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 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.     

Insurance demand in the presence of loss-dependent background risk

We analyze insurance demand when insurable losses come with an uninsurable zero-mean background risk that increases in the loss size. If the individual is risk vulnerable, loss-dependent background risk triggers a precautionary insurance motive and increases optimal insurance demand. Prudence alone is sufficient for insurance demand to increase in two cases: the case of fair insurance and the case where the smallest possible loss exceeds a certain threshold value (referred to as the large loss case). We derive conditions under which insurance demand increases or decreases in initial wealth. In the large loss case, prudence determines whether changes in the background risk lead to more insurance demand. We generalize this result to arbitrary loss distributions and find conditions based on decreasing third-degree Ross risk aversion, Arrow–Pratt risk aversion, and Arrow–Pratt temperance.     

Health insurers' use of quality improvement expenses to achieve a minimum medical loss ratio requirement

Health insurer medical loss ratios (MLRs) are the percentage of premium dollar spent on medical claims and healthcare quality improvement expenses (QIEs). QIEs include activities to improve patient health outcomes and safety, reduce medical errors, and prevent hospital readmissions. The Affordable Care Act mandates minimum MLRs in certain health insurance markets lest rebates be paid to policyholders. QIEs are reported in all markets regardless of whether that market is subject to minimum MLR requirements. Using health insurer statutory filings for a sample of group market insurers from 2010 to 2018, we employ a mixed regression discontinuity/regression kink approach to evaluate whether QIEs are used by insurers as a potential strategy for meeting the minimum MLR requirement. We show that health insurers' QIE increase in the loss ratio until meeting the minimum MLR requirement, have a significant discontinuous jump at the threshold, and decrease above the threshold after the introduction of the MLR mandate.