Biased samples yield biased results: What historical heights can teach us about past living standards

Howard Bodenhorn, Timothy Guinnane, Thomas Mroz 22 July 2015



At the core of most big questions about economic growth and development lies a concern with human welfare – how do we raise incomes and reduce poverty?

Economic historians have long asked how the early stages of the historical industrialisation process affected welfare. Although industrialisation in Europe and North America raised GDP per capita dramatically, it also generated some ‘bads’, including unhealthy cities and hard work under unpleasant conditions. Friederich Engels’ 1845 portrayal of English factory working conditions, for example, sounds as bad as anything in modern third-world sweatshops. By some economists’ accounts, the growth of real wages was too slow to offset the negative consequences of industrialisation, implying that those who lived through the Industrial Revolution were worse off than preceding generations.1

Measuring human welfare

A central problem for studying living standards in the past is familiar to all historical inquiry –limited empirical sources. Economic historians have constructed real wages to study purchasing power, and demographic historians study mortality and morbidity to better understand how industrialisation and urbanisation affected health. But these studies are hampered by small amounts of potentially unrepresentative data, as most data collected by contemporaries were for some purpose other than understanding well-being.

Building on the work of human biologists, the Nobel Prize-winning economic historian Robert Fogel pioneered an approach to the historical study of human welfare that relies on measurement of the human organism itself. His approach uses the fact that adult height reflects net nutrition in childhood and early adolescence.

To achieve its full height potential, the body requires nutrition that it can devote to growth after providing calories sufficient for metabolic function and work effort. Disease makes its own demands on nutritional input. Poor nutrition, hard work effort, and frequent illness make for short people. Fogel’s human height approach can draw on the records of millions of men and women whose heights were recorded over the past three centuries. Military recruiters, school administrators, prison officials, slave traders and many others kept records of people’s heights, mostly as a useful way to identify individuals. Fogel used these height records to document long-term trends in the human body’s reaction to economic developments such as industrialisation and urbanisation.

Fogel’s ideas were fruitful. His work led to hundreds of studies, a specialist journal, and radical reinterpretations of the implications of long-run economic growth. Most notably, Fogel and others point to a phenomenon that is know as the ‘industrialisation puzzle’. In the US, the UK, and some other European countries, people appeared to get shorter during the period of early industrialisation.

Figure 1 reports mean heights of soldiers for six countries over the 19th and 20th centuries. The US experience, where mean height apparently declined by about 5cm (about two inches) from 1830 to 1880, is an example of the industrialisation puzzle. This result supports an extremely pessimistic understanding of how industrialisation affects human welfare. It is one thing to argue that industrialisation’s benefits were unevenly distributed or at first sight. The industrialisation puzzle implies that at least in the short run, economic modernisation made the average person worse off.

Figure 1 Mean heights of volunteer soldiers in the US and in selected countries with conscription

How could this be? The finding that people shrank in a growing economy, as John Komlos puts it, led to a number of possible explanations for the puzzle. Most focus on the quality and availability of food supplies, the intensity of work effort, and the undeniably unhealthy living conditions of early industrial workers in both the US and Europe. The possibility that people could be worse off (as measured by their height) while real wages were increasing led Komlos to posit that the ‘biological’ and the economic standards of living might diverge during industrial revolutions.

Sample selection problems in historical heights data

Despite its emergence as a stylised fact, we doubt that the industrialisation puzzle is real. In pursuing the historical heights agenda, historians have learned a great deal about how people lived. And they have assembled millions of data points in doing so. But a common feature of most of these data sets is that they do not add up to representative samples of the underlying population.2

During the 18th and 19th centuries, most of these sources were subject to important selection forces. Consider soldiers, a favourite source of height data. No studies account for the fact that most armies in the past relied heavily on volunteers. Men willing to join the army in the economically dynamic US in the 1830s and 1840s, for example, did not amount to a random draw from the US population – in fact, they were probably men whose labour market opportunities were inferior to those who remained civilians.

To the extent that labour market opportunities reflect the same kinds of background traits and ‘health human capital’ that account for height, we would expect the soldiers to be shorter than the civilians. More importantly, the magnitude of this height difference would depend on variations in the tightness of civilian labour markets over time as well as the appeal of a life in the military. A small volunteer army in a weak civilian labour market might actually be taller than the population as a whole. Once we account for the self-selected nature of the samples, the phenomenon of ‘shrinking in a growing economy’ is not a puzzle – it is what one would expect.3

The basic idea extends to most of the other sources used to study heights in the past. Some of what we know about living conditions for chattel slaves in the US comes from the height data published to help identify runaways. But who could run away, and which runaway slaves were worth trying to recapture? Only relatively healthy slaves could escape, and only healthy and thus valuable slaves were worth trying to track down. In this case, the selection bias leads to an overestimation of the average slave’s height, and thus a too-rosy view of material conditions for slaves. Another important source for slave heights was the ‘coastwise manifest’ used to make sure that slaves transported between two US ports were not being imported from elsewhere, in violation of the 1808 prohibition on slave imports. Since shipping a slave involved a fixed cost, one would expect that only the healthier – and taller – were shipped, an example of the Alchian-Allen effect. Once again, the bias here is positive; relying on the manifests alone, we would overstate the heights of slaves.4

In fact, the only sources for historical height data that do not suffer this kind of bias come from the handful of countries that imposed a form of universal conscription. Figure 1 reports mean heights in five conscript armies, in addition to the US. The US did not have effective military conscription until World War I. The industrialisation puzzle, strikingly, does not appear in any country with conscription. The French military, for example, called up nearly all young men and measured them, and the mean height of measured French males grows monotonically throughout the 19th century.

New research

In a series of papers, we have explored the implications of these sample-selection issues for what Fogel’s approach has tried to deduce about living conditions in the past. The challenge for our research is this: we do not have random samples of the same populations for which we have heights, so we cannot directly test for selection on observable characteristics. And knowing whether there is selection on observables would only be half the battle. If unobservable factors affect the chance of joining an army, and if those un-observables are correlated with height, then we could also have selection bias, even without selection on observables.

To explore this issue, we adapt Roy’s famous occupational choice model to consider a stylised decision to join the army. We simulate the model to show that modest changes in civilian labour market conditions can create swings in mean military height similar to those labelled the industrialisation puzzle. We also devise a simple diagnostic for selection in military samples, based on the idea that if all men are of full adult height by a given age (say, 23), then the average heights of men born in a given year but who join the army at age 23 should not differ from those born in the same year but who join the army at age 24. Any difference in mean height suggests that the appeal of the army when the cohort was aged 23 was different from its appeal when the cohort was aged 24. Evidence of such age-specific height differentials varying across birth cohorts strongly suggests the influence of labour market alternatives on decisions to join the army, which in turn suggests that measured heights vary with changing economic conditions. While this approach cannot ‘correct’ for selection bias, we show, using a number of sources widely used in the heights literature, that most sources suffer from bias of this sort. Finally, a meta-analysis of nearly 200 published height studies demonstrates that the industrialisation puzzle and similar reversals in mean heights appear nearly always in samples that are selected and/or very small.5

Living standards during early industrialisation

So what do we know about living standards during early industrialisation? Fogel’s approach taught us a great deal, and studying the long-term history of the human organism remains a fruitful avenue of exploration. But one of Fogel’s early claims turns out to have, at best, a weak foundation. The measured decline of mean height during industrialisation reflects in large part the nature of the data sources, not necessarily changes in the heights of the underlying populations.

As economies grew, tight labour markets discouraged military enlistments by the most productive workers, with those enlisting (and being measured) increasingly over-representing the less advantaged members of society. The Industrial Revolution posed challenges for those facing the transformations it wrought, but it did not make people shorter.[RB1] 

Authors' note: The views expressed here are the authors’ and not necessarily those of the Federal Reserve Bank of Atlanta or the Federal Reserve System.


Asch, B J, J R Hosek, and J T Warner (2007), “New Economics of Manpower in the Post-Cold War Era”, in T Sandler and K Hartle (eds.) Handbook of Defense Economics Volume 2, 1077-1140.

Bodenhorn, H, T W Guinnane, and T A Mroz (2013), “Problems of sample-selection bias in the historical heights literature: a theoretical and empirical analysis”, SSRN No. 2261335.

Bodenhorn, H, T W Guinnane, and T A Mroz (2014), “Sample Selection Bias in the Historical Heights Literature”, Economic Growth Center Discussion Paper, Yale University.

Bodenborn, H, T W Guinnane, and T Mroz (2015), “Sample-selection biases and the ‘industrialization puzzle’”, NBER Working Paper No. 21249.

Feinstein, C H (1988), “Pessimism Perpetuated: Real Wages and the Standard of Living in Britain during and after the Industrial Revolution”, Journal of Economic History 58(3): 625-658.

Fogel, R W (1986), “Nutrition and the Decline in Mortality since 1700: Some Preliminary Findings”, in S L Engerman and R E Gallman (eds.), Long-Term Factors in American Economic Growth, Chicago: University of Chicago Press, 1986439-556.

Komlos, J (1998), “Shrinking in a Growing Economy? The Mystery of Physical Stature during the Industrial Revolution”, Journal of Economic History 58(3): 779-802.

Margo, R A and R H Steckel (1983), “Heights of Native-Born Whites during the Antebellum Period”, Journal of Economic History 43(1): 167-174.

Mokyr, J, and C Ó Gráda (1996), “Height and Health in the United Kingdom 1815–1860: Evidence from the East India Company Army”, Explorations in Economic History 33(2): 141-168.

Steckel, R H (1995), “Stature and the Standard of Living”, The Journal of Economic Literature XXXIII, December: 1903-1940.


1 Feinstein (1988) shows that real wages for the British working class increased by less than 15% from the 1780s to the 1850s

2 Steckel (1995) provides an overview of the methods and early findings of this approach

3 The US has faced a similar problem since it went to an all-volunteer military in 1973; during the positive parts of the business cycle, measured attributes of recruits decline (see Asch et al 2007).

4 Anthropometricians, as these scholars are called, have shown tremendous ingenuity in locating sources. Unfortunately, the selection problem arises in most of them. Men – and less often, women – imprisoned for crimes were typically measured and constitute the basis for many heights studies. Again, this is a choice-based sample and subject to the selection critique. Other samples, including passport holders and students, pertain to individuals who were far from representative of the general population

5 See Bodernhorn et al. (2014 and 2015). Mokyr and Ó Gráda (1996) long ago noted this selection problem in their study of men who joined the East India Company’s army in the early 19th century. The Irish soldiers turned out to be taller than those born in England and Wales, yet every other indicator suggested that Ireland was much poorer than England



Topics:  Economic history Health economics

Tags:  Height, well-being, living standards

Professor of Economics, Clemson University

Philipp Golden Bartlett Professor of Economic History, Yale University

Bernard B. and Eugenia A. Ramsey Chair of Private Enterprise, Georgia State University