Manifest 35
Nearly 60 million Europeans left for the Americas during the Age of Mass Migration. We find that people from larger families were more likely to emigrate, and use a model to explore how emigration may have eased population pressure and raised living standards in Europe.
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: every advance was eaten by the population it created.
What he was wrong about was the exit.
In the paper’s model, land is fixed: more workers leave less land per person, while higher income encourages population growth. A productivity gain therefore raises income at first, but some of the gain is eroded as the population grows. This captures the Malthusian mechanism the authors use to study the role of migration.
Europe in 1800, as the model sees it: income per head of $2,000, a population of 142 million, and about one person in twenty leaving in each generation. Four flat generations here, and it could as easily have been forty. Nothing moves 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 laboring 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.
Start with the fact Malthus never lived to see. Between 1850 and 1920, nearly sixty million Europeans crossed to the Americas — the largest voluntary movement of people there has ever been. In the 1920 United States census, the British Isles account for 2.2 million of the foreign-born, eastern Europe for 2.1 million, central Europe for 1.9 million, southern Europe for 1.8 million, Scandinavia for 1.3 million. France — which had entered the era with more people than any of them — accounts for 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. That century of restraint has a page of its own: Coitus Interruptus.
Nouvelle France
France provides a striking comparison: it experienced an early fertility decline and sent relatively few migrants across the Atlantic. The comparison is suggestive, though France also differed from other countries in many other ways.
The paper argues that population pressure alone was not enough to produce mass migration: the cost and difficulty of crossing the Atlantic also mattered. Steamships made the journey faster and, eventually, more accessible.
The Great Western, a wooden paddle steamer built by Brunel, left Bristol on 8 April 1838 and reached New York fifteen days later. Steamships made Atlantic crossings faster and more predictable, helping open the way to mass migration. In the model, a parameter governing the ease of migration captures this change.
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
Before 1825, the estimated association between log family size and the chance of dying in the New World is about 1.1 percentage points per log point. It is positive, but much smaller than for later cohorts.
For cohorts born after 1825, the corresponding association is 6.8 percentage points per log point. The change is consistent with the opening of cheaper transatlantic travel, although the comparison alone cannot isolate that cause.
The household was not always the one doing the arithmetic. In the Scottish Highlands the crofts had filled past what the land could feed — plots split among sons, then split again — and when the potato failed in 1846, the reckoning arrived all at once. It was the landlords who answered it: they cleared the townships for sheep, and they paid to make the people go. Between 1852 and 1857 the Highland and Island Emigration Society shipped some five thousand Highlanders to Australia, landlords covering a third of every fare — and its founding papers state the purpose in the era’s own words: to remove the “surplus population.”
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 no one in it chose the quay.
The Clearances remind us that migration was not always a free choice. Landlords could uproot communities and help pay for their passage; the pressures on land described here operated alongside coercion, famine, and unequal power. The genealogy data reveal where people were born and died, but not the full circumstances of each departure.
The paper also asks whether larger families were associated with moves elsewhere within Europe. The estimated relationship is small and statistically indistinguishable from zero in the main specifications, unlike the relationship with deaths in the New World. This contrast is consistent with the importance of opportunities across the Atlantic, although it does not by itself establish why people moved.
The paper turns from countries to people. It draws on a genealogy dataset of ten million linked individuals, then selects people born in Europe between 1750 and 1900 whose parents have sufficiently complete records of their children. The main individual regressions use roughly 225,000 people. The outcome is whether a person died in the New World, a proxy for migration.
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.
Family size is not random: income and other family characteristics can affect both fertility and the ability to pay for a passage. To address this problem, the paper uses two instruments for parental fertility. Each offers a different source of variation, and each depends on assumptions.
The first is a twin birth. Twins increase family size unexpectedly. The analysis uses opposite-sex twins to limit duplicate records; its causal interpretation assumes that a twin birth affects migration through family size, rather than through other channels. Twin-related selection and measurement remain concerns discussed in the paper.
The second is linguistic distance from French. France began limiting births early, and the fertility transition spread along lines of cultural proximity. The paper uses distance from French to predict parental fertility. The timing is consistent with diffusion, but the causal interpretation also requires that linguistic distance does not affect migration through other channels. The companion page French tells another story about language.
Using both instruments, the paper estimates that moving from a family of three children to four is associated with a 4.89 percentage point increase in a child’s probability of dying in the New World. For scale, the corresponding sample average rises from 6.6% among those born before 1825 to 17.1% among those born afterward. The estimate is large, but it does not mean that one extra sibling literally explains half of the historical increase. The instruments yield similar positive results; a test of their joint restrictions does not reject, though this cannot prove their validity. The twin-based estimate identifies a local average effect for families whose fertility responds to a twin birth, under the usual assumptions.
Inheritance offers another clue. Where land was divided equally, an additional child reduced each child’s potential share; under unequal inheritance, family size might matter less for a child who would not inherit the land. The paper finds a stronger relationship between family size and migration in places with equal inheritance norms.
These patterns are consistent with the paper’s explanation: when more children shared a family’s resources, later-born children had stronger incentives to seek opportunities elsewhere. The records cannot reveal the precise decision behind each departure.
Patrick Kennedy’s story gives the era a human face. Born in 1823 in County Wexford, he emigrated to Boston during the Great Famine, worked as a cooper, and died in 1858. His great-grandson became President of the United States. Like the genealogies, his story also reminds us that migration had many causes.
The paper calls these Malthusian migrations: population pressure can increase the incentive to seek land and work elsewhere. This is an economic explanation that complements, rather than rules out, wage differences and other reasons for migration.
The country-level evidence reveals a related pattern. Across seventeen sending countries and seventy years, a 1% higher marital fertility rate is associated with 4 to 6% more emigrants per head. The estimates also compare each country with itself over time.
The British Isles and Scandinavia go first and peak first. Scandinavia’s is the most violent wave in the data relative to population, peaking near four hundred emigrants 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 in the estimated distribution of ancestry today. Across Old World countries, a fertility transition one century later is associated with a 29 to 34% lower share of descendants living in their country of origin. This is a cross-country association, subject to the limitations of the ancestry data and the controls.
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.
The paper uses that relationship for an illustrative counterfactual: suppose France’s transition had begun in 1885, like England’s, instead of 1763. The estimated relationship implies 42.9% of French descendants would live in France, compared with 70.5% in the data. Combined with the assumption that France’s population grew at England’s rate after 1750, the arithmetic yields a diaspora of 320.4 million rather than 26.1 million. This is a scenario, not a forecast.
The assumptions compound. Applying England’s population growth rate gives 251.7 million residents, and combining that figure with the estimated diaspora share gives about 320.4 million descendants abroad. Together, the scenario implies 572 million people of French descent, compared with roughly 91 million in the data. These figures illustrate the potential scale of demographic differences; they do not identify where those hypothetical descendants would have lived.
The exercise suggests how differences in fertility and migration could have contributed to the very different reach of European diasporas. Colonial history, institutions, conflict and many other forces also shaped settlement in the Americas.
“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)
France also became a country of immigration. Between 1850 and 1890, immigration contributed more to French population growth than to American population growth. The paper argues that early fertility decline may have helped make France a destination for workers.
Return to the model from Part 1. The chart compares a productivity-level shock with a second scenario in which migration becomes easier two generations later.
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.
The chart above illustrates a productivity-level shock. The paper also studies a different exercise: a sustained increase in productivity growth, with and without easier migration. In that growth-shock calibration, productivity alone adds about $200 to long-run income per head and easier migration adds roughly another $500. Together, the two shocks account for more than half of Europe’s observed income increase from $2,006 in 1800 to $3,183 in 1880. These are model-based comparisons, not direct estimates of migration’s contribution.
The size of these contributions depends on the model and its calibration to European population, income and emigration. The exercise illustrates a possible mechanism by which migration could have accelerated growth alongside productivity gains.
The paper asks us to consider an additional connection between Europe and the Americas: migration offered Europeans access to land and opportunities overseas. That movement took place within a history of colonization, displacement and coerced labor.
In the model, emigration eases pressure on land in sending countries. With diminishing returns to labor, fewer workers sharing a fixed quantity of land can raise income per person. The size and persistence of that effect depend on the model’s assumptions.
The argument depends on diminishing returns to labor when land is fixed. Its strength in a modern economy, where capital, technology, and institutions also shape output, requires separate analysis; the historical model does not settle the effects of migration today.
The paper’s broader argument is that emigration could have given European economies time: population pressure eased while productivity rose and fertility began to fall. It is a different answer to the question Malthus posed, grounded in the particular conditions of the nineteenth century.