1. Fit a model (in the case Zipf's law) to a semi-related field (the size of non-financial companies).
2. Find that the model doesn't fit reality in the field you're interested in (financial companies).
3. Posit that your model is correct and reality is wrong, and invent over $30 trillion worth of invisible activity to account for the difference.
Alternatively... your model is just wrong?
The question is: how could one find evidence that justifies or refutes the idea that the scale of firms does in fact fit zipf and that measure is being obscured at the tail?
Also, I'd point out that the original post did not differentiate between financial and non financial companies in the way you do between points 1 and 2, so your characterization of what fields are related or "semi-related" is your own creation and not part of the original claim.
Well, I think to find that evidence, you would have to take a measurement of the amount of shadow banking from one of these firms. Objectively, you can't do that, since there is no agreed upon definition of what the term shadow banking means.
Cough cough… The correct word is not "reality", but "currently well established models".
This is less obvious than you make it out to be.
It's a world of difference
Evidence based on assets capped at a lower value than the power law implies probably implies either regulation is limiting asset size or otherwise distorting the market, OR the books are cooked and assets are considerably higher but accounting games are being played. Perhaps thats a good idea for future financial planning if many of the "hidden assets" are actually worthless unrealized mortgage loan losses. Or maybe they're just crooks.
Anyway its a pretty big leap to go from unusually low assets to therefore total aggregate transaction volume must be artificially low.
For those who can't tell the difference between assets and transaction volume, this is a slight simplification but the assets of the car lot at my car dealer are about 200 cars, varies a bit, but they're all of probably about the same order. Now the total transactional volume is totally different at each dealer, some sell one car per day and some sell ten cars per day. The total annual transaction volume better closely match the total annual car production. However the assets on hand merely equal a simple division problem and don't mean a whole heck of a lot. Its like comparing apples and oranges or OSes and DMBSes. They're kinda sorta related but not the same thing.