Zhaoyang Gu

Scale Factor, R2, and the Choice of Levels versus Returns Models

This paper analyzes a potential scale effect on the regression R2 to determine if a scale factor can reconcile the arguments concerning the choice between the price levels model and the returns model. Analytically, it is shown that the scale effect depends on the unknown scale-free economic relation and is generally unpredictable. This makes it difficult to choose one model over the other on the basis of controlling for a scale problem. Empirically, it is shown that a scale factor cannot explain the observed discrepancy between the R2 patterns from the levels and the returns models. The results support the view that the two models likely represent two different economic relations and that the model choice depends on the researchers belief and the research question at hand rather than any scale factor concerns.

Measuring the Pervasiveness of Earnings Management from Quarterly Accrual Volatility

Earnings management is a key issue for financial reporting. The purpose of this paper is to derive a set of indices to measure the pervasiveness of earnings management (PEM) using the properties of quarterly accrual volatility. The PEM index can be viewed as a quality measure of financial reporting and an effectiveness measure for financial monitoring. In contrast to mean-shifting studies in the literature, our measure based on accrual volatility yields two major advantages. First, it relieves us of the necessity of precise assumptions regarding economic events. Second, it provides a macro-perspective on the overall patterns in earnings management. The methodology based on accrual volatility can address issues like the earnings quality, the nature of the informational environment, and the effect of accounting standard setting. The seasonal pattern of accrual volatility can provide a trace of earnings management, even in the absence of further information about specific economic events and resulting managerial actions. Our working hypothesis is that pervasive earnings management leads to the first order stochastic dominance of fourth quarter accrual volatility over the other three quarters. We provide evidence on the relations between previously documented drivers of earnings management and seasonal accrual heteroskedasticity. These drivers include executive compensation, regulatory requirements, bond covenants, and political costs. This empirical support of our working hypothesis validates our application of Kolmogorov-Smirnov (KS) Distance to measure the pervasiveness of earnings management (PEM). We use raw total accruals as the basis for measuring PEM1 and use residuals from Jones? [1991] model to control for mechanical factors in our measurement of PEM2. The usefulness of controls is an empirical issue. Our results suggest that additional controls do not add much power to detect earnings management over and above the simplest measure based on total accruals. KS Distance is powerful in detecting the difference around the central locations of two distributions, but not powerful at the tail ends. We develop two other measures for PEM. First, we estimate the fraction of fourth quarter accruals volatility exceeding the 95th percentile value for the first three quarters (base period) distribution. This fraction, reduced by 5%, constitutes PEM3. Second, we design a simulation method to determine PEM4 as the percentage of firms with a given magnitude of accrual adjustment for the base period accrual volatility to match that of the fourth quarter. Both PEM3 and PEM4 are estimates of percentage of firms involved in earnings management of a given magnitude. However, we should note here that our PEM indices are more likely ordinal than cardinal measures. Though our methods of measuring PEM rely on indirect measurement, we provide direct evidence on the relevance of our method through a series of external validation checks. First, we use a subsample of firms subject to SEC actions relating to alleged earnings manipulation. This data was collected from Accounting and Auditing Enforcement Releases (AAERs) by the SEC. We compare PEM?s for the AAER sample to PEM?s for the COMPUSTAT sample to assess the power of our measures. The PEM indices for the AAER sample are two to three times as large as the PEM indices for the COMPUSTAT sample. Though we avoid interpreting the relative magnitudes literally, these differences do suggest a positive correlation between our PEM indices and the degree of earnings management. Second, we conduct case studies for 10 firms identified by fourth quarter accrual volatility as strongly suspect of earnings management. These studies show that suspect firms frequently engage in activities associated with earnings management, such as CEO turnover, restructuring, public offerings, or they experience losses. Applying our PEM indices to COMPUSTAT data, we find that pervasiveness of earnings management has been relatively stable in the period of 1988-1996.