A conditional independence test for causality in econometrics

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.