Howard Bodenhorn, Timothy W. Guinnane and Thomas A. Mroz
ABSTRACT
Long-run changes in living standards occupy an important place in development and growth economics, as well as in economic history. An extensive literature uses heights to study historical living standards. Most historical heights data, however, come from selected subpopulations such as volunteer soldiers, raising concerns about the role of selection bias in these results. Variations in sample mean heights can reflect selection rather than changes in population heights. A Roy-style model of the decision to join the military formalizes the selection problem. Simulations show that even modest differential rewards to the civilian sector produce a military heights sample that is significantly shorter than the cohort from which it is drawn. Monte Carlos show that diagnostics based on departure from the normal distribution have little power to detect selection. To detect height-related selection, we develop a simple, robust diagnostic based on differential selection by age at recruitment. A companion paper (H. Bodenhorn, T. Guinnane, and T. Mroz, 2017) uses this diagnostic to show that the selection problems affect important results in the historical heights literature.
INTRODUCTION
The causes and consequences of long-run economic growth remain central questions in economics. One important sub-question deals with changes in living standards: how does economic growth in general, or industrialization in particular, affect human welfare? Much of what we know about historical living standards comes from an extensive literature that uses measured human heights (and less often, other anthropometric measures) as a supplement to measures such as real wages. Unfortunately, many studies rely on choice-based samples of heights. This chapter studies the consequences of selection and proposes a diagnostic for detecting selection bias in real-world data.
This heights literature has been influential not just in economic history but in other areas of economics concerned with growth and development. R. Fogel’s (1994) Nobel Lecture, for example, presented a theory of long-run development based in important ways on the historical heights literature. D. Weil (2007) builds on measures drawn from compilations of historical heights. A. Deaton (2007) for modern Africa and Bozzoli, Deaton, and Quintana-Domeque (2009) for modern Europe and the United States attribute part of the lack of a height–income relationship in developing countries today to conclusions drawn from comparisons of the heights of British and Irish volunteers to the East India Company in the 1800s.
We do not dispute the central idea of the heights literature. Labor market studies find that taller individuals earn more because height is correlated with general health, cognitive ability, or both (A. Case & C. Paxson, 2008; P. Anderson, 2018). At the population level, adult height reflects the net nutrition available to individuals during the growing years. A cohort might be unusually short because its members had less food, or gross nutrition; because hard work during youth made greater caloric demands on gross nutrition, leaving less for growth; or because disease made demands on gross nutrition.
Many studies in the historical literature focus on “height reversals,” episodes where mean height apparently declines even though wages or other measures of living standards increase. Accounts of such reversals rely heavily on sources that only include individuals who made a choice resulting in a height measurement. The most abundant data comes from the records of volunteer military forces. In other cases, the sample reflects a different kind of choice; for example, the emancipation of an enslaved person or enrollment in a military academy. Estimation using choice-based samples always raises the possibility of selection bias. Our Roy-style model of such decisions demonstrates the role of sample selection bias in estimates of cohort heights. The model confirms the basic intuition underlying selection problems: for a choice-based sample, we cannot ordinarily distinguish between changes in population heights (the object of interest) and a change in the sampling rule that generates the sample at hand. Height reversals may well reflect the declining attractiveness of military service in a growing civilian economy, rather than, as anthropometricians often argue, some force that reduces net nutrition across cohorts. Simulations illustrate the extent of the potential problem. We also develop a simple, robust diagnostic that can detect (but not correct for) selection biases in real data.
We are not the first to notice the problem of selection bias in the historical heights literature. J. Pritchett and H. Freudenberger (1992, 2016) showed that the fixed cost of shipping slaves to the New Orleans market led to selection for unusually tall individuals; J. Pritchett and R. Chamberlain (1993) discuss other features of selection in that market. J. Mokyr and C. Ó Gráda (1996) fo...
