On the Testability of Causal Models With Latent and Instrumental Variables

By Judea Pearl. 1995

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.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Citations in the corpus

Causal inference in statistics: An overview (2009, methodology): “Pearl (1995a) has presented examples in which there exists no set of variables that is sufficient for adjustment and where the causal effect can nevertheless be estimated consistently.”
Generalized instrumental inequalities: testing the instrumental variable independence assumption (2020, background): “1) is the generalization of the discrete version of the instrumental inequality derived by Pearl (1994). To the best of our knowledge, this is the first time that inequalities (4.”
Theory-independent limits on correlations from generalized Bayesian networks (2014, background): “This model does not imply any conditional independences on A B Y { , , }, but in [28], it is shown that it can still be tested because for any ∈  P”
Nested Markov Properties for Acyclic Directed Mixed Graphs (2012, background): “n variable DAGs may induce additional inequality constraints which are not satisﬁed by all elements of the associated nested Markov model. The best known of these are the instrumental inequalities of Pearl (1995), which were generalized by Evans (2012). However, Evans (2015) shows that the nested Ma”
Bounds on Treatment Effects from Studies with Imperfect Compliance (1997, methodology): “These inequalities, when generalized to multivalued variables, assume the simple form max d X y max z P (y; djz) 1 which was called the instrumental inequality in (Pearl 1994).”
On the Testable Implications of Causal Models with Hidden Variables (2002, background): “This paper of fers a systematic way of identifying functional constraints and, thus, facilitates the task of testing causal models as well as inferring such models from data.”
Statistics and causal inference: A review (2003, methodology): “Pearl (1995a) has presented examples in which there exists no set of variables that is sufficient for adjustment and where the causal effect can nevertheless be estimated consistently.”
Bounds on causal effects in three‐arm trials with non‐compliance (2006, background): “Pearl (1995) provided a necessary condition on the probability distribution of .”
Margins of discrete Bayesian networks (2015, background): “d than equality constraints, and eﬀorts to characterize them fully in DAGs with latent variable models have been limited by computational challenges. Evans (2012), generalizing a result ﬁrst given by Pearl (1995), provides a graphical criterion for obtaining some inequalities, but deriving a complet”