I am not sure I understand your question.
By Maddala (1983) I presume you mean the book "Limited-Dependent and
Qualitative Variables in Econometrics".
It is my understanding that in that book, exception made for the last
chapter, there is a selection equation Y2*= a2X2 + e2 which does not depend
in any way from Y1, and it linked to Y1 only by the fact that Cov(e1, e2) is
different from 0, so the word "endogenous" in your email confuses me. It may
well be that it is me to be confused. The crown jewel of all the book,
except the last chapter, is probably the Heckman estimation method.
In the last chapter the model is expanded to allow for the possibilty that
the selection equation depends itself from the outcome variable. More
specifically Y2* depends on the difference between the value Y1 actually
takes and the value Y1 would have taken had the individual done the opposite
choice (a value we don't observe). I would call this one endogenous, but
(again) maybe it's me who doesn't have the terminology right. You can find
much more on this second topic in
Lee, Lung-Fei, 1979. "Identification and Estimation in Binary Choice Models
with
Limited (Censored) Dependent Variables," Econometrica, Vol. 47 (4) pp.
977-96
The papers that followed
Regardless of what you mean by endogenous, the following survey might be
worth reading
Vella, Francis (1998) "Estimating Models with Sample Selection Bias: A
Survey" Journal of Human Resources 33(1):127-169
Unfortunately, endogeneity in sample selection models did not receive enough
attention in standard econometrics text books (Greene, Davidson and
MacKinnon...). I think that for economists this is very unfortunate given
that we usually think that payoff relevant consequences (the Y1 that happens
and the Y1 that could have happened) are foundamental in the decision
itself.
I hope it helps.
Renzo Comolli
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