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

Author

Listed:
  • Howard Bodenhorn

    (Department of Economics, Clemson University)

  • Timothy W. Guinnane

    (Department of Economics, Yale University)

  • Thomas A. Mroz

    (Department of Economics, 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

  • Howard Bodenhorn & Timothy W. Guinnane & Thomas A. Mroz, 2013. "Problems of Sample-selection Bias in the Historical Heights Literature: A Theoretical and Econometric Analysis," Working Papers 1023, Economic Growth Center, Yale University.
    • Handle: RePEc:egc:wpaper:1023
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    More about this item

    Keywords

    self-selection; selection bias; heights; anthropometrics; standards of living; industrialization puzzle; long-run economic growth;
    All these keywords.

    JEL classification:

    • I00 - Health, Education, and Welfare - - General - - - General
    • N3 - Economic History - - Labor and Consumers, Demography, Education, Health, Welfare, Income, Wealth, Religion, and Philanthropy
    • 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
    • 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

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