Semi-Instrumental Variables: A Test for Instrument Admissibility

TL;DR

This paper introduces semi-instrumental variables and provides statistical tests to validate and identify instruments in causal models, enhancing the reliability of causal inference when domain knowledge is limited.

Contribution

It generalizes the concept of instruments to semi-instruments and develops algorithms to statistically test their validity and instrumentalness in additive models.

Findings

Algorithms for p-value estimation of semi-instrumental variables

Statistical tests for validating instruments based on distribution assumptions

Potential for automatic instrument identification

Abstract

In a causal graphical model, an instrument for a variable X and its effect Y is a random variable that is a cause of X and independent of all the causes of Y except X. (Pearl (1995), Spirtes et al (2000)). Instrumental variables can be used to estimate how the distribution of an effect will respond to a manipulation of its causes, even in the presence of unmeasured common causes (confounders). In typical instrumental variable estimation, instruments are chosen based on domain knowledge. There is currently no statistical test for validating a variable as an instrument. In this paper, we introduce the concept of semi-instrument, which generalizes the concept of instrument. We show that in the framework of additive models, under certain conditions, we can test whether a variable is semi-instrumental. Moreover, adding some distribution assumptions, we can test whether two semi-instruments are instrumental. We give algorithms to estimate the p-value that a random variable is semi-instrumental, and the p-value that two semi-instruments are both instrumental. These algorithms can be used to test the experts' choice of instruments, or to identify instruments automatically.