Understanding productivity growth in † the industrial revolution ∗ By NICHOLAS CRAFTS Economic History Review, 2021 Recent research relating to productivity growth during the British industrial revolution is reviewed. This confirms that there was a gradual acceleration rather than a ‘take-off’. The explanation for the speeding-up of technological progress remains controversial but the evidence base has improved considerably. In the face of a surge in population growth, slow growth of real wages during the industrial revolution may be seen as a good outcome which was underpinned by improved growth potential. Slow total factor productivity growth from the 1870s suggests that British technological capabilities at the end of the industrial revolution were still quite limited. he British industrial revolution was a landmark event in world economic T history. While it was once seen as a period of dramatic ‘take-off’, it is now generally accepted that it was an episode of gradual acceleration in labour productivity growth which eventually led to sustained increases in living standards. Even so, the unprecedented transition to modern economic growth which it entailed rightly continues to attract massive amounts of research effort, and the literature has evolved rapidly in recent years. Despite a considerable increase in the sophistication of analysis, important (and exciting) questions remain controversial. These include ‘why did productivity growth accelerate?’, ‘how soon did workers benefit from faster productivity growth?’, and ‘why did productivity growth experience a major slowdown as soon as the 1870s?’ Much progress has, however, been made and now is an opportune moment to take stock. This article will do so from a macro-economic vantage point informed by ideas from growth economics as well as economic history. Given the volume of research that has been produced, this will necessarily be a somewhat selective survey, which treats a few aspects in depth rather covering a wide terrain superficially. The article begins by setting out estimates of productivity growth derived from recent research and exploring them in a growth accounting framework. Given that the estimates of total factor productivity (TFP) growth in this period are underwhelming, it then proceeds by explaining why this is a plausible finding even though there were many famous inventions. It also explores the revised picture of sectoral growth rates that has emerged from recent research. It then reviews competing explanations for the move to faster productivity growth during the industrial revolution and the evidence for them. It also looks at the relationship ∗Author’s Affiliation: University of Sussex and University of Warwick. † I have received helpful advice and comments from Steve Broadberry, Morgan Kelly, Tim Leunig, Cormac Ó Gráda, John Styles, and John Turner. An anonymous referee made useful suggestions. The usual disclaimer applies. © Economic History Society 2021. Published by John Wiley & Sons Ltd, 9600 Garsington Road, Oxford OX4 2DQ, UK and 350 Main Street, Malden, MA 02148, USA. 2 NICHOLAS CRAFTS between productivity growth and real wage growth to develop some new insights into the standard of living debate. Finally, it considers why productivity growth soon declined from the rate achieved in the mid-nineteenth century at the end of the industrial revolution. The article’s main conclusions are as follows. First, improved estimates of labour quality and hours worked reinforce the conclusions of the revisionist literature of the 1980s that TFP growth during the industrial revolution was modest at least until the second quarter of the nineteenth century. Second, viewing labour productivity in terms of real GDP per hour worked highlights that there was a marked slowdown in productivity growth from the 1870s. This suggests that viewing the ‘climacteric’ as a post-1899 blip is seriously mistaken. Third, there has been much research on the hypotheses that improved productivity growth at the time of the industrial revolution was due to a ‘high-wage’ or an ‘enlightened’ economy. Neither is a fully persuasive hypothesis but viewing the industrial revolution through the lens of induced innovation in an economy with a responsive supply-side is attractive. Fourth, the pessimistic view of the impact of the industrial revolution on living standards fashionable in the last 20 years has gone too far. Slow real wage growth was a good outcome in the face of huge demographic pressure. I. Growth accounting estimates Growth accounting is a useful way to describe the proximate sources of economic growth.1 These are the growth of factor inputs (capital, labour, and land) weighted according to their importance in production and a residual contribution from TFP growth. The latter is often thought to represent the contribution of technological change but in practice will also reflect changes in efficiency and scale economies. If the industrial revolution is conceived as a great leap forward in technology with an economy-wide impact, then it might be expected that TFP growth would be very rapid, perhaps on a par with the rate achieved by the US around the mid-twentieth century.2 This would perhaps be the prior of T. S. Ashton’s famous (notorious?) schoolboy.3 The conventional growth accounting formula is: Y/Y = sKK/K + sLL/L + sNN/N + A/A (1) where Y is real GDP, K is capital, L is labour, N is land, and A/A is the rate of TFP growth which is obtained as a residual that balances the equation, while sK, sL,andsN are the factor shares of capital, labour, and land, respectively. This is the so-called ‘primal formula’ for the sources of growth but an equivalent so-called ‘dual formula’ can be derived as follows. The national income identity is: Y = πK + wL + rN (2) 1 For a detailed discussion of various refinements to and limitations of this technique as used in economic history, see Crafts and Woltjer, ‘Growth accounting’. 2 According to the estimates in Bakker, Crafts, and Woltjer, ‘Sources of growth’, tab. 3, American TFP growth peaked at 2.2% per year in 1960–73. 3 According to Ashton, Industrial revolution, p. 48, this schoolboy said that ‘a wave of gadgets swept over England’. © Economic History Society 2021 Economic History Review, 0, 0 (2021) UNDERSTANDING PRODUCTIVITY GROWTH 3 Tab l e 1 . Accounting for growth of real GDP: earlier estimates (% per year) Capital Labour Land TFP Real GDP contribution contribution contribution growth growth Feinstein 1760–1800 0.35×1.0 = 0.35 0.50×0.8 = 0.40 0.15×0.2 = 0.03 0.32 1.1 1800–30 0.35×1.4 = 0.49 0.50×1.4 = 0.70 0.15×0.4 = 0.06 1.45 2.7 1830–60 0.35×2.0 = 0.70 0.50×1.4 = 0.70 0.15×0.6 = 0.09 1.01 2.5 Crafts 1760–1800 0.35×1.0 = 0.35 0.50×0.8 = 0.40 0.15×0.2 = 0.03 0.22 1.0 1800–30 0.35×1.7 = 0.60 0.50×1.4 = 0.70 0.15×0.4 = 0.06 0.54 1.9 1830–60 0.35×2.5 = 0.88 0.50×1.4 = 0.70 0.15×0.6 = 0.09 0.83 2.5 Note: This table is constructed using the formula in equation 1. Sources: Feinstein, ‘Capital accumulation’, adjusted to 3-factor formula using land growth as in Crafts, British economic growth; Crafts, British economic growth with revisions based on Crafts and Harley, ‘Output growth’. where K is capital, π is the rate of profit, L is labour, w is the wage rate, N is land, and r is the land rental rate. So, taking logarithms and differentiating with respect to time: Y/Y = sK(π/π + K/K) + sL(w/w + L/L) + sN(r/r + N/N)(3) Rearranging equation 3 gives: Y/Y − sKK/K − sLL/L − sNN/N = sKπ/π + sLw/w + sNr/r (4) The left-hand side of equation 4 is the primal formula for TFP growth which is the rate of output growth minus the rate of growth of total factor inputs, while the right-hand side is the dual formula for TFP growth which is the sum of the factor-share-weighted factor rewards. Feinstein was an early exponent of growth accounting based on the primal formula in the context of the British industrial revolution. An adapted version of his estimates is reported in table 1.4 Also reported in that table are estimates based on the Crafts–Harley view of the industrial revolution. The main difference between them is that the latter found much lower growth of TFP in the 1800 to 1830 period compared with Feinstein. In turn, that mainly reflected a lower estimate of growth of real GDP based on a major revision of the earlier estimates made by Deane and Cole which Feinstein had used.5 Recently, the Crafts–Harley estimates of real GDP growth have been superseded by those of Broadberry et al., built up from the output side.6 Their work entails construction of new indices of real output for the agricultural, industrial, and services sectors which extend the coverage and improve the weighting of earlier estimates. Sectoral value-added weights are then used to obtain annual estimates of real GDP which had not previously been available. Broadberry et al. confirm that the earlier study by Deane and Cole, which deflated estimates of nominal income for benchmark years by an inappropriate price index, significantly overestimated 4 Feinstein, ‘Capital accumulation’. The dual formula was first employed by Antràs and Voth, ‘Factor prices’. 5 Deane and Cole, British economic growth. 6 Broadberry, Campbell, Klein, Overton, and van Leeuwen, British economic growth. © Economic History Society 2021 Economic History Review, 0, 0 (2021) 4 NICHOLAS CRAFTS Tab l e 2 .