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From |
Maarten buis <maartenbuis@yahoo.co.uk> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: About the Heckman selection model |

Date |
Wed, 17 Feb 2010 04:58:49 -0800 (PST) |

--- On Wed, 17/2/10, Maria Quattri wrote: > 1) Both the coefficients for the Probit and those for the > OLS seem to have no direct interpretation. Therefore, > I would consider the significance of marginal effects only: > Pr(y observed) for the Probit and E(y|y observed) for > the OLS. Is that right? No, especially E(y | y observed) is usually not the most interesting outcome, more often you would want to look at either E(y) (the dependent variable as one would observe them, thus including the censored observations), or E(y*) (the latent dependent variable). When trying to understand your results you want to look at all of them. > 2) Is there any way to test the bivariate normality of the > error terms for the maximum likelihood estimation in Stata? No, where would that information come from? Think about the selection equation: The empricial information about the distribution of the "error term" is only there in the form of the shape of the relationship between the probability and the explanatory variables. That is just not enough to build a reliable test. > 3) While Stata twostep option automatically corrects > standard errors after the inverse Mills ratio enters the > regression as estimated parameter (i.e. bootstrapping is not > necessary), the twostep does not allow robust estimation. > This seems to suggest that running Heckman manually > (Probit+OLS with robust s.e. and boostrap, say 1000 > replications) could be better option for inference. Is it > so? No, the bootstrap won't use the information from the robust standard errors, and point estimates will be exactly the same the models without robust standard errors. So this procedure will not get you what you want. Moreover, robust standard errors are not so great to be worth going through any special effort (with the danger of introducing bugs). Some people think that robust standard errors are the greatest thing since sliced bread, others think they are evil (and most hold a position somewhere in between). See for example: Freeman, D.A. (2006) On the So-Called "Huber Sandwich Estimator" and "Robust Standard Errors", The American Statistician, 60(4): 299--303. > 4) The robust MLE is less general than the two-step, yet it > seems to be preferred apart from when the estimated rho > approaches 1. Which value for rho is "big enough" to suggest > the use of the twostep procedure? Again, don't get too carried away with those robust standard errors. If you can use them without doing anything you don't want to do, then they probably don't do too much harm, otherwise just forget about them. Regarding rho, rho is a correlation, so when rho is close to 1 (or -1) it means that there is very little information you can use to distinguish between those two error terms. So use what you know about correlations to make that judgement. Hope this helps, Maarten -------------------------- Maarten L. Buis Institut fuer Soziologie Universitaet Tuebingen Wilhelmstrasse 36 72074 Tuebingen Germany http://www.maartenbuis.nl -------------------------- * * 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/

**References**:**st: About the Heckman selection model***From:*Maria Quattri <Maria.Quattri@manchester.ac.uk>

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