Long-run changes in living standards occupy an important place in development and growth economics, as well as in economic history. An extensive literature uses heights to study historical living standards. Most historical heights data, however, come from selected subpopulations such as volunteer soldiers, raising concerns about the role of selection bias in these results. Variations in sample mean heights can reflect selection rather than changes in population heights. A Roy-style model of the decision to join the military formalizes the selection problem. Simulations show that even modest differential rewards to the civilian sector produce a military heights sample that is significantly shorter than the cohort from which it is drawn. Monte Carlos show that diagnostics based on departure from the normal distribution have little power to detect selection. To detect height-related selection, we develop a simple, robust diagnostic based on differential selection by age at recruitment. A companion paper (H. Bodenhorn, T. Guinnane, and T. Mroz, 2017) uses this diagnostic to show that the selection problems affect important results in the historical heights literature.
For comments and suggestions, we thank Shameel Ahmad, Cihan Artunç, Gerard van den Berg, Claire Brennecke, Jeremy Edwards, William English, James Fenske, Amanda Gregg, Farly Grubb, Sukjin Han, Brian A’Hearn, Philip Hoffmann, Sriya Iyer, John Komlos, John Murray, Sheilagh Ogilvie, Jonathan Pritchett, Paul Rhode, Mark Rosenzweig, Gabrielle Santangelo, Richard Steckel, Jochen Streb, William Sundstrom, Werner Troesken, James Trussell, Christopher Udry, Marianne Wannamaker, John Warner, David Weir, and participants in seminars at the University of Michigan, the University of Nuremberg, Queen’s University (Ontario), the Rhein-Westfälisches Wirtschaftsintitut, Tulane University, and the 2012 Cliometrics meetings. We acknowledge financial support from the Economic Growth Center at Yale University and the Bernard B. and Eugenia A. Ramsey Chair of Private Enterprise at Georgia State University. Meng Liu, Yiming Ma, Adèle Rossouw and Lucas Zavala provided excellent research assistance. Direct correspondence to Guinnane: email@example.com. The views expressed here are the authors’ and not necessarily those of the Federal Reserve Bank of Atlanta or the Federal Reserve System.
Bodenhorn, H., Guinnane, T.W. and Mroz, T.A. (2019), "Theory and Diagnostics for Selection Biases in Historical Height Samples", Research in Economic History (Research in Economic History, Vol. 35), Emerald Publishing Limited, Bingley, pp. 59-89. https://doi.org/10.1108/S0363-326820190000035005
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