Comparing population distributions from bin-aggregated sample data: An application to historical height data from France

Institut d'Anàlisi Econòmica (CSIC), Barcelona, Spain.
Economics and human biology (Impact Factor: 2.46). 05/2011; 9(4):419-37. DOI: 10.1016/j.ehb.2011.05.002
Source: PubMed

ABSTRACT We develop a methodology to estimate underlying (continuous) population distributions from bin-aggregated sample data through the estimation of the parameters of mixtures of distributions that allow for maximal parametric flexibility. The statistical approach we develop enables comparisons of the full distributions of height data from potential army conscripts across France's 88 departments for most of the nineteenth century. These comparisons are made by testing for differences-of-means stochastic dominance. Corrections for possible measurement errors are also devised by taking advantage of the richness of the data sets. Our methodology is of interest to researchers working on bin-aggregated or histogram-type data, something that is still widely done since much of the information that is publicly available is in that form, often due to restrictions based on confidentiality concerns.

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    ABSTRACT: Since the pioneering study of Le Roy Ladurie and his team, the idea that mean height can be considered as a reliable indicator of the standard of living has emerged from a long debate among historians and economists. Considering height in this respect, nineteenth-century France, unlike most Western countries, did not pay an urban penalty. Thanks to a substantial set of individual data (105,324 observations), based on the draft lottery of Frenchmen born in the year 1848, we are able to prove that this “French exception” did not, in fact, exist. The larger the town, the shorter were the conscripts. Among the towns, Paris had the shortest conscripts. By combining individual data with the agricultural survey of 1852, we are able to identify those factors that compensated for this urban penalty—that were positively correlated with height: nutritional availability, the literacy rate, and life expectancy.
    Cliometrica 01/2014; DOI:10.1007/s11698-013-0095-1 · 0.48 Impact Factor

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