Before revision:  As a first contribution, it presents a proof confirming the conjecture in Pearl (1995), showing that \citet*{pearl1995testability}  the validity of an instrument indeed cannot be tested in the most general case when the endogenous variable is continuous.
After revision:  As a first contribution, it presents a proof confirming the conjecture in \citet*{pearl1995testability} the validity of an instrument indeed cannot be tested in the most general case when the endogenous variable is continuous.