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Past national prosperity predicts future national prosperity--- but is correlation causation?

Not if the Solow model and its cousins are correct when they teach this truth:

Nation's can't get permanently rich from past wealth, whether that wealth was earned or stolen.
A nation that expropriated its way to a huge capital stock (K) in the past stays rich for a while, but unless it has a way to continue expropriating that K continually...

...it won't be able to maintain that capital stock, which will depreciate and wear away.
In the modern U.S., over 90% of new capital investment goes to replacing depreciated, worn out capital.

A nation has to be great at making stuff, year in and year out, in order to maintain a huge capital stock.

Otherwise, it all wears out.
The classic Solow graph is a reminder:

Twice the machines mean twice the machines wearing out each year. [constant marginal cost of K]

But twice the machines produce less than twice the amount of new machines each year. [diminishing marginal benefits of K.]
So a theft of capital (K) that pushes a nation far above K* won't be self-sustaining-- over time, it will instead be self-cancelling.

All roads lead to K*.

And the only practical way to raise K* a lot is by boosting total factor productivity, the je ne sais quoi of macro.
There are a lot of claims that a nation's prosperity is...

rooted in
founded upon
built upon

...the many real crimes of the past.

Those crimes are real.

Yet the claim that those past crimes cause current prosperity is just a theory...

And one that conflicts with Solow.
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