On the testability of causal models with latent and instrumental variables

Authors:
Judea Pearl
Affiliations:
Cognitive Systems Laboratory, Computer Science Department, University of California, Los Angeles, CA
Venue:
UAI'95 Proceedings of the Eleventh conference on Uncertainty in artificial intelligence
Year:
1995

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Abstract

Certain causal models involving unmeasured variables induce no independence constraints among the observed variables but imply, nevertheless, inequality constraints on the observed distribution. This paper derives a general formula for such inequality constraints as induced by instrumental variables, that is, exogenous variables that directly affect some variables but not all. With the help of this formula, it is possible to test whether a model involving instrumental variables may account for the data, or, conversely, whether a given variable can be deemed instrumental.