Problems of Sample-Selection Bias in the Historical Heights Literature: A Theoretical and Econometric Analysis
Problems of Sample-Selection Bias in the Historical Heights Literature: A Theoretical and Econometric Analysis
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历史高峰文献中的样本选择偏差问题：理论和计量经济学分析
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
T. Mroz
中科院分区：
文献类型：
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作者：
H. Bodenhorn;T. Guinnane;T. Mroz
大量文献使用人体测量测量，通常是身高，来推断过去的生活水平。这些文学作品的影响超越了经济史；历史高度研究的结果是发展经济学及其相关领域的重要组成部分。历史文献通常依赖于从亚群体中抽取的微观样本，这些样本是自己选择的：例子包括志愿兵、囚犯和逃跑的奴隶等。身高文献的作者有时承认，他们的样本可能不是随机抽取的，而是仅仅依靠正态性来纠正样本中潜在的选择。我们使用一个简单的罗伊模型来表明，选择不能简单地通过增加截断样本来解决左尾短缺。偏离正态性的统计检验不能检测蒙特卡罗练习中对小到中等水平的自我选择的选择，从而避免了高度文献中选择的标准检验。我们利用18世纪末和19世纪英国士兵身高的微观数据，展示了强有力的选择证据。因此，文献中被广泛接受的结果可能不能反映士兵成长期生活水平的变化；观察到的高度可以主要由确定进入样品的选择过程决定。对当前历史文献的调查说明了三个最常见的问题来源：军事人员、奴隶和囚犯。
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.