Testing the identification of causal effects in observational data

TL;DR

This paper introduces a testable condition for identifying causal effects in observational data using observed covariates and a suspected instrument, with methods validated through simulations and an empirical application.

Contribution

It proposes a novel test for the validity of instruments based on conditional independence and demonstrates its effectiveness with machine learning methods.

Findings

The test can detect violations of instrument validity in simulated data.

Application to fertility and labor supply data suggests potential instrument invalidity.

Machine learning methods improve the power of the conditional independence tests.

Abstract

This study demonstrates the existence of a testable condition for the identification of the causal effect of a treatment on an outcome in observational data, which relies on two sets of variables: observed covariates to be controlled for and a suspected instrument. Under a causal structure commonly found in empirical applications, the testable conditional independence of the suspected instrument and the outcome given the treatment and the covariates has two implications. First, the instrument is valid, i.e. it does not directly affect the outcome (other than through the treatment) and is unconfounded conditional on the covariates. Second, the treatment is unconfounded conditional on the covariates such that the treatment effect is identified. We suggest tests of this conditional independence based on machine learning methods that account for covariates in a data-driven way and investigate their asymptotic behavior and finite sample performance in a simulation study. We also apply our testing approach to evaluating the impact of fertility on female labor supply when using the sibling sex ratio of the first two children as supposed instrument, which by and large points to a violation of our testable implication for the moderate set of socio-economic covariates considered.