Use of R2 in accounting research: measuring changes in value relevance over the last four decades, Journal of Accounting and Economics
Accounting research uses R2 frequently, for example, as a measure of value relevance. Our analytical results show that the metric is unreliable in the presence of scale effects. Specifically, we show that R2s in levels regressions are higher in the presence of scale effects. Moreover, R2 is increasing in the scale factor's coefficient of variation. We conclude that it is invalid to make between sample comparisons of R2, whether the samples are drawn cross-sectionally or over time, unless the researcher controls for differences in the coefficient of variation of the scale factor across samples. Applying this theory empirically, we show that the finding of increasing value relevance in Collins, Maydew, and Weiss (1997) and Francis and Schipper (1999) are attributable to increases in the coefficient of variation of scale over time. After controlling for these effects, we find that there has been a decline in value relevance, as measured by R2.
Stephen Brown, Kin Lo, Thomas Lys
Brown, Stephen, Kin Lo, and Thomas Lys. 1999. Use of R2 in accounting research: measuring changes in value relevance over the last four decades. Journal of Accounting and Economics. 28(2): 83-115.