Before the fall: quantity versus quality in pre–demographic transition Quebec (NR Online Session 3)

By Matthew Curtis (University of California, Davis)

This research is due to be presented in the third New Researcher Online Session: ‘Human Capital & Development’.


Map of East Canada or Quebec and New Brunswick, by John Tallis c.1850. Available at Wikimedia Commons.

While it plays a key role in theories of the transition to modern economic growth, there are few estimates of the quantity-quality trade-off from before the demographic transition. Using a uniquely suitable new dataset of vital records, I use two instrumental variable (IV) strategies to estimate the trade-off in Quebec between 1620 and 1850. I find that one additional child who survived past age one decreased the literacy rate (proxied by signatures) of their older siblings by 5 percentage points.

The first strategy exploits the fact that twin births, conditional on mother’s age and parity, are a random increase in family size. While twins are often used to identify the trade-off in contemporary studies, sufficiently large and reliable historical datasets containing twins are rare. I compare two families, one whose mother gave birth to twins and one whose mother gave birth to a singleton, both at the same parity and age. I then look at the probability that each older non-twin sibling signed their marriage record.

For the second strategy, I posit that aggregate, province-wide infant mortality rate during the year a younger child was born is exogenous to individual family characteristics. I compare two families, one whose mother gave birth during a year with relatively high infant mortality rate, both at the same parity and age. I then look at older siblings from both families who were born in the same year, controlling for potential time trends in literacy. As the two different IV techniques result in very similar estimates, I argue there is strong evidence of a modest trade-off.

By using two instruments, I am able to rule out one major source of potential bias. In many settings, IV estimates of the trade-off may be biased if parents reallocate resources towards (reinforcement) or away from (compensation) children with higher birth endowments. I show that both twins and children born in high mortality years have, on average, lower literacy rates than their older siblings. As one shock increases and one shock decreases family size, but both result in older siblings having relatively higher human capital, reinforcement or compensation would bias the estimates in different directions. As the estimates are very similar, I conclude there is no evidence that my estimates suffer from this bias.

Is the estimated trade-off economically significant? I compare Quebec to a society with similar culture and institutions: pre-Revolutionary rural France. Between  1628 and 1788, a woman surviving to age 40 in Quebec would expect to have 1.7 additional children surviving past age one compared to her rural French peers. The average literacy rate (again proxied by signatures) in France was about 9.5 percentage points higher than in Quebec. Assuming my estimate of the trade-off is a linear and constant effect (instead of just a local average), reducing family sizes to French levels would have increased literacy by 8.6 percentage points in the next generation, thereby eliminating most of the gap.

However, pre-Revolutionary France was hardly a human capital-rich society. Proxying for the presence of the primary educators of the period (clergy and members of religious orders) with unmarried adults, I find plausible evidence that the trade-off was steeper in boroughs and decades with greater access to education. Altogether, I interpret my results as evidence that a trade-off existed which explains some of the differences across societies.


Data Sources

Henry, Louis, 1978. “Fécondité des mariages dans le quart Sud-Est de la France de 1670 a 1829,” Population (French Edition), 33 (4/5), 855–883.

IMPQ. 2019. Infrastructure intégrée des microdonnées historiques de la population du Québec (XVIIe – XXe siècle) (IMPQ). [Dataset].Centre interuniversitaires d’études              québécoises (CIEQ).

Programme de recherche en démographie historique (PRDH). 2019. Registre de la population du Québec ancien (RPQA). [Dataset]. Département de Démographie, Université de Montréal.

Projet BALSAC. 2019. Le fichier BALSAC. [Dataset]. L’Université du Québec à Chicoutimi.

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