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st: MVprobit in an instrumental variable framework?


From   "Stephen P. Jenkins" <stephenj@essex.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: MVprobit in an instrumental variable framework?
Date   Thu, 24 May 2007 10:29:56 +0100

> ------------------------------
> Date: Wed, 23 May 2007 11:50:21 +0200
> From: "christoph t" <lehammock@googlemail.com>
> Subject: st: MVprobit in an instrumental variable framework?
> 
> Dear colleagues,
> 
> We want to estimate 3 equations (with binary dependent variables)
> simultaneously using mvprobit. However, we have a potential problem
> with self selection and unobserved characteristics (it's a migration
> paper and we only take the subsample of labour market inactive
> individuals). Therefore, we have thought to include a fourth
equation
> to instrument for the binary variable "migrant household", which
might
> be endogeneous (using migrant networks as an instrument).
> 
> Is this approach valid? I.e. will the inclusion of a 4th equation
with
> an instrument correct for potential biases just as in the biprobit?
Or
> is there a two-step procedure that would suit here?
> 
> We have thought long about this problem and searched around quite a
> bit. Therefore, we would be very grateful for any help.
> 
> Thank you in advance,
> Christoph Trebesch


The 'correction' via joint estimation in a -biprobit- estimation that
you allude to (and discussed, I think, in Hsiao's book on Panel Data)
also carries over to the case with > 2 equations.

However I gather that the definitive reference on coherency conditions
for systems of any such kind is: 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 in ISER working paper
series.]  We show how to estimate MV probit-like models faster than
with -mvprobit-, providing an egen command that uses a plugin.  (There
is an updated -mvprobit- downloadable from the Software Update section
of the same issue of the SJ.)


Stephen  (co-author of -mvprobit-)
-------------------------------------------------------------
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 Britain's new household panel survey, the United Kingdom
Household Longitudinal Study: http://www.iser.essex.ac.uk/ukhls/ 
Contribute to the consultation on content:
http://www.iser.essex.ac.uk/ukhls/consult/


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