The Explanatory Power of Explanatory Variables

Abstract

Abstract This paper examines the current empirical accounting research paradigm. We ask: In general, do the estimated regressions support the promoted narratives? We focus on a regression model’s main variable of interest and consider the extent to which it contributes to the explanation of the dependent variable. We replicate 10 recently published accounting studies, all of which rely on significant t-statistics, per conventional levels, to claim rejection of the null hypothesis. Our examination shows that in eight studies, 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. A closer examination of the data shows that the t-statistics produced reject the null hypothesis primarily due to a large number of observations (N). Empirical accounting studies often require N > 10,000 to reject the null hypothesis. To avoid the drawback of t-statistics’ connection with N, we consider the implications of using Standardized Regressions (SR). The magnitude of SR coefficients indicates 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.

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