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
The market price of the firm equals the expected value of the firm given the CEO’s earnings report. Thereby, the market rationally conjectures the CFO’s and the CEO’s optimal linear
reporting strategies in 3 and 4. Proposition 2 summarizes the equilibrium in the hierarchical reporting game.
Lemma 1. There
exists a linear equilibrium in which
i. the CFO chooses the reporting bias
2
1 ,
β ε
γ
⋅ + =
⋅ −
⋅
r F
F F
F
v b
x c
13
ii. the CEO chooses the reporting bias
2 2
2 2
2 2
2 2
2
,
ε ε
ε
λ κ σ σ
β κ σ
ε σ
σ σ
σ σ
σ ⋅ ⋅
+ ⋅
⋅ =
− ⋅
− ⋅ −
+ +
+ +
x v
E F
E F
F E
E v
F v
F
x b
x r
c 14
13 iii.
and the market pricing depends linearly on the CEO’s report with the positive weight β that is implicitly defined by the following equation:
2 2
2 2
2 2
2 2
2 2
2 2
4 2
2 2
2 2
2
. 1
1 1
1
v x
v F
v F
E F
v F
v F
c
ε ε
ε ε
σ β
σ σ
σ σ
κ β
σ σ
κ σ σ
γ σ
σ σ
σ σ
κ σ
=
+
+ −
⋅ +
+ − ⋅
⋅ + ⋅
+ ⋅
⋅ +
+ +
+ − ⋅
15
5. Earnings Quality
In the following, we analyze the quality of reported earnings. We highlight how earnings quality is linked to the uncertainty about the CFO’s and CEO’s cost of biasing, the uncertainty
about the CFO’s incentives and our primary variables of interest, the responsibilities of the CFO and the CEO for the CFO’s reporting bias.
We measure the quality of reported earnings as 1 value relevance of earnings and 2 price efficiency. Value relevance of earnings is typically measured as the slope coefficient in the
regression of market price on earnings e.g., Fischer Verrecchia 2000; Ewert Wagenhofer 2005. In our model, value relevance corresponds to the weight
β on the CEO’s earnings report in the market pricing function. Price efficiency captures the extent to which public and
private information is reflected in the market price. Therefore, price efficiency is related to the relative reduction of uncertainty about fundamental value due to the information included in
the market price
2
[ | ]
σ
v
Var v P
Fischer Verrecchia 2000. The measure reflects the remaining uncertainty in the market price after the issuance of the earnings report. To analyze
comparative statics for price efficiency, it is useful to define the following measure of price efficiency Heinle Verrecchia 2016:
2 2
2 2
2 2
2
1 [ | ]
1 .
v F
v v
F
Var v P V
ε ε
σ σ
κ σ β σ
σ σ
σ +
+ − ⋅
≡ − =
⋅ +
+
16 Some parameters in our model affect earnings quality in a predictable way consistent with the
prior literature. For example, in line with Fischer and Verrecchia 2000, increasing the CFO’s marginal cost of biasing
F
c deters earnings management and as a consequence increases value
relevance of earnings β and price efficiency V . As in Dye and Sridhar 2004, the CEO’s
marginal cost of biasing
E
c does not affect the quality of the reported earnings. In the
following, we focus on the distinctive parameters of our model. Lemma 2 summarizes the
14 comparative statics for the value relevance of earnings and the price efficiency with regard to
the key model parameters.
Lemma 2. Comparative statics
i. Variation in the value relevance of earnings β :
2
β σ
∂ ∂
E
;
2
β σ
∂ ∂
x
;
2
β σ
∂ ∂
F
; β
γ
∂ ∂
; β
κ
∂ ∂
. ii.
Variation in the price efficiency V :
2
σ
∂ ∂
E
V
;
2
σ
∂ ∂
x
V
;
2
σ
∂ ∂
F
V
; γ
∂ ∂
V
; κ
∂ ∂
V
. In our model, there are two sources of uncertainty that prevent the market from perfectly
inferring the reporting bias. First, the market observes the CEO’s incentive weight on the firm’s market price, but is uncertain about the incentives of the CFO Fischer Verrecchia
2000. Second, the CFO’s and the CEO’s cost of biasing is uncertain Dye Sridhar 2004. With regard to the uncertainty about the CFO’s incentives
2
σ
x
, we find that a higher uncertainty decreases the earnings quality as measured by the value relevance of earnings
β and price efficiency V . This result complements the finding of Fischer and Verrecchia 2000
in a non-hierarchical model that the uncertainty about managerial incentives negatively affects earnings quality. Thus, our result emphasizes the importance of transparency not only about
the CEO’s incentives, but also about the incentives of other top managers such as the CFO, and provides support for increased compensation disclosure requirements concerning the top
management team. The second source of uncertainty in our model that prevents the market from perfectly
inferring the reporting bias is the uncertainty about the CFO’s and the CEO’s cost of biasing,
2
σ
F
and
2
σ
E
respectively. As in Dye and Sridhar 2004, the uncertainty about the CEO’s cost of biasing the earnings report
2
σ
E
intuitively weakens the relation between reported earnings and market price. It thus decreases value relevance of earnings and price efficiency. The effect
of the uncertainty about the CFO’s cost of biasing earnings
2
σ
F
is more subtle. We discuss the effect of the uncertainty about the CFO’s cost of biasing as well as the effect of the key
variables of our model – the CFO’s and CEO’s responsibilities for CFO’s misreporting – in the next subsections.
15 Uncertainty about the CFO’s Cost of Biasing
The uncertainty about the CFO’s cost of biasing
2
σ
F
has an ambiguous effect on earnings quality. Price efficiency is unambiguously decreasing in the uncertainty about the CFO’s cost
of biasing. However, the relation between the reported earnings and market price may be strengthened or weakened with increasing uncertainty about the CFO’s cost of biasing.
Proposition 2 summarizes this result.
Proposition 2.
Earnings quality and the uncertainty about the CFO’s biasing costs a
Value relevance of earnings β may be increasing or decreasing in the uncertainty about
the CFO’s cost of biasing
2
σ
F
. Value relevance of earnings is more likely increasing in the uncertainty about the CFO’s cost of biasing
if i.
the CFO’s marginal cost of biasing,
F
c , is sufficiently low; ii.
the CFO’s responsibility for his reporting bias, γ , is sufficiently low; iii.
the uncertainty about the CFO’s incentives,
2
σ
x
, is sufficiently high; iv.
the uncertainty about the CEO’s cost of biasing,
2
σ
E
, is sufficiently low. b Price efficiency
V is decreasing in the uncertainty about the CFO’s cost of biasing. The ambiguous effect of the uncertainty about the CFO’s cost of biasing earnings results from
the hierarchical structure of our model. After observing the potentially biased interim report, the CEO may himself engage in earnings management before he forwards the final report to
the market. The uncertainty about the CFO’s cost of biasing thus has two opposing effects on the relation between the reported earnings and market price. On the one hand, all else equal,
increasing uncertainty about the CFO’s cost of biasing decreases the value of reported earnings in conveying information about true earnings. As a consequence, the value relevance of
reported earnings β decreases. On the other hand, the uncertainty about the CFO’s cost of
biasing affects the CEO’s response to the earnings reported by the CFO and thus the CEO’s optimal choice of bias. According to Proposition 1 i, the CEO’s discount of the interim report
is higher with increasing uncertainty about the CFO’s cost of biasing. This indirect effect increases the value relevance of the reported earnings.
Which effect dominates, depends on the CEO’s versus the CFO’s incentives and costs to bias the earnings report. The results i to iii in part a of the Proposition 2 address the CFO’s
16 incentives to bias the interim report. For sufficiently high CFO’s cost of biasing, sufficiently
high uncertainty about the CFO’s incentives and sufficiently low responsibility of the CFO for his own misreporting, the indirect effect dominates and the value relevance of earnings is
increasing in the uncertainty about the CFO’s cost of biasing. In this case, the CFO has particularly strong incentives to bias earnings which enhances the importance of the
supervision by the CEO. Anticipating higher incentives of the CFO to bias earnings, the CEO discounts the CFO’s interim report to a greater extent, strengthening the relation between the
reported earnings and market price. The last result in part a of the Proposition 2 relates to the CEO’s incentives to bias earnings.
If the uncertainty about the CEO’s cost of managing earnings,
2
σ
E
, is sufficiently low, the CEO has weak incentives to bias earnings. In this case, increasing uncertainty about the CFO’s cost
of biasing enhances the CEO’s incentives to correct the CFO’s interim report, thus strengthening the value relevance of earnings.
With regard to price efficiency, the result in part b of the Proposition 2 shows that the direct effect always dominates and the price efficiency is unambiguously decreasing in the
uncertainty about the CFO’s cost of biasing. CFO’s Responsibility for His Own Misreporting
The Sarbanes-Oxley Act of 2002, Section 302, “Corporate Responsibility for Financial Reports”, requires the CFO and the CEO of the firm to certify financial statements. Thereby,
Section 302 enhances the personal responsibility of the top executives. We first analyze the effect of the CFO’s responsibility for his own misreporting
γ on the quality of reported earnings. Proposition 3 provides the comparative static result.
Proposition 3. Value relevance of earnings
β and price efficiency V are increasing in the CFO’s responsibility for his own misreporting
γ . Proposition 3 confirms the intuition that higher responsibility of the CFO for his own
misreporting makes earnings more value-relevant and enhances price efficiency.
10
Our result highlights that in order to improve earnings quality, regulators should acknowledge the crucial
10
Similarly, Ewert and Wagenhofer 2005 find that increasing the tightness of accounting standards implies higher quality of reported earnings. However, they are concerned with the trade-off between accounting and
real earnings management and do not consider hierarchical reporting structures.
17 role the CFO plays in ensuring the appropriateness of financial reports and increase the CFO’s
accountability. Thus, Section 302 seems an important step towards achieving this goal. CEO’s Responsibility for the CFO’s Misreporting
Section 302 of the Sarbanes-Oxley Act of 2002 emphasizes the joint responsibility of the firm’s CFO and CEO for an appropriate presentation of the firm’s operations and financial
condition. As the CFO is primarily responsible for the preparation of the financial statements, the requirement to certify the accurateness of the financial statements enhances personal
responsibility of the CEO for his own misreporting as well for potential misreporting by the CFO. Proposition 4 presents the comparative static result for the effect of the CEO’s
responsibility for the CFO’s misreporting
κ
on the quality of reported earnings.
Proposition 4. Value relevance of earnings
β and price efficiency V may be increasing or decreasing in the CEO’s responsibility for the CFO’s reporting bias
κ
. Value relevance of earnings and price efficiency are more likely increasing in the CEO’s responsibility for the
CFO’s reporting bias if
i. the CFO’s marginal cost of biasing,
F
c , is sufficiently low; ii.
the CFO’s responsibility for his reporting bias, γ , is sufficiently low; iii.
the uncertainty about the CFO’s incentives,
2
σ
x
, is sufficiently high; iv.
the uncertainty about the CEO’s cost of biasing,
2
σ
E
, is sufficiently low. At first glance, the result in Proposition 4 seems counterintuitive. If the regulator aims at
increasing the earnings quality, it seems logical to increase the accountability of both executives who may manage earnings. Following this line of reasoning, we would expect that
enhancing the accountability of the CEO for potential misreporting by the CFO should help to unambiguously improve the quality of reported earnings. However, Proposition 4 highlights a
trade-off in making the CEO responsible for the CFO’s biasing. On the one hand, increasing the CEO’s responsibility for the CFO’s misreporting enhances the CEO’s incentives to correct
the CFO’s bias in the reported earnings. To illustrate this effect, consider the CEO’s optimal choice of bias for
κ
= : β ε
⋅ =
−
E E
E E
x b
c
. 17
18 If
κ
= , the CEO chooses the bias independently of the CFO and has no incentives to scrutinize the CFO’s interim report. The benefit of the CEO’s supervision is particularly high
if the CFO has strong incentives to manage earnings, i.e., if the CFO can bias earnings at low cost, if the CFO’s responsibility for his own misreporting is low and if the uncertainty about
the CFO’s incentives is high. On the other hand, increasing the CEO’s responsibility for the CFO’s misreporting also
increases the noise in the reported earnings, since the CEO’s costs of adjusting his bias are uncertain as well. This introduces additional noise into the final report. As a consequence, a
higher uncertainty about the CEO’s cost of biasing earnings results in a lower benefit of the CEO’s supervision.
Proposition 4 shows that, contrary to the expectation, the responsibility of the CFO γ and the
responsibility of the CEO
κ
for the CFO’s misreporting are substitutes instead of complements. All in all, the results in Proposition 4 show that increasing the responsibility of
both the CFO and the CEO does not necessarily imply higher earnings quality. Numerical Example on the Effects of the CEO’s Responsibility
Figures 2 and 3 illustrate the consequences of increasing CEO responsibility
κ
. Figure 2 shows the effect of higher CEO responsibility on value relevance graph on the left-hand side
and on price efficiency graph on the right-hand side depending on the variance of the CFO’s incentives. If the incentives of the CFO are perfectly known in the financial market
2
σ
=
x
, earnings quality and price efficiency are unambiguously decreasing in higher CEO
responsibility. In such cases, increasing responsibility is counter-productive. As the uncertainty about the CFO’s incentives increases, value relevance and price efficiency are
increasing for low levels of CEO responsibility. There are critical values of CEO responsibility, which maximize value relevance and price efficiency respectively.
11
Generally, higher uncertainty about the CFO’s incentives reduces earnings quality.
Figure 3 shows the interaction of CFO and CEO responsibility. If the CFO is largely responsible for his own misreporting, regulatory attempts to increase CEO responsibility
cannot significantly improve the results. Instead, higher levels of CEO responsibility reduce value relevance as well as price efficiency in the financial market. A beneficial effect of higher
11
Note that value relevance and price efficiency are not maximized by the same value of
κ
. This is obvious from the case
2
4
x
σ
= .
19 CEO responsibility occurs if the CFO is hardly responsible for his own misreporting decision.
This highlights the substitutive relationship between CEO and CFO responsibility regarding the informational value of the financial report.
FIGURE 2 Uncertainty about CFO incentives and the effect of increasing CEO responsibility
2 2
4
σ σ
= =
v F
,
2
1
ε
σ
=
, 1
µ =
=
E x
x ,
2
12
σ
=
E
, 0.5
= =
F E
c c
,
0.4
γ
=
FIGURE 3 The joint effect of CFO and CEO responsibility on earnings quality
2 2
4
σ σ
= =
v F
,
2
1
ε
σ
=
,
1 µ
= =
E x
x
,
2
12
σ
=
E
,
2
9
σ
=
x
,
0.5 =
=
F E
c c
20
6. Conclusion
