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Ever read a study claiming "we found no evidence that X affects Y"? Sounds like a non-result, but in finance it happens all the time. The catch: "statistically insignificant" doesn't mean "zero effect." It just means the data can't rule out zero — but can't rule out a bunch of other values either.

Imagine measuring a door's height with a bent ruler: if the result is "between 1.80 and 2.20 meters," you've learned little. But a precise ruler saying "between 1.99 and 2.01 meters" tells you the door is standard. The first interval is vacuous, the second is bounded and informative.

The author proposes a simple rule: before analyzing, declare the smallest effect that would matter in practice (e.g., "a 1% rate hike changes investments by at least $10M"). Then compare that number with the confidence interval's edges. If the interval excludes that effect, you have a real finding: the effect is too small to matter. If the interval includes it, the study says nothing.

Often one side of the interval is informative, the other vacuous. Saying "no effect" hides this split. Next time you see "not significant," ask: is the interval tight enough to rule out what counts?

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The paper distinguishes two types of "insignificant" results that look identical in standard regression tables. A "bounded null claim" has a confidence interval tight enough to exclude economically meaningful effects: a genuine finding proving the effect is too small to matter. A "vacuous null claim" has an interval so wide it includes meaningful effects: it establishes nothing, often due to low statistical power, weak data, or flawed identification.

The operational proposal is minimal: authors must pre-declare a "minimum consequential effect size" (MCES) in the dependent variable's units per a named increment of the regressor. Then compare the MCES with the confidence interval edges (typically 95%). If the interval excludes MCES on both sides → bounded null (informative). If it includes MCES on at least one side → vacuous null (uninformative).

A key insight: the symmetric phrase "no effect" hides split verdicts. Example: interest rates' effect on investment. MCES = -0.5% investment per +1% rate. 95% CI = [-0.8%, -0.1%]. Left edge excludes -0.5% (bounded), right edge includes -0.5% (vacuous). Verdict: large positive effects ruled out, large negative effects not ruled out. Saying "rates don't affect investment" is misleading.

The author is applying this framework to published null claims in top finance journals (JF, JFE, RFS, JFQA), starting with their own work. Preliminary results: a large fraction of null claims are vacuous on at least one side. Implication: many "non-findings" in the literature are not evidence of absence, but absences of evidence masked as definitive conclusions.

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Authors:
Ronnie SchöbAlfons J. WeichenriederJean-François Tremblay
Date Published:
Original Article arxiv.org
Fact-check verified on 03/10/2026 Primary Study / Original Source
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Creative Commons License CC BY-NC-SA 4.0

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