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st: mvprobit with autocorrelation and unobserved heterogeneity


From   <S.Jenkins@lse.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: mvprobit with autocorrelation and unobserved heterogeneity
Date   Sat, 25 May 2013 12:50:28 +0100

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

Date: Fri, 24 May 2013 18:35:07 +0200
From: "Bilge Karatas" <b.karatas@avans.nl>
Subject: st: mvprobit with autocorrelation and unobserved heterogeneity

Dear Statalisters,

I am estimating two structural equations having binary dependent
variables
in a panel data setting with small N and large T using  -mvprobit-
command.
 Is it possible to control for autocorrelation and unobserved
heterogeneity
 in the error terms of each equation in this estimation?

Best Regards,

Bilge Karatas
Tilburg University
=========================================

Please elaborate more precisely what you mean by "control for
autocorrelation and unobserved heterogeneity". What is the model?   (And
also please note the Statalist FAQ injunction to state the provenance of
programs that are cited.)

-mvprobit- fits a series of probit equations allowing the cross-equation
error terms to be correlated, with no restrictions on that error
structure. Essentially, each equation expresses the latent propensity
per individual subject to be a linear function of predictors plus a
subject-specific error term. Let's call this error e_i for subject i.

Do you want to express e_it as e_it = u_i + v_it, where v_it = r.v_it-1
+ z_it (say)?

In the panel case, -mvprobit- (or -cmp-) won't be able to fit such
models in which you wish to impose a particular error structure.

You might look at the article by Cappellari/Jenkins in the Stata Journal
2006, vol 6 issue 2 (freely downloadable from the Stata Journal
website).  The final example in the article is of a panel probit model
with unrestricted error structure.  One could place linear restrictions
on the variance-covariance matrix of error terms using -constraint-.
However, imposing an AR(1) structure would, I think, lead to non-linear
restrictions, and incorporating them would be much harder in programming
terms. (I haven't done it.) Note also the potential issue of 'initial
conditions'.

Alternatively ... you have 2 equations and so could be using built-in
-biprobit- rather than -mvprobit-. In the first instance, you could use
the -robust- option to "control". (But note that a -cluster(subject-id)-
option is not available.



Stephen (author of -mvprobit-)
------------------
Stephen P. Jenkins <s.jenkins@lse.ac.uk> 

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