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.
READER COMMENTS
Jon Murphy
Jul 9 2025 at 10:55am
Your post reminds me of the supreme silliness of whenever Michael Pettis (or others) claim that Chinese people saving too much is the cause of US trade deficits.
Kevin Corcoran
Jul 9 2025 at 11:16am
That’s exactly the sort of person (and claim) I had in mind when writing this post. It just makes me cringe with secondhand embarrassment when I see people talk that way.
steve
Jul 9 2025 at 4:40pm
This is well written but I think it goes over the top of the heads of 70%-80% of people, probably a third of those because they dont want to understand.
Steve
David Seltzer
Jul 9 2025 at 6:38pm
Kevin, Scott Sumner admonished readers to never reason from a price change. His quote;
“My suggestion is that people should never reason from a price change, but always start one step earlier—what caused the price to change.” Emphasis mine.
Knut P. Heen
Jul 10 2025 at 8:06am
I sometimes ask exam questions about how a firm can improve it’s profit. The answer I often get is cut costs and increase revenue, but that is just repeating the definition of profit. What happens to your pizza revenue if you drop the cheese? A more correct answer is that you should cut all the cost the customer is not willing to pay for and take on all the costs the customers is more than willing to pay for.
Kevin Corcoran
Jul 10 2025 at 9:56am
This is exactly correct. Another way to make the general point is by invoking the simplest accounting identity I can think of:
Beans bought = Beans sold
This is always and everywhere true – if one person adds up the number or beans bought and another adds up the number of beans sold and the two numbers don’t match, all that demonstrates is that (at least) one bean counter made a mistake somewhere. But if someone said “the increase in beans sold was caused by the increase in beans bought,” they’ve explained nothing. If they said “we can increase the amount of beans sold by increasing the number of beans bought,” they have made a useless statement devoid of any meaning. That’s the whole point of calling something an identity. The number of beans bought just is the number of beans sold, and vice versa. Neither can causally interact with the other, because they are one and the same thing. Attributing causation to an identity is just nonsense.
People who think they are deriving economic insight from accounting identities are making this fundamental mistake. There are more variables involved in most economic accounting identities than the bean sales identity above, and that can make the math involved look much more fancy, lending an appearance of scholarly rigor to those who have only a superficial understanding of the ideas involved, but ultimately it all boils down to the same error.
David Seltzer
Jul 10 2025 at 10:12am
Kevin: Excellent explanation.
Kevin Corcoran
Jul 10 2025 at 10:55am
Thank you David – I actually think that comment of mine makes the point I was trying to make even more clearly than the actual post. I just hadn’t thought to put it that way until I read Knut’s comment. And that’s one reason I’m glad the average quality of commenters at EconLog is so good!
Knut P. Heen
Jul 11 2025 at 8:25am
This one we hear often about the stock market. The price fell because investors sold. Who did they sell to?
David Seltzer
Jul 11 2025 at 10:32am
Knut asked, Who did they sell to? Buyers I believe. Completes the identity in equilibrium. Apologies Knut. I was just having a little fun.
Dylan
Jul 11 2025 at 8:58am
This reminded me of when we lived close to a Godfather’s Pizza in the late 80s/early 90s. I have fond memories of the whole family walking down there weekly. We remember the pizza being so good when we moved there, much better than the pizza where we had lived before. Then something happened, the crust started tasting a little stale or even moldy, the sauce wasn’t quite right, little things like that. We gave it a number of tries, because we at first thought it was our imagination or just a bad night, but after a few of those we just stopped going. And, we weren’t the only ones, pretty soon the place that had always been bustling was always empty, and it closed within a year or two. And, it wasn’t just that one, Godfather’s Pizza disappeared completely from the city. I had no idea they were even still in business anywhere until Herman Cain ran for president.
Many years later I met my wife and found out she worked at a different Godfather’s pizza at the time. She confirmed that they changed suppliers to save costs and the pizza quality took a nose dive. Not really related to Kevin’s post, but an example of where I’m fairly confident that cutting costs led to lower profits.
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