Use of R-Squared in Accounting Research: Measuring Changes in Value Relevance Over the Last Four Decades
Journal of Accounting & Economics, Vol 28, No 2, January 2000
Posted: 24 Jan 2000
The value relevance of accounting disclosures is the focus of numerous accounting studies. Frequently, the studies operationalize value relevance as the R2 from regressions of stock prices on per share values of accounting earnings and book values of equity. Intertemporal or cross-sample differences in R2 are used as indicators that value relevance of accounting disclosures has changed over time or that value relevance differs across disclosure regimes. The main purpose of this paper is to analyze whether R2 indeed captures the intuitive notion of value relevance sought by the authors.
We model the effect of scale formally and show that scale induces two related problems of interpretation. First, the R2 from a scale-affected regression will, under fairly general conditions, be higher than the R2 from the same regression without scale effects. The second problem of interpretation occurs when comparing R2 between samples with different scale effects. Specifically, we show that R2 increases in the coefficient of variation (CV) of the scale factor.
Consistent with the predictions of our model, we show that the R2 in regressions of price on EPS and BVPS is positively correlated with the cross-sectional CV of the scale factor. Moreover, we find that the CV of the scale factor has increased considerably over the last four decades. Since there is a relation between R2 and CV of the scale factor, if the latter increases, then an increase in R2 is induced, even when there may have been no change, or possibly a decrease, in value relevance. As a result, time series comparisons of R2 are likely to result in erroneous inferences. For example, Collins, Maydew, and Weiss (1997) (CMW) and Francis and Schipper (1999) examine R2 over the last four decades and conclude that value relevance has increased. By replicating CMW we show that their conclusions result from the impact of changes in scale on the regression R2.
We propose two modified research approaches to measure whether there has been a change in value relevance as measured by R2. Each controls for changes in scale effects. First, we estimate proxies for the CV of the scale factor in each of the sample periods. We then analyze differences in the R2 across samples, after controlling for the CV of the scale factor. Second, we remove scale effects from each sample by deflating all observations by proxies for the scale factor. In both instances we find that the conclusions drawn by CMW and FS reverse and that value relevance, as measured by the regression R2, has decreased over the last four decades.
Note: This is a description of the paper and not the actual abstract.
JEL Classification: C51, G10, G38, M41, M44
Suggested Citation: Suggested Citation