Problems of Sample-selection Bias in the Historical Heights Literature: A Theoretical and Econometric Analysis
Creators: name: Bodenhorn, Howard
name: Guinnane, Timothy
name: Mroz, Thomas
name: Bodenhorn, Howard
name: Guinnane, Timothy
name: Mroz, Thomas
Publisher: name: Unknown
Year: 2013
Subjects: subject: Health Economics and Policy
subject: International Development
subject: Labor and Human Capital
subject: Research Methods/ Statistical Methods
subject: self-selection
subject: selection bias
subject: heights
subject: anthropometrics
subject: standards of living
subject: industrialization puzzle
subject: long-run economic growth

description: An extensive literature uses anthropometric measures, typically heights, to draw inferences about living standards in the past. This literature's influence reaches beyond economic history; the results of historical heights research appear as crucial components in development economics and related fields. The historical heights literature often relies on micro-samples drawn from sub-populations that are themselves selected: examples include volunteer soldiers, prisoners, and runaway slaves, among others. Contributors to the heights literature sometimes acknowledge that their samples might not be random draws from the population cohorts in question, but rely on normality alone to correct for potential selection into the sample. We use a simple Roy model to show that selection cannot be resolved simply by augmenting truncated samples for left-tail shortfall. Statistical tests for departures from normality cannot detect selection in Monte Carlo exercises for small to moderate levels of self-selection, obviating a standard test for selection in the heights literature. We show strong evidence of selection using micro-data on the heights of British soldiers in the late eighteen and nineteenth centuries. Consequently, widely accepted results in the literature may not reflect variations in living standards during a soldier's formative years; observed heights could be predominantly determined by the process determining selection into the sample. A survey of the current historical heights literature illustrates the problem for the three most common sources: military personnel, slaves, and prisoners.
description: This paper was first circulated under a different title. For comments and suggestions we thank Shameel Ahmed, Cihan Artunç, Gerard van den Berg, Claire Brennecke, Jeremy Edwards, James Fenske, Amanda Gregg, Farly Grubb, Sukjin Han, Brian A'Hearn, Philip Hofmann, 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, David R. Weir, and participants in seminars at the University of Michigan, the University of Nuremberg, the Queen's University (Ontario), the Rhein-Westfälisches Wirtschaftsintitut, Tulane University, and the 2012 Cliometrics meetings. We acknowledge financial support from the Yale University Economic Growth Center. Meng Liu, Yiming Ma, and Adèle Rossouw provided excellent research assistance. Direct correspondence to Guinnane: timothy.guinnane@yale.edu.