On the Testability of Causal Models with Latent and Instrumental Variables
This addresses the challenge of validating causal models in fields like epidemiology or economics where unmeasured variables are common, but it is incremental as it builds on existing instrumental variable theory.
The paper tackles the problem of testing causal models with latent and instrumental variables, deriving a general formula to test if such models fit observed data or if variables can be considered instrumental.
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.