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


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/
-----------------------------------------


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