Manifest 35
For most of human history, better technology bought more people rather than richer ones. Then sixty million Europeans left for the Americas — and what pushed them out, this paper argues, was being born into a family with one child too many. These were Malthusian migrations, and by draining the surplus they may account for more than half of Europe’s rise in income per head in the nineteenth century. Malthus was asked whether emigration could do this. He said no.
Manifest 35
In 1798 an English clergyman explained why nobody was getting richer. Output grows slowly; people grow fast; so any gain in production is eventually divided among the extra mouths it feeds. Thomas Malthus was describing the world he lived in, and about that world he was right. For most of recorded history, technological progress translated into larger populations rather than better lives.
What he was wrong about was the exit.
The mechanism is not a metaphor. In an economy where most income comes out of the ground, land is fixed, so more workers means less land each and thinner output per person. And fertility rose with income: a good decade meant more children who lived to have children of their own. Prosperity was self-cancelling. That is the whole trap, and it held for as long as we have records.
Europe in 1800, as the model sees it: income per head of $2,006, a population of 141 million, and about one person in twenty leaving in each generation. Nothing is moving because nothing can.
Now give it the Industrial Revolution: productivity rises by 48%, which is roughly what Europe managed between 1800 and 1880. Income per head jumps immediately, to about $2,340.
And then the children arrive. Richer parents have more of them, and more of them survive. Population climbs from 142 million toward 208 million over the following six generations.
Which puts income back where it started. Eighty years of technological progress leaves income per head at $2,007 — seven dollars above 1800. Technology won the race; population collected the prize.
“The germs of existence contained in this spot of earth, with ample food, and ample room to expand in, would fill millions of worlds in the course of a few thousand years.” Thomas Malthus, An Essay on the Principle of Population (1798)
1507
There is, in principle, a door in the side of this machine. If some of the extra children leave, the land is divided among fewer people and the gain in living standards need not be handed back. In the 1820s this was live policy: Robert Wilmot-Horton, an under-secretary at the Colonial Office and a friend of Malthus, was campaigning for the state to pay poor families to emigrate to Canada.
He wrote to Malthus about it. Malthus refused. Wages, he replied, may be used “either so as to increase the comforts and improve the permanent condition of the labouring classes, or, to accelerate the rate of their increases; but as it is an acknowledged fact that with very few exceptions, population rapidly recovers itself, after any great loss which it has sustained, it must be allowed that experience shows the latter of the two results to be more probable than the former.” Empty a country and it fills back up. Emigration, he had already written, would prove “but a slight palliative.”
Hold on to that phrase. The rest of this page is a number attached to it.
Between 1850 and 1920 nearly sixty million Europeans crossed to the Americas. Counted in the 1920 United States census, the British Isles had sent 2.2 million, eastern Europe 2.1 million, central Europe 1.9 million, southern Europe 1.8 million, Scandinavia 1.3 million. France sent 150,000.
France was not short of people. In 1700 roughly one European in five was French. In 1750 it had 24.5 million inhabitants against England and Wales’ 5.5 million. It held the St Lawrence and the Mississippi, and it had the ports and the navy to move anyone it wanted to move. What it did not have was surplus children: French fertility began falling around 1763, a full century before anyone else’s.
Nouvelle France
So France is the control group, sitting inside the same century as everyone else with the same ocean in front of it and one variable turned off. Keep the flat line in mind. We come back at the end to what it cost.
If crowding pushes people out, the obvious question is why they waited three hundred years. The land was there, the labour shortage was there, and the pressure at home was there the whole time. What was missing was a way of getting across that an ordinary family could plan around.
What changed was the fare. The first transatlantic steam crossing was made in 1838, and steam quickly became the way people travelled. Under sail the westbound crossing had averaged five weeks, and might take three or might take twelve; by 1840 steam did it in a fortnight, and by 1900 in nine days. The American border stayed open until the quota acts of 1921. The paper models this as a single parameter — the ease of migration — and it is the only thing in the model that lets living standards rise for good.
Every voyage a logbook survives for, one dot each. The westbound crossing — into the prevailing wind, which is the direction that matters here — took anything from twelve days to eighty-eight. A hundred years of seamanship does not visibly improve it.
Now the steamships, one dot per vessel. They enter below the entire sailing cloud and keep descending. Brunel’s Great Western opened the run in 1838.
Look at the width of each cloud, not just its height. Steam was three times faster than sail; it was nearly ten times more predictable. That is what a household needs before it will put a son on a boat.
Steerage
An extra sibling barely moves the odds. Across cohorts born from 1750 to 1824 the effect averages 1.1 — statistically alive, economically nothing. In a world where the crossing costs more than a family owns, it does not matter how many children are competing for the farm.
For cohorts born after 1825 the same extra sibling is worth 6.8 — six times as much — and the effect keeps climbing to a peak of 10.2 for those born in the 1880s. Nothing about European families changed at 1825. Their children came of age with a steamship in front of them.
Which is a good moment to say that pressure was not the only thing loading those ships. In the Scottish Highlands, landlords cleared tenants off the land to make room for sheep, and the people evicted did not choose the quay.
1865This is Thomas Faed’s The Last of the Clan, painted in 1865. The ship has gone and the painter has kept the people it could not take: the old, the women, the children, left on the stones. It is the most famous image of the Highland Clearances, and it is not a picture of anybody’s decision.
The two forces are worth holding apart, and they point the same way. Eviction and a surplus of children both end at the same quay, and both leave the land behind divided among fewer people. The paper is about the second because the second can be measured across a continent — but the Clearances are the reminder that the pressure this page describes as arithmetic was, for a great many households, someone else’s decision about them.
One more test, and it is the one that convinces me. If crowding is what pushed people out, it should push them toward land and not merely away from home. And that is exactly what it does. Take the same extra sibling and ask whether it made a person more likely to die somewhere else in Europe: the answer is no — −0.6 by ordinary least squares, and indistinguishable from zero however it is instrumented. A brother too many did not send you to the next province, because the next province was just as crowded. It sent you across an ocean.
Everything so far is aggregates, and aggregates can agree by accident. So the paper goes down to people: ten million profiles from crowdsourced genealogies, linked parent to child, for everyone born in Europe between 1750 and 1900 whose siblings are all recorded. For each of them you know how many brothers and sisters they had, and where they died.
The relationship is close to a straight line in the logarithm of family size, and it does not flatten out: it is steepest past the third child. Between a household with one child and a household with sixteen, the chance that a given child dies in the New World roughly triples.
But family size is not handed out at random, and in a Malthusian world it is handed out by income — richer families had more children, and richer families could afford a passage. So the paper needs an instrument, and it has two good ones — which is the luxury that lets it check each against the other.
The first is twins. A twin birth is a shock nobody planned: it raises the number of children in a household and has no other business affecting where any of them dies. It moves family size by 0.47 of a child and it is as close to an experiment as this period offers.
The second is a language. France started limiting births a century before its neighbours, and the habit spread outward along lines of cultural proximity — places whose speech was closest to French adopted it earliest. So how far a village’s language sat from French predicts how many children its couples had. The test of whether that is an instrument or a coincidence is timing: the relationship should not exist before there is anything to copy.
Both instruments are strong — the twin birth moves family size by 0.47, linguistic distance by 0.15, with first-stage F-statistics from 27 to 385 — and, used together, they agree: the test of over-identifying restrictions cannot reject them, at p of 0.30 and above. Instrumented, the effect is about five times its ordinary-least-squares value — which is what you expect if income was pushing the two in opposite directions. Going from three children to four raises a child’s chance of ending up in the New World by 4.89 percentage points. For scale: across the Age of Mass Migration that chance went from 6.6% of a cohort to 17.1%. One extra sibling accounts for close to half of the whole increase.
If this is really about dividing a fixed inheritance, then it should matter how the inheritance was divided. Under primogeniture the eldest son takes the land and his brothers get nothing whether there are two of them or eight — so an extra sibling changes nobody’s prospects. Under equal division every extra child shrinks everybody’s portion. Europe had both systems, mapped village by village, and the pressure bites where you would expect.
So the household is not making one decision, it is making several, and they are not symmetric. The first-born stays because the farm is his. The fourth-born leaves because a quarter of a farm is not a living, and because a fare across the Atlantic has become something a family can raise.
This is why the paper calls them Malthusian migrations rather than economic ones. The push is not a wage gap. It is a birth order.
Back up to the continent, where the same fact is visible as a sequence. Across seventeen sending countries and seventy years, a 1% rise in marital fertility is worth 4 to 6% more emigrants per head — and the estimate rises, not falls, when you compare a country only with itself.
The British Isles and Scandinavia go first and peak first. Scandinavia is the most violent wave in the data relative to its population — a country of two and a half million sending people at four hundred per hundred thousand a year.
Germany, Switzerland, the Netherlands and Belgium begin limiting births around 1888. Their emigration, which had been running at a hundred per hundred thousand, falls away and never returns to that level.
Italy, Portugal and Spain transition last, around 1913, and their wave is the last one standing — still climbing when the borders close. Eastern Europe sits just ahead of them.
Everyone has noticed that European emigration moved northwest to south. The usual explanations are poverty and shipping routes. Put the transition dates on the chart and a simpler one appears: it is the order in which countries stopped having spare children, delayed by about a generation.
Ellis Island
Five hundred years of migration leave a mark you can still read. Take everyone alive in 1500, work out where their descendants live today, and ask what predicts the share who never moved. The answer is the date the country stopped having children: a century’s delay in the fertility transition costs 29 to 34% of the descendants who stayed home.
the raw matrix
The extremes are worth saying out loud. There are more English-descended people outside England than in it — 131.9 million worldwide, from a base of 5.5 million in 1750, of whom 53.2 million live in England. Only 11.4% of the descendants of the Irish of 1500 are still in Ireland. France is the mirror image: 70.5% of French descendants are still French residents, and there are twice as many people of French descent in France as in the rest of the world put together.
Which lets you ask the counterfactual. Suppose France had begun its fertility transition in 1885, when England did, instead of 1763. On the estimate above, the share of French descendants still living in France falls from 70.5% to 42.9% — almost exactly England’s 40.3%. And France would be a far larger country: at England’s growth rate from 1750 it would hold 251.7 million people rather than 65. Put the two together and the French diaspora today is 320.4 million people instead of 26.1 million — four times the size of the English one, and most of it in the Americas.
The two halves compound, and that is the part worth sitting with. A France that had kept having children until 1885 would hold 251.7 million people — the counterfactual of the companion paper — and would have sent 320.4 million descendants abroad. Together that is 572 million people of French descent alive today, against roughly 91 million. More than half a billion Frenchmen, most of them in the Americas, from a country that instead became the smallest of the great powers.
A counterfactual that large is not really about France. The New World was settled by whoever had children to spare, and the country best placed to spare them chose not to. Its language and its law are marginal in the Americas today for reasons that begin in French bedrooms in the reign of Louis XV — which is the subject of a companion page.
“The difference between France and other countries, this drying up of the sap at the moment of great expansion, is the most important fact of all her history; it has determined all subsequent development and is still in action today.” Alfred Sauvy, La prévention des naissances (1962)
And the mirror of a small diaspora is a large immigration. An early transition makes a country labour-scarce, which makes it a destination: between 1850 and 1890 immigration contributed more to French population growth than it did to American. The country that did not send became the country that received, for the same reason and at the same time.
Back to the machine from Part 1, with the door open. Same economy, same shock to productivity, same fertility response — and, two generations in, a steamship.
The solid lines are Part 1: productivity rises, population eats it, income comes home to $2,007. This is the world Malthus was describing, and the world he expected emigration to leave unchanged.
Now let the cost of leaving fall, two generations after the shock. Emigration jumps from one person in twenty to about one in four. Population turns over: instead of climbing to 208 million it falls to 119 million.
With fewer people dividing the same land, income per head does not slide back. It settles at $2,515 instead of $2,007 — a gap of $508. In the race between technology and population, emigration gives technology a head start.
That $508 is worth putting next to the thing it is meant to explain. Europe’s income per head went from $2,006 in 1800 to $3,183 in 1880. Productivity growth on its own, in this model, delivers about two hundred dollars of that. The escape valve delivers around five hundred. More than half of the observed rise needs the door.
Be clear about what that is and is not. It is a calibration, not a measurement: a model with five parameters, matched to European income, population and emigration in 1800 and 1880, and then asked what the same century looks like with one parameter held down. It does not displace the usual explanation for nineteenth-century growth, which is productivity. It says that productivity had help, and that the help came from the fact that there was somewhere to go.
Which adds something to a familiar list. What Europe took from the Americas is usually counted in silver, sugar, land and slave labour. It also took room. For a century the Americas absorbed the children European farms could not feed — and they arrived in the decades when there were more of those children than there had ever been.
Malthus pictured a single shipment: empty a parish, and the gap closes. What happened instead never stopped — sixty million people over seventy years, one generation after the next. And it lifted living standards for a narrow reason, not a general one. When output comes off a fixed quantity of land, each additional pair of hands has less of it to work, so the same harvest shared among fewer people leaves everyone with more. Diminishing returns to labour is doing all the work in that sentence. Take that assumption away and the argument collapses.
Which is exactly why none of it carries over. Once growth comes from machines and ideas rather than acres, people are no longer dividing a fixed thing between them — they are how it gets bigger, and a country with more of them is richer, not poorer. Europe’s nineteenth century was the last stretch of history in which the old arithmetic still held.
What the Americas gave Europe, then, was not a smaller population. It was time — a few generations in which incomes could rise before the land filled up again, and in which fertility began to fall on its own, so that it never did. Malthus had the mechanism right and the era wrong. He was writing at the end of the only world his own argument described.