
>>
>> Dear all
>>
>> I am using command xtivreg2. I have a couple of questions concerning
>> regressor endogeneity testing and I would be grateful if anyone could help
>> me with that.
>>
>> I want to estimate the following equation:
>>
>> y = b0 + b1x1 + b2x2 + b3x3 + u                         (1)
>>
>> Say that x1 is endogenous, x2 and x3 exogenous and that z1 is a potential
>> instrument for x1. The dataset is panel and the errors are heteroskedastic
>> and clustered.
>>
>> Given that my data is panel and the errors are not iid, I cannot use ivendog,
>> hausman or dmexogxt. The only choice I am left with is the option
>> endog(x1) in xtivreg2,
>> i.e. xtivreg2 y x2 x3 (x1=z1), fe endog(x1) cluster(id year)
>>
>> My questions are the following:
>>
>> 1. Is it correct to use endog when I have only one endogenous variable and
>> one instrument?
>
> Yes.
>
>> I may get a result from the option endog(x1) when running
>> xtivreg2 command, but I am wondering how are the Sargan statistics
>> calculated, given that my model is exactly identified?
>
> From the ivreg2 help file:
>
> "The endogeneity test implemented by ivreg2, is, like the C statistic, defined as
> the difference of two Sargan-Hansen statistics:  one for the equation with the smaller set of instruments, where the suspect regressor(s) are treated as endogenous, and one for the equation with the larger set of instruments, where the suspect regressors are treated as exogenous."
>
> In other words, you are contrasting
>
> xtivreg2 y x2 x3 (x1=z1), fe
>
> with
>
> xtivreg2 y x2 x3 x1 ( =z1), fe
>
> The first estimation is exactly identified (so the Sargan-Hansen stat is zero), but the second is overidentified because you have zero endogenous regressors and 1 excluded instrument.
>
>> 2. I read in the paper accompanying ivreg2 (2003) that when errors are iid,
>> the estimated C statistic (from endog) coincides with the Durbin-Wu-
>> Hausman chi^2 statistic (the one reported by ivendog). Is it correct to always
>> interpret this C-test like the Durbin-Wu-Hausman test?
>> In particular, may I argue that the C-test actually tests the same null, i.e. that
>> the coefficients in equation (1) are not significantly different when estimated
>> by OLS and when estimated by IV?
>
> Yes, that's right.  I am trying to remember where I've seen this discussed - I think Hayashi's (2000) "Econometrics" covers it (sort of), and Ruud's (200) "An Introduction to Classical Econometric Theory", but I am not sure.
>
> --Mark
>
>> If not, what is the proper non-technical
>> definition of the null hypothesis of the C-test in the option endog(.)?
>>
>> Any help would be greatly appreciated!
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