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

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  • Bodenhorn, Howard

    (Clemson University)

  • Guinnane, Timothy W.

    (Yale University)

  • Mroz, Thomas A.

    (Clemson University)

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.

Suggested Citation

  • Bodenhorn, Howard & Guinnane, Timothy W. & Mroz, Thomas A., 2013. "Problems of Sample-Selection Bias in the Historical Heights Literature: A Theoretical and Econometric Analysis," Working Papers 114, Yale University, Department of Economics.
  • Handle: RePEc:ecl:yaleco:114
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    References listed on IDEAS

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    Cited by:

    1. Lindert, Peter H. & Nafziger, Steven, 2014. "Russian Inequality on the Eve of Revolution," The Journal of Economic History, Cambridge University Press, vol. 74(03), pages 767-798, September.
    2. Baten, Joerg & Juif, Dácil, 2014. "A story of large landowners and math skills: Inequality and human capital formation in long-run development, 1820–2000," Journal of Comparative Economics, Elsevier, vol. 42(2), pages 375-401.
    3. Martine Mariotti, 2015. "Fathers' Employment and Sons' Stature: The Long-Run Effects of a Positive Regional Employment Shock in South Africa's Mining Industry," Economic Development and Cultural Change, University of Chicago Press, vol. 63(3), pages 485-514.
    4. Bailey, Roy E. & Hatton, Timothy J. & Inwood, Kris, 2014. "Health, Height and the Household at the Turn of the 20th Century," IZA Discussion Papers 8128, Institute for the Study of Labor (IZA).
    5. de Beer, Hans, 2016. "The biological standard of living in Suriname, c. 1870–1975," Economics & Human Biology, Elsevier, vol. 22(C), pages 140-154.
    6. Bailey, Roy E. & Hatton, Timothy J. & Inwood, Kris, 2016. "Atmospheric Pollution and Child Health in Late Nineteenth Century Britain," IZA Discussion Papers 10428, Institute for the Study of Labor (IZA).

    More about this item

    JEL classification:

    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C81 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Methodology for Collecting, Estimating, and Organizing Microeconomic Data; Data Access
    • I00 - Health, Education, and Welfare - - General - - - General
    • N30 - Economic History - - Labor and Consumers, Demography, Education, Health, Welfare, Income, Wealth, Religion, and Philanthropy - - - General, International, or Comparative
    • O15 - Economic Development, Innovation, Technological Change, and Growth - - Economic Development - - - Economic Development: Human Resources; Human Development; Income Distribution; Migration
    • O47 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - Empirical Studies of Economic Growth; Aggregate Productivity; Cross-Country Output Convergence

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