A large number of accounting studies have examined the occurrence of earnings management in various contexts. In most of these studies, the earnings management detection model is based on the linear regression model suggested by Jones (1991). A considerable problem with the Jones model is the requirement of long time series of financial statement data. An alternative to estimating the linear regression model coefficients with ordinary least squares (OLS) is to use fuzzy linear regression (FLR) instead. One of the main advantages with FLR described in the literature is its ability to handle small data sets. The purpose of this study is to compare the performance of the OLS-based Jones model with the performance of the FLR-based Jones model. The results show that the performance of both types of models decreases when the length of the time series decreases and that there is no significant difference in the estimated discretionary accruals between the models. The results also show that the FLR-based Jones model outperforms the OLS-based Jones model in detecting simulated earnings management when the estimation time series is short. Overall, the results show that the FLR-based Jones model is a feasible alternative to the OLS-based Jones model, especially when the length of the estimation time series is restricted by data availability.

A large number of accounting studies have examined the occurrence of earnings management in various contexts. There is, for example, evidence suggesting that firms manage earnings in order to avoid violating debt covenants (DeFond & Jiambalvo, 1994) or to influence initial public offering (IPO) valuations (Teoh, Welch, & Wong, 1998). A major challenge in earnings management studies is to find a measure for how much firms have managed their earnings. A common assumption is that earnings are managed through accounting accruals. With this assumption the measure of earnings management is the unexpected part of a firm’s total accruals. Various models have been suggested for dividing the total accruals into non-discretionary (expected) and discretionary (unexpected) accruals. Most of these models are based on the earnings management detection model suggested by Jones (1991). The Jones model is a linear regression model where the level of total accruals is assumed to be explained by property, plant and equipment and the change in sales. In the original Jones model, the regression coefficients are estimated using a firm specific time series comprising data prior to the event year. The expected level of accruals is then calculated using the estimated coefficients with event year data. A considerable problem with the Jones model is the requirement of long time series of financial statement data. Typically, in studies where the Jones model is used the requirement is set to at least ten years of data prior to the event year (e.g. Dechow et al., 1995 and Thomas and Zhang, 2000). This requirement might lead to several problems, such as survivorship bias and non-stationary regression coefficients (Peasnell et al., 2000 and Young, 1999). An alternative to estimating the firm specific regression coefficients with ordinary least squares (OLS) regression is using fuzzy linear regression (FLR), first introduced by Tanaka, Uejima, and Asai (1982). Contrary to probability theory-based OLS regression, FLR is based on possibility theory and fuzzy set theory. With FLR the objective is to minimize the fuzziness of the model rather than the sum of squared residuals. One of the main advantages with FLR described in the literature is its ability to handle small data sets (Shapiro, 2004). This was corroborated empirically by Kim, Moskowitz, and Koksalan (1996) who provided evidence that FLR outperforms statistical linear regression in predictive capability with small data sets. Thus, it is possible that the Jones model regression could be run with shorter time series using FLR. If this is the case, an FLR-based Jones model could reduce several problems originating from the requirement of long time series. The purpose of this study is to compare the performance of the OLS-based Jones model with the performance of the FLR-based Jones model. The focus is on the time series version of the Jones model and the comparison is made using different lengths of the time series. The remainder of this study is organized as follows. The basic operating principle of the linear regression-based accrual models is covered in Section 2. In Section 3 the estimation of FLR coefficients and prediction with FLR models are covered. The research design is presented in Section 4 and the results from the empirical study are presented in Section 5. Section 6 concludes the study.

The purpose of this study was to compare the performance of the OLS-based Jones model with the performance of the FLR-based Jones model. The two types of models were compared with different lengths of the estimation data set time series. The results show that the performance of both types of models decreases when the length of the time series decrease and that there is no significant difference in the estimated discretionary accruals between the models. The results also show that the FLR-based Jones model outperforms the OLS-based Jones model in detecting simulated earnings management when the estimation time series is short. Overall, the results show that the FLR-based Jones model is a feasible alternative to the OLS-based Jones model, especially when the length of the estimation time series is restricted by data availability. This study could be extended by assessing other fuzzy linear regression approaches besides the one suggested by Tanaka, Uejima, and Asai (1982). Furthermore, the performance of a cross-sectional FLR-based Jones model could be compared with the performance of cross-sectional and time series OLS-based Jones models.