considerable jump between zero and one (especially the latter); thus
it appears that managers strongly desire to be able to report strictly
positive earnings—as opposed to just breaking even.^29 The value of
the τ-statistic (based on the basic test in the appendix—the case in
which the likely threshold is far from the peak of the distribution)
confirms the observable pattern: at 1 cent per share, we obtain a τ
value of 4.36, confirming a discontinuity in the EPS distribution
there.^30
Finally, we can also detect an upward kink in the EPS distribu-
tion from −1 cent/share to 0 cents/share, indicating a secondary
threshold at zero, to “avoid red ink.” The τ-value for the secondary
kink, 3.84, also proves significant, although our visual impression is
that the threshold at zero is likely smaller than that at 1 cent/share.
In sum, we have established clear thresholds effects in the report-
ing of earnings, both visually and through statistical test results.
The three thresholds affecting the reporting of earnings are to “sus-
tain recent performance,” to “meet analysts’ forecasts,” and to “re-
port profits.”EARNINGS MANAGEMENT 653(^29) Note that this figure reinforces the impression of figure 1 in Hayn (1995), who, however,
scales EPS by price per share and thus obtains a confounding density estimate at zero (as dis-
cussed above in subsection 3A).
(^30) Since we have two suspected thresholds adjacent to one another, the neighborhood used
in the τ-tests here always excludes the observation corresponding to the other threshold obser-
vation.
Figure 18.7. Histogram of EPS: exploring the threshold “positive/zero profits”