To illustrate, we choose R 0 =0, β=1, γ=10, and δ=1; hence, f(R 1 )=
R 1 +v(R 1 ,0). Earnings have a normal distribution each period, with mean
of zero and standard deviation of 10.^18 The second-period cost from ma-
nipulation is k(M)=eM−1, which is greater than M,implying that any ma-
nipulation is costly on net. (If M<0, earnings are manipulated downward
in the first period and boosted in the second period—but the second-period
boost is smaller than the first-period hit.)
Figure 18.2 illustrates the executive’s optimal strategy as a function of la-
tent earnings L 1. The initial threshold is achieved where L 1 +M 1 =R 0 =0.
Our key finding is that, just below zero, the optimal strategy is to set
M 1 =−L 1 ; future earnings are borrowed to meet today’s earnings threshold.
At point Z, the payoff from choosing M 1 =−L 1 (and therefore a positive
M 1 , indicating borrowing) just equals the payoff from saving for a better
EARNINGS MANAGEMENT 643
Figure 18.2. Optimal amount of period 1 manipulation, M1,as a function of latent
period 1 earnings L 1. Latent earnings L 1 are normally distributed with mean zero
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 exactly when choosing the manipulation level M 1.
(^18) We assume stationarity in the latent earnings distribution. This might be considered un-
representative if the real earnings process has a random walk characteristic. If latent earnings
do follow a random walk and we keep the same ratcheting structure in the payoff function,
the manipulation behavior will be identical close to the threshold (M 1 =L 1 ). Away from the
threshold, firms will manipulate by a constant amount regardless of L 1 : ratcheting combined
with the random walk assumption ensures that the executive’s decision problem is invariant
toL 1.