RE: Antwort: Re: st: xtivreg2 with endogenous binary regressors

["Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk>]

Justina, your intuition is pointing in the right direction.

In fact, for consistency of IV estimation, the first stage regression not only doesn't have to represent an "economically sound" model, it doesn't even have to represent an "econometrically sound" model.

The coefficients in the first stage of 2SLS don't have to correspond to any sound model or be consistent estimates of any model coefficients.  The first stage is just a calculation method using a linear projection.  The only coefficients being estimated are those in the main equation, and the requirement is that Z is orthogonal to the error in the main equation.

You can go down the route of interpreting the first stage as the estimate of a structural model if you want to.  And you can add some structure to it if you want.  This can get you efficiency gains.  In that case, though, you are out of the single-equation land of 2SLS ("limited information estimation") and in the land of multiple equation estimation ("full information estimation").

One other point relevant to the discussion with Felipe and Javier - Wooldridge's panel data book (Econometric Analysis of Cross Section and Panel Data) discusses a procedure that obtains efficiency gains in this context by using a kind of first-stage probit to create a fitted value, and then using this fitted value as the instrument in IV/2SLS.  This procedure has the helpful practical advantage of not requiring ex post adjustment of the SEs.  I forget where exactly in the book this is discussed, but it's been mentioned on the list in the past and it shouldn't be hard to find.

--Mark

________________________________

	From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Justina Fischer
	Sent: 08 February 2011 10:18
	To: statalist@hsphsun2.harvard.edu
	Subject: Antwort: Re: st: xtivreg2 with endogenous binary regressors
	
	

	well, here it gets wobbly for me, too.
	
	My econometric intuition tells me (that may be wrong): the main purpose of the first stage regression is to have an econometrically sound model that predicts values for the endogenous variable X, using a valid instrument Z.
	It is not the purpose of the first stage to be economically sound, or to predict values of X that can be found in 'reality'.
	In that sense, obtaining predicted values beyond 0 or 1 should not cause any problem.
	
	But I am interested in knowing the opinion of the theorists in this list....
	
	Justina
	
	
	-----owner-statalist@hsphsun2.harvard.edu schrieb: -----
	
	An: statalist@hsphsun2.harvard.edu
	Von: Javier Pérez <gjavierperezv@googlemail.com>
	Gesendet von: owner-statalist@hsphsun2.harvard.edu
	Datum: 08.02.2011 11:06AM
	Thema: Re: st: xtivreg2 with endogenous binary regressors
	
	Felipe, you are right, the problem is the same. The issue is that with
	xtivreg2 you will always have a OLS first stage, even if your
	endogenous regressor is binary. What Justina says is that it is no a
	problem for the resons she pointed out. You can always try to do it
	manually estimating the probit and put the predicted values back in
	the main equation but, as you say, the correction of the SE is the
	issue, especially if you have a panel data.
	
	Anyway, if I understood correctly from Justina, getting the OLS first
	sate estimators would not be a problem in this case, but I am not sure
	to have understood the reason. Could you please Justina tell me a
	little more about that. The thing is that xtivreg2 uses the predicted
	values of the endogenous regressor X (binary), but estimating it by
	OLS there is no guarantee that the predicted value will be between 0
	and 1. Many thanks.
	
	
	2011/2/8 Filipe Silva <filipeourico@googlemail.com>:
	> Hi,
	>
	> Please correct me if wrong:
	> I am having a similar issue. However I'm using the fitted values from
	> a first step nl regression and using them as instrument for the
	> endogenous in the second step (see textbook Cameron & Trivedi, 2005
	> pp. 193). The problem is the correction of se in the second step.
	> Either you cumpute the V correction manually (not sure if there is an
	> appropriate package?) or use bootstrap.
	>
	> My question:
	> Could this also apply to the case of an ordinal endogenous variable,
	> since what is used is a linear projection?
	>
	> Many thanks,
	>
	> Filipe
	>
	>
	> 2011/2/8 Justina Fischer <JFischer@diw.de>:
	>
	>
	>> Hi
	>>
	>> you can use ivreg2 in that case.
	>>
	>> reason: you are only interested in predicting computationally correct values
	>> of the endogenous X, but not in getting the 'right' coefficients on Z.
	>> In a sense, the size of Z is of no interest to you; only its predictive
	>> power matters.
	>>
	>> Hope this helps
	>>
	>> Justina
	>>
	>>
	>>
	>>
	>> -----owner-statalist@hsphsun2.harvard.edu schrieb: -----
	>>
	>> An: statalist@hsphsun2.harvard.edu
	>> Von: Javier Pérez <gjavierperezv@googlemail.com>
	>> Gesendet von: owner-statalist@hsphsun2.harvard.edu
	>> Datum: 08.02.2011 10:23AM
	>> Thema: st: xtivreg2 with endogenous binary regressors
	>>
	>> I was wondering if anybody could please help me with the following
	>> issue: in my model I want to use the xtivreg2 Stata command, but in my
	>> case both the endogenous regressor and the instrument are binary; but
	>> the first stage with the xtivreg2 gives me only OLS estimators,
	>> instead of a logit or probit ones. Could you please give me any light
	>> about the potential solution? I saw one author with a similar
	>> situation just using the OLS first stage in this case, so the question
	>> could then become how can I justify using an OLS fisrt stage rather
	>> than logit or probit with the binary dep var.
	>>
	>> Many thanks in advance. Javier
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