Ebook Earnings Management? Sample Selection Bias, Averaging, and Scaling Lead to Erroneous Inferences
A vast literature following Hayn [1995] and Burgstahler and Dichev [1997] attributes the so-called “discontinuity” in earnings distributions around zero to earnings management. Durtschi and Easton [2005] show that, although earnings management is one possible explanation, the evidence suggests that these discontinuities are driven by sample selection bias and scaling. Jacob and Jorgensen [2007] introduce an alternate methodology and conclude that their findings suggest that “while scaling and associated selection biases might contribute to the observed discontinuities, they are not primarily responsible for these discontinuities.” We show that this conclusion is not supported by their analyses. Hence we reiterate the point in Durtschi and Easton [2005] that the shapes of frequency distributions of earnings metrics are not ipso facto evidence of earnings management, and assert that before one can draw conclusions regarding the presence/absence of earnings management, evidence beyond the shapes of these particular distributions must be bought to bear.
The Jacob and Jorgensen [2007] hereafter JJ methodology consists of comparing the distribution of fiscal year (t) earnings with a benchmark distribution, which is the average of the distributions of three “as-if” years of earnings. Each of the three “as-if” years span four consecutive quarters: (1) ending with quarter one of fiscal year t, (2) ending with quarter two of fiscal year t, and (3) ending with quarter three of fiscal year t. In other words, the Jacob and Jorgensen [2007] benchmark is a weighted average of quarterly earnings over the six quarters ending in the third quarter of year t. JJ argue that earnings measured over these alternate years are less likely to suffer from the effects of managerial income manipulation than earnings of the fiscal year; they claim that differences between the distribution of fiscal year earnings and the distribution of the average of the three “as-if” years of earnings is evidence of earnings management.
We show that JJ’s conclusions are not supported by their analyses for three reasons: (1) the JJ benchmark is not meaningful due to a) the characteristics of quarterly data and the fact that Compustat quarterly data are often restated, and b) the fact that averaging changes the shape of a distribution, (2) the JJ method, which relies on the availability of four continuous sets of quarterly data (four quarters per set) exacerbates sample selection problems, and (3) deflation by beginning-of-year market capitalization contributes to the final shape of the (deflated) earnings distributions.
Specifically, we argue that the weighted average earnings benchmark used by JJ is inappropriate because averaging across fiscal years does not make economic sense if, indeed, fiscal years are chosen for sound economic reasons and each year the firm faces different economic factors. We also note that the use of quarterly Compustat data is inappropriate because Compustat reports restated earnings, so that the data JJ analyze differs from the earnings data that was ostensibly managed and announced to the market. In addition, we argue that GAAP for interim financial statements differs from GAAP for the annual report. Finally we show that averaging smoothes the distribution of raw data by combining the idiosyncratic performance in one year with the idiosyncratic performance in the next year, and that averaging also draws observations toward the mean: therefore, differences between the distributions of the averaged “as-if” annual earnings and earnings of the fiscal year are likely due to the effects of averaging rather than due to earnings management.
To clarify and demonstrate the effects of averaging on the shape of frequency distributions, we introduce an analogy based on scores from the Australian Football League. Australian Rules Football has four quarters per game just as the fiscal year is divided into four quarters. We show that, by averaging team-scores across consecutive games, we produce the same effect as JJ observe when averaging net income (earnings per share) across consecutive fiscal years.
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