The slope coefficient in a rank-rank regression is a popular measure of intergenerational mobility. In this article, we first show that commonly used inference methods for this slope parameter are invalid. Second, when the underlying distribution is not continuous, the OLS estimator and its asymptotic distribution may be highly sensitive to how ties in the ranks are handled. Motivated by these findings we develop a new asymptotic theory for the OLS estimator in a general class of rank-rank regression specifications without imposing any assumptions about the continuity of the underlying distribution. We then extend the asymptotic theory to other regressions involving ranks that have been used in empirical work. Finally, we apply our new inference methods to two empirical studies on intergenerational mobility, highlighting the practical implications of our theoretical findings.

翻译：秩-秩回归中的斜率系数是衡量代际流动性的常用指标。本文首先证明，针对该斜率参数常用的推断方法是无效的。其次，当基础分布非连续时，OLS估计量及其渐近分布可能对秩中并列值的处理方式高度敏感。基于这些发现，我们在不施加任何基础分布连续性假设的前提下，针对一类广义的秩-秩回归设定，为OLS估计量建立了新的渐近理论。随后，我们将该渐近理论扩展至实证研究中涉及秩的其他回归模型。最后，我们将新的推断方法应用于两项关于代际流动性的实证研究，以凸显本理论发现的实际意义。