How Wealthy are the Rich?

Abstract

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 use 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 1 to 9 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 one hand, and statistical biases, on the other hand. 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.

Measures of Firm Performance and Concentration: Stylized Facts and a Dilemma of Data Reproduction

“…While this maneuver accentuates the tail behavior of the distribution we believe it is not necessary or helpful to top code data because it risks discarding important information. The long standing problems of top coded income and wealth data for the study of the income and wealth distribution clearly illustrate this point (Jenkins et al 2009, Schneider 2015, Schneider & Scharfenaker 2020, Schulz & Milaković 2021.…”

Top-End Wealth Accumulation: The <i>Forbes</i> Lists and Wealth Inequality

“…Abundant empirical study confirms that the wealthy do receive higher average returns on capital, even adjusted for risk (Saez & Zucman, 2020). As Schulz and Milakovic point out, whether the wealthier are wealthier because they obtain higher returns on their wealth, or whether they receive higher returns because they are wealthier, are observationally equivalent (Schulz & Milakovic, 2021). However, the data are consistent with a finding that the rates at which wealth increases rise with levels of wealth, much as income growth tends to increase in proportion to the level of income (Schulz & Milakovic, 2021).…”

“…As Schulz and Milakovic point out, whether the wealthier are wealthier because they obtain higher returns on their wealth, or whether they receive higher returns because they are wealthier, are observationally equivalent (Schulz & Milakovic, 2021). However, the data are consistent with a finding that the rates at which wealth increases rise with levels of wealth, much as income growth tends to increase in proportion to the level of income (Schulz & Milakovic, 2021). The evidence supports a conclusion that the rules governing the operation of capital markets favor those with the greatest wealth.…”