Fitting Pareto tails to wealth survey data: a practioners’ guide

Taking survey data of household wealth as our major example, this short article discusses some of the issues applied researchers are facing when fitting (Type I) Pareto distributions to complex survey data. The contribution of this article is threefold. First, we show how the ordering of the data vector is related to alternative definitions of the empirical CCDF. Second, we provide an intuitive reinterpretation of the bias-corrected estimator developed by Gabaix and Ibragimov (2011), in terms of the alternative definitions of the empirical CCDF, which allows us to generalize their result to the case of complex survey data. Third, we provide computational formulas for standard Kolmogorov-Smirnov (KS) and Cramer-von Mises (CvM) goodness of-fit tests for complex survey data. Taken together the article provides a concise and hopefully useful presentation of the fundamentals of Pareto tail fitting with complex survey data