To think that two and two are four / And neither five nor three / The heart of man has long been sore / And long ‘tis like to be. A.E. Housman.

In 1810, 81 per cent of the US labour force worked in agriculture, 3 per cent worked in manufacturing and 16 per cent worked in services. By 1950, the share of agriculture had fallen to 12 per cent, the share of manufacturing had peaked, at 24 per cent, and the share of services had reached 64 per cent. By 2020, the employment shares of these three sectors reached under 2 per cent, 8 per cent and 91 per cent, respectively. The evolution of these shares describes the employment pattern of modern economic growth. It is broadly what happens as countries become richer, whether they are big or small or run trade surpluses or deficits. It is an iron economic law.

What drives this evolution? In Behind the Curve — Can Manufacturing Still Provide Inclusive Growth?, Robert Lawrence of Harvard’s Kennedy School and the Peterson Institute for International Economics (PIIE) explains it in terms of a few numbers — the initial shares of employment in each of the three sectors, “income elasticities of demand” for their products, their “elasticities of substitution” and relative rates of growth of productivity. Income elasticities measure the proportional increase in demand for a category of goods or services relative to income. Elasticities of substitution measure the impact of changes in price on demand. A crucial consequence of the simple model that emerges is “spillovers”: what happens to a sector also depends hugely on what happens in the other sectors.