Across-Sample Incomparability of R2s and Additional Evidence on Value Relevance Changes Over Time

Abstract

Given the increasing popularity of across-sample R2 comparisons in accounting research, this paper illustrates why the regression R2s are incomparable across samples and the general nature of this problem. The regression residual dispersion with proper control for scale is proposed as the alternative measure of explanatory power for across-sample comparisons. In market-on-accounting variable regressions, this measure can be conveniently interpreted as the degree of accounting-based pricing errors and be used as a measure of value relevance of accounting information. As an application, the issue of over-time value relevance changes is re-visited. In contrast to prior mixed findings based on the R2 measure, a decline of value relevance since the early 1970's is robustly detected using the alternative measure.

Keywords: Econometric models, R2, residuals, pricing errors, value relevance

JEL Classification: C51, G10, M41