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

To |
statalist@hsphsun2.harvard.edu |

Subject |
RE: st: estimating the covariance matrix of probit two stage procedure |

Date |
Thu, 27 Dec 2007 13:09:39 +0000 (GMT) |

Ok, I think I (roughly) understand your question now. I am only going to give you very general advise here, and I am not going to implement it in Stata code, as I am in my final half year of my dissertation... Try to write down the entire likelihood function and maximize that with Stata -ml- command. In part those two-step methods were invented because computational power was so expensive at that time to make such short-cuts profitable. Now we can much more easily use the more general maximum likelihood methodology. When tyring to maximize the likelihood function you may find the following book invaluable: http://www.stata.com/bookstore/mle.html -- Maarten --- Guillermo Armelini wrote: > Sorry I express myself incorrectly, because looking at what I > proposed in the first email, you are completely right that this is > precisely the Heckman selection model > > What I'm trying to do is to estimate a model about how different > methods of customer acquisition affect customers profitability. I opt > for a kind of selection model because I have a set of "N" prospect in > the sample likely to adopt but, then only a number of them end up > adopting. This is the reason why in the first equation I proposed > using a probit model > > Z(i)=AV(i)+U(i) (equation 1) > > Z(i)=1 if Z(i)>0 > > Z(i)=0 if Z(i)<=0 > > where A is a vector of parametes and V is a set of covariates related > with different methods of customer acquisition (advertising, > publicity, referral, etc.) > > The second equation is a conditional regression: > > Y(i)=bX(i)+E(i) if Z(i)=1 (second equation) > > where "bs" are the coefficients to be estimated and "Xs" are the > covariates that affect customer profitability of those that were > already acquired (i.e. duration, degree of satisfaction, etc.) > > Up to here everything will be ok running a heckman selection model. > The problem is that Y(i) is not observed, for all observations, > because Y(i) is the variable of customer profitability, and in the > period that I'm taking into consideration, most of the customers are > still "alive", so this equation, by itself is censored. For that > reason, I think that in this case heckman model is not the correct > one to estimate what I wanted to do. > > There is an article by Lee, Maddala and Trost (1980) in which authors > proposed a method to calculate the correct variance covariance matrix > whenever there is a model like the one I would like to estimate. > > Asymptotic Covariance Matrices of Two-Stage Probit and Two-Stage > Tobit Methods for Simultaneous Equations Models with Selectivity > Lung-Fei Lee, G. S. Maddala, R. P. Trost Econometrica, Vol. 48, No. 2 > (Mar., 1980), pp. 491-503 ----------------------------------------- Maarten L. Buis Department of Social Research Methodology Vrije Universiteit Amsterdam Boelelaan 1081 1081 HV Amsterdam The Netherlands visiting address: Buitenveldertselaan 3 (Metropolitan), room Z434 +31 20 5986715 http://home.fsw.vu.nl/m.buis/ ----------------------------------------- __________________________________________________________ Sent from Yahoo! Mail - a smarter inbox http://uk.mail.yahoo.com * * 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/

**References**:**RE: st: estimating the covariance matrix of probit two stage procedure***From:*Maarten buis <maartenbuis@yahoo.co.uk>

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