David,
I am sitting on a similar problem and have not found an optimal solution
to it, too. But here are some ideas:
You may be able to estimate the full maximum likelihood estimator for
your problem using an autocorrelation and heteroscedasticity consistent
(cluster) covariance matrix by using the biprobit command in STATA if
you have intra-group autocorrelation.
The biprobit command is written for a SUR estimation but Greene (2000),
4th edition, Econometric analysis, p. 852, argues that the Likelihood
function is identical to one where an endogenous binary variable is
estimated. Wooldridge (2002), Econometric Analysis of cross section and
panel data, p. 477f tells what to write into the equations for biprobit,
e.g.
Biprobit (y1 x1 y2) (y2 z x1), mle cluster(group indicator)
The cluster option together with mle will give you the desired
estimator.
There are some kitchen sink approaches, too. There is an NBER Technical
Working Paper No. 248 by Joshua Angrist "Estimation of limited-dependent
variable models with dummy endogenous regressors: simple strategies for
empirical practice" that deals with alternative methods. I am not sure
whether they properly take into consideration autocorrelation, though.
Dieter
-----Original Message-----
From: [email protected]
[mailto:[email protected]] On Behalf Of David Leblang
Sent: Wednesday, April 12, 2006 2:32 PM
To: [email protected]
Subject: st: ivreg2 for dichotomous dependent variable
Dear All,
I am working with an instrumental variables model where the dependent
variable of the outcome (second stage) equation is dichotomous. I have
been using the ivprobit command but my data likely have serially
correlated errors. To that end I like the options and flexibility of
ivreg2 (with the bw option to deal with serial correlation) and wonder
about the optimality of using that command as a linear probability
model. I understand that I will have predictions that may range outside
of the (0,1) interval but I am more concerned about the efficiency and
bias of my estimates. Any thoughts or ideas would be most appreciated.
Thanks,
David Leblang
University of Colorado
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