论文标题
对未观察到的个体异质性的极端分位数的推断
Inference on Extreme Quantiles of Unobserved Individual Heterogeneity
论文作者
论文摘要
我们开发了一种对未观察到的个体异质性极端分位数进行推断（例如，异质系数，治疗效果）的方法。在这种情况下，推论是具有挑战性的：只有异质性的嘈杂估计值，并且中心极限近似在尾巴中的性能较差。我们得出了一种必要且充分的条件，在该条件下，嘈杂的估计值对极端分位数以及足够的速度和力矩条件提供了信息。在这些条件下，我们为嘈杂的估计值建立了一个极值定理和中间级定理。这些结果可为极端分位数提供简单的无优化置信区间。模拟表明，我们的置信区间具有良好的覆盖范围，而速率条件对于推断的有效性很重要。我们说明了该方法，该方法应用于密度和密度较小的面积之间的企业生产力差异。
We develop a methodology for conducting inference on extreme quantiles of unobserved individual heterogeneity (e.g., heterogeneous coefficients, treatment effects) in panel data and meta-analysis settings. Inference is challenging in such settings: only noisy estimates of heterogeneity are available, and central limit approximations perform poorly in the tails. We derive a necessary and sufficient condition under which noisy estimates are informative about extreme quantiles, along with sufficient rate and moment conditions. Under these conditions, we establish an extreme value theorem and an intermediate order theorem for noisy estimates. These results yield simple optimization-free confidence intervals for extreme quantiles. Simulations show that our confidence intervals have favorable coverage and that the rate conditions matter for the validity of inference. We illustrate the method with an application to firm productivity differences between denser and less dense areas.
