which we compare the empirical distributions below. The dark shaded
areas below the horizontal show shortfalls in the density, if any, relative to
the equidistant bin on the other side of the threshold (which, by construc-
tion, is at the peak of the latent symmetric distribution).
In results not shown, we explored the consequences of changing the pa-
rameter values of the model. We find that the changeover point Z(where
L 1 is negative and the payoff from borrowing to meet the threshold just
equals the payoff from taking the optimal sacrifice) moves to the left as the
discount factor increases since, the higher the executive’s discount rate, the
more valuable it is to get high earnings this period, and the costlier it is to
take a bath.
The more uncertain are second-period earnings, the more the executive
will manipulate to secure the bonus in the first period since big borrowings
are less likely to sacrifice the second year’s threshold. As the bonus for
crossing the threshold (indicated by γ) falls in importance relative to the re-
wards per unit of reported earnings (indicated by β), EM becomes more
costly and decreases. For any level of L 1 , as βincreases, the optimal M 1
moves closer to zero, and the dip below and pile-up above the threshold
EARNINGS MANAGEMENT 645 Figure 18.3. Simulated distributing of reported earnings R 1. Latent earning L 1 are
normally distributed with mean 0 and standard deviation 10. If reported earnings
R 1 =L 1 +M 1 reach at least R 0 =0, the executive reaps a bonus of 10. The period 2
cost of manipulation is k(M 1 )=eM−1. The executive knows L 1 imprecisely when
choosing the manipulation level M 1 (he has a probability distribution centered on
L 1 with a variance of one). The dark shaded areas below the horizontal show short-
falls relative to the equidistant bin on the other side of the threshold of zero.