Historical Height Samples with Shortfall: A Computational Approach

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Abstract
Research in economic history frequently uses human height as a proxy for net nutrition. This anthropometric method enables historians to measure time trends and differences in nutritional status. However, the most widely used data sources for historical heights, military mustering registers, cannot be regarded as random samples of the underlying population. The lower side of the otherwise normal distribution is eroded by a phenomenon called shortfall, because shorter individuals are under-represented below a certain threshold (truncation point). This paper reviews two widely used methods for analyzing historical height samples with shortfall - the Quantile Bend Estimator (QBE) and the Reduced Sample Maximum Likelihood Estimator (RSMLE). Because of the drawbacks of these procedures, a new computational approach for identifying the truncation point of height samples with shortfall, using density estimation techniques, is proposed and illustrated on an Austrian dataset. Finally, this procedure, combined with a truncated regression model, is compared to the QBE to estimate the mean and the standard deviation. The results demonstrate the deficiencies of the QBE again and cast a good light on the new method.

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