strategic delegation and the weaponization of …home.uchicago.edu/~mjbloomfield/jmp_ia.pdfstrategic...

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:


+ �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:



where Firmsj,t


j


t

and uj


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.



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)


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:



where Firmsj,t


j


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


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:



where Firmsj,t


j


t

and uj


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.



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)


Window 1998-2013 2002-2009 2003-2008



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:



where Firmsj,t


j


t

and uj


i,t



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)


Window 1998-2013 2002-2009 2003-2008



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.


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



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:



where Firmsj,t


j


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


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:



where Firmsj,t


j


t

and uj


i,t



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)


Window 1998-2013 2002-2009 2003-2008

Observations 663 382 296R-squared 0.510 0.531 0.565


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


j


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


27

strategic delegation and the weaponization of …home.uchicago.edu/~mjbloomfield/jmp_ia.pdfstrategic...

Documents