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Sample-Selection Bias and Height Trends in the Nineteenth-Century United States

Published online by Cambridge University Press:  14 March 2019

Ariell Zimran*
Ariell Zimran is Assistant Professor of Economics, Vanderbilt University, PMB 351819, 2301 Vanderbilt Place, Nashville, TN 37235-1819 and Faculty Research Fellow, National Bureau of Economic Research. E-mail:


After adjusting for sample-selection bias, I find a net decline in average stature of 0.64 inches in the birth cohorts of 1832–1860 in the United States. This result supports the veracity of the Antebellum Puzzle—a deterioration of health during early modern economic growth in the United States. However, this adjustment alters the trend in average stature in the same cohort range, validating concerns over bias in the historical heights literature. The adjustment is based on census-linked military height data and uses a two-step semi-parametric sample-selection model to adjust for selection on observables and unobservables.

Copyright © The Economic History Association 2019 

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I am indebted to Joel Mokyr, Joseph Ferrie, and Matthew Notowidigdo for encouragement and guidance, and to Ann Carlos (the editor), William Collins, and anonymous referees for detailed comments on several drafts of this paper. I also thank Ran Abramitzky, Hoyt Bleakley, Louis Cain, John Cawley, Stephanie Chapman, Carola Frydman, Seema Jayachandran, John Komlos, Peter Koudijs, Thomas Mroz, Aviv Nevo, Sangyoon Park, Pedro Sant’Anna, Yannay Spitzer, Richard Steckel, Benjamin Ukert, and Carlos Villareal for helpful suggestions and insightful comments. Thanks are also due to Roy Mill for access to the dEntry transcription system; to seminar participants at Northwestern University, the London School of Economics, Vanderbilt University, the University of Colorado Boulder, the University of Queensland, the Australian National University, the University of Melbourne, and Stanford University; to participants in the 2013 Asian Meetings of the Econometric Society, the 2015 Western Economic Association International Graduate Student Dissertation Workshop and Conference, the 2015 European Historical Economics Society Conference, the 2015 Illinois Economic Association Conference, the 2015 Social Science History Association Conference, and the 2015 H2D2 Research Day at the University of Michigan for helpful comments; and to Christie Jeung for excellent research assistance. This project was supported by the Northwestern University Center for Economic History, the Balzan Foundation, a Northwestern University Graduate Research Grant, and an Economic History Association Dissertation Fellowship. Computations were performed on the Social Sciences Computing Cluster at Northwestern University and on the Advanced Computing Cluster for Research and Education at Vanderbilt University. This project, by virtue of its use of the Union Army Data, was supported by Award Number P01 AG10120 from the National Institute on Aging. The content is solely the responsibility of the author and does not necessarily represent the official views of the National Institute on Aging or the National Institute of Health. This is a revised version of Chapter 2 of my dissertation. Previous versions of this paper were titled “New Perspectives on Historical Standards of Living: Evidence from US Military Enlistment in the Late Nineteenth Century,” “Does Sample-Selection Bias Explain the Industrialization Puzzle? Evidence from Military Enlistment in the Nineteenth-Century United States,” and “Does Sample-Selection Bias Explain the Antebellum Puzzle? Evidence from Military Enlistment in the Nineteenth-Century United States.” All errors are my own.



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