ABSTRACT It is common to assume that worker productivity is normally distributed, but this assumption is rarely, if ever, tested. We estimate the distribution of worker productivity, where individual productivity is measured with error, using the productivity of teachers as an example. We employ a nonparametric density estimator that explicitly accounts for measurement error using data from the Tennessee STAR experiment, and longitudinal data from North Carolina and Washington. Statistical tests show that the productivity distribution of teachers is not Gaussian, but the differences from the normal distribution tend to be small. Our findings confirm the existing empirical evidence that the differences in the effects of individual teachers on student achievement are large and the assumption that the differences in the upper and lower tails of the teacher performance distribution are far larger than in the middle of the distribution. Specifically, a 10 percentile point movement for teachers at the top (90th) or bottom (10th) deciles of the distribution is estimated to move student achievement by 8–17 student percentile ranks, as compared to a change of 2–7 student percentile ranks for a 10 percentile change in teacher productivity in the middle of the distribution.

中文翻译：

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论工人生产力的分配：以教师效能与学生成就为例

摘要通常假设工人的生产率是正态分布的，但是这种假设很少（如果有的话）经过检验。我们以教师的生产率为例，估算了工人生产率的分布，其中用误差衡量了个人生产率。我们使用非参数密度估计器，该模型使用田纳西州STAR实验的数据以及北卡罗来纳州和华盛顿州的纵向数据明确说明了测量误差。统计检验表明，教师的生产力分布不是高斯分布，但与正态分布的差异较小。我们的发现证实了现有的经验证据，即个别教师对学生成绩的影响差异很大，并且假设教师绩效分布的上下尾部差异远大于分布中间的差异。具体来说，在分布的顶部（第90位）或底部（第10位）教师的10个百分点的变动估计会使学生的学习成绩提高8-17个学生百分点，而变化幅度为2-7个学生分布中间的教师生产率变化了10％。