Non-Linearity and Specification Problems in Unexpected Earnings Response Regression Model - C. S. Agnes Cheng; William S. Hopwood; James C. McKeown (The Accounting Review, 1992)
[In the last two decades of accounting research, many studies have investigated the relation between accounting variables and risk-adjusted security returns. The earliest studies (e.g., Ball and Brown 1968) used simple, nonparametric methods and focused mainly on the question of whether accounting earnings are associated with residual equity returns. Subsequent studies made methodological refinements in both the measurement and the statistical techniques. One important statistical refinement was the "unexpected earnings response regression model" (UERRM), a linear statistical model that uses the unexpected earnings variable as a regressor to explain risk-adjusted returns. The UERRM has become well-known, and many recent studies (e.g., Cornell and Landsman 1989, 686; Daley et al. 1988, 580; Doran et al. 1988, 392; Landsman and Damodaran 1989, 107; McNichols 1989, 15) have used some form of it as a "benchmark" model, against which to compare more complicated models. In one paradigm (so popular that it has become almost standard practice), various accounting variables are added to the UERRM, and their "incremental information content" is assessed by testing the statistical significance of their coefficients. The inferences derived from this procedure are, of course, conditional on the degree to which the UERRM is correctly specified. A critical problem caused by using a misspecified UERRM is that its least squares estimator can lead to erroneous inferences in the research design. Despite the UERRM's popularity, researchers have expressed concerns regarding its specification. For example, Lev (1989) recently surveyed a large number of research papers that used some form of an UERRM and found that for the most part R2 s were low and often bordered on "the negligible." His table 1, which includes statistics from 19 studies, indicates that most reported R2 s are less than 10 percent. Although low R2 s are not proof of major specification problems, Lev does suggest that they are a cause for concern and may be the result of specification problems. Investigation of multiple specification problems is an important aspect of the present study because the various specification issues are interrelated. For example, nonnormality can be associated with nonlinearity, which, in turn, can be associated with heteroscedasticity or variation in the coefficients (Judge et al. 1985, 455, 814, 839). Thus, ad hoc tests for a single specification problem can be misleading and can fail to identify the fundamental problems. To our knowledge, no studies have comprehensively and formally evaluated the specification of the cross-sectional, ordinary least squares model that relates unexpected earnings to risk-adjusted security returns. Therefore, the purpose of this study is to test such a model systematically and empirically for specification problems. Specifically, this study tests for nonlinearity, heteroscedasticity, residual nonnormality, omitted variables, and interfirm systematic and random coefficient variation. Also, when appropriate, adjusted R2 -statistics are included to indicate the degree of misspecification-information that is not directly observable from the tests themselves. A high degree of generality is obtained by using three samples of earnings forecasts as proxies for expected earnings. These were obtained from IBES financial analyst consensus forecasts, Value Line financial analyst forecasts, and COMPUSTAT-based time-series forecasts. Daily and monthly security returns are considered for short and long event-windows, respectively. In addition, one study recently published in The Accounting Review (Cornell and Landsman 1989) is replicated. The findings from all of the samples and the replication indicate that the specification error is large enough to affect conclusions regarding economic relationships. For example, in the replication, the specification problems are shown to lead to substantial instability in inferences from the model.]