The math of the logistic (S-Curve) model is simple. f(x) = 1 / (1 + e-x).
It's the sort of math that can emerge out of a lot of complexity. The CDF of a gaussian, for example, is a sigmoid a la style du logistique, but the gaussian arises as described by the central limit theorem, as the asymptotic distribution of a mean of (functionally) random processes. And that concept of randomness may conceal a chaotic process - arguably always does, given axiomatic physical determism. Or it might just be, for example, a lotka-volterra system in which the quasiperiodic factors are on incomensurate time scales, and hence not evident above the noise of observation.
Given that the system described (the living economy) is an agent system physically, I don't think you can have a satisfactory understanding of the domain of applicability of a simple model, unless you can show how it is caused by the agent interactions. When I say satisfactory, I mean a model such that you know when it must apply, and when it may or must fail to apply.
Make no mistake, I like the model. I think it is useful - until it is no longer useful; and, I think it is even
more useful to have a principled understanding of why and (hopefully, even) when it will cease to be useful. Meanwhile, it can serve as a pretext or stimulus to hypothesize theories which explain why the model is presently applicable, an important creative process, but one which should include in its scope hypotheses which imply evanescent application.
TL;DR: I just don't want anyone to be mislead into thinking that because a model is elegantly simple, and a good fit, that therefore it is reliable. It is often a precondition of, or indicator of reliability. It is rarely an assurance of reliability. When the model is the result of a sound theory, then reliability is indicated more strongly, and its conditions begin to be understood.
