Yes, that’s essentially the stylised model I use – i.e. I understand the long-run history of GDP per capita growth at the frontier as a transition from stagnation (/a very low rate) into sustained growth at a roughly constant rate. And it is very stylised (and I allow that the take-off may have been quite gradual), but I still think it works quite well as a basic framework.
And I agree that Romer’s backwards projection implies that the rate of GDP per capita growth at the frontier has increased over time; but it doesn’t prove that this took the form of a constant acceleration across all of history, rather than a roughly discrete acceleration (described above).
I don’t yet think that the Maddison data supports the idea of accelerating frontier growth across millennia. I think we need better country and year coverage to establish that claim. Better country coverage because the country at the frontier changes over time. Even if we see constant acceleration in country X’s GDP per capita growth rate between (say) 1-1800AD, it is unlikely that it was consistently at the frontier. We need to splice together data from various countries to get a timeseries of frontier growth. And better year coverage to avoid us relying on data points which may just so happen to be at a low or high point in a fluctuating cycle. We might have a higher estimate of GDP per capita in country Y for AD1000 than AD1, but I’d need more convincing to interpret that as long-run growth rather than our data point for AD1000 incidentally being a good year (or at the high point of a cycle which may span generations) and/or our data point for AD1 incidentally being a bad year (/low point in a cycle).
FWIW, this Jones & Romer paper names “accelerating growth” as one of the key stylized facts that growth models should explain. See pp. 13–16.
One example of accelerating progress they give is from Nordhaus’s famous “price of light” paper:
Between 38,000 B.C. and 1750 B.C., the real price of light fell by a total of about 17%, based on the transition from animal or vegetable fat to sesame oil as a fuel. The use of candles and whale oil reduced the price by a further 87% by the early 1800s, an average annual rate of decline of 0.06% per year. Between 1800 and 1900, the price of light fell at an annual rate that was 38 times faster, 2.3%, with the introduction of the carbon filament lamp. And then in the 20th century, the price of light has fallen at the truly remarkable pace of 6.3% per year with the use of tungsten filaments and fluorescent lighting.
Yes, that’s essentially the stylised model I use – i.e. I understand the long-run history of GDP per capita growth at the frontier as a transition from stagnation (/a very low rate) into sustained growth at a roughly constant rate. And it is very stylised (and I allow that the take-off may have been quite gradual), but I still think it works quite well as a basic framework.
And I agree that Romer’s backwards projection implies that the rate of GDP per capita growth at the frontier has increased over time; but it doesn’t prove that this took the form of a constant acceleration across all of history, rather than a roughly discrete acceleration (described above).
I don’t yet think that the Maddison data supports the idea of accelerating frontier growth across millennia. I think we need better country and year coverage to establish that claim. Better country coverage because the country at the frontier changes over time. Even if we see constant acceleration in country X’s GDP per capita growth rate between (say) 1-1800AD, it is unlikely that it was consistently at the frontier. We need to splice together data from various countries to get a timeseries of frontier growth. And better year coverage to avoid us relying on data points which may just so happen to be at a low or high point in a fluctuating cycle. We might have a higher estimate of GDP per capita in country Y for AD1000 than AD1, but I’d need more convincing to interpret that as long-run growth rather than our data point for AD1000 incidentally being a good year (or at the high point of a cycle which may span generations) and/or our data point for AD1 incidentally being a bad year (/low point in a cycle).
FWIW, this Jones & Romer paper names “accelerating growth” as one of the key stylized facts that growth models should explain. See pp. 13–16.
One example of accelerating progress they give is from Nordhaus’s famous “price of light” paper: