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Height and the normal distribution: evidence from italian military data

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  • Brian A’hearn
  • Franco Peracchi

    ()

  • Giovanni Vecchi

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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Suggested Citation

  • Brian A’hearn & Franco Peracchi & Giovanni Vecchi, 2009. "Height and the normal distribution: evidence from italian military data," Demography, Springer;Population Association of America (PAA), vol. 46(1), pages 1-25, February.
  • Handle: RePEc:spr:demogr:v:46:y:2009:i:1:p:1-25
    DOI: 10.1353/dem.0.0049
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    File URL: http://hdl.handle.net/10.1353/dem.0.0049
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    References listed on IDEAS

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    1. Arcaleni, Emilia, 2006. "Secular trend and regional differences in the stature of Italians, 1854-1980," Economics & Human Biology, Elsevier, vol. 4(1), pages 24-38, January.
    2. 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.
    3. Fogel, Robert W, 1994. "Economic Growth, Population Theory, and Physiology: The Bearing of Long-Term Processes on the Making of Economic Policy," American Economic Review, American Economic Association, vol. 84(3), pages 369-395, June.
    4. Federico, Giovanni, 2003. "Heights, calories and welfare: a new perspective on Italian industrialization, 1854-1913," Economics & Human Biology, Elsevier, vol. 1(3), pages 289-308, December.
    5. Borjas, George J, 1987. "Self-Selection and the Earnings of Immigrants," American Economic Review, American Economic Association, vol. 77(4), pages 531-553, September.
    6. Angus Deaton, 2008. "Height, Health, and Inequality: The Distribution of Adult Heights in India," American Economic Review, American Economic Association, vol. 98(2), pages 468-474, May.
    7. Hatton, Timothy J. & Williamson, Jeffrey G., 1998. "The Age of Mass Migration: Causes and Economic Impact," OUP Catalogue, Oxford University Press, number 9780195116519.
    8. Anne Case & Christina Paxson, 2008. "Stature and Status: Height, Ability, and Labor Market Outcomes," Journal of Political Economy, University of Chicago Press, vol. 116(3), pages 499-532, June.
    9. 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.
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    More about this item

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • J11 - Labor and Demographic Economics - - Demographic Economics - - - Demographic Trends, Macroeconomic Effects, and Forecasts
    • N33 - Economic History - - Labor and Consumers, Demography, Education, Health, Welfare, Income, Wealth, Religion, and Philanthropy - - - Europe: Pre-1913

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