The Empirical Results of the Relationship Between the Stakeholders and Earnings Manipulation Around the Zero-Earnings Threshold
5. Additional Tests
5.1 Annual Earnings Histogram
Regarding the application of prospect theory, Hayn (1995) addresses
discontinuities around the zero-earnings threshold in annual earning histograms.
Burgstahler and Dichev (1997) identify the discontinuities around zero in the 1976 and 1994 data of US firms, which confirms that they manipulated earnings around the zero-earnings threshold.30 In examining these empirical results, Durtschi and Easton (2005) suspect that such discontinuities are false readings attributable to scaling. Jacob and Jorgensen (2007) expand on the study by Burgstahler and Dichev (1997) and formulate a different research design, which confirms the existence of discontinuities in the histograms and supports the conclusion of Burgstahler and Dichev (1997).
The research design of Jacob and Jorgensen (2007) involves using two approaches to measure annual earnings: fiscal annual earnings and nonfiscal annual earnings (i.e., total earnings from the second quarter to the first quarter of the following year, from the third quarter to the second quarter of the following year, or from the fourth quarter to the third quarter of the following year). A nonfiscal annual earnings histogram was created to predict the distribution of fiscal annual earnings (i.e., an earnings histogram without earnings management).
The results show that loss manipulation occurred only in the fiscal annual earnings but not in the nonfiscal annual earnings. Jacob and Jorgensen (2007) maintain that nonfiscal annual earnings are less likely to be affected by earnings management. If fiscal year earnings are managed in the fourth quarter and if the earnings management effects reverse in subsequent quarters, then this alternate annual earnings figure might represent the economic earnings for a year more accurately than the fiscal year earnings reported in firms’ annual financial statements.
Jacob and Jorgensen (2007) indicate that the greatest challenge of testing for earnings management lies in specifying comparison standards in the absence of manipulation (i.e., under the null hypothesis). Most studies that examine earnings management through accrual manipulation adopt the model employed by Jones (1991) to estimate discretionary accruals under the null hypothesis. However,
30 The research method of Burgstahler and Dichev (1997) is employed in further studies to investigate earnings manipulation around the threshold (Dichev and Skinner, 2002;
Roychowdhury, 2006; Jacob and Jorgensen, 2007; Lin, 2001).
Kothari, Leone, and Wasley (2005) identify potential errors in the model specifications used by Jones (1991) to test firms demonstrating extreme performance. Similarly, specification problems are present in histograms of earnings without manipulation when they are used to test earnings management.
Jacob and Jorgensen (2007) indicate that flaws may exist in the approach of Burgstahler and Dichev (1997), in which the average of the number of firms in the adjacent partitions of the first partition to the left of the zero-earnings threshold is taken as the expected frequency.31 The potential flaws include the following: (a) if earnings manipulation around the threshold is identified, then the frequencies in partitions adjacent to the threshold may also be affected by the manipulation. (b) If earnings management is identified in more than one partition, then using the average number of neighboring firms on the two sides of the partition to obtain the expected distribution may not enable detecting earnings management. (c) If the potential partition of earnings management is also the peak of the earnings distribution, then the expected distribution that is calculated may not be applicable.
Therefore, Jacob and Jorgensen (2007) incorporate three quarters of the nonfiscal annual earnings histogram as the expected fiscal earnings distribution (i.e., earnings histograms without earnings management) to conduct z tests of discontinuity around the zero-earnings threshold, as follows:
]
where pi(q) represents the proportion of the samples of earnings in the annual period ending in Quarter q in Partition i (q = 1, 2, 3, 4);
Diff is a test statistic
i31 In statistical testing to identify discontinuities around zero-earnings thresholds, Burgstahler and Dichev (1997) designate the first interval on the left of the threshold (Interval 0) as the interval of firms with small negative earnings closest to the threshold. If the actual frequency distribution of the firms in Interval 0 is significantly lower than that of the predicted frequency distribution (the average frequency distribution of the firms in Partitions -1 and 1), and the z test fulfills the level of significance (Burgstahler and Dichev, 1997, p. 103, Note 6), then the firms are confirmed to have managed earnings to avert losses.
and represents the difference between the actual distribution and the expected distribution;
VAR represents the asymptotic variance of Diff;
iZ represents the
i asymptotic distribution (standard normal distribution); and N represents the number of observations.The higher the absolute value of z is, the greater the difference between the actual distribution and the expected distribution. Therefore, a greater negative value in Partition 0 indicates that the sample ratio of fiscal group in the partition is significantly lower than the corresponding sample ratio of nonfiscal group (expected distribution); a greater positive value in Partition 1 indicates that the sample ratio of fiscal group in the partition is significantly higher than the corresponding sample ratio of nonfiscal group. Thus, a discontinuity is identified around the zero-earning threshold in the annual earnings histogram and confirms that firms have manipulated the threshold to avert losses.
Currently, no studies adopt the model of Jacob and Jorgensen (2007) to verify whether loss-aversion earnings management in Taiwanese listed firms can be attributed to scaling.32 The additional test in this study uses the model of Jacob and Jorgensen (2007) to formulate a cross-sectional earnings histogram and to conduct a statistical test of earnings manipulation around the zero-earnings threshold. Durtschi and Easton (2005) maintain that analysts and financial media typically report earnings per share (EPS) rather than net incomes.33 Therefore, the earnings histograms in this study are presented in terms of EPS.34 With mean EPS as the center, two standard deviation values were designated on each side of the mean, with 150 partitions being divided among these four standard deviation
32 Studies that incorporate the earnings histogram of Burgstahler and Dichev (1997) reveal that earnings management is prevalent in Taiwanese firms. However, excluding the histogram of the electronics industry by Lin (2001), all other studies in Taiwan involving earnings histograms are Master’s theses and are therefore not displayed in detail.
33 Durtschi and Easton (2005) suggest that the discontinuity in earnings histograms may be caused by selection bias. Because no consensus among scholars has been reached regarding the EPS data from the I/B/E/S (Degeorge, Patel and Zeckhauser, 1999) and Compustat DBs (Burgstahler and Dichev, 1997), we adopt single-quarter and cumulative financial statements from the TEJ Finance DB to avoid this problem.
34 In the sensitivity test, we also plotted earnings histograms by using net and ordinary incomes after subtracting equity market capitalizations. Discontinuity was identified around the zero-earnings threshold in each histogram, confirming the reports on EPS.
intervals.35 The total number of samples in the chart is 42,151, including 10,457 fiscal and 31,604 nonfiscal observations.36
Figures 1-1 to 1-5 show the earnings histograms based on EPS. Discontinuity was identified around the zero-earnings threshold in the fiscal earnings histograms (Figure 1-4), but the patterns around the thresholds in the fiscal earnings histograms ending at the end of the first, second, and third quarters (Figures 1-1–
1-3) and the combined nonfiscal chart (Figure 1-5) are relatively smooth.
Specifically, the annual earnings histograms of Taiwanese listed firms plotted according to the model of Jacob and Jorgensen (2007) are consistent with their empirical findings; the discontinuities around zero in the annual earnings histograms do not support the assertion of Durtschi and Easton (2005) that they may be attributable to scaling.
Table 4 lists the actual and the expected frequencies of fiscal annual earnings (EPS) for 20 partitions around the zero-earnings threshold. The expected frequencies are the average frequencies of the nonfiscal groups. The partitions below the zero-earnings threshold were labeled Partitions 0 to -10. Among the 11 frequencies in these partitions, 10 showed negative variance in the actual frequency from the expected frequency for fiscal annual earnings. The partitions above the zero-earnings threshold were labeled Partitions 1 to 9. Eight frequencies in these partitions showed positive variance in the actual frequency from the expected frequency. Moreover, the deviation from the expected frequency ratio is significantly negative in Partition 0 (z = -5.77412) and significantly positive in Partition 1 (z = 6.18599). The frequency of small negative earnings (Partition 0) is
35 The class interval of the EPS histograms obtained using the four annual earnings measurement approach is approximately .08 (.0848 for Figure 1-1, .0852 for Figure 1-2, .0860 for Figure 1-3, and .0859 for Figure 1-4). Figure 1-5 combines the histograms for nonfiscal annual earnings (i.e., the frequency totals of the corresponding pairs of samples on both sides of the zero-earnings threshold in Figure 1-1–1-3): annual earnings calculated at the end of the first (Figure 1-1), second (Figure 1-2), and third quarters (Figure 1-3). Therefore, no class intervals exist in Figure 1–5. In addition, the intervals among the four standard deviation values were divided into 100 or 200; the results are consistent with the empirical results of this study.
36 There were a total of 31,604 data points for the nonfiscal group, including 10,517 data points on the total earnings from the second quarter to the first quarter of the following year, 10,529 data points on the total earnings from the third quarter to the second quarter of the following year, and 10,558 data points on the total earnings from the fourth quarter to the third quarter of the following year.
Figure 1
Figure 1-1
Earnings (EPS) Histograms for Nonfiscal Year Ending at the End of the
First Quarter
Figure 1-2
Earnings (EPS) Histograms for Nonfiscal Year Ending at the End of the Second
Quarter
Figure 1-3
Earnings (EPS) Histograms for Nonfiscal Year Ending at the End of the
Third Quarter
Figure 1-4
Earnings (EPS) Histograms for fiscal Year
Figure 1-5
Earnings (EPS) Histograms for Nonfiscal Year Ending at the End of the
First, Second, and Third Quarter