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The historical fertility transition is the process by which much of Europe and North America went from high to low fertility in the nineteenth and early twentieth centuries. This transformation is central to recent accounts of long-run economic growth. Prior to the transition, women bore as many as eight children each, and the elasticity of fertility with respect to incomes was positive. Today, many women have no children at all, and the elasticity of fertility with respect to incomes is zero or even negative. This paper discusses the large literature on the historical fertility transition, focusing on what we do and do not know about the process. I stress some possible misunderstandings of the demographic literature, and discuss an agenda for future work.

The Human Tide: How Population Shaped the Modern World, by Paul Morland, argues for the importance of demography in both historical events and our current situation. Intended for a general audience, the book traces demographic developments from the late eighteenth century, arguing that the timing and pace of demographic change helps to explain why some countries became powerful and others did not. The author continues the story into the twentieth century, discussing the changes in age structure and internal ethno-religious balances that are consequences of demographic patterns. Many readers will find the questions and themes in The Human Tide interesting. Unfortunately, the book misrepresents some research findings and is confused about important demographic concepts. The Human Tide deals with fundamental changes in human society over the past two centuries, but for a clear account of those changes, readers will have to go elsewhere.

Economists have reported results based on populations for every country in the world for the past two thousand years. The source, McEvedy and Jones’ Atlas of World Population History, includes many estimates that are little more than guesses and that do not reflect research since 1978. McEvedy and Jones often infer population sizes from their view of a particular economy, making their estimates poor proxies for economic growth. Their rounding means their measurement error is not “classical.” Some economists augment that error by disaggregating regions in unfounded ways. Econometric results that rest on McEvedy and Jones are unreliable. “… we haven’t just pulled the figures out of the sky. Well, not often.” —McEvedy and Jones (1978, p. 11)

Understanding long-term changes in human well-being is central to understanding the consequences of economic development. An extensive anthropometric literature purports to show that heights in the United States declined between the 1830s and the 1890s, which is when the U.S. economy modernized. Most anthropometric research contends that declining heights reflect the negative health consequences of industrialization and urbanization. This interpretation, however, relies on sources subject to selection bias. Our meta-analysis shows that the declining height during industrialization emerges primarily in selected samples. We also develop a parsimonious diagnostic test that reveals, but does not correct for, selection bias in height samples. When applied to four representative height samples, the diagnostic provides compelling evidence of selection.

Economists have long argued that introducing social insurance will reduce fertility. The hypothesis relies on standard models: if children are desirable in part because they provide security in case of disability or old age, then State programs that provide insurance against these events should induce couples to substitute away from children in the allocation of wealth. We test this claim using the introduction of social insurance in Germany in the period 1881–1910. Bismarck's social insurance scheme had three pillars: health insurance, workplace accident insurance, and an old‐age pension. Earlier studies typically focus on the pension alone; we consider all three pillars. We find that Bismarck's social insurance system affected fertility overall only via its effects on the incentive to marry. The old‐age insurance by itself tended to reduce marriages, but the health and accident insurance components had the opposite effect. For people exposed to all three pillars of social insurance, the two effects cancelled each other and the aggregate effect on fertility was muted. fertility transition; economics; social insurance

Sample-selection bias (SSB) arises when the process that selects observations into a sample involves a correlation with the question of interest. SSB affects many quantitative historical sources and has analogues in other forms of historical inquiry. Three extensive literatures in quantitative history raise important issues of SSB: the anthropometric literature that uses height as a proxy for material welfare; family-reconstitution studies that derive demographic rates from parish registers; and the more recent \"linking\" literature that creates longitudinal data sets from cross-section sources such as censuses. The linking literature, unlike the first two, has yet to come to grips with SSB.

The most common business enterprise form in Germany today is the Gesellschaft mit beschränkter Haftung (GmbH). The GmbH offers entrepreneurs the flexibility of a partnership combined with limited liability, capital lock-in, and other traits associated with corporations. Authorized in 1892, the GmbH appeared during a period of ferment in German enterprise law and was an early example of the private limited-liability company prevalent in many economies today. The new form reflected challenges created by the corporation reform of 1884, problems in German colonial companies, and the view that British company law had put German firms at a competitive disadvantage. Significant sections of the financial and legal community harbored strong reservations about this legal innovation.

Recent research disputes the view that the joint-stock corporation played a crucial role in historical economic development, but retains the idea that the costless firm dissolution implicit in non-corporate forms deterred investment. A multi-armed bandit model demonstrates the benefits of costless dissolution in an environment where potential business partners are not fully informed. Experimentation creates a spike in dissolution rates early in firms’ lives, as less productive matches break down and agents look for better matches. Many of the better matches adopt the corporate form, whose higher dissolution cost functions as a commitment device. We test the model’s predictions using firm-level data on 12,000 enterprises established in Egypt between 1910 and 1949. The partnership reflected a trade-off between committing to a partner and sorting into potentially better matches, fostering the formation of more productive enterprises.

Our 2017 article in this Journal stresses the pitfalls of using choice-based samples in economic history. A prominent example is the literature addressing the so-called antebellum puzzle. Heights researchers claim that Americans grew shorter in the first half of the nineteenth century, a period of robust economic growth. We argue that this result relies on choice-based samples. Without knowing the process that led to inclusion in the sample, researchers cannot properly estimate conditional mean heights. We proposed a diagnostic that can detect, but not correct for, selection bias. Komlos and A’Hearn’s interpretation of our analysis confuses diagnosis with cure. We dispute their view that selection bias has been appreciated in the heights literature.