I believe there exists an equilibrium relationship between three variables: the position of the Gas pedal; the Speed of the car; the position of the speedometer Needle. I have verified this relationship empirically. I have a crude theory of how cars work that can explain this relationship. But any automotive engineer would laugh at my crude theory. I can state my theory in words. I could maybe state my theory as a mathematical relationship, but little would be gained, and much would be lost, if I simply wrote down: aN(t) = bS(t) = cG(t)+dS(t-1), and added a few exogenous shocks to account for hills and things.
According to my theory of how cars work, if I press down on the gas pedal, that will cause the speed to increase, and that will cause the speedometer needle to rotate clockwise. But if I grab the speedometer needle, and rotate it clockwise, this will not cause the speed to increase and the gas pedal to go down. I admit I have never tried doing this, to test my theory empirically, but I am 99.99% sure it won't work. But according to the equations I have just written down, it should work just fine. Simply read the same equation from right to left.
My theory of how cars work, though very crude, is much richer than that equilibrium relationship. Something important is lost in translation when I write down only that equation that describes the equilibrium relationship and leave everything else out. Some causal relationships are not reversible. My theory tells me this one is not reversible.
I am a very amateur auto mechanic. On a good day, if it's something simple, I can maybe diagnose and fix a problem with my car. I am a professional economist. But I understand how cars work better than I understand how economies work. I can diagnose and fix cars better than I can diagnose and fix economies.
The gas pedal is the growth rate in the money supply. The speed is the inflation rate. The speedometer needle is the nominal interest rate. If you increase the growth rate of the money supply, that will cause the inflation rate to rise, and that in turn will cause the nominal interest rate to rise. The analogy isn't perfect though.
Because for the last 20 years, the Bank of Canada has succeeded in keeping the car at a roughly constant speed, at almost exactly the speed on average it said it wanted to target, by grabbing hold of the speedometer needle and turning it. But here's the weird thing. The Bank of Canada says (and I have no reason to think they are lying) that when it wants the car to increase speed it turns the speedometer needle counterclockwise, which is the opposite direction that the equilibrium relationship would suggest. If the Bank of Canada had been muddled, and should have been turning the needle clockwise to make the car speed up, it would be an amazing fluke that the average speed of the car was almost exactly what the Bank had previously said it was targeting. That is an important bit of empirical evidence about the negative relationship between nominal interest rates and inflation when we reverse the direction of causation. It supplements the observed positive correlation between a clockwise speedometer needle and speed that we see in long run data and cross-country data.
(I think I understand why the relationship between speedometer needle and speed changes sign when we reverse the direction of causation, though I'm not sure my explanation is right.)
So if another amateur auto mechanic writes down "aN(t) = bS(t)", and tells me that that equation is all I need to know if I want to understand why turning the speedometer needle clockwise will increase the car's speed. And isn't interested in my story about why it won't work, because it's only a story, and in words not equations, and refuses to tell me a different story of his own.....I think he's wrong.
[Update: as I was driving down Autoroute 5, pressing the gas pedal, watching the speedo, I suddenly remembered Andy Harless had made a similar point a couple of years back about umbrellas not causing rain. Sorry Andy. (But cars are cooler than umbrellas).
Question: there must be some relation between: instability of equilibrium when you swap the control lever; and the sign of the relationship reversing. A regular pendulum is stable, and you move the top end north if you want the bottom end to move north. But an inverted pendulum is unstable, and you move the bottom end south initially, then north, if you want the top end to move north. (But the people in an economy, unlike a pendulum, have expectations and act on them, so there are leads as well as lags.)