No you cannot test the exclusion restriction; if you invent such a test that
would be noble prize material. That is why IV papers always end up in
endless discussions about why an instrument is valid or not
What you can test is:
First stage identification: Regress the instrumented variable on the
instrument and the covariates and see whether the instrument has some
predictive power (some say an F test above 10 is good, others say it
depends). But if your instrument is not at all correlated with the
instrumented variable, you enter the ugly world of weak instruments and you
have to switch the estimators (see Imbens and Rosenbaum: Robust, accurate
confidence intervals with a weak instrument: quarter of birth and education)
Sensitivity to violations of the exclusion restriction: induce some
correlation between the instrument and the outcome (conditional on the other
vars) and see how much violation of the exclusion restriction you need to
make the effect go away. There are a couple of such tests available (see
Wand, J. 2002. Evaluating the Consequences of Assumptions Using
Simulations," The Political Methodologist, vol. 11, no. 1, 21, or Robins JM,
Scharfstein D, Rotnitzky A. (1999). Sensitivity Analysis for Selection Bias
and Unmeasured Confounding in Missing Data and Causal Inference Models.
Statistical Models in Epidemiology: The Environment and Clinical Trials.
Halloran, M.E. and Berry, D., eds. NY: Springer-Verlag, pp. 1-94).
jens
From: Viridiana R?os [mailto:viridianarios at
gmail.com]
Sent: Tuesday, April 08, 2008 7:34 PM
To: Jens Hainmueller; Jose Luis Romo Cruz
Subject: Instrument validity
Hi Jens,
I am trying to use a new instrument that theoretically should work better. I
run my new model and apparently, results are better than in the original
paper. However, there is a possibility that instrument is in fact correlated
with y. Is there a causality tests or something that I can use to prove the
validity of my instrument?
Best,
Viridiana R?os
617-997-2471