Large-scale simultaneous testing with hypergeometric inverted-beta priors

We develop a new class of distributions for use in large-scale simultaneous testing. These priors are based on hypergeometric inverted-beta priors, and have two main attractive features: heavy tails, and computational tractability. The family is a four-parameter generalization of the normal/inverted-beta prior, and is the natural conjugate prior for a shrinkage coefficients in a hierarchical normal model. Our results emphasize the usefulness of these of heavy-tailed priors in large multiple-testing problems, as they have mild rate of tail decay in the marginal likelihood m(y)—a property long recognized to be important in testing. We apply our proposed methodology by testing historical patterns of ROA (return on assets) for a cohort of 11,298 publicly traded firms across 93 countries. Our goal is to determine which firms, if any, have systematically outperformed their peer groups over the past 45 years. We find evidence that demonstrably superior performance is quite rare. We compare our findings with the popular literature on corporate success. By our reckoning, these books appear to be studying a sample wherein the majority of firms have performance profiles that are statistically indistinguishable from random chance. These conclusions are consistent with other recent studies on the subject (e.g. Henderson et al., 2009).