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

• Authors: Josée Leblanc, David Sahn and Jean-Yves Duclos.
• BSE Working Paper: 381 | September 15
• Keywords: welfare , health inequality , health , aggregate data , 19th-century France
• JEL codes: C14, C81, D3, D63, I1, I3, N3
• welfare
• health inequality
• health
• aggregate data
• 19th-century France

This paper develops a methodology to estimate the entire population distributions from bin-aggregated sample data. We do this 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 distribution of height data from potential army conscripts across France’s 88 departments for most of the nineteenth century. These comparisons were 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 historical as well as contemporary 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 due to political sensitivity and/or confidentiality concerns.