Japanese inflation is only a recent phenomenon. Prior to the pandemic, they were experiencing deflation and the BoJ was doing everything in its power to get some inflation. The falling birth rate, on the other hand, has been going on for far longer than monetary inflation.

Falling birth rates are often correlated with discretionary income levels and women's education.

> wonder when people will make the connection between monetary inflation and birth rates

It's been studied. The connections are as non-obvious as they are fascinating.

In the Pacific Islands, a "1% increase in CPI (inflation) will decrease total fertility rate by 0.41%" [1]. (This effect was much stronger than female education and real GDP changes.) This supports your hypothesis.

When we look at rich countries, however, we find that "an increase in annual inflation of 1 percentage point would bring an increase of 0.06 percentage point in the annual growth of the total population" [2]. Inflation increases fertility!

A clue as to why might be found in the U.K., where among "home owners" they found "evidence of positive but temporary effects of house prices on fertility," with "a 10% increase in the average house price in a given month increases the fertility of home owners by 2.4% in the following year" [3]. Among renters, on the other hand, "fertility rates are lower by the order of 2 to 4%. Fertility rates for this group remain lower three years later, suggesting house price increases affect completed fertility as well as the timing of births."

[1] https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8457485/ Table 8

[2] https://www.sciencedirect.com/science/article/abs/pii/S10590...

[3] https://www.bristol.ac.uk/cmm/research/housing/publications/...