规模报酬人工递增与对数正态抽样问题
Artificial Increasing Returns to Scale and the Problem of Sampling from Lognormals
摘要：
我们展示了如何在城市规模化中人为地、系统地、可预测地出现规模收益递增，而不需要任何排序或正外部性。我们采用了一个模型，其中个人生产率是独立的，在所有城市的对数正态分布的随机变量。我们使用极值理论来分析证明规模收益递增的矛盾出现时，对数生产率的方差大于两倍的对数规模的最小城市的人口规模的横截面回归。我们的贡献是推导出一个分析预测的人工标度指数所产生的这种机制，并制定一个简单的统计测试，试图告诉一个给定的估计是真实的或文物。我们的分析结果验证分析模拟和真实的微观数据的工资在哥伦比亚的城市。我们展示了一个人工标度指数出现在哥伦比亚的数据时，每个市的工人随机样本的大小是$1\%$或更少的总大小。
英文摘要：
We show how increasing returns to scale in urban scaling can artificially emerge, systematically and predictably, without any sorting or positive externalities. We employ a model where individual productivities are independent and identically distributed lognormal random variables across all cities. We use extreme value theory to demonstrate analytically the paradoxical emergence of increasing returns to scale when the variance of log-productivity is larger than twice the log-size of the population size of the smallest city in a cross-sectional regression. Our contributions are to derive an analytical prediction for the artificial scaling exponent arising from this mechanism and to develop a simple statistical test to try to tell whether a given estimate is real or an artifact. Our analytical results are validated analyzing simulations and real microdata of wages across municipalities in Colombia. We show how an artificial scaling exponent emerges in the Colombian data when the sizes of random samples of workers per municipality are $1\%$ or less of their total size.
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