Extreme Value Estimation for Heterogeneous Data

We develop a universal econometric formulation of empirical power laws possibly driven by parameter heterogeneity. Our approach extends classical extreme value theory to specifying the tail behavior of the empirical distribution of a general data set with possibly heterogeneous marginal distributions. We discuss several model examples that satisfy our conditions and demonstrate in simulations how heterogeneity may generate empirical power laws. We observe a cross-sectional power law for US stock losses and show that this tail behavior is largely driven by the heterogeneous volatilities of the individual assets.本研究构建了一种通用的计量经济学公式，以解析可能由参数异质性驱动的经验幂律。该方法将经典极值理论扩展至界定一般数据集经验分布的尾部行为，其中边缘分布可能存在异质性。我们讨论了满足条件的多类模型示例，并在模拟中展示了异质性如何产生经验幂律。我们观察到美国股票损失的横截面幂律，并表明这种尾部行为主要受个别资产异质波动性的驱动。