A Consistent Research Design for Value Relevance Studies

We argue that Ohlson's linear solution to the residual earnings (RE) equation, a crucial component of widely used value relevance research designs, is not necessarily a linear regression. Moreover, its coefficients are firm-dependent. As such, its empirical specifications, the price-levels and the returns-earnings regressions are structurally ill-suited for consistent inference in cross-sections. We prove the existence of a non-linear regression solution to the RE equation and propose a valuation-based research design that builds on such a solution and warrants a consistent estimation of the empirical specification. Its estimation turns out to be an optimal implementation of the price-to-book (P/B) multiple valuation, an easy-to-apply technique familiar to the accounting community. The proposed regression view on multiple valuation identifies the P/B value with a price that incorporates earnings expectations formed only on the basis of the current levels of the RE drivers. Using a large sample of US non-financial firms over almost 40 years, we document the usefulness of the alternative research design through a comparative testing of two economically-motivated and intuitively-appealing predictions: earnings volatility and the quality of accruals are value-relevant. While the standard research design does not validate them, the approach based on the regression solution to the RE shows a significant association between prices and the two attributes for most of the years in the sample.