The Effects of Scale Differences on Inferences in Accounting Research : Coefficient Estimates, Tests of Incremental Association, and Relative Value Relevance

Firms' financial data vary considerably with the size of their operations. Such scale differences potentially confound several types of inferences, of which this paper analyzes three. This paper evaluates two potential solutions to these inference problems suggested by theory: (i) deflating the data by a proxy for scale; and (ii) including a scale proxy as an independent variable. First, simulations of bivariate and multivariate regressions show that deflating the data mitigates coefficient bias as effectively as including that proxy as an independent variable. Reconciling this result with the conclusions of Barth and Kallapur (1996, Contemporary Accounting Research) reveals that the prior study (unknowingly) made assumptions that are both economically and statistically unreasonable. Second, deflation results in more accurate tests in terms of mean squared error. Third, deflating by a scale proxy results in well-specified tests of relative association using Vuong's (1989) Z-statistic for non-nested models whereas including the scale proxy as an independent variable results in overstated significance. These results suggest that deflating scale-affected variables is at least as good, and under some statistical criteria, superior to an alternative that uses a scale proxy as a regressor