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RE: st: Sequential correlated probits


From   jpferg@MIT.EDU
To   statalist@hsphsun2.harvard.edu
Subject   RE: st: Sequential correlated probits
Date   Fri, 20 Jun 2008 15:35:09 -0400

Quoting "Stephen P. Jenkins" <stephenj@essex.ac.uk>:

------------------------------

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

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.
I suspect that -mvprobit- could estimate this model. -findit mvprobit-
to find latest version of -mvprobit-. (Original version discussed in a
2003 Stata Journal article by Cappellari and Jenkins; downloadable from
DJ website.)

Read the help file in conjunction with the definitive reference on
coherency conditions for systems of such kinds: James J. Heckman "Dummy
Endogenous Variables in a Simultaneous Equation System", Econometrica,
Vol. 46, No. 4. (July, 1978), pp. 931-959. I recommend that you read
this article and check that your case 'fits'.  (I presume that you also
have suitable instruments available so that you can appeal to
appropriate exclusion restrictions.

I suggest that you also check out  Cappellari, L. and S.P. Jenkins.
2006. Calculation of multivariate normal probabilities by simulation,
with applications to maximum simulated likelihood estimation. The Stata
Journal 6(2). [Pre-print of article is in ISER working paper
series; URL below signature. We show to estimate MV probit-like models
faster than with -mvprobit-, providing an egen command that uses a
plugin. ]


Stephen
-------------------------------------------------------------
Professor Stephen P. Jenkins <stephenj@essex.ac.uk>
Director, Institute for Social and Economic Research
University of Essex, Colchester CO4 3SQ, U.K.
Tel: +44 1206 873374.  Fax: +44 1206 873151.
http://www.iser.essex.ac.uk
Survival Analysis using Stata:
http://www.iser.essex.ac.uk/teaching/degree/stephenj/ec968/
Downloadable papers and software: http://ideas.repec.org/e/pje7.html

Learn about the UK's new household panel survey, the United Kingdom
Household Longitudinal Study: http://www.iser.essex.ac.uk/ukhls/



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Professor Jenkins, this is exactly what I was looking for. I had indeed
overlooked it. Thank you for the reference--and for co-authoring the routine!

Best,
John-Paul Ferguson
MIT
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