Proportion of bounded and vacuous null claims in finance

Determine the proportion of published “no effect” claims in finance that are bounded nulls rejecting consequential effect sizes versus vacuous null claims that fail to distinguish zero, negligible, and meaningful effects.

Background

The paper distinguishes bounded null claims, in which a confidence interval excludes economically consequential effect sizes, from vacuous null claims, in which consequential effects remain compatible with the data alongside zero. It notes that the existing finance literature contains an unknown proportion of each type, because conventional reporting typically treats statistical insignificance as evidence of no economic effect without examining the confidence interval’s economically relevant bounds.

The paper states that identifying which published null claims are bounded or vacuous is an empirical and answerable question requiring only the reported coefficient and standard error. The author describes an ongoing systematic audit of null claims in leading finance journals, with results intended for a companion paper.

References

There is an unknown proportion of “no effect” claims of each kind: i) bounded nulls that were undersold as mere insignificance, and ii) vacuous null claims that were oversold as evidence of absence. Which claims are which is an empirical question, and an answerable one.

— Two Kinds of Nothing: What Insignificant Results in Finance Actually Show  (2608.30490 - Tan, 31 Aug 2026) in Section 5, “Implications, and the audit ahead”