Labour input growth is the most forecastable term in the whole decomposition, because the people who will be working in 2040 are already born. It is also the term that has changed sign for most of the rich world and will change sign for India within the lifetime of a terminal value.
How is the dependency ratio calculated?
The instrument is the dependency ratio: the population aged under 15 plus the population aged 65 and over, divided by the population aged 15 to 64, conventionally expressed per 100 of working age. A demographic dividend is the period during which that ratio falls, because the share of the population in work rises and output per head rises even with output per worker flat.
Take three stated profiles (United Nations population projections, 2024 revision; check before quoting):
| Economy and year | Youth | Old age | Total dependency | Working-age share |
|---|---|---|---|---|
| India 2024 | 36.5 | 10.5 | 47.0 | 0.680272 |
| India 2035 | 30.0 | 14.0 | 44.0 | 0.694444 |
| India 2050 | 25.0 | 25.0 | 50.0 | 0.666667 |
| United States 2024 | 27.5 | 28.5 | 56.0 | 0.641026 |
| Japan 2024 | 17.5 | 54.5 | 72.0 | 0.581395 |
India's working-age share rises 2.083% between 2024 and 2035, which is 0.188% a year of free GDP per head. It then falls 4.000% between 2035 and 2050, which is minus 0.272% a year. The swing between the two legs is 0.459 points a year of growth in output per head, arriving without any change in productivity, policy or investment.
The dividend is a window rather than a permanent feature, and its closing date is already in the projections.
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What does a shrinking labour force do to growth?
The other side of the same arithmetic is what a shrinking labour force does. Take an economy with labour input falling 0.6% a year, capital growing 1.5%, a residual of 1.0% and α = 0.35. The labour contribution is minus 0.390 points, the capital contribution plus 0.525, and aggregate output grows 1.135%. If the population is falling 0.4% a year, output per head grows 1.535%.
The two numbers differ by the whole population growth rate, and reading the first as the economy's performance while citing the second as its living standards is how one country gets described as stagnant and as comfortable in the same week. Both descriptions are arithmetically correct.
For a valuation, aggregate growth is what caps a company's revenue growth and per-head growth is what drives its pricing and mix. Use the one the cash flow actually depends on.