Height and the normal distribution: evidence from italian military data

Abstract

Researchers modeling historical heights have typically relied on the restrictive assumption of a normal distribution, only the mean of which is affected by age, income, nutrition, disease, and similar influences. To avoid these restrictive assumptions, we develop a new semiparametric approach in which covariates are allowed to affect the entire distribution without imposing any parametric shape. We apply our method to a new database of height distributions for Italian provinces, drawn from conscription records, of unprecedented length and geographical disaggregation. Our method allows us to standardize distributions to a single age and calculate moments of the distribution that are comparable through time. Our method also allows us to generate counterfactual distributions for a range of ages, from which we derive age-height profiles. These profiles reveal how the adolescent growth spurt (AGS) distorts the distribution of stature, and they document the earlier and earlier onset of the AGS as living conditions improved over the second half of the nineteenth century. Our new estimates of provincial mean height also reveal a previously unnoticed "regime switch "from regional convergence to divergence in this period.

Height and health in late eighteenth-century England

“…Figure 5 shows the overall distribution of heights. The distribution is not completely normal, possibly because it includes men from quite a wide age range (18–45), where some had not yet reached adult height (A’Hearn et al 2009 ). However, as expected, there was no evidence of any truncation that would suggest the operation of a minimum height requirement.…”

Sample-Selection Biases and the Historical Growth Pattern of Children

“…While most enlistment or conscription records would not include many adolescents under the age of 16 or 17, these records could be used to understand the growth pattern after the pubertal growth spurt and notably when individuals stopped growing. A'Hearn et al (2009b) use Italian military registration records to trace changes in the growth pattern from age 17 onward for birth cohorts from 1855 to 1910. In addition, many studies have noted that military recruits appeared to be growing into their early to mid-twenties suggesting a much longer growing period than is typical of modern, healthy populations (Beekink and Kok 2017;Cinnirella 2008;Floud et al 1990: 153-54).…”

“…Clearly, any estimation strategy that imposes normality on these distributions, such as the QBE or the truncated maximum likelihood estimator, will have difficulty in matching the untruncated distribution. A'Hearn et al (2009b) develop a semiparametric approach that does not require the distributions to be normal, which might be of greater use when dealing with truncated distributions of children's heights, if it could be adapted to account for the truncation points and expected shifting skewness of the distribution. A final source of bias is the misreporting of ages.…”

The effect of disease burden on the speed of aging: an analysis of the Sardinian mortality transition

“…4 ) confirm the above. Together with Basilicata, Sardinia was the Italian region with the lowest average height (A’Hearn et al 2009 ; Arcaleni 1998 , 2006 ; Sanna 2002 ; Sanna et al 1993 ). In particular, data from the conscript records reveal that the average of the Sardinian cohorts born between 1861 and 1927, ranged at 20 years of age, between 160 and 162 cm, without any substantial upward trend in the time series.…”