Nonlinearity in the Returns‐Earnings Relation: Tests of Alternative Specifications and Explanations*

. Several authors recently challenged the linearity of the returns-earnings relation. In this article, we test the adequacy of alternative nonlinear specifications and examine the validity of various explanations put forth for the returns-earnings nonlinearity. Our main findings are (1) that the nonlinearity persists even when the returns-earnings relation is estimated on annual data (most previous studies used quarterly data) and by a nonparametric procedure that does not impose a specific functional form on the relation; (2) that some nonlinearity exists in the relation between stock returns and earnings levels (previous studies have considered earnings surprises), although it is much less pronounced than the returns-earnings surprise nonlinearity; (3) that the main nonlinear estimation methods used in previous studies and in the current one appear to characterize equally well the underlying returns-earnings relation; predictions of subsequent stock returns based on each of the three specifications the authors examined are largely indistinguishable with respect to their accuracy; (4) that although “special items,” usually identified as transitory by the accountants, appear to contribute to the nonlinearity, there are probably additional contributing factors; the authors find that when all extraordinary items and “special items” are removed from earnings, the returns-earnings relation still exhibits nonlinearity, (5) that the inclusion of cash flow or accrual information also does not eliminate the nonlinearity; and (6) that the returns-cash flow relation is also nonlinear. The authors conclude that nonlinearity of the returns-earnings relation is quite robust across several alternative specifications. However, the candidate explanations they examined do not fully explain the observed nonlinearity. The search for the underlying cause of nonlinearity must therefore continue. Resume. Plusieurs auteurs remettaient recemment en question la linearite de la relation rendements-benefices. Les auteurs de l'article qui suit verifient, pour leur part, si les formes non lineaires envisageables sont appropriees et examinent la validite de diverses explications mises de l'avant pour eclairer la non-linearite de la relation rendements-benefices. Leurs principales observations sont les suivantes: (1) la non-linearite persiste meme lorsque la relation rendements-benefices est estimee a partir de donnees annuelles (la plupart des etudes precedentes s'appuyaient sur des donnees trimestrielles) et au moyen d'un procede non parametrique qui n'impose pas de forme fonctionnelle precise a la relation; (2) une certaine non-linearite existe dans la relation entre le rendement des actions et les niveaux de benefice (les chercheurs avaient, jusque-la, pris en consideration les benefices inattendus), bien que cette non-linearite soit beaucoup moins accentuee que la non-linearite des rendements-benefices inattendus; (3) les principales methodes d'estimation non lineaire utilisees dans les etudes precedentes et dans la presente etude semblent definir tout aussi bien la relation sous-jacente rendements-benefices; les predictions relatives aux rendements subsequents des actions en fonction de chacune des trois formes que les auteurs ont examinees sont, dans la majorite des cas, impossibles a differencier en ce qui a trait au degre d'exactitude; (4) bien que des elements ≪ exceptionnels ≫, habituellement definis comme etant provisoires par les comptables, semblent contribuer a la non-linearite, d'autres facteurs y contribuent probablement aussi; selon les auteurs, lorsque tous les elements extraordinaires et les ≪ elements exceptionnels ≫ sont exclus des benefices, la relation rendements-benefices demeure non lineaire; (5) la relation demeure aussi non lineaire si l'on tient compte de l'information relative aux flux de tresorerie ou aux engagements; et (6) la relation rendements-flux de tresorerie est egalement non lineaire. Les auteurs concluent que la non-linearite de la relation rendements-benefices, envisagee sous plusieurs formes differentes, resiste assez bien a l'analyse. Toutefois, les causes possibles qu'ils ont choisi d'examiner n'expliquent pas entierement la non-linearite observee, et les recherches doivent se poursuivre.