How Wealthy Are the Rich?

Underreporting and undersampling biases in top tail wealth, although widely acknowledged, have not been statistically quantified so far, essentially because they are not readily observable. Here we exploit the functional form of power law-like regimes in top tail wealth to derive analytical expressions for these biases, and employ German microdata from a popular survey and rich list to illustrate that tiny differences in non-response rates lead to tail wealth estimates that differ by an order of magnitude, in our case ranging from one to nine trillion euros. Underreporting seriously compounds the problem, and we find that the estimation of totals in scale-free systems oftentimes tends to be spurious. Our findings also suggest that recent debates on the existence of scale- or type-dependence in returns to wealth are ill-posed because the available data cannot discriminate between scale- or type- dependence on the one hand, and statistical biases on the other. Yet both economic theory and mathematical formalism indicate that sampling and reporting biases are more plausible explanations for the observed data than scale- or type-dependence.