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The passage around this formula

Allen’s analysis of the same period gives the mechanism a name. Across 1760–1913 he finds a two-stage evolution of inequality in which, over the first half of the nineteenth century, “the real wage stagnated while output per worker expanded”, the profit rate roughly doubled, and profits’ share of national income rose at the expense of labour and land; only after mid-century did real wages resume growing in line with productivity, with factor shares stabilising [ 8 ] . The gap between output per worker and the real wage is an accounting identity once the labour share is admitted: $\Delta \ln w \;=\; \Delta \ln\!\left(\frac{Y}{L}\right) \;+\; \Delta \ln s_{L}$. where w is the real wage, Y/L output per worker, and $s_L$ labour’s share of value added.…

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