When I was in high school (approximately 730 years ago, or so it feels these days) I first learned basic trigonometry. A common type of problem in homework and tests involved situations where you had to find the length of one side of a triangle based on other values provided. For example, a problem might tell you that there is a post of unknown height. The problem then tells you there is a shadow of such and such length being cast from that post by a light source at such and such an angle. The given information could then be combined with various trigonometric identities to work out the missing information. I always enjoyed these sorts of questions, and found it very satisfying how they worked in any direction. If you tell me the height of the post and length of the shadow, I can tell you the angle of the light – or if you tell me the angle of the light and the length of the shadow, I can tell you the height of the post.
But, upon working out that the post is six feet tall, suppose you wanted to know why the post is six feet tall – what caused the post to be that height? It would be really weird if I were to try to tell you that the angle of the light and the length of the shadow caused the height of the post. More than just weird – it would be such a confused answer that it’s not even wrong. Trigonometric identities are true, and the math behind them is impeccable. The relationships among these variables are ironclad. But it would be the height of nonsense to answer a question about what caused the light to be at its current angle by attributing that to the height of the post or the length of the shadow. If I move the light to a new position, the length of the shadow will change. If I hammer the post down into the ground by six inches, the light will hit at a different angle and the shadow will be a different length. But you can stare at the mathematical equations all day and not be able to say what caused the change in the angle of the light or the height of the post. Trigonometric identities are not causal mechanisms.
Unfortunately, there is no shortage of economics commentators who have failed to absorb this very basic point, and speak as though setting out an accounting identity and then solving a math problem is the height of economic insight. Every time someone who styles themselves as a sophisticated dealer in economics talks as though levels of private or public debt are caused by the trade balance, the world becomes a more tediously confused place. Accounting identities are not causal mechanisms.
