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 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 historical as well as contemporary bin-aggregated or histogram-type data, something that 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.
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Find related papers by JEL classification: C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods C81 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Microeconomic Data D3 - Microeconomics - - Distribution D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement I1 - Health, Education, and Welfare - - Health I1 - Health, Education, and Welfare - - Health N3 - Economic History - - Labor and Consumers, Demography, Education, Income, and Wealth
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