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From |
"A. Mushfiq Mobarak" <ahmed.mobarak@colorado.edu> |

To |
<statalist@hsphsun2.harvard.edu>, <leblang@sobek.colorado.edu> |

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

Date |
Tue, 8 Apr 2003 11:20:01 -0600 |

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/

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