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st: Sequential correlated probits


From   John-Paul Ferguson <jpferg@MIT.EDU>
To   statalist@hsphsun2.harvard.edu
Subject   st: Sequential correlated probits
Date   Tue, 17 Jun 2008 22:06:03 -0400

Hello,

Twice in the last year I have found myself modeling three-stage processes where
there was some risk of endogeneity between the outcomes of the stages. An
example from American labor markets:

1. A labor union files an election petition. It can choose to withdraw the
petition or go to election.

2. The union can lose the election or win.

3. The union can fail or succeed to negotiate a contract with the employer.

Observations are lost at each stage because failures at earlier stages do not
proceed to later ones. At the same time, there is some risk of endogeneity. In
particular, unions may choose to withdraw their election petitions when they
think they are going to lose the election.

Because there is such endogeneity, a simple sequential logit or probit will
yield biased estimates. A model that allows for correlation would be better.
Several pieces of research, including Lillard and Willis (1994), Upchurch et
al. (2002) and Waelbroeck (2005) have developed and implemented such models. In
all of these cases, the authors have either used aML or programs they rolled
themselves.

My understanding is that aML is popular for such multi-level and/or
multi-process models; that is after all what it was designed for. I myself used
aML to model the process described above. Yet I use Stata for the rest of my
statistical work, and while I haven't paid much attention I know that versions
9 and 10 have brought considerable advances in, for example, hierarchical
linear models.

So my question: to your knowledge, has something like a correlated sequential
probit model been implemented in the more recent versions of Stata? Has it been
there for a while and I just missed it? I always suspect there are options deep
within -ml- that I haven't explored enough...

Any suggestions anyone has would be appreciated.

Best,
John-Paul Ferguson
Massachusetts Institute of Technology

References:

Lee A. Lillard and Robert J. Willis. 1994. Intergenerational educational
mobility: Effects of family and state in Malaysia. Journal of Human Resources
29(4): 1126-1166.

Dawn M. Upchurch, Lee A. Lillard and Constantijn W.A. Panis. 2002. Nonmarital
childbearing: Influences of education, marriage and fertility. Demography
39(2): 311-329.

Patrick Waelbroeck. 2005. Computational issues in the sequential probit model: A
Monte Carlo study. Computational Economics 26: 141-161.
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