Thread by @JWMason1

This is something I think about a lot. I'm really delighted to see someone write it up formally. I am definitely going to be talking about the piranha theorem from now on.

stat.columbia.edu/~gelman/resear…

I will try to write up (my understanding) of the argument better tomorrow, but the essential point is that there cannot be a very large number of independent important causes of the same outcome x, because there is only so much variation in x to be explained.

One nice thing about the paper is that they put a number on this. Basically, if a is a correlation between x and y that represents a genuine causal link, then x must be one of the 1/(a^2) most important influences on y.

Unlike a lot of mathematical results one sees in statistics and econometrics, this is a really strong and general claim. It is literally impossible for - for example - more than 10 independent factors to each explain 30% of the same outcome.

This by itself rules out a lot of strong claims for "nudges". Small causes cannot *systemactically* produce large effects. There are too many possible causes!

They don't say this and might not agree, but to me this points strongly in the direction of narrative as a critical form of validation for causal claims in economics and other social sciences.

The test of a theory is not whether one can isolate variation in x and then show it has some correlation with y, but rather one can take a concrete important evolution of y and give an account of the most important of all the causes of it.

I think there's a strong argument that this is how persuasion works in practice in economics. Theories succeed not by performing better on some econometric test but by offering a more compelling story about some salient historical development.