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From |
"Steven Stillman (LMPG)" <Steven.Stillman@lmpg.dol.govt.nz> |

To |
"'statalist@hsphsun2.harvard.edu'" <statalist@hsphsun2.harvard.edu> |

Subject |
RE: st: Inverse Mills Ratio after MLOGIT |

Date |
Fri, 18 Apr 2003 12:37:41 +1200 |

David, Mushfiq: While Mushfiq advice on calculating the Inverse Mills Ratios for an mlogit model is correct, your approach of calculating the IMR and using them as regressors in a second-stage logit model will not give you consistent estimates of this model. The two-step approach to estimating selection models using IMR only produces consistent estimates when the second-stage is a linear regression model. If as in your case the second stage model is a non-linear model, the system of equations needs to be estimated using ML-methods. This is why the stata command heckprob has no two-step option. Steve > -----Original Message----- > From: A. Mushfiq Mobarak [SMTP:ahmed.mobarak@colorado.edu] > Sent: Wednesday, April 09, 2003 5:20 AM > To: statalist@hsphsun2.harvard.edu; leblang@sobek.colorado.edu > Subject: RE: st: Inverse Mills Ratio after MLOGIT > > David, > > Let me answer the second question first. To my knowledge, the IMR are a > function of the predicted probabilities of the various outcomes in your > first stage mlogit regression. > > For your four outcomes, you first have to create variables for your > predicted probabilities of each outcome. Right after running the mlogit, > you can type: > > predict p0 if e(sample), outcome(0); > predict p1 if e(sample), outcome(1); > predict p2 if e(sample), outcome(2); > predict p3 if e(sample), outcome(3); > > You then have to use p0,p1,p2,p3 to create the 3 mills ratio terms. > According to formulas given by Dubin and McFadden (Econometrica circa > 1984), the following code would create the mills terms: (you should > check whether the formulas below are appropriate for your particular > problem) > > gen trnsp0=(p0*ln(p0))/(1-p0); > gen trnsp1=(p1*ln(p1))/(1-p1); > gen trnsp2=(p2*ln(p2))/(1-p2); > gen trnsp3=(p3*ln(p3))/(1-p3); > > gen millsp1=3*ln(p1)+ trnsp0 +trnsp2 +trnsp3; > gen millsp2=3*ln(p2)+ trnsp0 +trnsp1 +trnsp3; > gen millsp3=3*ln(p3)+ trnsp0 +trnsp1 +trnsp2; > > You can plug in millsp1-millsp3 in your second stage logit. If you are > interested in the standard errors for the mills ratio terms in the > second stage logit, then more work has to be done - you should probably > bootstrap errors. > > As to your first question, in my opinion, this is a fine thing to do, as > long as you have a variable that helps identify the covariance in the > first and second stage error terms. If you're using the exact same set > of variables in your first and second stages, then only the > non-linearity of the Mills ratio terms is used for identification, and > according to the literature on selection correction, this is not a good > way to proceed. There's a paper in the Journal of Economic Surveys on > the Heckman selection correction that discusses these issues. > > -Mushfiq > > A. Mushfiq Mobarak > Assistant Professor of Economics > University of Colorado at Boulder > 303-492-8872 > > Date: Mon, 07 Apr 2003 08:52:28 -0600 > From: David Leblang <leblang@sobek.colorado.edu> > Subject: st: Inverse Mills Ratio after MLOGIT > > Listers, > > I am trying to estimate a selection type model in the tradition of the > heckprob command however where the first stage has multiple outcomes > (four) and the second stage is a standard logit/probit. My approach to > this is to estimate the first stage as a multinomial logit, get the > predicted probabilities, and plug them into the second stage logit. > However, because I assume that the errors from the first and second > stage models are correlated, I want to generate the inverse mills ratio > (IMR) from the first stage multinomial logit and add those in the second > > stage equation (this is discussed in Millimet's faq on endogeniety). > Here are my questions: > > 1. from a statistical point of view, does this make sense? > > 2. how can I obtain the IMR after the mlogit? I have searched the > faqs, etc but cannot find an answer. > > Thanks, > > David Leblang > University of Colorado > > > > > * > * 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/ The information contained in this document is intended only for the addressee and is not necessarily the views nor the official communication of the Department of Labour. All final/official papers which are sent from the Department will be sent by non-electronic means, on appropriate letterhead, signed by authorised personnel. * * 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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