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From |
"Renzo Comolli" <[email protected]> |

To |
<[email protected]> |

Subject |
Re: st: Heckman & simultaneous Equations procedures (?) |

Date |
Mon, 27 Dec 2004 19:17:17 -0500 |

Dear Rashid: The reason why we are going through this procedure rather than using -reg3- is that migration/not-migration is a zero-one decision. It is probably possible to use -reg3- (but you should check for other issues) if you were prepared to use a linear probability model for the migration/non-migration step. That is to say, if you use -reg3- it is possible that the predicted probability of migration is either higher than one or smaller than zero. That's why usually people don't use -reg3- for this type of problems. The procedure that I referred to is "close in spirit" to -reg3-. Rather than describing here the whole thing myself (that would take several pages) I refer you to one or more of the following references. Greene "Econometrics Analysis". The section is called "treatment effect". If you have the 5th edition it is at page 787, but I suggest you read the chapter on limited dependent variables from the beginning. I you read the whole chapter the logic will be pretty clear and you should be pretty clear on how comes that the endogeneity of the wage differential is taken care of. Greene stops short of the final step though. Maddala "Limited-dependent and qualitative variables in econometrics" explains the procedure under the heading "Lee's binary choice model". Note though that, for historical reasons, equation 11.20 is set up with a negative sign in front of the error; this might confuse you because it switches the signs of the inverse mills ratios. Also the fact that there is a typo in formula 11.23 does not help (the typo is that the minus in front of sigma2epsilon* should be a plus) The original references are Lee, Lung-Fei (1978) "Unionism and Wage Rates: A Simultaneous Equations Model with Qualitative and Limited Dependent Variables", International Economic Review, Vol. 19(2), pp. 415-433 Lee, Lung-Fei (1979) "Identification and Estimation in Binary Choice Models with Limited (Censored) Dependent Variables", Econometrica, Vol. 47, pp.415-433. I want to point out that the first step as you describe it here is NOT correct. The correct first step involves estimating a probit of migration on the migration regressors AND THE WAGE EQUATIONS REGRESSORS (but not the wages per se). You see now how this procedure is closer in spirit to -reg3- Also be sure that in step two you compute the right inverse mills ration (each equation has its own) I gave a sketch of the code here http://www.stata.com/statalist/archive/2004-11/msg00622.html http://www.stata.com/statalist/archive/2004-11/msg00626.html but this sketch presupposes you have a knowledge of the material and you just want to see the code. You could also use the command -movestay- that does full-information maximum likelihood, but as I point out here http://www.stata.com/statalist/archive/2004-11/msg00453.html there is a bug in the code for -mspredict-. If the bug were fixed, you could use -movestay- to estimate the reduced form migration equation and the two wage equation, then use -mspredict- to predict the wage in two regimes and could then estimate the structural form probit. But I received no confirmation that the way that I have proposed to correct the bug is right, so I don't suggest you rely on this procedure. To learn about -movestay- M. Lokshin and Z. Sajaia "Maximum likelihood estimation of endogenous switching regression models" Stata Journal 4(3):282--289 Best, Renzo Comolli ---------------------------------------------------------------------------- ---- *From Rashid Memon <[email protected]> To [email protected] Subject st: Heckman & simultaneous Equations procedures (?) Date Mon, 27 Dec 2004 13:39:55 +0000 (GMT) ---------------------------------------------------------------------------- ---- Dear All I am looking at the effect of the rural-urban wage differential on rural-urban migration. I am following the methodology Renzo Conelli posted some time ago: I first estimate the probit (migration on its dependent variables except the wage differential). Calculate the inverse mills ratio and then plug it in the wage equations. Estimate the wage equations and get predicted values to calculate the wage differential Plug in the wage differential in the migration Probit again. My concern is this: Since the wage differential is endogenous, should'nt a simultaneous equation procedure be used. I am a bit confused on how to combine a ML methodology (probit) with a simultaneous equation procedure (say, reg3) Any assistance will be appreciated. Thanks Rashid * * 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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