An alternative interpretation of the discontinuity in earnings distributions

The term “discontinuity” is shorthand terminology for an unusually low frequency of small loss observations and an unusually high frequency of small profit observations, relative to the frequencies in the adjacent intervals of the earnings distribution. It does not imply that the cumulative distribution function is discontinuous at zero.

Property-casualty insurers are excluded from the current study’s sample.

See McNichols and Wilson (1988), and McNichols (2000) for further discussion of earnings management research designs.

Prior research, however, finds that the discontinuity exists in samples of nonlisted firms (e.g., Beaver et al. 2003), inconsistent with the exchange listing argument, and that the discontinuity is not sensitive to alternative deflators, such as assets, book value of equity, and net sales (e.g., BD), inconsistent with the market value deflator argument.

We assume that the mean of υ _t is negative, and therefore transitory items affect both the mean and the variance of the distribution of earnings for loss firms.

The choice of a simulation approach represents a trade-off between the potential for over-fitting the data when parameters are allowed to vary by earnings interval versus the potential for outliers in extreme earnings intervals to exert an undue influence on the results in the intervals immediately around zero when parameters are allowed to vary only for profit and loss observations.

An alternative, and econometrically equivalent, specification to the model in Eq. (1) uses the tax provision as the dependent variable instead of net income. We adopt the given specification because it parallels our other analyses comparing the distributions of net income and pretax income.

The Compustat manual indicates that data item #17 includes, among other things, significant nonrecurring items, write-downs or write-offs of receivables and intangibles, inventory write-downs when reported as a separate line item or called nonrecurring, items specifically called “restructuring/reorganization,” “special,” or “nonrecurring,” and nonrecurring profit or loss on the sale of assets, investments, and securities.

After applying all other sample selection criteria, there were 19 observations with one or more of the earnings measures exactly equal to zero.

Although the economic interpretation of ETR for loss firms is unclear, we are merely interested in the income statement effect of income taxes, and for this purpose ETR is a reasonable measure. However, the results in Table 2 are robust to measuring the tax component as income tax expense scaled by beginning-of-the-year market value of common equity. Dhaliwal et al. (2004) examine whether firms manage ETR’s to meet consensus analyst earnings forecasts for a sample of firms with positive pretax income. In contrast, the purpose of our study is to examine whether the accounting treatment of income taxes contributes to a discontinuity in the distribution of earnings.

BD state in their footnote 6 that the variance of the difference between the observed and expected number of observations for interval i is Np _i  (1 − p _i ) + (1/4) N (p _i − 1 + p _i + 1) (1 − p _i − 1 − p _i + 1). The correct variance, however, is Np _i  (1 − p _i ) + (1/4) N (p _i − 1 + p _i + 1) (2 − p _i − 1 − p _i + 1). Because of the difference in the first term in the last parentheses, the estimated standard deviation used in BD and related papers is understated, resulting in an overstatement of the standardized difference test statistic. We report all results using the correct standard deviation, and thus our standardized difference test statistics are somewhat lower than reported in BD.

As discussed earlier, in addition to the discontinuity at zero, there is a decline in the frequency of small loss observations in the bin just below zero relative to the bins to the left of zero and a decline in the frequency of small profit observations to the right of the bins just to the right of zero. Our analysis is silent on the factors that give rise to these differences in frequency.

The drop in mean ETR in the two intervals immediately below zero is due to a decline in the relative proportion of observations with a zero ETR as well as an increase in the relative proportion of observations with a negative ETR (i.e., recognizing tax expense on a pretax loss).

Although the findings are not as visually striking as the comparison of the PRETAX and NI distributions in Fig. 2, the results in Table 3, Panel B (discussed further below) show that there are 1,149 observations in the interval just above zero in the PRESPC distribution compared with 852 in the interval just below zero, a difference of 297 observations. In contrast, there are 1,208 observations in the interval just above zero in the PRETAX distribution compared with 722 in the interval just below zero, a difference of 486 observations. Thus, the gap between the frequency of small profit and small loss firms is nearly twice as large in the PRETAX distribution, primarily due to a decrease in the frequency of small loss observations.

Results are presented after the deletion of statistical outliers. However, none of our inferences is altered if these outliers are retained. In addition, following BD, the tabulated results are for estimations that define the small profit (loss) region to include six intervals immediately above (below) zero. However, none of our inferences is altered if we define the small profit (loss) region to include only one interval immediately above (below) zero. In additional robustness checks, we permitted separate intercepts for each of the four regions of the earnings distribution and estimated the regression using scaled earnings variables, both with no change in inferences.

Ceteris paribus, the standardized difference increases approximately linearly with the square root of sample size. Although sample sizes in Table 5 vary somewhat due to missing items for some of the alternative deflators, the variation is small enough to permit direct comparison across the various tests.

In other portions of their paper, Durtschi and Easton (2005) report t-tests for differences in frequencies between earnings intervals which assumes the expected number of observations in those intervals is equal, i.e., the distribution is flat in the region immediately around zero. This contrasts to BD’s standardized difference test statistic which assumes the expected number of observations in a given interval is the average of the two immediately adjacent intervals, i.e., the distribution is smooth in the region immediately around zero.

An examination of the financial statements for a sample of these observations indicates these firms are typically development stage companies or otherwise had no operations during the years in question.

An examination of 10-K filings for a sample of observations missing current price confirms that their common equity was not listed during the years in question.

Inferences are similar for the number of shares used to calculate basic earnings per share (Compustat data item #54). Because of substantial missing data for the number of shares used to calculate diluted earnings per share (Compustat data item #171), we do not examine this variable.

Untabulated results for the other deflators discussed in this section, ASSETS, CE, and SALES are all quite similar to the MVE results reported in Fig. 5, Panel B.

To insure comparability, all regressions were estimated using the primary sample of observations. However, the results for the share deflators are unchanged if estimated using all observations with earnings and share data available on Compustat, i.e., ignoring the other sample selection criteria.

We note, however, that special items are also reported by relatively few firms, and yet the results indicate their inclusion does affect the earnings distribution and the discontinuity at zero.

As with our analysis of income taxes and special items, we examine each of the earnings components within the usual context in which the component enters into the calculation of earnings. As noted above, this approach allows us to focus on commonly reported measures of earnings. An alternative approach simply adjusts bottom-line net income for each of the earnings components. This approach, however, results in arbitrarily computed earnings numbers that have no commonly understood meaning and are thus not widely used or reported (e.g., earnings after income taxes and special items but before depreciation).

Several recent papers (e.g., Phillips et al. 2003; Frank and Rego 2003; Burgstahler et al. 2003) examine whether firms use discretion in accounting for deferred taxes to meet earnings thresholds. However, none of these papers considers the implications of asymmetries in income taxes for profit and loss firms.