# The lost millennium

*Note: This post is speculative, and you should take the claims in it with a grain of salt.*

Throughout human history, we know that economic growth, for which population growth was a good proxy under Malthusian conditions, has accelerated many times. Indeed, we can see this just by extrapolating current growth rates backward: given that there are only so many people in the world and they are only at a finite multiple of subsistence income per person, it would not be possible for economic growth rates on the order of 3% per year to have lasted for more than a thousand years or so.

Though it's difficult to do so, people have also come up with estimates for exactly how this growth happened in the past. One such estimate is from [the HYDE dataset](https://www.pbl.nl/en/image/links/hyde), also available at [Our World In Data](https://ourworldindata.org/population-sources); and a whole collection of other estimates [can be found here](https://www.census.gov/data/tables/time-series/demo/international-programs/historical-est-worldpop.html). 

Let's examine the HYDE dataset first. The data before 1 AD is given per millennium, and looking at the growth rates gives us the table below:

| Millennium         | Mean annual population growth rate (percent) |
|--------------------|-----------------------------------------|
| 10000 BC - 9000 BC |                                 0.0236% |
| 9000 BC - 8000 BC  |                                 0.0254% |
| 8000 BC - 7000 BC  |                                 0.0279% |
| 7000 BC - 6000 BC  |                                 0.0320% |
| 6000 BC - 5000 BC  |                                 0.0368% |
| 5000 BC - 4000 BC  |                                 0.0411% |
| 4000 BC - 3000 BC  |                                 0.0435% |
| 3000 BC - 2000 BC  |                                 0.0489% |
| 2000 BC - 1000 BC  |                                 0.0415% |
| 1000 BC - 1 AD     |                                 0.0746% |

Aside from a slight reversal in the second millennium BC[^1], the estimates suggest a gradual acceleration in the growth rate of population. This would be consistent with e.g. a hyperbolic model for population growth, but here I don't want to make any such assumption and just look at the raw data.

What is surprising, then, is the next entry that should be in this table: in the first millennium, 1 AD - 1000 AD, population growth is estimated to have averaged a mere 0.033%/year. In other words, according to this dataset, even the fifth millennium BC had faster population growth than the first millennium!

Something like this result turns out to be robust to changing the dataset we're using. McEvedy and Jones report a mean growth rate of 0.044%/year for the first millennium, compared to 0.137%/year from 1000 BC to 200 BC and 0.062%/year from 200 BC to 1 AD. This more granular data in the first millennium BC, not available in the HYDE dataset, suggests that the slowdown in population growth likely started before the first millennium. To find a millennium with slower population growth in this dataset, we have to go back to the fourth millennium BC (5000 BC - 4000 BC).

All datasets I've looked at report substantial acceleration in population growth with the turn of the second millennium. The Mongol conquests and the Black Death appear to have weighed on population growth from 1200 to 1400, but despite that growth from 1000 to 1500 still averages 0.08%/year, which is faster than the first millennium BC. 

[The Lost Decade](https://en.wikipedia.org/wiki/Lost_Decades) was a name used in Japan to refer to the ten-year period of economic stagnation following the Japanese stock market crash of 1991. Following this convention, it might be appropriate to call the first millennium "the lost millennium". If we believe in some kind of stochastic hyperbolic growth model of economic history, a la [Roodman (2020)](https://www.openphilanthropy.org/research/modeling-the-human-trajectory/), this means that humanity got "very unlucky" in the first millennium, possibly due to persistent adverse social shocks.

This story is purely quantitative, looking at population growth, but it's worth keeping in mind that under Malthusian conditions we expect population growth to track technological progress and capital formation. The more productive we are, the more children people should have until the population increases sufficiently for the marginal product of labor to fall back to subsistence levels. A millennium is more than enough time for Malthusian dynamics to play out, so the lack of robust population growth over the first millennium also suggests a slowdown in productivity-increasing factors such as innovation and capital accumulation.

The important question then becomes: *why did this happen?*, or perhaps *how did this happen?* We have good explanations for other slowdowns in population growth, e.g. the Mongol conquests and the Black Death for the period 1200 to 1400. However, the slowdown in the first millennium looks like a complete mystery. I can come up with some explanations but none of them fit the data that well. Even if it was "bad luck", I'd like to be able to say more about it than that.

[^1]: Perhaps due to the [Late Bronze Age collapse](https://en.wikipedia.org/wiki/Late_Bronze_Age_collapse)?