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Re: st: IV estimation for probit models with binary endogenous variable...?
From |
Antoine Terracol <[email protected]> |
To |
[email protected] |
Subject |
Re: st: IV estimation for probit models with binary endogenous variable...? |
Date |
Thu, 02 Apr 2009 14:48:04 +0200 |
I forgot to include this part of -cmp-'s help file in my previous message:
So some Stata estimation commands have wider applicability than
many realize. sureg (X=Y) (Y=Z), isure
typically matches ivreg X (Y=Z) exactly even though the
documentation does not describe sureg as an
instrumental variables (IV) estimator. (Iterated SUR is not a true
ML estimator, but it converges to
the same solution as ML-based SUR, as implemented, for example, in
the demonstration command mysureg.
See Pagan (1979) on the LIML-iterated SUR connection.) And biprobit
(X=Y) (Y=Z) will consistently
estimate an IV model in which X and Y are binary.
Antoine
Antoine Terracol wrote:
Kit, I miht have misunderstood your comment, but I read in -cmp-'s help
file that:
As a matter of algorithm, cmp is an SUR (seemingly unrelated
regressions) estimator. It treats the
equations as independent from each other except for modeling their
underlying errors as jointly normally
distributed. Mathematically, the likelihood it computes is
conditioned on observing all right-side
variables, including those that also appear on the left side of
equations. However, it can actually fit
a much larger class of models. Maximum likelihood (ML) SUR
estimators, including cmp, are appropriate
for an important class of simultaneous equation models, in which
endogenous variables appear on the
right side of structural equations as well as the left. Models of
this kind for which ML SUR is
nevertheless consistent must satisfy two criteria:
1) They are recursive. In other words, the equations can be
arranged so that the matrix of
coefficients of the dependent variables in each others'
equations is triangular. As emphasized
above, this means the models have clearly defined stages, though
there can be more than one equation
per stage.
2) Dependent variables in one stage enter subsequent stages only
as observed. Returning to the
example in the first paragraph, if C is a categorical variable
modeled as ordered probit, then C,
not the latent variable underlying it, call it C*, must figure
in the model for D.
In the following example, -cmp- and -biprobit- give the same results
/*---------------------------*/
clear
set obs 1000
drawnorm e1 e2, cov(1,0.5\0.5,1)
drawnorm x1 x2 z1 z2
g endog=(1+z1+z2+e1>0)
g y=(1+endog+x1+x2+e2>0)
cmp (y = endog x1 x2) (endog = z1 z2), ind(4 4)
biprobit (y = endog x1 x2) (endog = z1 z2)
/*---------------------------*/
Antoine
Kit Baum wrote:
<> Antoine said
If you are ready to assume joint normality, then -biprobit- should do
the trick:
/*------------------------------*/
clear
set obs 10000
set seed 987654321
drawnorm e1 e2, cov(1,0.5\0.5,1)
drawnorm x1 x2 z1 z2
g endog=(1+z1+z2+e1>0)
g y=(1+endog+x1+x2+e2>0)
probit y endog x1 x2 /*biased*/
biprobit (y= endog x1 x2) (endog=z1 z2)
I'm not so sure. Stata will allow you to estimate that model, but it
calls it the "seemingly unrelated bivariate probit" model. That model
is described in Greene, Econometric Analysis 6ed (p. 817), as
analogous to SUR ("in the same spirit as the seemingly unrelated
regression model"): that is, two equations in which there are nothing
but exogenous explanatory variables. The way in which Antoine has
written the model is one in which you surely could use cmp, as it is
recursive (y depends on endog, but endog does not depend on y). But
I'm not sure that the assumptions of the SUBP model are satisfied here.
Greene (p. 817) describes a model in which an endogenous regressor is
binary as a 'treatment effects' model and suggests that it should be
treated as a selection problem.
Kit Baum | Boston College Economics & DIW Berlin |
http://ideas.repec.org/e/pba1.html
An Introduction to Stata Programming
| http://www.stata-press.com/books/isp.html
An Introduction to Modern Econometrics Using Stata |
http://www.stata-press.com/books/imeus.html
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