What's stopping investments outside the empire?

Investors like to get their money back.

"Outside the empire" means "outside a legal framework which I can use to obtain recourse against people who default on our business dealings."

Because the ability to reliably obtain recourse against people who default on your business dealings is a pretty good working definition of the difference between "inside" and "outside" the empire.

(Lots of building still needed across the world.)

The point is not that there is a lack of investment opportunities. The point is that there are fewer than there used to be, and this shifts power toward rentiers. This power is then used to change the rules of the game to be more favorable to rentiers, which further shifts power to rentiers.

Just like, in the expanding empire, producers gain power from exploiting previously unclaimed (by stakeholders internal to the empire) economic niches, and then change the rules to favor producers, which opens up even more previously unclaimed niches to exploitation.

Your post implies that the whole set of economic theories basically only works while you have an expanding empire.

Yes. Why is this surprising?

Growing empires attempt to explain their world, in order to better realize opportunities, since power resides with those who have a vested interest in opportunities being realized.
NB: This is not necessarily (or even typically) the same group of people as the ones who do the actual work of realizing the opportunities.

Stagnant empires invent excuses for looting.

An economic theory which "works," in the sense of providing actionable explanations for what drives economic activity, is actively contrary to the interests of those who guide the direction of a stagnant empire.

After that the rate of growth limited by productivity isn't a zero-sum game, but very close to being so?

I suppose that is a matter of taste. Personally, I find that one per cent per year compounding adds up to quite a nice positive sum over a few decades.

But relative to the expanding empire? Absolutely.

- Jake

Friends come and go. Enemies accumulate.