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Does Economic History Point Toward a Singularity?

I agree with much of this. A few responses.

As I see it, there are a couple of different reasons to fit hyperbolic growth models — or, rather, models of form (dY/dt)/Y = aY^b + c — to historical growth data.

I think the distinction between testing a theory and testing a mathematical model makes sense, but the two are intertwined. A theory will tend naturally to to imply a mathematical model, but perhaps less so the other way around. So I would say Kremer is testing both a theory and and model—not confined to just one side of that di... (read more)

3Ben Garfinkel1yJust on this point: For the general Kremer model, where the idea production function is dA/dt = a(P^b)(A^c), higher levels of technology do support faster technological progress if c > 0. So you're right to note that, for Kremer's chosen parameter values, the higher level of technology in the present day is part of the story for why growth is faster today. Although it's not an essential part of the story: If c = 0, then the growth is still hyperbolic, with the growth rate being proportional to P^(2/3) during the Malthusian period. I suppose I'm also skeptical that at least institutional and cultural change are well-modeled as resulting from the accumulation of new ideas: beneath the randomness, the forces shaping them typically strike me as much more structural.
Does Economic History Point Toward a Singularity?

Thank you Ben for this thoughtful and provocative review. As you know I inserted a bunch of comments on the Google doc. I've skimmed the dialog between you and Paul but haven't absorbed all its details. I think I mostly agree with Paul. I'll distill a few thoughts here.

1. The value of outside views

In a previous comment, Ben wrote:

My general feeling towards the evolution of the economy over the past ten thousand years, reading historical analysis, is something like: “Oh wow, this seems really complex and heterogeneous. It’d be very surprising if we could mo

... (read more)
3Ben Garfinkel1yHi David, Thank you for this thoughtful response — and for all of your comments on the document! I agree with much of what you say here. (No need to respond to the below thoughts, since they somehow ended up quite a bit longer than I intended.) This is well put. I do agree with this point, and don’t want to downplay the value of taking outside view perspectives. As I see it, there are a couple of different reasons to fit hyperbolic growth models — or, rather, models of form (dY/dt)/Y = aY^b + c — to historical growth data. First, we might be trying to test a particular theory about the causes of the Industrial Revolution (Kremer’s “Two Heads” theory, which implies that pre-industrial growth ought to have followed a hyperbolic trajectory).[1] [#fn-vpS4ChwAKePtJ9zZf-1] Second, rather than directly probing questions about the causes of growth, we can use the fitted models to explore outside view predictions — by seeing what the fitted models imply when extrapolated forward. I read Kremer’s paper as mostly being about testing his growth theory, whereas I read the empirical section of your paper as mostly being about outside-view extrapolation. I’m interested in both, but probably more directly interested in probing Kremer’s growth theory. I think that different aims lead to different emphases. For example: For the purposes of testing Kremer’s theory, the pre-industrial (or perhaps even pre-1500) data is nearly all that matters. We know that the growth rate has increased in the past few hundred years, but that’s the thing various theories are trying to explain. What distinguishes Kremer’s theory from the other main theories — which typically suggest that the IR represented a kind of ‘phase transition’ — is that Kremer’s predicts an upward trend in the growth rate throughout the pre-modern era.[2] [#fn-vpS4ChwAKePtJ9zZf-2] So I think that’s the place to look. On the other hand, if the purpose of model fitting is trend extrapolation, then there’s no particular reas