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Height and the normal distribution: Evidence from Italian military data

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Author Info
Brian A'Hearn (Franklin & Marshall College)
Franco Peracchi () (Faculty of Economics, University of Rome "Tor Vergata")
Giovanni Vecchi () (Faculty of Economics, University of Rome "Tor Vergata")

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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.

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Publisher Info
Paper provided by Tor Vergata University, CEIS in its series CEIS Research Paper with number 124.

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Length: 37 pages
Date of creation: 14 Jul 2008
Date of revision: 14 Jul 2008
Handle: RePEc:rtv:ceisrp:124

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Postal: CEIS - Centre for Economic and International Studies - Faculty of Economics - University of Rome "Tor Vergata" - Via Columbia, 2 00133 Roma
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Related research
Keywords: Human height; normal distribution; semi-parametric modelling; Italy;

Find related papers by JEL classification:
C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods
J11 - Labor and Demographic Economics - - Demographic Economics - - - Demographic Trends and Forecasts
N33 - Economic History - - Labor and Consumers, Demography, Education, Income, and Wealth - - - Europe: Pre-1913

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References listed on IDEAS
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  1. Angus Deaton, 2008. "Height, Health, and Inequality: The Distribution of Adult Heights in India," American Economic Review, American Economic Association, vol. 98(2), pages 468-74, May. [Downloadable!]
    Other versions:
  2. Robert W. Fogel, 1994. "Economic Growth, Population Theory, and Physiology: The Bearing of Long-Term Processes on the Making of Economic Policy," NBER Working Papers 4638, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
    Other versions:
  3. Anne Case & Christina Paxson, 2006. "Stature and status: Height, ability, and labor market outcomes," Working Papers 27, Princeton University, Woodrow Wilson School of Public and International Affairs, Center for Health and Wellbeing.. [Downloadable!]
    Other versions:
  4. Arcaleni, Emilia, 2006. "Secular trend and regional differences in the stature of Italians, 1854-1980," Economics and Human Biology, Elsevier, vol. 4(1), pages 24-38, January. [Downloadable!] (restricted)
  5. Federico, Giovanni, 2003. "Heights, calories and welfare: a new perspective on Italian industrialization, 1854-1913," Economics and Human Biology, Elsevier, vol. 1(3), pages 289-308, December. [Downloadable!] (restricted)
  6. Vittorio Daniele & Paolo Malanima, 2007. "Il prodotto delle regioni e il divario Nord-Sud in Italia (1861-2004)," Rivista di Politica Economica, SIPI Spa, vol. 97(2), pages 267-316, March-Apr. [Downloadable!]
  7. Yoko Akachi & David Canning, 2007. "The Height of Women in Sub-Saharan Africa: the Role of Health, Nutrition, and Income in Childhood," PGDA Working Papers 2207, Program on the Global Demography of Aging. [Downloadable!]
  8. Danubio, Maria Enrica & Amicone, Elisa & Vargiu, Rita, 2005. "Height and BMI of Italian immigrants to the USA, 1908-1970," Economics and Human Biology, Elsevier, vol. 3(1), pages 33-43, March. [Downloadable!] (restricted)
  9. Borjas, George J, 1987. "Self-Selection and the Earnings of Immigrants," American Economic Review, American Economic Association, vol. 77(4), pages 531-53, September. [Downloadable!] (restricted)
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  10. Vecchi, Giovanni & Coppola, Michela, 2006. "Nutrition and growth in Italy, 1861-1911: What macroeconomic data hide," Explorations in Economic History, Elsevier, vol. 43(3), pages 438-464, July. [Downloadable!] (restricted)
    Other versions:
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