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From |
Antoine Terracol <Antoine.Terracol@univ-paris1.fr> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: IV estimation for probit models with binary endogenous variable...? |

Date |
Thu, 02 Apr 2009 14:48:04 +0200 |

I forgot to include this part of -cmp-'s help file in my previous message:

estimate an IV model in which X and Y are binary. Antoine Antoine Terracol wrote:

Kit, I miht have misunderstood your comment, but I read in -cmp-'s helpfile that:As a matter of algorithm, cmp is an SUR (seemingly unrelatedregressions) estimator. It treats theequations as independent from each other except for modeling theirunderlying errors as jointly normallydistributed. Mathematically, the likelihood it computes isconditioned on observing all right-sidevariables, including those that also appear on the left side ofequations. However, it can actually fita much larger class of models. Maximum likelihood (ML) SURestimators, including cmp, are appropriatefor an important class of simultaneous equation models, in whichendogenous variables appear on theright side of structural equations as well as the left. Models ofthis kind for which ML SUR isnevertheless consistent must satisfy two criteria:1) They are recursive. In other words, the equations can bearranged so that the matrix ofcoefficients of the dependent variables in each others'equations is triangular. As emphasizedabove, this means the models have clearly defined stages, thoughthere can be more than one equationper stage.2) Dependent variables in one stage enter subsequent stages onlyas observed. Returning to theexample in the first paragraph, if C is a categorical variablemodeled as ordered probit, then C,not the latent variable underlying it, call it C*, must figurein the model for D.In the following example, -cmp- and -biprobit- give the same results /*---------------------------*/ clear set obs 1000 drawnorm e1 e2, cov(1,0.5\0.5,1) drawnorm x1 x2 z1 z2 g endog=(1+z1+z2+e1>0) g y=(1+endog+x1+x2+e2>0) cmp (y = endog x1 x2) (endog = z1 z2), ind(4 4) biprobit (y = endog x1 x2) (endog = z1 z2) /*---------------------------*/ Antoine Kit Baum wrote:<> Antoine said If you are ready to assume joint normality, then -biprobit- should do the trick: /*------------------------------*/ clear set obs 10000 set seed 987654321 drawnorm e1 e2, cov(1,0.5\0.5,1) drawnorm x1 x2 z1 z2 g endog=(1+z1+z2+e1>0) g y=(1+endog+x1+x2+e2>0) probit y endog x1 x2 /*biased*/ biprobit (y= endog x1 x2) (endog=z1 z2)I'm not so sure. Stata will allow you to estimate that model, but itcalls it the "seemingly unrelated bivariate probit" model. That modelis described in Greene, Econometric Analysis 6ed (p. 817), asanalogous to SUR ("in the same spirit as the seemingly unrelatedregression model"): that is, two equations in which there are nothingbut exogenous explanatory variables. The way in which Antoine haswritten the model is one in which you surely could use cmp, as it isrecursive (y depends on endog, but endog does not depend on y). ButI'm not sure that the assumptions of the SUBP model are satisfied here.Greene (p. 817) describes a model in which an endogenous regressor isbinary as a 'treatment effects' model and suggests that it should betreated as a selection problem.Kit Baum | Boston College Economics & DIW Berlin |http://ideas.repec.org/e/pba1.htmlAn Introduction to Stata Programming| http://www.stata-press.com/books/isp.htmlAn Introduction to Modern Econometrics Using Stata |http://www.stata-press.com/books/imeus.html* * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

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**References**:**Re: st: IV estimation for probit models with binary endogenous variable...?***From:*Kit Baum <baum@bc.edu>

**Re: st: IV estimation for probit models with binary endogenous variable...?***From:*Antoine Terracol <Antoine.Terracol@univ-paris1.fr>

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