Dear all,
First, a public thanks to Gustavo Sanchez and Jonathan Beck (who replied
in private) for answering my initial question. I hope you have some
time to answer more questions regarding the biprobit model I am working
on. I would be very grateful.
I have the following model:
p = a1X + b1s + c1Z
s = a2X + b2p.
The variables p and s are binary. The first thing I did is to run a
biprobit model (all runs are with pweight) like this:
p = a1X
s = a2X,
which I implemented in Stata as
[1] . biprobit p s X
and
[2] . biprobit (p = X s) (s = X p),
with the second one constained with [p]s = 0 and [s]p = 0.
1. They produce the same result in terms of the coefficients and
everything else on that table. However, they differ in computing the
(log-)likelihood functions. The first one produces a "Comparison: log
pseudolikelihood" of -1576 while the second reports -1528. Why is this
different and which one is the correct specification? Does it make a
difference at all, considering that the coefficients are the same,
anyway?
2. -mfx- is able to compute the marginal effects of the first
specification (with standard errors, too). However, when I try it on
the constrained -biprobit-, it responds with "warning: derivative
missing; try rescaling variable p". How could this happen?
Next, I ran
[3] . biprobit (p = X s) (s = X p),
with the constraint that [athrho]_cons = 0.
3. Would this be equivalent to running a two separate probits? I ran
". probit p X s" and did not get the same results.
4. -mfx- is able to compute the marginal effects but fails for the
standard error, returning "warning: predict() expression unsuitable for
standard error calculation". Can I still be confident in interpreting
the marginal effects in this case?
Since rho is effectively a test for exogeneity [Fabbri et al., 2004;
also discussed in Statalist previously], what I want to do is to test
whether p and s are exogenous. So, I run
[4] . biprobit (p = X s Z) (s = X p)
to test whether s is exogenous to the first equation, with the
constraint that [s]p = 0. I include Z for identification purposes
(should I have done this for [2], too?). If the output of [2] says that
rho is significantly different from zero and the output of [4] says that
it is not, then I can conclude that s is exogenous. Similarly, to
examine whether p is exogenous, I must run
[5] . biprobit (p = X s Z) (s = X p)
with the constraint [p]s = 0. I get the essentially same result (the
rho has become zero) so I can conclude that p is exogenous to the second
equation.
5. Is this how the test for exogeneity should be implemented?
6. s is significant in [4] and p is significant in [5]. This means
that the the reason why rho is significant in [2] is that p and s are
the omitted variables that make the error terms correlated. Thus, I can
run
[6] . probit p = X s Z
[7] . probit s = X p.
7. The thing is, s is a significant regressor and p is also a
significant regressor. Does this not, in fact, tell us to estimate the
two equations jointly? I am unsure of what to do next.
Please let me know (kindly?) where I have committed the disastrous
blunder. :)
--
Paloys
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