Strategic Delegation and the Weaponization of Executive Pay
Evidence from Revenue-Based Performance Evaluation
Internet Appendix
Matthew J. BloomfieldMay 15, 2017
A Analytical Framework of Strategic Delegation
Here, I present the analytical framework from which I derive my hypotheses. In Section A.1, I
present a stylized model of the Cournot oligopoly to demonstrate the entangled roles of disclosure
and product market competition in determining the optimal executive compensation contract. In
Section A.1.1, I solve the model exactly as originally formulated by Fershtman and Judd (1987),
with all contracts being common knowledge. I then alter the model, in Section A.1.2, by assuming
that contracts are private information but that principals and agents form rational conjectures
regarding their rivals contracts. In Section A.2, I generalize the model presented in Section A.1 and
discuss when the main predictions would and would not be expected to hold, in real world settings.
Lastly, In Section A.3 I provide the sketch of a proof showing that, even in dynamic settings in
which agents can reveal their incentives through their actions, disclosure is still necessary in order
for a pay package to be an e↵ective commitment mechanism.
A.1 Stylized Nash Game: The Cournot Oligopoly
Consider a Cournot oligopoly, comprised of N principal-agent pairs. Each principal owns one firm,
but delegates to a risk-neutral and e↵ort-neutral agent the responsibility of running the firm. The
game has two periods; in the first period, principals simultaneously choose their contracts, and in
the second period, agents make simultaneous quantity decisions.1
Each agent’s task is to choose a production quantity, qi
at a constant marginal cost, c. The
per-unit price at which any firm, i, can sell its goods is given by:
pi
= a� b(qi
+ �X
j 6=i
qj
), (1)
where qi
is agent i’s quantity decision,Pj 6=i
qj
, hereafter denoted as Qi
, is the collective quantity
decision of all product market rivals, and � is the parameter of substitutability in the product
1For ease of discussion, I refer to principals as “she”/“her,”, and agents as “he”/“his.”
1
market. When � = 1, the goods are perfect substitutes, and when � = 0, each firm is e↵ectively a
monopolist. For ease of analysis, I will assume � = 1, however the model is equally tractable for
any � 2 [0, 1].2
Each principal’s problem is to maximize her firm’s value by providing the optimal incentives to
her agent, in the form of a linear contract:
wi
= �i
⇡i
+ (1� �i
)Ri
, (2)
where ⇡i
and Ri
represent firm i’s profits and revenues, and the principal’s choice variable, �i
,
parameterizes agent i’s incentive to maximize profit versus revenue. Equations (1) and (2) combine
to define each agent’s objective function:
�i
qi
(p� c) + (1� �i
)(qi
p)
=�i
qi
(a� b(qi
+Qi
)� c) + (1� �i
)qi
(a� b(qi
+Qi
)� c)
=qi
(a� b(qi
+Qi
)� �i
c). (3)
In what follows, I characterize the entangled roles of product market competition and disclosure
in shaping the incentive equilibrium of a Cournot oligopoly.
A.1.1 Disclosed Contracts
In this subsection, I present the model, as originally formulated by Fershtman and Judd (1987).
Contracts are disclosed, and therefore common knowledge to all agents.
Begin by di↵erentiating each agent’s objective function with respect to his own quantity decision
to define the system of best response functions:3
q⇤i
(Qi
) =a� bQ
i
� �i
c
2b. (4)
In order to determine the equilibrium quantity decisions, aggregate over all best response func-
2Equilibrium results are qualitatively similar for any 0 < � 1.3An agent’s “best response function” describe the agent’s optimal action as a function of the actions taken by all
other agents—or in this case, a representative rival agent.
2
tions by summing them up:
X
i
q⇤i
(Qi
) ⌘ Q =X
i
a� bQi
� �i
c
2b
=
aN � b(NQ�Pi
q⇤i
)�Pi
�i
c
2b
=aN � b(N � 1)Q� ⇤c
2b, (5)
where N is the number of product market competitors, Q is the total quantity produced, and ⇤ is
the sum over all �i
.
Solving for Q yields the unique equilibrium solution:
Q =aN � ⇤c
b(N + 1). (6)
Further defining ⇤i
⌘ ⇤� �i
, note that:
Qi
= Q� qi
=aN � ⇤c
b(N + 1)� q
i
=aN � (⇤
i
+ �i
)c
b(N + 1)� q
i
, (7)
which can be substituted into the original first order condition, eq. (4), to produce an expression
for agent i0s optimal quantity decision, purely as function of �i
and ⇤i
:
q⇤⇤i
=a� bQ
i
� �i
c
2b
=a� b(aN�(⇤i+�i)c
b(N+1) � q⇤⇤i
)� �i
c
2b(8)
=) q⇤⇤ =a� c(N�
i
� ⇤i
)
b(N + 1). (9)
Each principals’ problem is to maximize profit by choosing �i
. That is, the each principal has an
objective function:
⇡i
= q⇤⇤i
⇥ (pi
� c)
=(a+ c(�
i
+ ⇤i
�N � 1))(a+ c(⇤i
�N�i
))
b(N + 1)2. (10)
The first order condition with respect to �i
yields the system of best response functions:
�⇤i
(⇤i
) =a� aN + c(⇤
i
+N(1� ⇤i
+N))
2Nc. (11)
3
Finally, by leveraging the symmetric nature of the product market, we can assume that �⇤⇤i
= �⇤⇤,
for all firms, which would imply that ⇤i
= (N � 1)�⇤⇤. Using this fact, we can characterize the
incentive equilibrium:
�⇤⇤ =a� aN + c((N � 1)�⇤⇤ +N(1� (N � 1)�⇤⇤ +N))
2Nc(12)
=) �⇤⇤ =a� aN + cN + cN2
c(1 +N2). (13)
This expression, illustrated graphically in Figure IA1, has a number of useful properties:
1. �⇤⇤(1) = 1
2. limN!1 �⇤⇤(N) = 1
3. �⇤⇤ is strictly increasing in N , for N > 1.
This result demonstrates how oligopolistic interdependencies, coupled with public disclosure,
can drive a wedge between the agency cost minimizing contract and the profit maximizing contract.
In this setting, the agency cost minimizing contract is � = 1; agents are neither risk averse nor
e↵ort averse, so there is no friction preventing costless incentive alignment. But providing such
a contract would be suboptimal, because it would fail to leverage one key element of a disclosed
compensation contract: the e↵ect of the contract on rivals’ actions. Shifting weight towards revenue
(i.e., lowering � below 1) commits the agent to over-production, relative to profit maximization.
This commitment, in turn, forces product market rivals to curtail production, which keeps market
prices higher, ultimately elevating the firm’s profits.
In essence, a firm can gain a quasi “first mover advantage” (a la Stackelberg, 1934) by com-
mitting, in an observable way, to a more aggressive response function. Of course, in equilibrium,
all firms attempt to get this first mover advantage and no firm manages to gain a strategic edge.
Rivals instead engage in an even more aggressive Nash game—a social dilemma.
A.1.2 Private Contracts
In this subsection, I alter the preceding analysis with one crucial distinction: contracts are no
longer disclosed publicly. Instead, choices of � are private information, observed only within a
principal-agent pair.
As before, each agent’s optimal quantity decision is a function of the quantity decisions made,
simultaneously, by all other agents. However, in contrast to the case of disclosed contracts, agents
cannot rely on observing their rivals’ contracts to ascertain their rivals’ actions. Instead, agents
must form conjectures of their rivals’ contracts and corresponding quantity decisions.
4
Taking these conjectures as given, the first order condition describing agent i’s optimal quantity
choice can be represented as:
q⇤i
(Qi
) =a� bQ
i
� �i
c
2b, (14)
where ‘hats’ denote conjectures.
Due to the private nature of rivals’ contracts, determining the correct quantity conjectures
requires solving a complicated higher order beliefs problem—an agent’s quantity choice is not only
a function of his own contract, �, but also of his conjecture regarding all rivals’ contracts, �, as
well as his conjecture about his rivals’ conjectures, ˆ�, and so on ad infinitum. In order to make this
higher order beliefs problem analytically tractable, I impose that all conjectures are “rational” in
the sense that they will be sustained in equilibrium.
The assumption of rational conjectures does a great deal to collapse the parameter space and
simplify the problem. First, it guarantees that, for any firm i, all rivals share a common “first order
conjecture,” �i
, of firm i’s contract and qi
of firm i’s quantity decision—if rivals had divergent
conjectures, at least one conjecture would not be sustained in equilibrium. Moreover, it assures
that every conjecture about a conjecture, or “higher order conjecture,” will be equivalent to the
corresponding first order conjecture. That is,
�i
= ˆ�i
= ... =
...ˆ�i
= ..., 8i, (15)
and similarly,
qi
= ˆqi
= ... =
...ˆqi
= ..., 8i. (16)
These facts simplify the analysis (and notation) immensely. The only distinctions which must be
retained are those between choice variables, q’s and �’s, and the corresponding first order conjectures
which relate to these choice variables, q’s and �’s.
Lastly, I leverage symmetry to further simplify the parameter space. The symmetry of the
product market implies that all rivals’ decisions will be identical, in equilibrium. Thus, any agent
i 6= j will form equivalent conjectures qj
and �j
for all product market rivals.
Jointly, the first order conditions on qi
, the rationality conditions on conjectures, and the
symmetry of the product market imply that all agent’s quantity choices can be fully described by
5
the following system of simultaneous equations:
q⇤i
=a� b(N � 1)q
j
� c�i
2b(17)
qi
=a� b(N � 1)q
j
� c�i
2b(18)
qj
=a� b((N � 2)q
j
+ qi
)� c�j
2b. (19)
Solving this system of simultaneous equations yields:
q⇤i
=2a� c(�
i
(N + 1) + (N � 1)(�i
� 2�j
))
2b(N + 1)(20)
qj
=a+ c(�
i
� 2�j
)
b(N + 1)(21)
qi
=a� c(�
i
N � �j
N + �j
)
b(N + 1). (22)
Using the expressions for q⇤i
and qj
, we can calculate firm i’s profit, as a function of �i
:
⇡i
=qi
⇥ (pi
� c)
=2a� c(�1(N + 1) + (N � 1)(�
i
� 2�j
))
2b(N + 1)
⇥ (a� b(2a� c(�
i
(N + 1) + (N � 1)(�i
� 2�j
))
2b(N + 1)+ (N � 1)
a+ c(�i
� 2�j
)
b(N + 1))� c). (23)
Di↵erentiating the profit function with respect to �i
yields:
@⇡i
@�i
= �c2(�i
� 1)
2b(24)
indicating that profit is maximized by choosing �i
= 1, the agency cost minimizing contract.
In this setting, the principal i’s choice variable, �i
, only a↵ects profit through its a↵ect on
qi
. In order to manipulate rivals’ behavior, the principal would need to change �i
, which is not a
parameter the principal has power to influence, sans disclosure. Without the ability to use contracts
strategically, there is no reason to deviate from the agency cost minimizing contract—in this case,
pure profit maximization.4 A summary of the equilibrium outcomes, with and without disclosure
can be found in Table IA1.4In repeated games, it is possible for agents to reveal their incentives through their actions (a la Spence, 1973).
However, the possibility for signaling in this manner does not justify deviations from the agency cost minimizingcontract, sans disclosure. See proof in Section A.3.
6
A.2 Generalizability/Discussion
The preceding analysis leveraged a highly stylized model of product market competition to pro-
vide tight predictions regarding the relations among product market competition, disclosure and
revenue-based compensation. In order to gauge the plausibility of such relations manifesting in
real-world data, it is critical to assess the generalizability of the underlying intuition.
While the exact nature of the incentive equilibrium is sensitive to the specifics of the model,
the core intuition—that contract disclosure pushes Nash competitors to overweight revenue—holds
fairly broadly. Formally, In a Nash oligopoly with linear incentives based on profit and revenue, the
following three assumptions are su�cient to demonstrate that disclosure leads to a greater weight
on revenue:
(1) @⇡
i(xi,xj)@xi
<@R
i(xi,xj)@xi
(2) @⇡
i(xi,xj)@xj
< 0
(3) @
2⇡
i(xi,xj)@xi@xj
< 0
where ⇡i and Ri are firm i’s [convex] profit and revenue functions, with respect to its own product
market aggressiveness, xi
, and a representative rival’s product market aggressiveness, xj
.
Proof. Let wi
= �i
⇡i + (1 � �i
)Ri be agent i’s objective function. Taking the total derivative of
firm profits, ⇡i, with respect to the contract, �i
, yields:
d⇡i(xi
, xj
)
d�i
=@⇡i
@xi
· @xi@�
i
+@⇡i
@xj
· @xj@x
i
· @xi@�
i
, (25)
when contracts are disclosed. And,
d⇡i(xi
, xj
)
d�i
=@⇡i
@xi
· @xi@�
i
, (26)
when contracts are private information. The optimal contract, �⇤i
is defined as the one satisfies:
d⇡i(xi
, xj
)
d�i
= 0. (27)
By the convexity of the profit function, strictly increasing (decreasing) d⇡
i(xi,xj)d�i
reduces (increases)
the optimal weight on revenue. Thus, whether disclosure increases or decreases the weight on
revenue depends only on the sign of:@⇡i
@xj
· @xj@x
i
· @xi@�
i
. (28)
7
This expression can be easily signed. The terms @⇡
i
@xj, @xj
@xiand @xi
@�iare each negative by assumptions
(2), (3) and (1), respectively. Thus, when contracts are disclosed, there is a gain to be made by
decreasing �i
by a strictly positive amount (i.e., shifting weight towards revenue-based pay).
With an additional assumption that the magnitude of the strategic interaction, abs�@
2⇡
i(xi,xj)@xi@xj
�,
grows with market concentration, the proof further shows the attenuating e↵ects of competition.
Assumptions (1) and (2) are mild and will hold broadly. In plain English, (1) simply states
that, holding rivals’ behavior fixed, a more aggressive action increases a firm’s expenses (e.g., selling
more and/or higher quality goods results in a higher cost of goods sold). Assumption (2) states
that, holding rivals’ behavior fixed, a more aggressive action decreases rivals’ profits (e.g., selling
equivalent goods at a lower price will draw consumers—and therefore profits—away from rivals).
Assumption (3) is less innocuous—that rivalrous firms’ strategic actions are substitutes. That
is, as one firm engages in more aggressive product market behavior, rivals optimally respond by
curtailing their own aggressiveness. A game in which rivalrous agents make simultaneous quantity
decisions, as in Fershtman and Judd (1987), is the canonical way to satisfy this condition. However,
many other strategic environments admit similar properties, such as strategic horizontal positioning
in a spatial competition game, or rivalrous quality choices in a vertical di↵erentiation game. In
such games, observably committing to a more aggressive behavior is strategically beneficial, as this
commitment begets reduced competition from rivals.
When strategic actions are complements instead of substitutes (i.e., @
2⇡
i(xi,xj)@xi@xj
> 0), the logic
reverses. There can still be a strategic incentive to deviate from the agency cost minimizing contract,
but in the opposite direction; firms will want to observably commit to reducing their aggressiveness
in the product market (i.e., setting � > 1). The canonical instance of strategic complementarity is
“di↵erentiated Bertand,” in which rival firms compete to sell horizontally di↵erentiated goods by
strategically setting prices. In this game, a contract that o↵ers a bonus based on profit margins
or imposes a penalty for costs of goods sold will result in higher equilibrium prices (both from the
firm, and from its product market rivals), and thus greater profits.5
In most industries, the reality is likely to fall somewhere in between the two extremes. Strategic
actions are not always substitutes, nor are they always complements. What matters is whether
strategic actions are predominantly one or the other. For example, in a two-period spatial com-
petition model, where firms first choose their locations, and then compete with one another by
choosing prices, there are two opposing forms of competition. Location choices are strategic sub-
stitutes; as one firm moves towards a particular point in the product space, rivals will optimally
spread themselves further away from that location, so as to mitigate the competitive forces they
5My data does not allow me to cleanly observe these types of contracts. Thus I am unable to assess whether ornot this kind of collusive strategic delegation takes place, as well.
8
endure. However the prices they charge are strategic complements; when one firm raises (lowers)
its price, rivals will optimally respond by raising (lowering) their own prices. Many other games
will admit similar properties, for example a two stage game in which firms choose a production
capacity, and then compete on price. Whether firms prefer to observably commit to more or less
aggressive behavior depends on the relative importance of the two forms of competition.
A.3 Dynamic Decision Making
The model laid out in Sections A.1 and A.2 assumes that agents take actions only once. In many
real-world scenarios, actions are taken numerous times over the course of a contract period. For
example, in Bertrand competition, incentive contracts might be determined annually but prices
might be adjusted monthly, or weekly, or even daily. Thus, a reasonable reader might wonder
whether contract disclosures are necessary for strategic delegation to occur. Two questions that
arise are: (1) In lieu of disclosure, can agents credibly signal their contractual terms through their
actions? And (2) if so, does that make revenue-based pay a viable precommitment tool that a
profit-seeking principal would rational implement, even without disclosure? The answer to the
former question is “yes,” while the answer to the latter remains “no.” Below, I sketch a proof
by contradiction demonstrating that, in the absence of disclosure, the possibility for repeated play
does not make the strategic use of a revenue-based pay a viable profit-maximizing strategy.
Proof. Let each principal, i, delegate an unobservable type, ✓i, to her agent. Each agent then takes
a sequence of T observable actions, {xi1(✓i, ✓j
1), ..., xi
T
(✓i, ✓jT
)}, to maximize his terminal payo↵,
wi = ✓iRi + (1 � ✓i)⇡i, where Ri is revenue, ⇡i is profit, and ✓jt
is the agent’s belief about a
representative rival’s type based on information available at time t.
Lastly, assume that there exists a fully revealing equilibrium in which each agent’s initial action,
xi1 fully reveals his type. Once the types are revealed, a unique sequence of equilibrium actions will
ensue. Thus, the outcomes of the game can be expressed as a function of the initial actions and
their e↵ect on beliefs. Each principal has an objective function:
⇡i(xi1(✓i), ✓i(xi1(✓
i))), (29)
while each agent has an objective function:
wi(xi1(✓i), ✓i(xi1(✓
i)); ✓i)
=✓iRi(xi1(✓i), ✓i(xi1(✓
i))) + (1� ✓i)⇡i(xi1(✓i), ✓i(xi1(✓
i))) (30)
Note that the existence of a fully revealing equilibrium implies that there exists a pair of
9
functions, x(✓) and ✓(x) such that:
✓(x(✓)) = ✓, 8✓, (31)
and
w(x(✓), ✓; ✓) > w(x(✓0), ✓0; ✓), 8✓0 6= ✓. (32)
Suppose there exists some type ✓⇤ > 0 that yields greater profits than type ✓ = 0.6 That is,
⇡i(x(✓⇤), ✓⇤) > ⇡i(x(0), 0), (33)
This implies that an agent of type ✓ = 0 can achieve a greater payo↵ by playing the strategy of
an agent of type ✓⇤ > 0. Therefore, there exists a ✓⇤ > 0 such that:
w(x(0), 0; 0) < w(x(✓⇤), ✓⇤; 0) (34)
)(
This is a contradiction, as it violates the conditions of a fully revealing equilibrium, specified in
eq. (32). Thus, there cannot exist some ✓⇤ > 0 such that greater profits are achieved. Therefore,
the principal would never choose to delegate anything other than her own type, ✓ = 0.
Intuitively, this result can be thought of in the following way. Agents can use overly aggressive
initial actions as costly signals of their type. However, to sustain an fully-revealing equilibrium, an
agent of type ✓ > 0 has to destroy more profit through his signal, x(✓), than he gains by revealing
his type. That is, ⇡(x(✓), ✓) < ⇡(x(0), 0). If not, an agent of type 0 would prefer to take action
x(✓) instead of x(0), which would violate the conditions of a fully-revealing equilibrium. Thus, a
profit-seeking principal would not choose to give her agent any type ✓ > 0 because doing so would
result in lower profits.
B Sensitivity Analyses
This section provides tabulated results from my sensitivity analyses. Unless otherwise specified, all
sensitivity analyses are based on the eq. (7) of the manuscript:
RevenueBonusi,t = ↵+ �1log(Firmsj,t)⇥ Postt ⇥ Subsj + �2Postt ⇥ Subsj + �3log(Firmsj,t)⇥ Postt
+ �4log(Firmsj,t)⇥ Subsj + �5log(Firmsj,t) + Xi,t + ⌧t + uj + µi + "i,j,t,
6This is the only scenario in which the principal would engage in strategic delegation.
10
where Firmsj,t
is the number of competitors in industry j in year t, Post is an indicator variable
that takes a value of one during and after 2006, Subsj
is an indicator variable which takes a value
of one (zero) if industry j is estimated to be a substitute (complement) industry, X represents the
agency theoretic controls, fully interacted with Post, Subs and the Post⇥Subs interaction, and ⌧t
and uj
are year and industry fixed e↵ects. Note that the main e↵ects of Post and Subs are implicitly
included by way of year and industry fixed e↵ects. The dependent variable, RevenueBonusi,t
, is
an indicator variable equal to one if the CEO of firm i in year t is given absolute performance
incentives tied to revenue.
Logit Specification
Despite a binary left-hand side variable, I use a linear probability model as my main specifica-
tion. This approach confers advantages in the form of easier interpretability and greater stability
with dense fixed e↵ect structures and lots of interactions (Neyman and Scott, 1948; Lancaster,
2000; Ai and Norton, 2003). However, there are well-documented issues associated with linear
probability models (e.g., Maddala, 1986; Horrace and Oaxaca, 2006), and accordingly I employ a
logit analysis to verify that my results are not sensitive to my econometric specification. I find that
my inferences are una↵ected by this alteration, as shown in Table IA2.
Standard Errors
In the preceding analyses, I cluster standard errors by industry-year. This is a natural choice
given that the primary measure of competition is industry-year. However, if errors are strongly
correlated across industries within a year, or over time within an industry or firm, this approach can
yield spurious inferences. To verify that my inferences are not sensitive to my choice of standard
error calculation, I replicate the main analysis using several alternative approaches: clustering by
firm, clustering by industry, clustering by fiscal year, and bootstrapping. Across all specifications,
results remain significant at the 5%-level, and in the majority of cases the 1%-level. Thus, it
seems unlikely that unaddressed error correlations drive my inferences. These results are shown in
Table IA3.
The bootstrap procedure is as follows: (1) randomly code each FIC-50 industry as a substitute
or complement industry, based on the empirical frequency of each; (2) use the triple di↵erences
design to estimate a placebo treatment e↵ect based on this random coding; and (3) repeat 999
more times to obtain the distribution of treatment e↵ects that attain using this random coding.
I then compare the true estimated treatment e↵ect against this placebo distribution to determine
the likelihood that such a result would occur due to random chance.
Propensity Score Matched Sample
11
The theoretical relation between competition intensity and revenue based pay depends on
whether strategic actions are substitutes or complements—an endogenous industry characteris-
tic. This endogeneity does not pose a concern for my results as long as it does not lead to a
violation of my identifying assumption. However, to assess the possibility that substantive, agency
theoretic di↵erences across substitute and complement industries drive my results, I replicate my
main analysis on a propensity score matched sample.
I perform a 1-to-1 match of firms in substitute industries to firms in complement industries,
with a 0.0001 caliper. The match variables are log(Firms) and all of the agency theoretic control
variables (Age, Ads, R&D, log( �⇡�R
) and log(Inc.Info.)). This procedure reduces the sample size
substantially, but the results remain statistically significant and increase in magnitude, as shown
in Table IA4.
Alternative Industry Sizes
I use Hoberg and Phillips’ FIC-50 to define industries, in my main analyses. I chose this
definition because it is su�ciently broad to avoid the theoretical non-monotonicities associated
with monopolists (as seen in Figure IA1), and because it is comparable in breadth to the oft-used
Fama and French 48 industry classification. To ensure that my findings are not specific to the FIC-
50 industry definition, I replicate the triple di↵erences analysis using multiple di↵erent FIC-levels
to define industries: FIC-25, FIC-100 and FIC-200. I find that my inferences are stable across the
various definitions, as shown in the Table IA5.
Fama-French Industry Classification
The previous tests show that my inferences are robust to various industry breadths, within
the Hoberg and Phillips fixed industry classification. To verify that my inferences also hold with
more conventional industry definitions, I replicate my triple di↵erences analysis using the Fama
and French 48 industry classification to define each industry, and find similar results. These results
are presented in Table IA6.
Herfindahl-Hirschman Index
I use the number of competitors as my primary measure of product market competition. I
choose this measure as it ties most closely to my motivating theory, which used the number of
competitors, N , as the driver of equilibrium incentives. However, to ensure that my results are not
overly sensitive to my choice of competition metric, I use the Herfindahl-Hirschman Index as an
alternative measure of industry competition and find that my results are robust to the use of this
alternative competition measure. These results are shown in Table IA7.
12
Competition From Private Firms
In my main analyses, I use Compustat-based measures to quantify the competition each firm
faces in the market place. One shortcoming of this approach is that it ignores the e↵ects of private
firms on product market competition. Following Ali et al. (2009) I use industry concentration ratios
provided by the Census Bureau to get a more holistic measure of product market competition.
Specifically, I proxy for competition intensity using the natural logarithm of the proportion sales
attributable to the 50 largest firms with a 3-digit NAICS industry, as measured in the 2007 Census.
I replicate my triple di↵erences analysis using this alternative measure and find that results are
consistent, as shown in Table IA8. For this sensitivity analysis, I do not include the interacted
agency theoretic controls; without time series variation in industry competition, there is insu�cient
variation to include them.
Alternative Measures of Strategic Direction
Determining whether strategic actions are substitutes or complements is an important element
of my research design, as it dictates the theoretical e↵ect of enforced pay package disclosures.
Unfortunately, there is no widely accepted method of classifying industries according to the game
being played. In my main analyses, I rely on Kedia’s (2006) methodology for estimating whether
strategic actions are substitutes or complements. This measure is conceptually ideal for two reasons:
(1) it is based on the slopes of firms’ best response functions, which dictate whether firms would
choose to prefer to commit to more aggressive or more passive behavior; and (2) it is flexible enough
to reflect strategic interdependencies across a wide array of possible games (e.g., Cournot; Bertrand;
vertical di↵erentiation; spacial competition; advertising; etc...). However, in practice, this measure
has a number of drawbacks. Most notably, its complicated construction makes it somewhat of a
black box. This in turn makes assessing the validity of my empirical design somewhat di�cult. To
reiterate, any issues of measurement error will not bias towards my hypotheses unless they vary
systematically with competition intensity and the determinants of revenue-based pay, and these
systematic biases change di↵erentially around the introduction of the CD&A.
To verify that my results are robust to alternative approaches, I use two additional [simpler]
proxies for strategic direction. The first alternative proxy is based on the importance of capital
investment. Kreps and Sheinkman (1983) show that Bertrand competition is equivalent to Cournot
if firms must precommit through investment to a production capacity. Dixon (1985) elaborates
that “[i]t has long been recognized that flexibility of production lies at the heart of the distinction
between Bertrand and Cournot models. The most natural application of the Cournot model would
seem to be in the case where output in fixed in the short run” (pg. 1).7 In this spirit, I construct
7See also: Maggi (1996).
13
an alternative measure of strategic direction based on the flexibility of production, as captured by
capital investment. I measure capital investment as the book value of a firm’s Property, Plant and
Equipment, scaled by total assets. I then code industries with lower-than-average (greater-than-
average) production flexibility as as substitute (complement) industries.8
The second alternative proxy is based on the degree of product di↵erentiation. Singh and
Vives (1984) show that the benefits of Cournot competition over Bertrand competition rise as
product substitutability increases. That is, given the ability to choose the mode of competition,
firms would be increasingly likely to choose to compete in quantities (rather than prices) the
more homogenous their goods. Moreover, the pressure to engage in endogenous product di↵eren-
tiation is “orders of magnitude” larger for firms engaged in Bertrand competition (Brander and
Spencer, 2015). Both of these features point towards a greater degree of product di↵erentiation
in complement industries, relative to substitute industries. Accordingly, I measure each firm’s de-
gree of di↵erentiation as 1 minus the cosine similarity of the most similar rival (as provided by
the Hoberg and Phillips Data Library), and code industries with greater-than-average (lower-than-
average) di↵erentiation as complement (substitute) industries. 9
I find that both alternative proxies are highly correlated with the primary Subs measure
(⇢ > 0.20, p < 0.01), but are not significantly correlated with each other (⇢ = 0.0251, t = 0.63).
Their high correlation with the primary measure reassures me that Subs indeed reflects the com-
petitive natures of the industry. Conversely, their low correlation with each other reassures me
that these two alternative proxies o↵er an e↵ective triangulation of the true underyling construct.
Results, presented in Table IA9, align closely with the main analyses. Across all six specifica-
tions, there is an economically large and statistically significant negative coe�cient on the triple
di↵erence.
Single Segment Firms
My triple di↵erences analyses depend on the ability of my competition proxies to successfully
capture product market competition. For many firms, these measures will naturally convey a lot of
information about the product market competition a firm faces. However, for more complex firms
with many segments spanning multiple industries, these measures can fail. To mitigate this concern,
I replicate the triple di↵erences analysis on the subset of single-segment firm-years. The documented
e↵ect is much larger for this subsample, as shown in Table IA10. This finding is consistent with
8This approach to coding industries generates an intuitive ranking. The least flexible industries are mining;construction; utilities; and transportation. The most flexible industries are pharmaceuticals; software; film; andfinancial services.
9This approach to coding industries generates an intuitive ranking. The least di↵erentiated industries are com-modities; (e.g., precious metals, coal, minerals, oil/gas); utilities; transportation; holding companies; and hotels. Themost di↵erentiated industries are newspapers/periodicals/books; groceries; clothing; general merchandise; architec-ture/engineerng and; electronics.
14
the notion that competition proxies provide a much cleaner measure of true competition intensity
for firms which operate in only one industry. It is also consistent with strategic delegation being
a more e↵ective commitment mechanism in simpler firms where the CEO’s incentives are likely to
have more a more direct role in shaping the firm’s product market policies.
Placebo Analysis: Executive Pay Levels
The triple di↵erences design relies on the assumption that agency theoretic determinants of
executive pay are not changing di↵erentially in concentrated substitute industries, around the
introduction of the CD&A. While this assumption cannot be explicitly tested, it is possible to
approximate a test by examining the behavior of other outcome variables that are likely e↵ected
by any changes in agency theoretic considerations. In this vein, I replicate my triple di↵erences
analysis using three alternative outcome variables related to executive pay levels. The estimating
equation is:
< PayLevel >i,t= ↵+ �1log(Firmsj,t)⇥ Postt ⇥ Subsj + �2Postt ⇥ Subsj + �3log(Firmsj,t)⇥ Postt
+ �4log(Firmsj,t)⇥ Subsj + �5log(Firmsj,t) + ⌧t + uj + "i,j,t. (35)
where ⌧t
and uj
are year and industry fixed e↵ects. I use three dependent variables: (1) total pay;
(2) fixed pay and (3) bonus pay. In each specification I deflate the outcome variable by average
total assets use the natural logarithm to adjust for skewness. Results can be found in Table IA11.
Across all nine specifications, the estimated triple di↵erence coe�cient is economically tiny and
statistically indistinguishable from zero.10
Null results for these three outcome variables provide comfort that no major violations of the
parallel trends assumption occur. While I cannot entirely rule out the possibility that some violation
occurs in a manner that alters the optimal mix of metrics used in pay packages without altering
the level of pay, such a violation seems unlikely. I note that finding a null result on pay levels does
not contradict prior work by Gipper (2016), nor does it imply that agency theoretic considerations
are constant over this period. The null result simply shows that any changes in agency theoretic
considerations (that are relevant in determining the level of pay) do not change di↵erentially in
concentrated substitute industries.
10While some of the economic magnitudes looks comparable to those of the prior tests, it is important to note thatthe standard deviations of the placebo outcome variables are roughly times times larger than the standard deviationof RevenueBonus. After adjusting for the standard deviation of the outcome variable, the estimated triple di↵erencecoe�cients in Table 5 (which provides the most similar basis for comparison) are, on average, 6.16 times greater inmagnitude. When compared to Tables 6-8 the di↵erence in economic magnitudes is even more stark.
15
Figure IA1: Equilibrium Incentives as a Function of the Number of Product Market Competitors
This figure presents a graphical representation of the function linking product market competition
to equilibrium incentives, when contracts are publicly disclosed, as derived in the Appendix, Sec-
tion A.1.1 The function is �⇤⇤ = a�aN+cN+cN
2
c(1+N
2)where N is the number of product market rivals, a
is the level of demand, c is the marginal cost of production and � is the relative weight of profit ver-
sus revenue in the compensation contract, with � = 1 (� = 0) representing a pure profit (revenue)
contract.
16
Table IA1: Equilibrium Outcomes—E↵ect of Disclosure on Contract and Product Market
This table summarizes the theoretical predictions which attain from the stylized model in the Appendix, Section A.1. I present theformulae which characterize each equilibrium outcome. I also provide the signs of the main e↵ects of disclosure and competition(operationalized by the number of competitors, N), as well as the sign of their interactive e↵ect. Other model primitives are the level ofdemand, a; the sensitivity of price to output, b; and the marginal cost of production, c. The relative weight on profit is given by �.
Outcome w/o Disclosure w/ Disclosure Disc. Main N Main Interaction
� 1 �aN+a+cN2+cN
cN2+c
� 0 +
Quantity a�cbN+b
aN�cNbN2
+b+ � �
Price a+cNN+1
a+cN2
N2+1
� � +
Revenue (a�c)(a+cN)
b(N+1)
2
N(a�c)(a+cN2)b(N2
+1)2 + � �
COGS c(a�c)bN+b
cN(a�c)
b(N2+1)
+ � �
Markup a�cN+1
a�cN2
+1
� � +
Profit (a�c)2
b(N+1)
2N(a�c)2
b(N2+1)
2 � � +
17
Table IA2: Event Study—Triple Di↵erences (Logit)
This table presents logit results from the “triple di↵erences” event study analysis, with interactedagency theoretic controls. The sample comes from the intersection of Compustat, Incentive Labsand the Hoberg and Phillips Data Library. Specification 1 utilizes the full sample while specifi-cations 2 and 3 winnow the sample to symmetric 4-year and 3-year windows around the CD&A’sintroduction in 2006. The estimating equation is the logit specification:
Pr(RevenueBonusi,t) = f(↵+ �1log(Firmsj,t)⇥ Postt ⇥ Subsj + �2Postt ⇥ Subsj + �3log(Firmsj,t)⇥ Postt
+ �4log(Firmsj,t)⇥ Subsj + �5log(Firmsj,t) + Xi,t + ⌧t + uj + "i,j,t),
where Firmsj,t
is the number of competitors in industry j in year t, Post is an indicator variablethat takes a value of one during and after 2006, Subs
j
is an indicator variable which takes a valueof one (zero) if industry j is estimated to be a substitute (complement) industry, X represents theagency theoretic controls, fully interacted with Post, Subs and the Post⇥Subs interaction, and ⌧
t
and uj
are year and industry fixed e↵ects. Note that the main e↵ects of Post and Subs are implicitlyincluded by way of year and industry fixed e↵ects. The dependent variable, RevenueBonus
i,t
, is anindicator variable equal to one if the CEO of firm i in year t is given absolute performance incentivestied to revenue. Industries are defined by the Hoberg and Phillips FIC-50. In all specifications, theconstant term is not reported as it is subsumed by the fixed e↵ects. Standard errors are clusteredby industry-year.
(1) (2) (3)VARIABLES Prediction R. Bonus R. Bonus R. Bonus
log(Firms)⇥Post⇥Subs – �0.655⇤⇤⇤ �0.699⇤⇤⇤ �0.696⇤⇤⇤(�4.418) (�3.713) (�3.502)
Post⇥Subs 2.294⇤⇤ 2.346⇤⇤ 2.243⇤(2.465) (1.975) (1.890)
log(Firms)⇥Post 0.386⇤⇤⇤ 0.418⇤⇤⇤ 0.387⇤⇤⇤(3.683) (3.310) (3.041)
log(Firms)⇥Subs 0.565⇤ �0.108 �0.879(1.816) (�0.219) (�1.432)
log(Firms) �0.229 0.503 0.779(�0.795) (1.199) (1.589)
Year FE’s Yes Yes YesIndustry FE’s Yes Yes YesInteracted Controls Yes Yes Yes
Window 1998-2013 2002-2009 2003-2008
Observations 10,798 5,630 4,302t-statistics, clustered by industry-year, in parentheses
*** p<0.01, ** p<0.05, * p<0.1
18
Table IA3: Event Study—Triple Di↵erences (Standard Error Calculations)
This table presents results from the“triple di↵erences” event study analysis, with interacted agency theoretic controls using four alternativestandard error calculations: cluster by industry, cluster by firm, cluster by year and bootstrap. The sample comes from the intersectionof Compustat, Incentive Labs and the Hoberg and Phillips Data Library. Specification 1 utilizes the full timeseries while specifications 2and 3 winnow the sample to symmetric 4-year and 3-year windows around the CD&A’s introduction in 2006. The estimating equationis:
RevenueBonusi,t = ↵+ �1log(Firmsj,t)⇥ Postt ⇥ Subsj + �2Postt ⇥ Subsj + �3log(Firmsj,t)⇥ Postt
+ �4log(Firmsj,t)⇥ Subsj + �5log(Firmsj,t) + Xi,t + ⌧t + uj + "i,j,t,
where Firmsj,t
is the number of competitors in industry j in year t, Post is an indicator variable that takes a value of one during andafter 2006, Subs
j
is an indicator variable which takes a value of one (zero) if industry j is estimated to be a substitute (complement)industry, X represents the agency theoretic controls, fully interacted with Post, Subs and the Post ⇥ Subs interaction, and ⌧
t
and uj
are year and industry fixed e↵ects. Note that the main e↵ects of Post and Subs are implicitly included by way of year and industryfixed e↵ects. The dependent variable, RevenueBonus
i,t
, is an indicator variable equal to one if the CEO of firm i in year t is givenabsolute performance incentives tied to revenue. For brevity, only the coe�cient on the two-way interaction (�1) is reported, as this isthe coe�cient which relates directly to my hypotheses. For each specification and standard error method, I report the number of clusters(if applicable), t-statistics and two-sided p-values. Industries are defined by the Hoberg and Phillips FIC-50.
(1) (2) (3)Coe�cient Estimate -0.146 -0.145 -0.132Window 1998-2013 2002-2009 2003-2008Standard Errors Clusters t-stat p-value Clusters t-stat p-value Clusters t-stat p-value
Cluster by Firm 1,487 (�3.098) 0.002 1,290 (�2.805) 0.005 1,243 (�2.441) 0.015Cluster by Industry 49 (�3.628) 0.001 49 (�3.416) 0.001 49 (�3.085) 0.003Cluster by Year 16 (�4.776) <0.001 8 (�3.424) 0.011 6 (�2.609) 0.048Bootstrap (�3.905) <0.001 (�2.859) 0.002 (�2.205) 0.020
19
Table IA4: Event Study—Triple Di↵erences (Propensity Score Matched Sample)
This table presents results from the propensity score matched “triple di↵erences” event studyanalysis, with interacted agency theoretic controls. The sample comes from the intersection ofCompustat, Incentive Labs and the Hoberg and Phillips Data Library. Specification 1 utilizes thefull timeseries while specifications 2 and 3 winnow the sample to symmetric 4-year and 3-yearwindows around the CD&A’s introduction in 2006. The estimating equation is:
RevenueBonusi,t = ↵+ �1log(Firmsj,t)⇥ Postt ⇥ Subsj + �2Postt ⇥ Subsj + �3log(Firmsj,t)⇥ Postt
+ �4log(Firmsj,t)⇥ Subsj + �5log(Firmsj,t) + Xi,t + ⌧t + uj + "i,j,t,
where Firmsj,t
is the number of competitors in industry j in year t, Post is an indicator variablethat takes a value of one during and after 2006, Subs
j
is an indicator variable which takes a valueof one (zero) if industry j is estimated to be a substitute (complement) industry, X represents theagency theoretic controls, fully interacted with Post, Subs and the Post⇥Subs interaction, and ⌧
t
and uj
are year and industry fixed e↵ects. Note that the main e↵ects of Post and Subs are implicitlyincluded by way of year and industry fixed e↵ects. The dependent variable, RevenueBonus
i,t
, isan indicator variable equal to one if the CEO of firm i in year t is given absolute performanceincentives tied to revenue. In each specification, the sample is composed of a 1-to-1 match offirms in substitute industries to firms in complement industries, with a 0.0001 caliper. The matchvariables are log(Firms) and all of the agency theoretic control variables (Age, Ads, R&D, log( �⇡
�R)
and log(Inc.Info.)). Industries are defined by the Hoberg and Phillips FIC-50. In all specifications,the constant term is not reported as it is subsumed by the fixed e↵ects. Standard errors are clusteredby industry-year.
(1) (2) (3)VARIABLES Prediction R. Bonus R. Bonus R. Bonus
log(Firms)⇥Post⇥Subs – �0.184⇤⇤⇤ �0.193⇤⇤⇤ �0.350⇤⇤⇤(�3.952) (�2.874) (�4.876)
Post⇥Subs 0.703⇤⇤⇤ 0.719⇤ 1.252⇤⇤⇤(2.723) (1.947) (3.133)
log(Firms)⇥Post 0.120⇤⇤⇤ 0.171⇤⇤⇤ 0.165⇤⇤⇤(3.813) (3.755) (3.692)
log(Firms)⇥Subs 0.147⇤ �0.189 0.211(1.729) (�1.047) (0.779)
log(Firms) �0.068 0.145 0.158(�0.949) (1.096) (0.824)
Year FE’s Yes Yes YesIndustry FE’s Yes Yes YesInteracted Controls Yes Yes Yes
Window 1998-2013 2002-2009 2003-2008
Observations 4,282 1,842 1,400R-squared 0.174 0.181 0.198
t-statistics, clustered by industry-year, in parentheses*** p<0.01, ** p<0.05, * p<0.1
20
Table IA5: Event Study—Triple Di↵erences (Alternative Industry Sizes)
This table presents results from the “triple di↵erences” event study analysis for a variety of industry definitions. The sample comes fromthe intersection of Compustat, Incentive Labs and the Hoberg and Phillips Data Library. Specifications 1, 4 and 7 utilize the full samplewhile specifications 2, 5 and 8 (3, 6 and 9) winnow the sample to symmetric 4-year (3-year) windows around the CD&A’s introductionin 2006. The estimating equation is:
RevenueBonusi,t = ↵+ �1log(Firmsj,t)⇥ Postt ⇥ Subsj + �2Postt ⇥ Subsj + �3log(Firmsj,t)⇥ Postt
+ �4log(Firmsj,t)⇥ Subsj + �5log(Firmsj,t) + Xi,t + ⌧t + uj + "i,j,t,
where Firmsj,t
is the number of competitors in industry j in year t, Post is an indicator variable that takes a value of one during andafter 2006, Subs
j
is an indicator variable which takes a value of one (zero) if industry j is estimated to be a substitute (complement)industry, X represents the agency theoretic controls, fully interacted with Post, Subs and the Post ⇥ Subs interaction, and ⌧
t
and uj
are year and industry fixed e↵ects. Note that the main e↵ects of Post and Subs are implicitly included by way of year and industryfixed e↵ects. The dependent variable, RevenueBonus
i,t
, is an indicator variable equal to one if the CEO of firm i in year t is givenabsolute performance incentives tied to revenue. In specifications 1-3 (4-6) [7-9], industries are defined by the Hoberg and Phillips FIC-25(FIC-100) [FIC-200]. In all specifications, the constant term is not reported as it is subsumed by the fixed e↵ects. Standard errors areclustered by industry-year.
(1) (2) (3) (4) (5) (6) (7) (8) (9)VARIABLES Pred. R. Bonus R. Bonus R. Bonus R. Bonus R. Bonus R. Bonus R. Bonus R. Bonus R. Bonus
log(Firms)⇥Post⇥Subs – �0.087⇤⇤⇤ �0.073⇤⇤ �0.084⇤⇤ �0.120⇤⇤⇤ �0.088⇤⇤⇤ �0.114⇤⇤⇤ �0.095⇤⇤⇤ �0.075⇤⇤ �0.079⇤⇤(�3.206) (�1.978) (�2.162) (�5.085) (�2.769) (�3.248) (�4.322) (�2.457) (�2.296)
Post⇥Subs 0.347⇤ 0.314 0.371 0.636⇤⇤⇤ 0.184 0.309 0.401⇤⇤⇤ 0.291 0.362⇤⇤(1.847) (1.226) (1.395) (4.511) (0.985) (1.574) �3.067 �1.63 �1.976
log(Firms)⇥Post 0.013 0.023 0.036 0.078⇤⇤⇤ 0.071⇤⇤⇤ 0.091⇤⇤⇤ 0.071⇤⇤⇤ 0.071⇤⇤⇤ 0.074⇤⇤(0.706) (0.954) (1.375) (4.059) (2.784) (3.227) �3.766 �2.775 �2.569
log(Firms)⇥Subs 0.004 �0.037 0.013 0.065 �0.106 �0.006 0.063 0.125 0.149(0.065) (�0.340) (0.073) (1.222) (�1.086) (�0.049) �1.232 �1.473 �1.418
log(Firms) 0.052 0.090 0.101 �0.054 0.118⇤ 0.067 �0.086⇤⇤ �0.185⇤⇤⇤ �0.249⇤⇤⇤(0.803) (0.988) (0.638) (�1.330) (1.727) (0.809) (�2.012) (�2.824) (�3.067)
Year FE’s Yes Yes Yes Yes Yes Yes Yes Yes YesIndustry FE’s Yes Yes Yes Yes Yes Yes Yes Yes YesInteracted Controls Yes Yes Yes Yes Yes Yes Yes Yes Yes
Industry Level FIC-25 FIC-25 FIC-25 FIC-100 FIC-100 FIC-100 FIC-200 FIC-200 FIC-200Window 1998-2013 2002-2009 2003-2008 1998-2013 2002-2009 2003-2008 1998-2013 2002-2009 2003-2008
Observations 10,798 5,630 4,302 10,798 5,630 4,302 10,798 5,630 4,302R-squared 0.200 0.181 0.190 0.236 0.231 0.245 0.253 0.245 0.255
t-statistics, clustered by industry-year, in parentheses*** p<0.01, ** p<0.05, * p<0.1
21
Table IA6: Event Study—Triple Di↵erences (Fama-French 48)
This table presents the results from the “triple di↵erences” event study analysis using an alternativeindustry classification system. The sample comes from the intersection of Compustat, IncentiveLabs and the Hoberg and Phillips Data Library. Specification 1 utilizes the full sample whilespecifications 2 and 3 winnow the sample to symmetric 4-year and 3-year windows around theCD&A’s introduction in 2006. The estimating equation is:
RevenueBonusi,t = ↵+ �1log(Firmsj,t)⇥ Postt ⇥ Subsj + �2Postt ⇥ Subsj + �3log(Firmsj,t)⇥ Postt
+ �4log(Firmsj,t)⇥ Subsj + �5log(Firmsj,t) + Xi,t + ⌧t + uj + "i,j,t,
where Firmsj,t
is the number of competitors in industry j in year t, Post is an indicator variablethat takes a value of one during and after 2006, Subs
j
is an indicator variable which takes a valueof one (zero) if industry j is estimated to be a substitute (complement) industry, X represents theagency theoretic controls, fully interacted with Post, Subs and the Post⇥Subs interaction, and ⌧
t
and uj
are year and industry fixed e↵ects. Note that the main e↵ects of Post and Subs are implicitlyincluded by way of year and industry fixed e↵ects. The dependent variable, RevenueBonus
i,t
, is anindicator variable equal to one if the CEO of firm i in year t is given absolute performance incentivestied to revenue. Industries are defined by the Fama and French 48 Industry Classification. In allspecifications, the constant term is not reported as it is subsumed by the fixed e↵ects. Standarderrors are clustered by industry-year.
(1) (2) (3)VARIABLES Prediction R. Bonus R. Bonus R. Bonus
log(Firms)⇥Post⇥Subs – �0.057⇤⇤⇤ �0.069⇤⇤⇤ �0.066⇤⇤⇤(�3.620) (�3.507) (�3.087)
Post⇥Subs 0.127 0.243 0.204(1.151) (1.588) (1.224)
log(Firms)⇥Post 0.034⇤⇤⇤ 0.031⇤⇤⇤ 0.029⇤⇤(4.104) (2.743) (2.515)
log(Firms)⇥Subs �0.073 �0.140 �0.401⇤⇤⇤(�1.082) (�1.149) (�2.808)
log(Firms) 0.004 0.121 0.303⇤⇤(0.076) (1.198) (2.583)
Year FE’s Yes Yes YesIndustry FE’s Yes Yes YesInteracted Controls Yes Yes Yes
Window 1998-2013 2002-2009 2003-2008
Observations 10,739 5,602 4,280R-squared 0.225 0.215 0.224
t-statistics, clustered by industry-year, in parentheses*** p<0.01, ** p<0.05, * p<0.1
22
Table IA7: Event Study—Triple Di↵erences (HHI)
This table presents the results from the “triple di↵erences” event study analysis using theHerfindahl-Hirschman index as my measure of industry concentration. The sample comes fromthe intersection of Compustat, Incentive Labs and the Hoberg and Phillips Data Library. Specifi-cation 1 utilizes the full sample while specifications 2 and 3 winnow the sample to symmetric 4-yearand 3-year windows around the CD&A’s introduction in 2006. The estimating equation is:
RevenueBonusi,t = ↵+ �1log(Firmsj,t)⇥ Postt ⇥ Subsj + �2Postt ⇥ Subsj + �3log(Firmsj,t)⇥ Postt
+ �4log(Firmsj,t)⇥ Subsj + �5log(Firmsj,t) + Xi,t + ⌧t + uj + "i,j,t,
where Firmsj,t
is the number of competitors in industry j in year t, Post is an indicator variablethat takes a value of one during and after 2006, Subs
j
is an indicator variable which takes a valueof one (zero) if industry j is estimated to be a substitute (complement) industry, X represents theagency theoretic controls, fully interacted with Post, Subs and the Post⇥Subs interaction, and ⌧
t
and uj
are year and industry fixed e↵ects. Note that the main e↵ects of Post and Subs are implicitlyincluded by way of year and industry fixed e↵ects. The dependent variable, RevenueBonus
i,t
, is anindicator variable equal to one if the CEO of firm i in year t is given absolute performance incentivestied to revenue. Industries are defined by the Hoberg and Phillips FIC-50. In all specifications, theconstant term is not reported as it is subsumed by the fixed e↵ects. Standard errors are clusteredby industry-year.
(1) (2) (3)VARIABLES Prediction R. Bonus R. Bonus R. Bonus
log(HHI)⇥Post⇥Subs + 0.118⇤⇤⇤ 0.085⇤ 0.071(3.274) (1.939) (1.555)
Post⇥Subs 0.031 �0.047 �0.044(0.235) (�0.273) (�0.242)
log(HHI)⇥Post �0.100⇤⇤⇤ �0.084⇤⇤ �0.063(�2.949) (�2.037) (�1.504)
log(HHI)⇥Subs �0.106⇤⇤⇤ �0.075⇤ �0.042(�3.168) (�1.806) (�0.927)
log(HHI) 0.109⇤⇤⇤ 0.105⇤⇤⇤ 0.073⇤(3.512) (2.727) (1.783)
Year FE’s Yes Yes YesIndustry FE’s Yes Yes YesInteracted Controls Yes Yes Yes
Window 1998-2013 2002-2009 2003-2008
Observations 10,798 5,630 4,302R-squared 0.208 0.193 0.202
t-statistics, clustered by industry-year, in parentheses*** p<0.01, ** p<0.05, * p<0.1
23
Table IA8: Event Study—Triple Di↵erences (Private Firms)
This table presents the results from the “triple di↵erences” event study analysis using Prop50 asmy measure of industry concentration. The sample comes from the intersection of Compustat,Incentive Labs and the Hoberg and Phillips Data Library. Specification 1 utilizes the full samplewhile specifications 2 and 3 winnow the sample to symmetric 4-year and 3-year windows aroundthe CD&A’s introduction in 2006. The estimating equation is:
RevenueBonusi,t = ↵+ �1log(Prop50j)⇥ Postt ⇥ Subsj + �2Postt ⇥ Subsj
+ �3log(Prop50j)⇥ Postt + ⌧t + uj + "i,j,t,
where Prop50j
is the proportion of sales generated by the largest 50 firms within industry j in2007, Post is an indicator variable that takes a value of one during and after 2006, Subs
j
is anindicator variable which takes a value of one (zero) if industry j is estimated to be a substitute(complement) industry, and ⌧
t
and uj
are year and industry fixed e↵ects. Note that the e↵ectsof Post, Subs, log(Prop50) and log(Prop50) ⇥ Subs are implicitly included by way of year andindustry fixed e↵ects. The dependent variable, RevenueBonus
i,t
, is an indicator variable equal toone if the CEO of firm i in year t is given absolute performance incentives tied to revenue. Dueto the time-invariant nature of the competition measure, I do not include the agency theoreticcontrol variables. Industries are defined 3-digit NAICS. In all specifications, the constant term isnot reported as it is subsumed by the fixed e↵ects. Standard errors are clustered by industry-year.
(1) (2) (3)VARIABLES Prediction R. Bonus R. Bonus R. Bonus
log(Prop50)⇥Post⇥Subs + 0.079⇤ 0.116⇤⇤ 0.130⇤⇤(1.868) (2.072) (1.997)
Post⇥Subs �0.376⇤⇤ �0.509⇤⇤ �0.573⇤⇤(�2.289) (�2.319) (�2.252)
log(Prop50)⇥Post �0.066⇤⇤ �0.082⇤ �0.106⇤⇤(�2.052) (�1.850) (�2.016)
Year FE’s Yes Yes YesIndustry FE’s Yes Yes YesInteracted Controls No No No
Window 1998-2013 2002-2009 2003-2008
Observations 10,931 5,404 4,142R-squared 0.213 0.192 0.195
t-statistics, clustered by industry-year, in parentheses*** p<0.01, ** p<0.05, * p<0.1
24
Table IA9: Event Study—Triple Di↵erences (Alternative Measures of Strategic Direction)
This table presents results from the “triple di↵erences” event study analysis using two alternative measures of strategic direction. Thesample comes from the intersection of Compustat, Incentive Labs and the Hoberg and Phillips Data Library. Specifications 1 and 4utilizes the full sample while specifications 2 and 5 (3 and 6) winnow the sample to symmetric 4-year (3-year) windows around theCD&A’s introduction in 2006. The estimating equation is:
RevenueBonusi,t = ↵+ �1log(Firmsj,t)⇥ Postt ⇥ Subsj + �2Postt ⇥ Subsj + �3log(Firmsj,t)⇥ Postt
+ �4log(Firmsj,t)⇥ Subsj + �5log(Firmsj,t) + Xi,t + ⌧t + uj + "i,j,t,
where Firmsj,t
is the number of competitors in industry j in year t, Post is an indicator variable that takes a value of one during andafter 2006, Subs
j
is an indicator variable which takes a value of one (zero) if industry j is estimated to be a substitute (complement)industry, X represents the agency theoretic controls, fully interacted with Post, Subs and the Post ⇥ Subs interaction, and ⌧
t
and uj
are year and industry fixed e↵ects. Note that the main e↵ects of Post and Subs are implicitly included by way of year and industryfixed e↵ects. In odd (even) numbered specifications, the Subs variable is an indicator variable equal to one in industries of above averagecapital intensity (product market homogeneity). The dependent variable, RevenueBonus
i,t
, is an indicator variable equal to one if theCEO of firm i in year t is given absolute performance incentives tied to revenue. Industries are defined by the Hoberg and PhillipsFIC-50. In all specifications, the constant term is not reported as it is subsumed by the fixed e↵ects. Standard errors are clustered byindustry-year.
(1) (2) (3) (4) (5) (6)VARIABLES Pred. R. Bonus R. Bonus R. Bonus R. Bonus R. Bonus R. Bonus
log(Firms)⇥Post⇥Subs – �0.111⇤⇤⇤ �0.076⇤⇤ �0.085⇤⇤ �0.155⇤⇤⇤ �0.115⇤⇤⇤ �0.103⇤⇤(�4.003) (�2.194) (�2.292) (�5.228) (�2.925) (�2.180)
Post⇥Subs 0.403⇤⇤ 0.302 0.390⇤ 0.801⇤⇤⇤ 0.574⇤⇤ 0.609⇤⇤(2.482) (1.520) (1.945) (4.800) (2.549) (2.313)
log(Firms)⇥Post 0.028 0.022 0.027 0.042⇤⇤ 0.038⇤ 0.038(1.527) (0.915) (1.031) (2.467) (1.671) (1.435)
log(Firms)⇥Subs 0.039 �0.014 0.070 0.183⇤⇤⇤ 0.176⇤⇤⇤ 0.157⇤⇤⇤(0.675) (�0.141) (0.587) (6.582) (4.589) (3.452)
log(Firms) 0.040 0.108⇤ 0.084 �0.010 0.025 0.016(1.107) (1.761) (1.135) (�0.334) (0.519) (0.253)
Year FE’s Yes Yes Yes Yes Yes YesIndustry FE’s Yes Yes Yes Yes Yes YesInteracted Controls Yes Yes Yes Yes Yes Yes
Measure of Subs vs Comps Capital Capital Capital Prod. Di↵. Prod. Di↵. Prod. Di↵.Window 1998-2013 2002-2009 2003-2008 1998-2013 2002-2009 2003-2008
Observations 10,621 5,528 4,226 10,621 5,528 4,226R-squared 0.207 0.191 0.200 0.207 0.194 0.202
t-statistics, clustered by industry-year, in parentheses*** p<0.01, ** p<0.05, * p<0.1
25
Table IA10: Event Study—Triple Di↵erences (Single Segment Firms)
This table presents results from the “triple di↵erences” event study analysis, with interacted agencytheoretic controls, based only on single segmet firms. The sample is single segmet firms from theintersection of Compustat, Incentive Labs and the Hoberg and Phillips Data Library. Specification1 utilizes the full timeseries while specifications 2 and 3 winnow the sample to symmetric 4-yearand 3-year windows around the CD&A’s introduction in 2006. The estimating equation is:
RevenueBonusi,t = ↵+ �1log(Firmsj,t)⇥ Postt ⇥ Subsj + �2Postt ⇥ Subsj + �3log(Firmsj,t)⇥ Postt
+ �4log(Firmsj,t)⇥ Subsj + �5log(Firmsj,t) + Xi,t + ⌧t + uj + "i,j,t,
where Firmsj,t
is the number of competitors in industry j in year t, Post is an indicator variablethat takes a value of one during and after 2006, Subs
j
is an indicator variable which takes a valueof one (zero) if industry j is estimated to be a substitute (complement) industry, X represents theagency theoretic controls, fully interacted with Post, Subs and the Post⇥Subs interaction, and ⌧
t
and uj
are year and industry fixed e↵ects. Note that the main e↵ects of Post and Subs are implicitlyincluded by way of year and industry fixed e↵ects. The dependent variable, RevenueBonus
i,t
, is anindicator variable equal to one if the CEO of firm i in year t is given absolute performance incentivestied to revenue. Industries are defined by the Hoberg and Phillips FIC-50. In all specifications, theconstant term is not reported as it is subsumed by the fixed e↵ects. Standard errors are clusteredby industry-year.
(1) (2) (3)VARIABLES Prediction R. Bonus R. Bonus R. Bonus
log(Firms)⇥Post⇥Subs – �0.397⇤⇤⇤ �0.507⇤⇤⇤ �0.312⇤(�3.076) (�3.458) (�1.798)
Post⇥Subs 1.984⇤⇤⇤ 2.261⇤⇤ 0.939(2.716) (2.580) (0.900)
log(Firms)⇥Post 0.324⇤⇤⇤ 0.470⇤⇤⇤ 0.437⇤⇤⇤(3.047) (4.209) (3.307)
log(Firms)⇥Subs 0.431 0.736⇤ 0.099(1.603) (1.821) (0.155)
log(Firms) �0.814⇤⇤⇤ �1.211⇤⇤⇤ �1.067⇤⇤(�3.088) (�3.199) (�2.024)
Year FE’s Yes Yes YesIndustry FE’s Yes Yes YesInteracted Controls Yes Yes Yes
Window 1998-2013 2002-2009 2003-2008
Observations 663 382 296R-squared 0.510 0.531 0.565
t-statistics, clustered by industry-year, in parentheses*** p<0.01, ** p<0.05, * p<0.1
26
Table IA11: Placebo Event Study—Triple Di↵erences Design (Executive Pay Levels)
This table presents results from the “triple di↵erences” event study analysis using executive pay levels as the dependent variables. Thesample comes from the intersection of Compustat, Incentive Labs, ExecuComp and the Hoberg and Phillips Data Library. Specifications1, 4 and 7 utilize the full sample while specifications 2, 5 and 8 (3, 6 and 9) winnow the sample to symmetric 4-year (3-year) windowsaround the CD&A’s introduction in 2006. The estimating equation is:
< PayLevel >i,t
= ↵+ �1log(Firmsj,t
)⇥ Postt
⇥ Subsj
+ �2Postt
⇥ Subsj
+ �3log(Firmsj,t
)⇥ Postt
+ �4log(Firmsj,t
)⇥ Subsj
+ �5log(Firmsj,t
) + Xi,t
+ ⌧t
+ uj
+ "i,j,t
,
where Firmsj,t
is the number of competitors in industry j in year t, Post is an indicator variable that takes a value of one during andafter 2006, Subs
j
is an indicator variable which takes a value of one (zero) if industry j is estimated to be a substitute (complement)industry, X represents the agency theoretic controls, fully interacted with Post, Subs and the Post ⇥ Subs interaction, and ⌧
t
and uj
are year and industry fixed e↵ects. Note that the main e↵ects of Post and Subs are implicitly included by way of year and industryfixed e↵ects. In specifications 1-3 (4-6) [7-9], the dependent variable is total pay (fixed pay) [bonus pay] awarded to the CEO of firm ifor fiscal year t. In each specification, the dependent variable is deflated by average total assets, and logged. Industries are defined bythe Hoberg and Phillips FIC-50. In all specifications, the constant term is not reported as it is subsumed by the fixed e↵ects. Standarderrors are clustered by industry-year.
(1) (2) (3) (4) (5) (6) (7) (8) (9)VARIABLES Pred. Total Pay Total Pay Total Pay Fixed Pay Fixed Pay Fixed Pay Bonus Pay Bonus Pay Bonus Pay
log(Firms)⇥Post⇥Subs 0 �0.059 �0.076 �0.034 �0.088 �0.102 �0.021 �0.030 �0.087 �0.076(�0.725) (�0.789) (�0.341) (�1.066) (�1.102) (�0.219) (�0.320) (�0.761) (�0.643)
Post⇥Subs 0.202 0.257 0.028 0.324 0.408 �0.008 0.056 0.288 0.216(0.483) (0.526) (0.055) (0.773) (0.878) (�0.017) (0.115) (0.499) (0.362)
log(Firms)⇥Post 0.003 0.018 �0.021 �0.019 0.029 0.005 0.046 0.058 0.023(0.069) (0.296) (�0.327) (�0.352) (0.510) (0.094) (0.869) (0.772) (0.296)
log(Firms)⇥Subs �0.043 �0.242 �0.432 0.083 0.077 0.067 �0.116 �0.312 �0.462(�0.236) (�0.705) (�1.229) (0.396) (0.237) (0.180) (�0.559) (�0.773) (�1.143)
log(Firms) 0.097 �0.046 0.121 �0.052 �0.405 �0.260 0.157 0.041 0.155(0.615) (�0.142) (0.418) (�0.275) (�1.386) (�0.849) (0.901) (0.111) (0.459)
Year FE’s Yes Yes Yes Yes Yes Yes Yes Yes YesIndustry FE’s Yes Yes Yes Yes Yes Yes Yes Yes Yes
Window 1998-2013 2002-2009 2003-2008 1998-2013 2002-2009 2003-2008 1998-2013 2002-2009 2003-2008
Observations 8,945 4,619 3,524 8,945 4,619 3,524 8,945 4,619 3,524R-squared 0.270 0.275 0.285 0.206 0.243 0.253 0.226 0.221 0.233
t-statistics, clustered by industry-year, in parentheses*** p<0.01, ** p<0.05, * p<0.1
27