Slope coefficients in rank-rank regressions are popular measures of intergenerational mobility. In this paper, we first point out two important properties of the OLS estimator in such regressions: commonly used variance estimators do not consistently estimate the asymptotic variance of the OLS estimator and, when the underlying distribution is not continuous, the OLS estimator may be highly sensitive to the way in which ties are handled. Motivated by these findings we derive the asymptotic theory for the OLS estimator in a general rank-rank regression specification without making 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 three empirical studies. We find that the confidence intervals based on estimators of the correct variance may sometimes be substantially shorter and sometimes substantially longer than those based on commonly used variance estimators. The differences in confidence intervals concern economically meaningful values of mobility and thus may lead to different conclusions when comparing mobility across different regions or countries.

翻译：秩-秩回归中的斜率系数是代际流动性的常用度量指标。本文首先指出此类回归中普通最小二乘（OLS）估计量的两个重要性质：常用的方差估计量无法一致地估计OLS估计量的渐近方差；当基础分布非连续时，OLS估计量可能对结的处理方式高度敏感。基于这些发现，我们在不假设基础分布连续性的前提下，推导了一般秩-秩回归设定中OLS估计量的渐近理论。随后，我们将渐近理论扩展至实证研究中涉及的其他秩回归模型。最后，我们将新的推断方法应用于三项实证研究。研究发现，基于正确方差估计量构建的置信区间，有时可能显著短于、有时又显著长于基于常用方差估计量构建的置信区间。这些置信区间的差异涉及具有经济意义的流动性数值，因此在比较不同地区或国家间的流动性时，可能导致不同的结论。