New Delhi, Nov. 3 -- The dominant demographic story about India is that it is a country of young people. Statistically, that is true: India's median age is estimated to be 29.2 years. It has close to a billion people of working age (15 to 64 years). But that is set to change. There are slow, yet significant, shifts in population structure that will lead to a demographic transition in the coming years.

To understand why, visualize the country in terms of three age slabs: children (0 to 14 years), working-age population (15 to 59 years) and older adults (60 years and above). The number of babies in India born peaked sometime in the early-2000s; by 2011, the share of children in the population had started declining. The share of working-age...