I suppose a world without law at all would be one in which people habitually defect on the Prisoner’s Dilemma. Even when it’s the least ‘true’ a PD can be and still be a PD (so, iterated, with reputational incentives, all that stuff). There are no Schelling points, and thus no coördination: Nash equilibria and Moloch for all.
The “rule of law”, perhaps, is a list of particular properties of the law (collection of Schelling points): that they contain no proper nouns, for example (the same law binds the King), that they do not discriminate on irrelevant/prejudicial grounds, etc. That is to say, that the law is neither arbitrary nor capricious (I will hereonin refer to this synecdochically as: the law is just). Of course, a society’s beliefs about justice will be reflected in its informal law; thus a society will typically only see itself as lacking the rule of law inasmuch as its legislation, as enforced, is contrary to the principles of its informal law.
This is in contrast with your definition, under which (if I understand correctly) a society without the rule of law is one where enforcement doesn’t follow the written legislation. Of course, the patterns in this mismatch are themselves part of (my-model) law; so if everyone agrees that a piece of legislation (say, the Fugitive Slave Law) is unjust and the refusal to enforce it is just, then the society has (or believes it has) my-rule-of-law but does not have your-rule-of-law (unjust legislation is not enforced).
Conversely, if the legislation is enforced even though most people believe it’s unjust, then the society has your-rule-of-law but not (it believes) my-rule-of-law (unjust legislation is enforced).
If just legislation is enforced, then the society has both kinds of rule of law (since successful enforcement of legislation makes it law). If the legislation is just but selectively enforced in a way that is unjust, then the society has neither (because the selective enforcement creates law that is unjust).
Appeals to justice, and hence arguments based on my-rule-of-law, are subjective. But I would argue (had I not spent long enough on this response already) that justice itself is objective, even if we have not yet discovered all of its principles — and thus the same is true of my-rule-of-law.
I’m not quite sure how you’re defining “causal model” here, but the bit about “get paid to build a factory, which then produces goods, meanwhile you don’t consume the goods you were paid” seems causal to me. By not consuming the proceeds of your work, you have caused society to have more capital than otherwise. Heck, the paragraph beginning “But suppose…” is also describing a series of causes and effects, although it glosses over exactly how removing money from circulation drives up the value of money (that’s just basic microecon, though, I’m assuming you already understand that).
The rate of GDP growth isn’t really the right thing to use (GDP is the total value of all transactions in the economy, which is fundamentally a meaningless number and is certainly irrelevant here). Burying the money creates capital that grows at the rate of return on capital. Investing the money does the exact same thing. The only difference is to whom the interest is paid.
Actually, on re-reading your post, I see another sign of confusion where you talk about “real value” and claim that trades can’t create it. Value is a two-argument function; when you buy the stock, it’s because the stock (or rather, the future consumption-opportunity it represents) is worth more to you than the present consumption you could buy with it. Meanwhile, the seller values present consumption (or whatever else he buys with the money today, which may even be just the security of having larger reserves of liquid currency as opposed to holding less-liquid, potentially risky shares of stock) more than the future consumption the stock represents. Value has been created, not by creating ‘stuff’, but by moving existing stuff to higher-valued uses.
Similarly, when you defer consumption into the future, you are moving current stuff from consumption to capital uses (because at least some of the resources you are no longer consuming will end up as capital formation (though not all of it because the price of consumption goods will fall slightly relative to the price of capital goods, but it can only do so because the equilibrium quantities shift)), and simultaneously moving future stuff (some of which is created by the capital uses of the current stuff) to consumption uses. As long as the rate of return on capital × your value ratio of future to present consumption is greater than 1, the combined effect is an increase in value. If you invest the money saved, then you capture the value thereby created (you’re trading your future consumption against your current consumption); if you bury it, you don’t: you’re trading society’s future consumption against your current consumption, but if you’re a selfless utilitarian that’s irrelevant.