  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.
