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Re: RE: st: Instrumental Variable Method and Probit

From   [email protected] (Vince Wiggins, StataCorp)
To   [email protected]
Subject   Re: RE: st: Instrumental Variable Method and Probit
Date   Mon, 24 Jan 2005 18:31:37 -0600

When Roger Harbord <[email protected]> suggested the user-written
command -qvf- as a solution to a probit model with endogenous variables, Scott
Merryman <[email protected]> noted that I had warned him two years ago
against using -qvf- for such problems.

As background, -qvf- is part of the suite of estimators for data with
measurement errors written by Ray Carroll, James Hardin <[email protected]>,
and Henrik Schmiediche <[email protected]>.  -qvf- estimates Generalized
Linear Models (GLMs) by the method of instrumental variables (IV) and to my
knowledge there is no question about its methods or efficacy for such
problems.  The question is whether the IV method can be applied to the more
general problem of endogenous covariates, rather than covariates with
measurement error.

The extent of my involvement in -qvf- was my private email to Scott of some
time back, and I can't speak for the intent of the authors of -qvf-, but here
is what I do know about applying IV estimation to such problems.

    1) For the specific case of a probit model, 
       -family(binomial) link(probit)- it is known that the IV estimator
       produces coefficient estimates that are scaled by the unestimated
       conditional correlation of the dependent and endogenous variable(s);
       see, for example, Wooldridge (2002, 472-477).  What this means is:

	1a)  the coefficients are not generally interpretable, being mixed
	     with an unestimated quantity; however,

	1b)  the coefficients can be tested for significance against the null
	     hypothesis that they are 0; put simply this test is not affected
	     by scaling.

     2) We have convincing simulation evidence supporting (1) for -qvf-.

     3) We have some simulation evidence that 1a) and 1b) apply to 
        a standard Poisson model, -family(poisson) link(log)-, estimated by
        IV with -qvf-, but we do not know of a citation for this result.

     4) We have some simulation evidence that a model with a poisson
        distribution and identity link is estimated by IV with -qvf- without
        scaling problems; meaning that the coefficients have their normal
        interpretation.  This is consistent with the results for linear
	regression models with endogenous variables.

     5) We do not know of any reference discussing the general case of 
        instrumental variables and GLM estimation.

-- Vince
   [email protected]

Wooldridge, J.M. 2002.  Econometric Analysis of Cross Section and Panel Data.
    Cambridge, MA:  MIT Press.
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