On the Testability of Causal Models with Latent and Instrumental Variables

Certain causal models involving unmeasured variables induce no independence constraints among the observed variables but imply, nevertheless, inequality contraints on the observed distribution. This paper derives a general formula for such 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 variables can be deemed instrumental.