If the escape from the Malthusian trap was the sharpest change in human history, the first thing to ask is how fast it actually went, and the honest answer disappoints almost everyone who asks it.
The previous lesson left English population growing at rates no earlier century had reached while wages failed to collapse. That is the thing to be explained. Explaining it requires knowing its shape: when growth began, how quickly it accelerated, and where in the economy it was happening. Those questions have been answered twice, with different numbers, and the second answer is the one now used.
Two sets of national accounts
Britain has no official national accounts before 1948. Everything said about growth in 1780 is a reconstruction, assembled from tax records, port books, output series for individual trades and guesses about everything else, and the quality of the answer depends entirely on how those pieces are weighted.
The first serious attempt was Phyllis Deane and William Cole's British Economic Growth 1688 to 1959, published in 1962 and the standard for a generation. Their picture matched the textbook story: industrial output accelerating hard from about 1780, growing above 3 per cent a year, with national income following it upward. A reader of Deane and Cole would conclude that Britain took off somewhere around 1780 and that the takeoff was visible in the aggregate figures.
Nicholas Crafts and Knick Harley rebuilt the estimates in the 1980s and published the joint revision in 1992, and the picture changed. Industrial output growth in the late eighteenth century came down to roughly 2 per cent a year. Growth of output per head came down further. The revised series has British output per head rising at about 0.2 per cent a year between 1760 and 1801, about 0.5 per cent between 1801 and 1831, and about 1.3 per cent between 1831 and 1873.
Look at what those rates do over the periods they cover. Compounded across the forty-one years to 1801 the first gives a total rise of 8.5 per cent, which is less than the fluctuation between a good harvest and a bad one. The second gives 16 per cent over thirty years. Only the third, running from the 1830s, produces the 72 per cent rise that a lifetime would notice. On these numbers the classic period of the Industrial Revolution, 1760 to 1830, is not a period of rapid growth in living standards at all.
Why the first estimate was too high
The revision was not a matter of finding new documents. It was a matter of weights, and the mechanism is worth understanding because it recurs whenever anyone builds an index of a changing economy.
Deane and Cole had good output series for exactly the industries that were transforming: cotton, iron, coal. They had almost nothing for building, food processing, leather, clothing, retailing, domestic service and the hundreds of small urban trades that together employed far more people. Where a series was missing they filled the gap by assuming the missing sector moved with something they could measure, and the things they could measure were the fast ones. The result was an index that gave the exciting industries more weight than their share of the economy justified.
Crafts and Harley's correction was to weight each sector by its actual contribution to value added, using the 1841 census of occupations and contemporary estimates of output per worker to pin the shares down. The fast sectors did not slow down under the new treatment. They simply stopped standing for the whole.
Example. Suppose an economy is 10 per cent modern industry growing at 6 per cent a year and 90 per cent everything else growing at 0.5 per cent. What is aggregate growth in the first year, and what is it on average over thirty years?
In the first year the aggregate rate is the share-weighted average, per cent. The modern sector is growing twelve times as fast as the rest and moves the total by half a percentage point, because nine tenths of the economy is not doing what it is doing. Over thirty years the arithmetic changes, though, and in the direction that matters. Starting from 10 and 90 units, the modern sector reaches and the rest reaches . Total output has gone from 100 to 161.9, an average of 1.62 per cent a year, and the modern sector is now 35 per cent of the economy rather than 10. Slow aggregate growth and violent sectoral change are perfectly consistent, and the aggregate accelerates on its own as the fast sector's weight rises, with no change in any underlying growth rate.
Now you. Run the same economy on for another thirty years at the same two sectoral rates. What is the modern sector's share then, and what is aggregate growth over that second period?
Answer
The modern sector reaches and the rest reaches , so total output goes from 161.9 to 451.0. That is an average of 3.47 per cent a year, and the modern sector is now 73 per cent of the economy. Nothing has been added to the model: the same two constant sectoral rates produce 1.05 per cent growth at the start, 1.62 per cent across the first generation and 3.47 per cent across the second, purely through the shift in weights. This is the single most useful thing to carry out of the lesson, because it dissolves the apparent conflict between historians who say the change was gradual and those who say it was explosive. Both are describing the same arithmetic from different ends.
The economy underneath
What the revised accounts describe, then, is a dual economy, and the duality is the finding rather than an inconvenience.
On one side sit three or four industries growing at rates no economy had sustained before. Raw cotton consumption in Britain rose from about 6.8 million pounds in 1780 to about 56 million in 1800, which is 11.1 per cent a year for twenty years. Pig iron output went from about 68,000 tons in 1788 to about 244,000 in 1806, 7.4 per cent a year. Coal output roughly tripled across the eighteenth century.
On the other side sits the great majority of British work, doing more or less what it had always done. In the 1851 census, the largest single occupation for women in Britain was domestic service, with over a million of them; agriculture was still the largest employer of men; and the numbers in the celebrated cotton factories were around half a million across the whole United Kingdom. A visitor to Manchester in 1835 was looking at the future, but a visitor to almost anywhere else in Britain was not.
This is why the period will not resolve into a single adjective. The rate of aggregate growth was modest by any modern standard. The rate of change inside particular industries was without precedent. And the structural shift, the movement of workers out of one kind of activity into another, was enormous and permanent.
What the occupations say
The best evidence for that structural shift is not output at all. It is what people did for a living, which the Cambridge Group's reconstruction of English occupational structure has now traced back well before the census.
The startling number is the starting one. By around 1710, only about 35 per cent of the English male labour force worked in agriculture. That is already an extraordinarily low figure for a pre-industrial society, far below France or anywhere in eastern Europe, and it means England had begun shedding farm labour long before any machine was involved. By 1817 the share was near 29 per cent, and by 1851 it was under a quarter.
The other landmark is urban. In the 1851 census, slightly more than half the population of England and Wales lived in towns, which made Britain the first society in history where the majority of people did not live in the countryside. Nothing in the growth rates prepares you for that. It is a change of kind rather than of degree, and it happened while output per head was growing at rates a modern economy would consider a recession.
Example. Deane and Cole put late eighteenth century industrial growth above 3 per cent a year; Crafts and Harley put it near 2 per cent. Neither found new records for the missing trades. What kind of evidence decided between them?
Evidence about shares rather than about rates. The disagreement was never over how fast cotton grew, which both sides took from the same import figures, but over how much of the economy behaved like cotton. Crafts and Harley pinned the shares down with the occupational census, since the number of people working in a trade is a usable proxy for its contribution when direct output data are missing, and that is a source Deane and Cole had underused. The general lesson applies well beyond this argument: when a composite index is disputed, look first at the weights, because a weighting assumption is usually doing more work than any individual series and is far less visible. It is also the reason the revision has itself been revised repeatedly since 1992, always by a percentage point or two, never back to Deane and Cole.
Now you. Someone objects that if aggregate growth was really only 0.2 per cent a year to 1801, the Industrial Revolution is a myth. What is wrong with the inference?
Answer
It confuses the growth rate with the transformation. Three things happened in that period which no growth rate captures: a set of industries changed their production methods by factors of hundreds rather than percentages, the composition of the labour force shifted permanently out of agriculture, and, most importantly, growth stopped stopping. Every previous economy had produced episodes of growth and then given them back, which is exactly what the previous lesson's four flat centuries consist of. What is new after 1780 is not the height of the rate but the fact that it never returns to zero, and a rate of 1.3 per cent that persists multiplies output per head by 6.9 in a century and a half. The myth would be a sudden leap in living standards, and there was not one. The revolution is the change in the machinery of the economy, and it is real.
Where the growth came from
One more piece of accounting sharpens the question the rest of the course has to answer. Growth can come from more workers, more capital per worker, or better use of both, which economists call total factor productivity, and Crafts's decomposition assigns it.
For 1760 to 1830 the striking result is how little total factor productivity contributed: something like 0.1 to 0.2 per cent a year, most of it traceable to a handful of industries. Capital accumulation did not carry the period either, because Britain's investment rate rose only modestly, from perhaps 6 per cent of national income in the mid eighteenth century to around 12 per cent by the 1830s. Britain did not industrialise by saving furiously. It industrialised by changing how a few things were made, and by having many more people to make them.
That last clause matters. Much of the raw output growth in this period came simply from a population rising at 1 per cent a year and more, which is why output per head grew so much more slowly than output. Britain got bigger before it got richer.
Example. England's population was about 6.15 million in 1761 and about 8.66 million in 1801, on Wrigley and Schofield's reconstruction. With output per head growing at 0.2 per cent a year, how fast did total output grow, and how much of that growth was simply more people?
Population growth is per cent a year. Total output is population multiplied by output per head, so its growth rate is the sum of the two, per cent a year. Of that, 0.86 points out of 1.06, or 81 per cent, is extra people rather than extra product per person. This is the arithmetic behind almost every disagreement about how impressive the period was. Someone quoting aggregate output is quoting a figure that is four fifths demography; someone quoting output per head is quoting the fifth that is left. Both are correct and they describe different things, which is why the honest practice is to say which one you mean every time.
Now you. Across those same forty years population rose 41 per cent and output per head rose 8.5 per cent. In the model of the previous lesson, what should have happened instead, and what does its failure to happen tell you?
Answer
In the Malthusian model land is fixed, so each additional worker adds less than the one before, and a 41 per cent rise in numbers drives output per head and therefore the real wage down. That is what four previous centuries of English data show. Between 1761 and 1801 it did not happen: output per head crept upward while population grew faster than in any earlier period on record. So the escape shows up first as an absence, the penalty for population growth simply not being collected, rather than as any dramatic gain. And notice how small the gain is. Eight and a half per cent over forty years is not prosperity, it is the difference between a good year and a bad one. This is the strongest reason not to date the arrival of industrial living standards to 1800: what had changed by then was the constraint, not the standard of living, and the two come apart by roughly two generations.
So what needs explaining
The question has now been narrowed twice. It is not, why did Britain grow fast, because it did not grow fast for the first seventy years. It is: why did a handful of British industries change their methods so radically, and why did the resulting growth, unlike every earlier episode, never stop?
Both halves have to be answered in the right order. Before any account of machines can start, though, a prior condition has to be met, and the occupational figures have already flagged it. An economy where two thirds of men are not farming is an economy where somebody else is producing their food. England was that economy by 1710, before the first cotton mill existed, and how it managed that is the next lesson.