Two Kinds of Nothing: What Insignificant Results in Finance Actually Show

Abstract

Claims of the form "we find no evidence that X affects Y" appear throughout the applied finance literature, yet whether such a claim contains evidence of absence or absence of evidence depends entirely on its confidence interval. The term "statistically insignificant" is routinely read to mean zero economic effect. However, a more honest description is that zero could not be rejected along with a range of other coefficient effect sizes. The crucial question is whether effect sizes in that range are consequential. This note distinguishes two kinds of insignificant results that are indistinguishable in a standard regression table: bounded null claims where the intervals reject effect sizes of consequence and thus represent a genuine finding, and vacuous null claims where even consequential effects remain unrejected and therefore establish nothing. I propose a minimal reporting standard for regression results in applied finance, where the smallest consequential effect size is stated (in the units of the decision, per a named increment of the regressor) alongside the descriptive statistics and compared with the relevant edges of the confidence intervals of null claims. Using only the reported coefficient and standard error, authors can distinguish bounded (informative) null claims that reject consequential effect sizes from vacuous null claims that establish no information, perhaps due to deficiencies in data or the identification strategy. The symmetric phrase "no effect" conceals, in particular, the frequent split verdict: bounded in one direction, vacuous in the other. In ongoing work, I apply this framework to published null claims in leading finance journals, beginning with my own.