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RE: st: Sequential correlated probits


From   "Stephen P. Jenkins" <stephenj@essex.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   RE: st: Sequential correlated probits
Date   Fri, 20 Jun 2008 18:31:15 +0100

> ------------------------------
> 
> 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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