Measurement error and rank correlations

This paper characterizes and proposes a method to correct for errors-in-variables biases in the estimation of rank correlation coeffcients (Spearman's ρ and Kendall's τ). We first investigate a set of suffcient conditions under which measurement errors bias the sample rank correlations toward zero. We then provide a feasible nonparametric bias-corrected estimator based on the technique of small error variance approximation. We assess its performance in simulations and an empirical application, using rich Swedish data to estimate intergenerational rank correlations in income. The method performs well in both cases, lowering the mean squared error by 50-85 percent already in moderately sized samples (n = 1,000).