The Explanatory Power of Explanatory Variables

Abstract

This paper concerns potential disparities between narratives and statistical evidence in empirical accounting research. We focus on the extent to which a regression model’s main variable of interest contributes incrementally to the explanation of the dependent variable. We replicate ten recently published accounting studies, all of which base their conclusions on t-statistics and statistical significance. In eight of the replicated studies, we find that the incremental explanatory power contributed by the main variable of interest is effectively zero. For the remaining two, the incremental contribution is at best marginal. These findings highlight the apparent overreliance on t-statistics as the primary evaluation metric. T-statistics tend to reject the null hypothesis primarily due to a large numbers of observations (N), a point we examine in detail. As a potential remedy, we evaluate the use of Standardized Regressions (SR). The magnitudes of estimated SR coefficients indicate variables’ relevance directly. Empirical analyses establish a strong correlation between a variable’s estimated SR coefficient magnitude and its incremental explanatory power, without reference to N or t-statistics.