C. Conditional Distributions: Interaction among ThresholdsIf executives pay attention to more than one threshold, as seems likely, is
one threshold more important than another? Is there a discernible hierar-
chy among them?
To investigate interactions between thresholds, an issue that appears to
have been ignored by the literature, we analyze the conditional distributions
of EPS, ∆EPS, and FERR, when each of the other thresholds is met or failed.
For example, suppose that we find a significant threshold in the EPS distribu-
tion when we condition it on making the analysts’ forecast, as well as when
we condition it on failing to reach the analysts’ forecast; and suppose that we
also find that one of the “parallel” distributions of FERR (that is, FERR con-
ditional on EPS>0, and FERR conditional on EPS<0) exhibits no threshold
effect: in this hypothetical example, we would conclude that “to report prof-
its” is a more important threshold than “make the analysts’ forecast.”
Twelve conditional distributions are of interest (three individual distri-
butions×conditioning on the other two×two levels). We attend to the
problem that there may be little or no room to meet or fail a threshold
when another threshold is met or failed. For example, if the ∆EPS thresh-
old is met, and analysts have predicted earnings below last year, there is no
possibility of missing the FERR threshold. We thus focus only on samples
where there is at least a 5-cent range within which the threshold could be
failed or met. While this conditioning reduces the available sample size, we
are assured that inferences in the neighborhood of the threshold are valid.
For our positive earnings threshold, we focus on the case of 1 cent in EPS
(though the 0-cent threshold also appears important). Our other two thresh-
olds imply a 0-cent threshold in the distribution of ∆EPS and FERR. Our re-
sults appear in the 12 panels of conditional distributions in figure 18.8, where
the vertical lines indicate the thresholds.
To illustrate our requirements for inclusion, consider the second panel in
the second row of figure 18.8 where we examine the ∆EPS threshold condi-
tional on the EPS being positive. Since we want to have a 5-cent range
where the firm could fall short of the ∆EPS threshold in this subsample, we
consider only cases where lag(EPS)>5. This provides a range of 1–5 cents/
share where the current EPS can be positive and still fail to attain the ∆EPS
threshold. Each of our 12 cases looks at performance relative to one thresh-
old conditional on another threshold having been failed or met. When the
conditional threshold is failed (met), we preserve a 5-penny range on the up
(down) side.^31
654 DEGEORGE, PATEL, ZECKHAUSER
(^31) The restrictions we impose on included conditions influences the shape of our his-
tograms. Considering the upper-right-hand diagram, for example. Apart from thresholds, it
is unlikely that earnings will be nine cents when the analysts’ forecast (AF)<−4, whereas − 9
is not so unlikely even though FERR≥0. Our statistical test, which only looks at earnings in
a range of 10 cents, mitigates this problem.