A conditional independence test for causality in econometrics

TL;DR

This paper introduces a heuristic conditional independence test for causality in econometrics, relaxing the strict independence requirement of the traditional Y-test, and demonstrates its application and limitations in economic models.

Contribution

It proposes a new heuristic test for causality that is easier to apply than the traditional Y-test and discusses its practical usefulness and limitations.

Findings

Test is informative with linear Gaussian models

Can be misleading outside linear Gaussian contexts

Useful for falsifying control set assumptions

Abstract

The Y-test is a useful tool for detecting missing confounders in the context of a multivariate regression.However, it is rarely used in practice since it requires identifying multiple conditionally independent instruments, which is often impossible. We propose a heuristic test which relaxes the independence requirement. We then show how to apply this heuristic test on a price-demand and a firm loan-productivity problem. We conclude that the test is informative when the variables are linearly related with Gaussian additive noise, but it can be misleading in other contexts. Still, we believe that the test can be a useful concept for falsifying a proposed control set.