st: Controlling for sample selection in three stages including a count based model

[Paul Gerrans <pcmmpa@hotmail.com>]

Hello,
I have a sample selection question involving three stages with an initial logit/probit, a count based regression, and another logit/probit.
I would like to model how sophisticated a person’s investment portfolio is. To do this I make an assessment of how the stocks are weighted in 
their portfolio when they change their portfolio from a starting (default) portfolio which only has one stock in it. I can only assess sophistication 
when there is more than one stock in a portfolio change. Hence I have three stages and I wish to ensure sample selection bias is controlled for.

Approx 80% don’t make any changes – they stay in the starting (default) portfolio. For those who do make a change approx 40% use just one stock again. 
I then assess the 60% of those who use more than one stock and classify their choice as sophisticated or not. I was wishing to make predictions at each 
stage using a limited set of regressors and don’t have a strong basis for including one regressor in one stage and not the other. 
 
My estimators at each stage are:
1. Predict make a change from default portfolio (1,0 logit probit) 
2. Predict number of stocks in portfolio for those who make a change (over dispersed count of ones therefore use zero truncated negative binomial) – 20% of original sample 
3. Predict sophistication of portfolio for those who choose more than one stock in a change (1,0 logit/probit) – 60% of sample 2 or 12% of original sample.

Would appreciate any suggestions.
Thanks
Paul 		 	   		  
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