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

[Austin Nichols <austinnichols@gmail.com>]

Mark, Justina, Felipe and Javier --
See Procedure 18.1 on page 623 in EACSAP2002
(http://www.stata.com/texts/eacsap/).
But note that overID and weak instruments tests are vitiated if not
destroyed by the procedure.
See also e.g. this thread:
http://www.stata.com/statalist/archive/2010-01/msg00138.html

On Tue, Feb 8, 2011 at 8:41 AM, Schaffer, Mark E <M.E.Schaffer@hw.ac.uk> wrote:
> 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

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