Use of R-squared in Accounting Research: Measuring Changes in Value Over the Last Four Decades

Use of R-squared in Accounting Research: Measuring Changes in Value Over the Last Four Decades
Author(s): Brown, Stephen and Lo, Kin and Lys, Thomas
Year: 1999
Paper Number: GBS-ACC-1999-001
Goizueta Department: Accounting

Abstract

This study examines the properties of the R-squared metric frequently used in accounting research as a measure of value relevance. Analytical results show that the metric is unreliable in the presence of scale effects. Specifically, we show that the metric is upwardly biased for accounting studies, and the bias is increasing in the scale factor's coefficient of variation. We conclude that it is invalid to make cross-sample comparisons of R-squared, whether the samples are drawn cross-sectionally or over time, unless the researcher controls for differences in the coefficient of variation across the samples. Applying this theory empirically, our results show that the finding of increasing value relevance in Collins, Maydew, and Weiss (1997) and Francis and Schipper (1998) are attributable to over time increases in the coefficient of variation of scale. After controlling for these effects, we find that there has been a decline in value relevance as measured by R-squared.