Everybody knows that if you press down on the gas pedal the car goes faster, other things equal, right? And everybody knows that if a car is going uphill the car goes slower, other things equal, right?
But suppose you were someone who didn’t know those two things. And you were a passenger in a car watching the driver trying to keep a constant speed on a hilly road. You would see the gas pedal going up and down. You would see the car going downhill and uphill. But if the driver were skilled, and the car powerful enough, you would see the speed stay constant.
So, if you were simply looking at this particular “data generating process”, you could easily conclude: “Look! The position of the gas pedal has no effect on the speed!”; and “Look! Whether the car is going uphill or downhill has no effect on the speed!”; and “All you guys who think that gas pedals and hills affect speed are wrong!”
If the driver is doing his job right, and correctly adjusting the gas pedal to the hills, you should find zero correlation between gas pedal and speed, and zero correlation between hills and speed. Any fluctuations in speed should be uncorrelated with anything the driver can see. They are the driver’s forecast errors, because he can’t see gusts of headwinds coming. And if you do find a correlation between gas pedal and speed, that correlation could go either way. A driver who over-estimates the power of his engine, or who under-estimates the effects of hills, will create a correlation between gas pedal and speed with the “wrong” sign. He presses the gas pedal down going uphill, but not enough, and the speed drops.
While these ideas are nominally formulated on monetary and fiscal policy, I can’t help but wonder whether there’s some “big data stuff” in there as well…