Problems of Sample-Selection Bias in the Historical Heights Literature: A Theoretical and Econometric Analysis

101 Pages Posted: 9 May 2013

See all articles by Howard Bodenhorn

Howard Bodenhorn

National Bureau of Economic Research (NBER); John E. Walker Department of Economics, Clemson University

Timothy W. Guinnane

Yale University - Department of Economics; CESifo (Center for Economic Studies and Ifo Institute)

Thomas A. Mroz

Department of Economics, Andrew Young School of Policy Studies

Date Written: May 5, 2013

Abstract

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.

Keywords: self-selection, selection bias, heights, anthropometrics, standards of living, industrialization puzzle, long-run economic growth

JEL Classification: I00, N3, O15, O47, C46, C52, C81

Suggested Citation

Bodenhorn, Howard and Guinnane, Timothy W. and Mroz, Thomas A., Problems of Sample-Selection Bias in the Historical Heights Literature: A Theoretical and Econometric Analysis (May 5, 2013). Yale Economics Department Working Paper No. 114, Yale University Economic Growth Center Discussion Paper No. 1023, Available at SSRN: https://ssrn.com/abstract=2261335 or http://dx.doi.org/10.2139/ssrn.2261335

Howard Bodenhorn

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
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John E. Walker Department of Economics, Clemson University ( email )

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United States

Timothy W. Guinnane (Contact Author)

Yale University - Department of Economics ( email )

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New Haven, CT 06520-8268
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(203) 432-3616 (Phone)
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HOME PAGE: http://sites.google.com/site/timothywguinnanec/

CESifo (Center for Economic Studies and Ifo Institute)

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Germany

Thomas A. Mroz

Department of Economics, Andrew Young School of Policy Studies ( email )

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Atlanta, GA 30302-3992
United States

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