What indeed can be tested with an instrumental variable?
An astronomer, a physicist and a mathematician are on a train in Scotland. The astronomer looks out of the window, sees a black sheep standing in a field, and remarks, “How odd. All the sheep in Scotland are black!” “No, no, no!” says the physicist. “Only some Scottish sheep are black.” The mathematician rolls his eyes at his companions’ muddled thinking and says, “In Scotland, there is at least one sheep, at least one side of which appears to be black from here some of the time”.
British Heart Foundation (None)
Medical Research Council (MC_UU_00002/7)
Wellcome Trust (204623/Z/16/Z)