10 To obtain a tractable solution to our reporting game, we restrict the analysis to linear equilibria.
The equilibrium consists of the CFO’s and the CEO’s earnings reports and the market price reaction to the CEO’s report. We assume the following linear strategies:
ε
λ λ λ
λ ε =
+ ⋅ + ⋅ + ⋅
F e
x F
F
b e
x ,
3
ε
ε = + ⋅ + ⋅
+ ⋅
E r
F x
F E
b v
v r v x
v ,
4 α β
= + ⋅
E
P r
. 5
3. CFO’s and CEO’s Reporting Strategies
The CFO’s Problem and Optimal Reporting Bias The CFO chooses the bias
F
b to maximize his expected utility in 1 given the earnings e , the
realization of the incentive weight
F
x and the cost of biasing the report
F
ε
and given the conjectures about the CEO’s final report ˆ
E
r and the resulting market price ˆ ˆ
E
P r :
8
2 2
ˆ ˆ arg max
, ,
2 γ
ε ε
∈ ⋅
− ⋅ ⋅
+
F
F F
F E
F F
F F
b
c b
E x P r
b e x
. 6
The CFO conjectures that the CEO’s final report ˆ
E
r and the price of the firm ˆ ˆ
E
P r are linear
strategies as given in equations 4 and 5. Then, the first-order condition yields the CFO’s choice of bias in his earnings report:
9
2
1
β ε
γ
⋅ + =
⋅ −
⋅
r F
F F
F
v b
x c
. 7
Given the linear structure of the CFO’s bias in equation 3, we can conclude: λ = ,
λ =
e
,
2
1
β λ
γ
⋅ + =
⋅
r x
F
v c
, and 1
ε
λ = − . 8
The CFO’s choice of bias in the interim report is independent of actual earnings Fischer Verrecchia 2000, Ewert Wagenhofer 2005 and decreases in the realization of
ε
F
Dye Sridhar 2004. In line with Fischer and Verrecchia 2000, a higher market response to the
earnings report β and a lower CFO’s cost of biasing the report
F
c result in a higher amount
8
The caret “” denotes a conjecture.
9
All proofs are in the Appendix.
11 of CFO’s earnings management. Intuitively, the CFO’s degree of responsibility for biasing the
interim report decreases the bias. Since the interim report is evaluated by the CEO prior to being issued to the market, the coefficient on the CFO’s incentive weight also depends on the
CEO’s reaction to the interim report. In particular, the bias increases as the CEO’s conjectured reaction
r
v to the CFO’s report increases.
The CEO’s Problem and Optimal Reporting Bias The CEO chooses the bias
E
b to maximize his expected utility in 2 given the realization of
the CFO’s incentive weight
F
x , the interim earnings report
F
r , the cost of biasing the report
E
ε and given the conjecture about the market price ˆ ˆ
E
P r :
2
ˆ ˆ
arg max ,
, 2
κ ε
ε
∈
⋅ −
⋅ ⋅ +
+
E
E E
E E
F E
E F
F E
b
c b
E x P r
b b
r x .
9 The CEO’s cost of biasing the report to the market depends on the realization of the cost of
biasing the report
E
ε
. However, if the CEO is partially responsible for reporting bias potentially introduced by the CFO, i.e.,
κ
, the CEO’s expected cost of bias also depends on the CFO’s biasing decision. While the CEO does not directly observe the bias chosen by
the CFO, he makes a conjecture based on the observation of the CFO’s incentives
F
x and the
CFO’s interim report
F
r . The CEO’s optimal choice of bias in the final report follows from
the first-order condition:
,
β κ λ ε
ε
⋅ =
− ⋅ ⋅
− −
E E
x F
F F
F E
E
x b
x E
r x c
, 10
where the conditional expectation of the CFO’s cost of biasing earnings is given by:
2 2
2 2
2 2
2 2
,
ε ε
σ σ
ε λ
σ σ
σ σ
σ σ
= −
⋅ + ⋅ ⋅
+ +
+ +
F F
F F
F F
x F
v F
v F
E r x
r x
. 11
Comparing this result to the linear equilibrium strategy in 4 shows that β
= ⋅
E E
v x
c
,
2 2
2 2
ε
σ κ
σ σ
σ = − ⋅
+ +
F r
v F
v ,
2 2
2 2
2
ε ε
λ σ σ
κ σ
σ σ
⋅ +
= − ⋅ +
+
x v
x v
F
v , and
1
ε
= − v
. 12
The CEO’s reaction to the interim report,
r
v , plays a crucial role in the reporting game. The
CEO discounts the earnings reported by the CFO, i.e.,
r
v , and thus tries to correct the
12 overstatement bias in the CFO’s interim report. However, the CEO corrects the CFO’s report
only if he is partially accountable for the CFO’s misreporting, i.e.,
κ
. The CEO’s bias can be positive or negative depending on the CEO’s discount of the interim report.
Proposition 1 summarizes the results concerning the CEO’s response to the CFO’s report.
Proposition 1. Holding the financial market reaction
β constant
,
the CEO’s discount of the CFO’s interim report increases if
i. the responsibility of the CEO for the CFO’s misreporting
κ
increases; ii.
the uncertainty about the CFO’s cost of biasing
2
σ
F
increases. The CEO’s responsibility for the CFO’s earnings management determines his reaction to the
interim report. The higher the CEO’s responsibility for the CFO’s reporting bias, the more the CEO optimally reduces his bias in response to the CFO’s report. While the CEO is aware of
the CFO’s incentives to bias earnings, there is some remaining uncertainty about his cost of biasing the report. As long as the CEO is accountable for the CFO’s reporting bias, he chooses
a lower level of bias if the uncertainty about the CFO’s cost of managing earnings increases. Interestingly, the CEO’s reaction to the CFO’s report is independent of the CFO’s
responsibility for his own misreporting, i.e., γ
∂ =
∂
r
v
.
4. Market Pricing Function and Equilibrium
