Gaussian Rank Correlation and Regression

Abstract

We study the statistical properties of Pearson correlation coefficients of Gaussian ranks, and Gaussian rank regressions -- OLS applied to those ranks. We show that these procedures are fully efficient when the true copula is Gaussian and the margins are non-parametrically estimated, and remain consistent for their population analogues otherwise. We compare them to Spearman and Pearson correlations and their regression counterparts theoretically and in extensive Monte Carlo simulations. Empirical applications to migration and growth across US states, the augmented Solow growth model, and momentum and reversal effects in individual stock returns confirm that Gaussian rank procedures are insensitive to outliers.