Good, great, or lucky? Screening for firms with sustained superior performance using heavy-tailed priors

TL;DR

This study analyzes the long-term performance of over 53,000 firms worldwide, revealing that truly superior performance is rare when accounting for statistical complexities, and introduces a new heavy-tailed prior for large-scale testing.

Contribution

It introduces a novel class of heavy-tailed priors based on the hypergeometric inverted-beta family for improved large-scale multiple testing in performance analysis.

Findings

Superior firm performance is quite rare after adjustments.

Heavy-tailed priors improve large-scale testing accuracy.

Methodology is applicable to global firm performance data.

Abstract

This paper examines historical patterns of ROA (return on assets) for a cohort of 53,038 publicly traded firms across 93 countries, measured over the past 45 years. Our goal is to screen for firms whose ROA trajectories suggest that they have systematically outperformed their peer groups over time. Such a project faces at least three statistical difficulties: adjustment for relevant covariates, massive multiplicity, and longitudinal dependence. We conclude that, once these difficulties are taken into account, demonstrably superior performance appears to be quite rare. We compare our findings with other recent management studies on the same subject, and with the popular literature on corporate success. Our methodological contribution is to propose a new class of priors for use in large-scale simultaneous testing. These priors are based on the hypergeometric inverted-beta family, 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 shrinkage coefficients in a hierarchical normal model. Our results emphasize the usefulness of these heavy-tailed priors in large multiple-testing problems, as they have a mild rate of tail decay in the marginal likelihood $m(y)$---a property long recognized to be important in testing.