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st: MVprobit in an instrumental variable framework?
> Date: Wed, 23 May 2007 11:50:21 +0200
> From: "christoph t" <firstname.lastname@example.org>
> 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
> to instrument for the binary variable "migrant household", which
> be endogeneous (using migrant networks as an instrument).
> Is this approach valid? I.e. will the inclusion of a 4th equation
> an instrument correct for potential biases just as in the biprobit?
> 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 <email@example.com>
Director, Institute for Social and Economic Research
University of Essex, Colchester CO4 3SQ, U.K.
Tel: +44 1206 873374. Fax: +44 1206 873151.
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