Re: st: Question on Wooldridge's Procedure 18.1

[Brent Gibbons <brent.gibbons@gmail.com>]

Hopefully the list server will recognize this response in the correct
thread. I was trying to use nabble (and only get the digest) but it
wasn't allowing me to respond. In case it doesn't recognize it
correctly, the last 2 threads are below.

Austin, thanks for your response. Let me see if I can explain a bit better.

I was partly trying to ask why exactly you have stated weak instrument
tests for proc. 18.1 are problematic. You mention that "weak
instrument diagnostics should come from straight IV, not procedure
18.1--note that procedure 18.1 would go through if Z was pure noise,
and the predicted value of your endogenous variable could be very
highly correlated with the endogenous variable, leading you to think
you had very strong instruments."

As I understand the 18.1 procedure, mainly coming from Wooldridge
(2002), you have an extra component in the predicted probabilities
besides what is specified in the probit model, which Wooldridge says
allows for identification in the subsequent 2SLS even if there are no
instruments (p. 624). The extra component comes from the probit
estimator's "nonlinear function of x" - which is what I figured you
were referring to with 'pure noise'. Hence my first question - is it
this reason alone that the weak instrument tests are problematic?

My second question relates to a scenario where you have both strong
instruments and this same component from above, that is also highly
correlated with the endogenous variable. So you can test the strength
of the instruments with the linear 2SLS. But is there any reason to
worry that this extra component could bias the result? I don't think
so, but I'm having trouble explaining why to myself.

Thanks again for all comments, Brent

Below posted Aug. 7, 2012

B.Gibbons <brent.gibbons@gmail.com>:
This question is not clear to me--the point is that weak IV
diagnostics work fine for the linear probability model but not
Procedure 18.1, as evidenced by a thought experiment (or simulation)
using white noise variables as excluded instruments as in my 2010
post. When you say "can't test the exclusion restriction" you are
apparently confusing several tests of quality of inference in
instrumental variables. I have no idea what you mean by "the
non-linearity in the probit may be correlated with..." (did you mean
some component of the error? a generalized residual?)

Below posted Aug. 2, 2012

Hi Austin, I'm currently using the 18.1 method in a project and have seen
your warnings about using tests of instrument strength through the 18.1
method.

My 1st question is whether those warnings are solely because of the
potential that the non-linearity in the probit may be correlated with the
binary endogenous variable - and falsely show good instrument strength.

2nd - what if there is both strong correlation between the non-linearity in
the probit AND strong instruments in the model: is there reason to worry
about this non-linearity as having a potential bias, especially since you
can't test the exclusion restriction for that?

Thanks for any comments, Brent
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