Note: Actually looking at the graphs in Farmer & Lafond (2016), many of these do sure seem pretty S-curve shaped. As do many of the diagrams in Nagy et al. (2013). I would have to run some real regressions to look at it, but in particular the ones in Farmer & Lafond seem pretty compatible with the basic s-curve model.
Overlapping S-curves are also hard to measure because obviously there are feedback effects between different industries (see my self-similarity comment above). Many of the advances in those fields are driven by exogenous factors, like their inputs getting cheaper, with no substantial improvements in their internal methodologies. One of my models of technological progress (I obviously also share the model of straightforward exponential growth and assign it substantial probability) is that you have nested and overlapping S-curves, which makes it hard to just look at cost/unit output of any individual field.
For analyzing that hypothesis it seems more useful to hold inputs constant and then look at how cost/unit develops, in order to build a model of that isolated chunk of the system (and then obviously also look at the interaction between industries and systems to get a sense of how they interact). But that’s also much harder to do, given that our data is already really messy and noisy.
Thanks for poking at this, it would be quite interesting to me if the “constant exponential growth” story was wrong. Which graphs in Farmer & Lafond (2016) are you referring to? To me, the graph with a summary of all trends only seems to have very few that at first glance look a bit like s-curves. But I agree one would need to go beyond eyeballing to know for sure.
I agree with your other points. My best guess is that input prices and other exogenous factors aren’t that important for some of the trends, e.g. Moore’s Law or agricultural productivity. And I think some of the manufacturing trends in e.g. Arrow (1971) are in terms of output quantity per hour of work rather than prices, and so also seem less dependent on exogenous factors. But I’m more uncertain about this, and agree that in principle dependence on exogenous factors complicates the interpretation.
To me, the graph with a summary of all trends only seems to have very few that at first glance look a bit like s-curves. But I agree one would need to go beyond eyeballing to know for sure.
Yeah, that was the one I was looking at. From very rough eye-balling, it looks like a lot of them have slopes that level off, but obviously super hard to tell just from eye-balling. I might try to find the data and actually check.
Note: Actually looking at the graphs in Farmer & Lafond (2016), many of these do sure seem pretty S-curve shaped. As do many of the diagrams in Nagy et al. (2013). I would have to run some real regressions to look at it, but in particular the ones in Farmer & Lafond seem pretty compatible with the basic s-curve model.
Overlapping S-curves are also hard to measure because obviously there are feedback effects between different industries (see my self-similarity comment above). Many of the advances in those fields are driven by exogenous factors, like their inputs getting cheaper, with no substantial improvements in their internal methodologies. One of my models of technological progress (I obviously also share the model of straightforward exponential growth and assign it substantial probability) is that you have nested and overlapping S-curves, which makes it hard to just look at cost/unit output of any individual field.
For analyzing that hypothesis it seems more useful to hold inputs constant and then look at how cost/unit develops, in order to build a model of that isolated chunk of the system (and then obviously also look at the interaction between industries and systems to get a sense of how they interact). But that’s also much harder to do, given that our data is already really messy and noisy.
Thanks for poking at this, it would be quite interesting to me if the “constant exponential growth” story was wrong. Which graphs in Farmer & Lafond (2016) are you referring to? To me, the graph with a summary of all trends only seems to have very few that at first glance look a bit like s-curves. But I agree one would need to go beyond eyeballing to know for sure.
I agree with your other points. My best guess is that input prices and other exogenous factors aren’t that important for some of the trends, e.g. Moore’s Law or agricultural productivity. And I think some of the manufacturing trends in e.g. Arrow (1971) are in terms of output quantity per hour of work rather than prices, and so also seem less dependent on exogenous factors. But I’m more uncertain about this, and agree that in principle dependence on exogenous factors complicates the interpretation.
Yeah, that was the one I was looking at. From very rough eye-balling, it looks like a lot of them have slopes that level off, but obviously super hard to tell just from eye-balling. I might try to find the data and actually check.