Hi statalisters,
I have two instrumental variables that I'm considering, Instrument A
and Instrument B. In theory, instrument A is more likely to be
correlated with the outcome variable on the left-hand side and so i
created a variation of instrument A (which is instrument B), thinking
that it might have a better chance to pass the overid test. Now
surprisingly, across many different specifications that I've tried, it
turns out that instrument A has a better chance of having a smaller
Hansen J statistic (and thus a greater p-value) and of passing the
overid test. So my question is, even if in theory the instrument is
very likely to be correlated with the variable on the left-hand side,
if it passes the overid test, can I argue that this is a valid
instrument? Both instruments reject the joint F-statistic, even though
in most cases the statistic is smaller than 10, which implies that
both instruments are not very strong. Can I just hold onto the
instrument that passes the joint F-test as well as the overid test?
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