Earlier this week, I made a throwaway comment about China’s one-child policy, saying that revoking one-child probably wouldn’t help redress China’s looming demographic crunch, and made some mention of building a model of China’s population.

So here we go.

The short answer: **I was wrong.** China’s birth rate is low, but the population isn’t particularly old – so they’re not facing a demographic crunch any time in the next thirty years, one-child-policy or no. After that point, though, unless birth rates increase in the meantime, they will have a problem. And no matter what happens to demographics, the population probably won’t grow much beyond 1.5 billion.

Here’s the Excel model – hit the link to download. It’s in Excel 2003 format, but doesn’t use any funny VBScript, so it should work OK with other versions and Excel for Mac.

After the jump – the model methodology, and the results! (**Warning: VERY NERDY.** Proceed at your own risk.)

The model projects three possible paths for population growth in China, and the changes in population distribution that would result from each of those three paths.

The assumption’s going to be that the one-child policy is removed in one shot in 2010, and China experiences a sudden gap higher in birth rate, which then trails off over the period to 2040 as economic development causes the country’s birth rate to fall.

The “DE Paradox Model” worksheet shows three possible paths for Chinese crude birth rates given GDP per capita. (I’m using crude birth rate here as a proxy for fertility, because it’s tricky to translate a total fertility rate into a year-by-year birth rate, but TFR shows a very similar relationship to GDP per capita.) They are:

- The “Fitted curve” case fits a power law curve to the set of world GDP/birth rate pairs (I’ve left out three outliers – Angola, Saudi Arabia, and Israel – all of which have significantly higher birth rates than their GDP would predict); it’s a “worldwide average” path for the Chinese birth rate to follow;
- The “High case” represents a very high birth rate for a given GDP. This would probably significantly overstate Chinese birth rates for GDP between $15,000 and $35,000, but it represents a pretty firm upper bound for growth;
- The “low case” represents a low birth rate for a given GDP. I’ve fitted it to exactly match China’s current birth rate, and it represents the birth rates we’d expect to see if the one-child policy remains in place – or if the one-child policy was removed but birth rates
*didn’t*increase. (Given that East Asian countries have the lowest fertility rates in the world, this is not entirely implausible.)

That gives us an upper and lower bound and a middle case for China’s birth rate given GDP per capita.

Now, to get the actual birth rates, we have to predict how fast China’s GDP is going to grow.

The “Birth rate trajectories” sheet uses a simple linear growth rate to project GDP growth thirty years into the future. Again, there’s three different scenarios, and each one uses a different curve to relate GDP growth to birth rates. Since faster GDP growth leads to slower population growth and vice versa, the fast-GDP-growth projection uses the “low case” birth rate curve – that establishes a firm lower bound on population growth. Conversely, the slow-GDP-growth projection uses the “high case” birth rate curve, to put an upper bound on population.

As a note, the “slow growth” projection assumes GDP growth of just 2% a year over the next thirty years. While China’s GDP growth rate has to slow from its current white-hot 10% (just because it’s starting from a higher base), a 2% growth rate over thirty years would imply multiple spectacular recessions in that period. I’m not exactly a bull on China, but I think that’s pretty unlikely. 4-5% seems more likely to me.

Then comes the magic…

The “Population projections” sheet takes China’s current population distribution, and for each five year timestep:

- Nudges the current population five years forward;
- Creates five years’ worth of new babies,
*at the birthrate projected by the previous two steps;* - Applies a fixed death rate to bump off some of the population.

(One problem with this approach is the “fixed death rate” assumption. Death rates aren’t fixed – they tend to decrease as GDP increases – so the net population growth and the number of old people in the high-GDP scenarios will be underestimated. I don’t think this effect is major, but it’s worth keeping in mind.)

The total population is in column V, the annualised growth rate in column W, and column AA has the crucially important “dependency ratios” – the ratio of non-working-age people to working age people (15-65). Lower ratios are better – they mean each working-age person supports fewer non-working-age people.

China’s current dependency ratio is somewhere below 40 – very low by global standards, because right now they’re at the peak of their demographic dividend years. The aging populations of Western Europe and Japan have dependency ratios in the mid-50s; the impoverished countries of sub-Saharan Africa have extremely young populations, mostly below working age, so they have even higher dependency ratios (above 90 in the worst cases, which means that each non-working person has just one working-age person to support them, compared to two or three workers per non-worker in the first world).

**The results…**

Under **the median scenario** – a world-average birth rate, and 4% p.a. GDP growth – China’s demographics are fine for the next thirty years. By 2040, there’s a large cohort of people aged 50-70 and about to retire, but there’s a similarly large cohort of people aged 10-30, born just after the hypothetical removal of the one-child policy and entering their prime working years.

The birthrate will be dropping, and the population growth will be slightly negative (maxing out around 1.5 billion), but dependency ratios aren’t out of line with the rest of the world.

(Meanwhile, Paul Ehrlich will still be tearing his hair out over “unchecked population growth”.)

Under **the high-growth scenario**, China will have a severe dependency ratio problem. Population growth will jump from its current level around 0.5% p.a. to 1.5% p.a, creating a large number of children (and possibly an infant mortality problem). The low GDP in this scenario also implies that living standards will be low relative to the rest of the world, so living conditions for all of these new children will be sub-par.

This scenario, though, is unlikely. It assumes an instant doubling of birth rates and a sudden, sharp drop in GDP growth – in fact, it’d need GDP growth to drop to 2-3% sometime in the next two years, and stay there for the next thirty.

The **low-population-growth scenario**, though, is much more likely to occur, and brings with it its own problems.

Under this scenario, China’s strong GDP growth will continue, and GDP per capita will reach 2010-USA standards by 2040 – but there will have been a steady, commensurate drop in birth rates. Population growth will have turned negative sometime around 2020, and total population will never have significantly exceeded the current level of 1.35 billion.

In the years until 2040, this won’t have been a problem, because the bulk of the Chinese population will have been of working age. But by 2040, the babies born before the one-child policy in 1980 will all be at least sixty – either retired or on the brink of retiring – and the declining birth rates will mean there’s been no second peak of population growth to create new workers. This is a similar situation to the one Japan finds itself in right now, and would have the same unhappy results (do click that link, it’s a sensational travelogue of dying rural Japan).

All that would have to happen for this situation to rear its head is for birthrates to continue their current trend, and for GDP growth to trend linearly down from 10% to 4% over the next thirty years. This is well within the realms of probability.

**So what does it all mean?**

China is not currently in danger of a population crunch. The population born before one-child was introduced in 1980 have plenty of working years ahead of them, and even under a lower-bound rate of population growth, it’ll take at least thirty years for China to face a problem.

But China needs to unwind the one-child policy within the next decade, and it needs to encourage birth-rates to return to global average levels. A median-growth scenario looks good for China; the babies born after one-child was removed would enter the workforce just as the pre-one-child population left it.

High growth would cause a “too many children” problem, and this was originally what the one-child policy aimed to avert. Unfortunately, it’s been too successful – and removing one-child probably would *not* lead to a recurrence. Chinese GDP is high enough and growing strongly enough that birth-rates will continue to fall under any scenario.

If John Garnaut’s article is right, the removal of one-child should be good news for China’s long-term growth prospects.