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Height and the Normal Distribution: Evidence from Italian Military Data

37 Pages Posted: 26 May 2008  

Brian A'Hearn

Pembroke College, Oxford

Franco Peracchi

University of Rome, Tor Vergata - Centre for International Studies on Economic Growth (CEIS); EIEF

Giovanni Vecchi

University of Rome, Tor Vergata - Faculty of Economics

Abstract

Height data offer insights into the well-being of populations and historical periods for which other indicators are lacking. Researchers modeling historical heights have typically relied on the restrictive assumption of a normal (Gaussian) distribution, only the mean of which is affected by age, income, nutrition, disease, and similar influences. We develop a different approach, in which covariates - age in particular - are allowed to affect the entire distribution without imposing any parametric shape. We apply this method to a new database of height distributions for Italian provinces drawn from conscription records. The data are of unprecedented length and geographic disaggregation, but suffer from a variety of statistical problems: variation in the age at measurement in particular. Our method allows us to standardize distributions to a single age and calculate moments of the distribution that are comparable through time. The distribution of heights at age 20 is not normal over most of our sample. Our method also allows us to generate counterfactual distributions for a range of ages, from which we derive age-height profiles. These reveal how the adolescent growth spurt (AGS) distorts the distribution of stature, and 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.

In the light of this evidence, previous assumptions about regional economic development during Italian industrialization will need to be reexamined.

Keywords: Human height, normal distribution, semi-parametric modelling, Italy

JEL Classification: C14, J11, N33

Suggested Citation

A'Hearn, Brian and Peracchi, Franco and Vecchi, Giovanni, Height and the Normal Distribution: Evidence from Italian Military Data. CEIS Working Paper No. 124. Available at SSRN: https://ssrn.com/abstract=1136771 or http://dx.doi.org/10.2139/ssrn.1136771

Brian A'Hearn

Pembroke College, Oxford ( email )

Department of Economics
Manor Road
Oxford, OX1 3UQ
United Kingdom

Franco Peracchi (Contact Author)

University of Rome, Tor Vergata - Centre for International Studies on Economic Growth (CEIS) ( email )

Via Columbia, 2
Rome, I-00133
Italy

EIEF ( email )

via Sallustiana 62
Rome, 00187
Italy

Giovanni Vecchi

University of Rome, Tor Vergata - Faculty of Economics ( email )

Via Columbia n.2
Rome, rome 00100
Italy
+39 6 7259 5730 (Phone)
+39 6 2020 500 (Fax)

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