Arthur is making some important points. If the decline in working people does not look nearly as scary as it does with simple age ratios, that would be reassuring.
It is of course a matter of opinion if a declining population and slower growth are a problem or not. But younger people acting rationally should try to minimize their contribution to pay-as-you-go pension systems because they will hardly see benefits commensurate with their contributions. That in turn undermines the system itself.

The two studies, however, tell us nothing about the effect of family-friendly policies on fertility.

The Nature study does not disaggregate HDI into its components. What's more, it explicitly states that its findings don't apply to Japan (p. 4): "While there are clear exceptions, as for instance Japan, the trajectories for the large majority of countries (18 out of 24, representing 74% of the population in the 24 countries included in Figure 2) are in accordance with our hypothesis: as development has continued and countries have attained an advanced HDI level of 0.9 or higher, the trend in the total fertility rate has reversed."

The Feyrer, Sacerdote, and Stern study uses cross-sectional data to investigate the effect of something that changes over time (supportive policies).
This means that all the variation observed comes from differences between countries, and is largely due to slow-changing institutional, social and cultural factors. This approach and their data simply do not allow an estimation of the relative contribution of policies vs other factors. Also, supportive policies and greater share of household work done by men are extremely highly correlated (p. 16): "Societies that are more effective at sharing the burden of children across the genders also tend to be more generous in supporting children in the public sphere." On top of that their sample size is (wait for it) 18 observations. I'm mildly amused that this got published at all.

To see how policies affect fertility, we need at time-series, or even better panel data, so that we can compare countries before and after a policy was introduced, controlling for cohort size and other things.

There aren't many studies like that, but one that demonstrates the considerable effect of "subsidizing the Stork" is this: Milligan, Kevin. 2005. "Subsidizing the Stork: New Evidence on Tax Incentives and Fertility." The Review of Economics and Statistics
87(3): 539-555. http://www.jstor.org/stable/40042947

So why doesn't Japan implement such policies? Aside from the general issue of gender relations in Japan, we may be beyond the point where such policies are politically implementable.

For a study that attempts a political economy explanation of why Japan does so little to support families with children, see Aoki, R., and R.
Vaithianathan. 2010. "Political Economy of Low Fertility and Changing Population Age Structure-Case of Japan."
(http://www.ier.hit-u.ac.jp/~aokirei/documents/aoki_vai
thianthan110302.pdf)

Now you might question that people are so selfish that they effectively undermine the likelihood of them being grandparents, but there is plenty of evidence in other domains as well. For example, disbelief in climate change is highly correlated with age.

Lastly, on today's 50-year old being as healthy as yesterday's 70-year olds. That may be true, but labour productivity estimates show that individuals reach their productivity peak between 30 and 50 years. By 57+ years a worker is no more productive than a 25-year old, and the decline continues. This means that the retirement age cannot be pushed indefinitely higher in terms of years. Still, moving the actual retirement age to 68 or even 70 would likely solve the fiscal problem in developed countries relying on pay-as-you-go pensions, because the effect of every year delay is enormous.

Best,

Mark

Dr Mark S MANGER
Lecturer in International Political Economy International Relations Department London School of Economics