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From |
vwiggins@stata.com (Vince Wiggins, StataCorp) |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: RE: st: Instrumental Variable Method and Probit |

Date |
Mon, 24 Jan 2005 18:31:37 -0600 |

When Roger Harbord <roger.harbord@bristol.ac.uk> suggested the user-written command -qvf- as a solution to a probit model with endogenous variables, Scott Merryman <smerryman@kc.rr.com> 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 <jhardin@gwm.sc.edu>, and Henrik Schmiediche <henrik@stat.tamu.edu>. -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 vwiggins@stata.com Wooldridge, J.M. 2002. Econometric Analysis of Cross Section and Panel Data. Cambridge, MA: MIT Press. * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

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