Understanding the Limits of Mathematical Relationships in Economics
Reflecting on my high school days (which feels like an eternity ago), I remember my first encounter with basic trigonometry. Homework and tests often presented scenarios where one had to deduce the length of a triangle’s side using provided values. Take, for instance, a problem involving a post of unknown height casting a shadow of a specified length, influenced by a light source at a particular angle. By employing various trigonometric identities, one could unravel the mystery of the missing variable. I found these problems immensely satisfying; whether given the post’s height and shadow length or the angle of light and shadow length, the relationships remained consistent and reliable.
However, suppose we determine that the post is six feet tall, and we then ask ourselves why it stands at this height. To attribute the post’s height to the angle of the light or the length of the shadow would not only be peculiar but utterly misguided. The mathematical relationships are sound—trigonometric identities are indeed true—but they don’t provide causal explanations. If I shift the light, the shadow changes. Hammer the post deeper into the ground, and the angle of light will shift accordingly. Yet, no matter how many equations one studies, they won’t reveal the cause of the light’s angle or the post’s height. Trigonometric identities serve to illustrate relationships, not to explain causation.
Unfortunately, the world of economic commentary is littered with voices who seem oblivious to this fundamental distinction. When self-proclaimed economic experts present an accounting identity and then solve a mathematical problem as if it reveals profound economic insight, they only add to the confusion. Each time someone asserts that levels of private or public debt are dictated by the trade balance, we plunge deeper into a tedious haze. Just as trigonometric identities do not indicate causation, neither do accounting identities serve as mechanisms for economic causality.
