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Executive compensation: the trend toward one size fits all

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Executive compensation: the trend toward one size fits all

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Content Executive Compensation: The Trend Toward One Size Fits All
by
Felipe Cabez on
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulllment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(BUSINESS ADMINISTRATION)
May 2021
Acknowledgements
I am especially grateful to Jerry Hoberg, John Matsusaka, and Kevin J. Murphy for their in-
valuable advice. I would also like to thank Kenneth Ahern, Francisco Cabezon, Tom Chang,
Constantin Charles, Alex Edmans, Alberto Etchegaray, Wayne Guay (discussant), Sandy Klasa,
Gabriel Natividad, Katya Neretina, Marcus Opp, Oguzhan Ozbas, Giorgo Sertsios, Richard Sloan,
and participants at the FOM Conference, the MFA Conference, the SFS Cavalcade Conference, the
USC PhD Conference, the Uandes Corporate Finance Conference, and seminar participants at USC
Marshall School of Business, Foster School of Business, UGA Terry College of Business, Pamplin
College of Business, KU School of Business, ESCP Business School, PUC School of Business, and
UAI Business School for helpful comments and suggestions.
ii
Contents
Acknowledgements ii
List of Tables v
List of Figures vi
Abstract vii
1 Introduction 1
2 Data and Methodology 7
2.1 Measure of Contract Similarity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3 Major Trends 12
3.1 The Convergence of Executive Compensation Plans . . . . . . . . . . . . . . . . . . 12
3.2 Discussion and Institutional Background . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.3 Suggestive Evidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4 Evidence from the frequency of mandatory Say-on-Pay 33
4.1 Dierence-in-dierence Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
4.2 Regression Discontinuity Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
5 Economic Consequences of the Convergence of Compensation Structures 45
5.1 Instrumental Variable Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
6 Conclusion 54
Bibliography 56
iii
A Appendices 63
A.1 Variable denitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
A.2 Variance of Similarity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
A.3 Alternative Measures of Similarity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
A.4 SOP: Di-in-di with entropy balanced matching . . . . . . . . . . . . . . . . . . . . 68
A.5 IV Estimation: First Stage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
iv
List of Tables
1 Cosine Similarity of Compensation Packages . . . . . . . . . . . . . . . . . . . . . . . 13
2 Summary statistics of cosine similarity of CEO compensation . . . . . . . . . . . . . 14
3 Cosine Similarity of Compensation Packages . . . . . . . . . . . . . . . . . . . . . . . 20
4 CEO compensation similarity and the in
uence of Proxy Advisory Firms . . . . . . 31
5 Similarity to ISS simulated preferred compensation scheme . . . . . . . . . . . . . . 32
6 Votes on the frequency of Say-on-Pay in the rst Say-on-Pay vote . . . . . . . . . . . 33
7 Eects of the frequency of Say-on-Pay on similarity of CEO compensation. Dierence-
in-dierence analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
8 Summary Statistics in 2011 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
9 Eects of the frequency of Say-on-Pay on similarity of CEO compensation. Dierence-
in-dierence analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
10 Regression discontinuity design estimation: CEO similarity . . . . . . . . . . . . . . 42
11 Summary Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
12 CEO compensation similarity and economic consequences . . . . . . . . . . . . . . . 47
13 CEO compensation similarity and directors serving on the board of other rms . . . 51
14 Cosine Similarity of Compensation Packages . . . . . . . . . . . . . . . . . . . . . . . 64
15 KL Divergence test and KS test of Compensation Packages . . . . . . . . . . . . . . 67
16 Instrumental Variable Estimation: First Stage . . . . . . . . . . . . . . . . . . . . . . 69
v
List of Figures
1 Cosine similarity of CEO compensation plans (mean) . . . . . . . . . . . . . . . . . . 2
2 Kernel density estimate of the ratio of equity CEO compensation . . . . . . . . . . . 9
3 Box plot of each component of compensation . . . . . . . . . . . . . . . . . . . . . . 9
4 Average standard deviation of cosine similarity of CEO compensation plans . . . . . 13
5 Cosine similarity of CEO compensation and rm characteristics . . . . . . . . . . . . 15
6 Cosine similarity of CEO compensation by industry . . . . . . . . . . . . . . . . . . 17
7 Cosine similarity of executive compensation plans within industry . . . . . . . . . . 18
8 Cosine similarity of CEO compensation excluding one element at a time . . . . . . . 19
9 Cosine similarity of CEO compensation including pension . . . . . . . . . . . . . . . 20
10 Cosine similarity of CEO compensation distinguishing restricted and performance-
based stock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
11 Cosine similarity of CEO compensation excluding new and exiting rms . . . . . . . 21
12 Cosine similarity of CEO compensation comparable before and after 2006 . . . . . . 22
13 Cosine similarity of CEO compensation considering stock and options awards together 23
14 Cosine similarity of CEO compensation and the Discussion of Say-on-Pay . . . . . . 25
15 Cosine-similarity of rms' compensation plan and a simulated ISS's preferred com-
pensation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
16 Say-on-Pay: dierence-in-dierence analysis . . . . . . . . . . . . . . . . . . . . . . . 37
17 Say-on-Pay: RDD analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
18 Histogram of the vote dierence between 1-year and 3-year Say-on-Pay . . . . . . . . 43
19 Representation of the instrumental variable . . . . . . . . . . . . . . . . . . . . . . . 52
20 Statistical distribution similarity of executive compensation plans . . . . . . . . . . . 66
vi
Abstract
This paper reports the prevalence of a \one-size-ts-all" trend in the structure of executive com-
pensation plans. The way rms distribute total compensation across dierent components of pay
{salary, bonus, stock awards, option awards, non-equity incentives, pensions, and perquisites{ is
becoming more similar since 2006. In particular, 25% of the variation across rms disappeared
in the last ten years. Using close votes surrounding Say-on-Pay's implementation, I nd that
shareholders' in
uence on management decisions causes part of this convergence. This nding is
robust in both dierence-in-dierence and RDD estimations. Additional evidence suggests that
proxy advisors play a role by pushing towards standardization. The convergence has economic
consequences. The more similar a rm's compensation structure becomes to the others, the
higher the pay and the lower its sensitivity to the rm performance and the risk taken. Addi-
tionally, the rm innovates less {invests less in R&D and is less likely to patent{ and reduces
its market value.
vii
1 Introduction
In principle, the optimal incentive contract is a function of many parameters that are not the
same for every rm. Yet many observers worry that executive compensation is homogenizing, with
contracts converging on a \one-size-ts-all" template (Gordon (2009), Hou, Priem, and Goranova
(2017), Murphy and Jensen (2018)). This paper conducts an empirical investigation to determine
to what extent executive contracts are converging, explain why this might be happening, and its
consequences for corporate performance.
Trends in total compensation are easy to observe, but measuring convergence in the structure
of compensation is challenging because of the multidimensionality of contracts. I propose a direct
measure of contract similarity based on a spacial representation of contracts, which is analogous to
the spatial representation of industries in Hoberg and Phillips (2016). Executives receive compensa-
tion in many dierent forms, including salaries, bonuses, long-term incentives, stock, stock options,
retirement benets, and dierent types of perquisites. Thus, to compare compensation plans across
rms, for each rm, I create a multidimensional vector that includes the participation of each type
of compensation in the total compensation. Then I measure how similar one rm is to another
rm by calculating the dot product of their two vectors (Bhattacharya (1946), Salton and McGill
(1983), Hoberg and Phillips (2016)), taking values from zero (the two vectors are orthogonal) to
one (the two vectors have the same orientation). For each rm, I calculate the average similarity
of its compensation relative to all other rms.
I nd that the structure of compensation of public rms is converging, and the amount of the
convergence is economically large. Figure 1 shows the time-series of the mean of compensation
similarity. The average similarity increased from 0.5 in 2007 to 0.63 in 2016, which implies that
25% of the compensation variation across rms disappeared in the last 10 years.
This convergence is an economy-wide phenomenon. Firm characteristics do not explain it, and
1
Figure 1: Cosine similarity of CEO compensation plans (mean)
it does not respond to industry-specic forces. I nd similar levels and trends of convergence if
I separate the sample based on rm size, age, and protability. Additionally, all industries are
converging at similar rates, and the magnitude of convergence within-industry is similar to the
whole-economy convergence. Moreover, the results are also robust to excluding any element of
compensation, implying that there is no single type of pay that can explain the convergence by
itself.
An economy-wide change of this nature and magnitude raises two questions: why is this con-
vergence happening, and is it a good or bad thing? The bulk of this paper attempts to answer
these two questions.
I rst show evidence that this convergence is partly an unintended consequence of recent regu-
lations to get shareholders involved in the design of compensation plans. Indeed, public companies
have to disclose their executive compensation plans, and shareholders have an advisory vote on
them (the so-called Say-on-Pay (SOP)). The existence of shareholders' vote on compensation plans
might increase convergence in the structure of pay if shareholders have homogenous preferences
2
or are inadequately informed about optimal variation. The reason is that management has to
consider their preferences as a new element in the optimization process of dening the rm's best
compensation structure.
Even though many of the major investors make their own voting decisions, the empirical ndings
suggest that shareholders routinely rely on proxy-advisory rms for recommendations on how to
vote and that rms do react to their recommendations (McCahery, Sautner, and Starks (2016), Er-
timur, Ferri, and Oesch (2013), Malenko and Shen (2016), Larcker, McCall, and Ormazabal (2015)).
The existence of a small number of proxy advisors and the limited time to provide recommendations
on thousands of proxy meetings has created a growing concern of a \best compensation practices"
regime pushing towards a \one-size-ts-all" trend (Gordon (2009), Hou, Priem, and Goranova
(2017), Murphy and Jensen (2018)).
The existence of Say-on-pay combined with an increase in institutional investors ownership and
an increase in proxy advisory rms' activity are likely to explain part of the convergence. To test
this hypothesis, I use the frequency of Say-on-Pay voting as a quasi-natural experiment. In 2011,
when the SEC implemented the mandatory Say-on-Pay vote, it also required that shareholders vote
on the frequency of that voting. In particular, in the rst year of Say-on-Pay (and every six years
after that), shareholders voted on whether Say-on-Pay votes will occur every one, two, or three
years. Firms with a higher frequency of Say-on-Pay voting are exposed to shareholders' in
uence
more frequently. If the increase in similarity is due to more in
uential shareholders, rms with
Say-on-Pay every year should have higher levels of similarity than rms with Say-on-Pay every two
or three years.
I rst run a dierence-in-dierence analysis in which the treated rms are those with Say-on-Pay
every year, and the control rms those with Say-on-Pay every three years. However, one concern
with this approach is that the shareholder's vote on Say-on-Pay periodicity might be endogenous
3
to omitted characteristics of the rm. To improve the identication, I restrict the sample to rms
where the election between one-year-SOP and three-year-SOP was close. The intuition of this
identication strategy is that rms in which a one-year-SOP won against a three-year-SOP by a
narrow margin can be a good counterfactual for those rms in which the opposite occurred (a
three-year-SOP won against a one-year-SOP by a narrow margin). Using this more rigorous test, I
nd that after the implementation of SOP in 2011, treated rms increased compensation similarity
by 8%.
I nd similar results after implementing a sharp regression discontinuity estimation. Specically,
I create a variable that measures the one-year-SOP margin of victory {dened as the vote share
of the one-year-SOP minus the vote share of the three-year-SOP{. The value of this variable
goes from -1 to +1, with positive values meaning the victory of one-year SOP frequency. At
the zero-threshold, the frequency of Say-on-Pay sharply changes from three to one. I use the
compensation similarity in the next period as the dependent variable. The estimated coecient
shows an increase in almost 10% of compensation similarity when a rm has a one-year frequency
SOP instead of a three-year frequency. These results {both from the dierence-in-dierence and the
RDD analysis{ are signicant at a 95% condence level and are robust to all alternative measures
of similarity (compensation similarity within industry, compensation similarity including pensions,
and compensation similarity distinguishing restricted and performance-based stocks).
The Say-on-Pay result suggests that an increase in shareholders' in
uence on management
decisions plays an important role in explaining the convergence of compensation. Exploring further,
four tests provide evidence suggesting that proxy advisory rms' recommendations are likely driving
this result at least in part.
First, the ratio of shares owned by passive institutional investors positively correlates with com-
pensation similarity. Most of the empirical literature shows that passive institutional investors are
4
the shareholders most likely to follow proxy advisers' recommendations (Bushee and Noe (1999),
Larcker, McCall, and Ormazabal (2015) and Malenko and Shen (2016)). Second, I nd that com-
pensation similarity increases more if the rm received a negative Say-on-Pay recommendation
from ISS in the past. Third, I nd that the less similar is the compensation package of a rm,
the more likely the rm will receive a negative Say-on-Pay recommendation from ISS in the next
period. Fourth, I create a simulated vector that mimics the implicitly preferred vector behind the
ISS's recommendation on Say-on-Pay. I nd that all rms' compensation structure is converging
to the simulated vector that ISS most recommends to vote in favor of.
I nd evidence that convergence has real eects on CEO behavior and rm performance. In
particular, I nd that when a CEO compensation plan becomes more homogenous, that CEO gets
higher pay, and this payment is less sensitive to the rm performance (delta) and the risk taken
(vega).
The positive correlation between compensation similarity and pay level suggests that rms
standardize their plans by increasing the low components rather than reducing the high components
(Murphy and Sandino (2020)). The negative association with delta suggests that standardization
may be pushing compensation plans to a contract that is less linked to performance. The negative
association between similarity and vega suggests that rms are converging to a contract that does
not incentivize executives to get involved in risk-taking activities. Exploring further, I examine the
relationship between compensation similarity and innovation since innovation is likely to be aected
by risk-taking incentives. In line with lower risk-taking behavior, I nd a negative correlation
between compensation similarity and both R&D investment and the number of patents reported
in the next two years.
The standardization in CEO pay structure is associated with less innovation and less pay-
performance sensitivity. Whether this is good or bad depends on the optimal level of innovation
5
and delta of each company. The methodology of this paper does not allow to make such a claim.
However, I do nd evidence of possible value-destruction consequences. Specically, I nd a negative
association with Tobin's Q: the more similar a rm's compensation plan becomes to the others, the
lower its market value. This result, however, should be considered with caution since, even though
it is statistically signicant, its magnitude is considerably smaller than the eects on innovation
and pay sensitivities.
My empirical analysis considers within-rm variation, it does not control for time-variant omit-
ted variables. To overcome these endogeneity issues, I propose an instrument that is related to
convergence but is unlikely to be related to rm policies. There is evidence that directors can in
u-
ence the design of executive compensation plans based on their experiences on the board of other
rms. For example, Fernandes, Ferreira, Matos, and Murphy (2013) show that, for non-US rms
with a high fraction of directors who also sit on boards of US rms, the CEO pay is similar to that
of the US CEOs. I take advantage of these peer eects to build an instrument for compensation
similarity.
Specically, I dene an overlapping-board rm as a rm that is both (i) in a dierent industry
and (ii) shares a director with the focal rm, and I consider the standardization of the compensation
plan of the overlapping-board rm as an instrument for the standardization of the compensation
plan of the focal rm. The idea of this instrument is that if the director of a rm participates on the
board of another rm with a very standard compensation structure, she might in
uence the focal
rm to mimic that structure. The exclusion restriction relies on assuming that the compensation
similarity of a dierent rm in a dierent industry is unlikely to be related to the focal rm's policy.
Based on this identication strategy, I run a Two-Stage least squares (2SLS) instrumental
variable regression with rm and year xed eects and nd a positive eect of similarity on total
CEO compensation. Similarly, I nd a negative impact on delta, vega, Tobin's Q, R&D investment,
6
and the number of patents. These results are stronger both in magnitude and statistical power than
those obtained without instrumentation, suggesting that compensation convergence exacerbates the
severity of agency problems for treated rms.
I contribute to the empirical literature on the interaction between corporate governance and
executive compensation plans. My ndings also relate to a large debate among both academics and
practitioners on what causes the observed trends in executive pay (Frydman and Jenter (2010),
Murphy (2013), and Edmans, Gabaix, and Jenter (2017)). The results support the perspective
that institutional forces shape pay. Unlike the shareholder-value and rent-extraction views, which
contradict each other, institutional in
uences overlay both views. Under the \shareholder value"
view, my ndings of the harmful eects of a \one-size-ts-all" trend imply that rms are being
pushed away from optimal contracts. Under the rent-extraction view, they imply that standard-
ization makes rent extraction easier. Finally, my paper complements Kalpathy, Nanda, and Zhao
(2019) and Jochem, Ormazabal, and Rajamani (2020). They report that, since 2006, CEOs with
lower pay have experienced a far sharper increase in pay than those with higher pay. My ndings
show the existence of convergence in the structure of the compensation as well.
2 Data and Methodology
I obtain data on executive compensation from Execucomp, collected directly from each company's
annual proxy (DEF14A SEC form). The rms' universe covers the S&P 1500 plus companies that
were once part of the 1500 plus companies removed from the index that are still trading. I merge the
Execucomp sample to other datasets using the Global Company Key {or GVKEY{ rm identier.
I base the main analysis on six elements of compensation: salary, bonus, stock awards, option
awards, non-equity incentives, and other compensation. Salary and bonus re
ect the amount
received for the scal year. Stock awards are evaluated at the grant-date value using the grant-date
7
market value, including both time-lapse restricted stock and performance shares. Options awards
are evaluated at grant-date value using dierent variant of the Black and Scholes (1973) formula.
Non-equity incentives are evaluated at the target level (or the average of minimum and maximum
if target not reported). Other compensation includes perquisites, signing bonuses, termination
payments, and above the market interest paid on deferred compensation.
Following the existing studies in corporate nance, I exclude nancial rms and regulated
utilities (SIC 6000-6999 and 4900-4999, respectively) from the sample. All variables are winsorized
at 1% and 99% level. The baseline subsample includes 2,021 rms between 2006 and 2016, with a
total of 16,747 rm-year observations.
2.1 Measure of Contract Similarity
Perhaps the main challenge in examining if executive compensation is converging is that executives
receive compensation in many dierent forms. As a motivational exercise, and only to look for
some very broad trends, I group each form of compensation in two types: equity and non-equity
compensation. Given this distinction, Figure 2 shows the Kernel density function of the share of
total compensation that is equity, at dierent moments. Over time, density increases around the
mean, and tales become thinner. This trend suggests that rms have become more similar, at least
on how they allocate compensation between equity and non-equity.
Examining each element of compensation separately, I nd that the variance in most components
of pay decrease over time. Figure 3 shows a time series graph with the mean and interquartile ranges
for the participation in total compensation of each component of pay on a yearly basis. In the case
of salary, options, non-equity incentive plans, and other compensation, the gure shows a clear
reduction in the size of the box. This reduction is especially notorious after 2010. In the case of
stock, the gure shows an increase and then a reduction in the size of the box. More than 75% of
8
rms set bonus to zero after 2008.
Figure 2: Kernel density estimate of the ratio of equity CEO compensation
The gure shows the Kernel density function of the share of total compensation that is equity (stock+options), at dierent
moments of time.
0 .5 1 1.5 2
Density
0 .2 .4 .6 .8 1
Equity compensation CEO
2006
2009
2012
2015
kernel = epanechnikov, bandwidth = 0.0493
Kernel density estimate
Figure 3: Box plot of each component of compensation
The gure shows a time series graph with the mean and interquartile ranges for each component of pay. The upper hinge of
the box corresponds to the 75th percentile, the lower hinge to the 25th percentile, and the center line is the median. The
adjacent values are dened as the lowest and highest observations that are still inside the region dened by +/- 1.5 time the
interquartile range.
(a) Salary (b) Bonus (c) Stock
(d) Options (e) Non-equity Incentive Plans (f) Other compensation
The previous analysis only examine one component of compensation at a time and, thus, do
not allow to examine a similarity in the whole structure of compensation. To compare the whole
9
structure of compensations of dierent rms, it is necessary to look at several elements at the
same time. Furthermore, the methodology should allow to examine changes at a rm level and not
only at the economy level. In this section, I suggest a measure of similarity that fullls these two
conditions.
For each rm, I create a vector that includes the six primary components of compensation {
salary, bonus, stock awards, option awards, non-equity incentives, and other compensation{, based
on the \Summary Compensation Table" and the \Grants of Plan-Based Awards Table" reported
by each company in its annual proxy statement. Because each of these elements is measured with
a monetary value, the vector of payments is comparable across rms. I scale each element by the
total compensation, such that the sum of all the elements of each vector equals one. In this way,
the vector measures the structure of the compensation plan rather than the level.
v
it
=

salary
it
total
it
;
bonus
it
total
it
;
stock
it
total
it
;
options
it
total
it
;
non eq
it
total
it
;
other
it
total
it

(1)
total
it
=salary
it
+bonus
it
+stock
it
+options
it
+non eq
it
+other
it
I then compute the similarity between the compensation vectors of every possible pair of rms
in each given year. To measure the similarity between two vectors, I calculate the dot product of
the two vectors. This measure of similarity is also known as cosine similarity, and it is the most
widely reported measure of vector similarity when the magnitude of the vectors does not matter
(Bhattacharya (1946), Salton and McGill (1983), Hoberg and Phillips (2016)).
Similarity(i;j) =
6
P
n=1
v
n
it
v
n
jt
s
6
P
n=1
v
n
it
s
6
P
n=1
v
n
jt
withv
n
ij
=n
th
element ofv
ij
(2)
10
Cosine similarity is a measure of similarity between two non-zero vectors of an inner product
space that measures the cosine of the angle between them. Cosine similarity can take values from
zero to one. Two vectors with the same orientation have a cosine similarity of one; two vectors
orthogonal relative to each other have a similarity of zero. For each rm, I calculate the average
cosine similarity with respect to all other rms in each year.
Compensation Similarity
i
=
N
P
j=1
Similarity(i;j)
N
withN = all rms in Execucomp (3)
This methodology has many advantages. It allows us to compare the structure of contracts
at a rm-level considering all pay elements simultaneously. Importantly, it compares element by
element in a multidimensional way. In other words, it measures spatial representation considering
each element as a dierent axis. For the same reason, it has an easy interpretation since it is
analogous to a measure of geographic distance.
One limitation, however, is that it captures realizations of pay, not the contingencies in the
contract itself. This limitation is dicult to overcome, given how the dataset is built. Nevertheless,
I reduce it as much as possible. I use grant-date values of equity payments instead of realized values
(realized compensation as measured at the time the stock vests and the options are exercised).
However, the use of grant-date values has its own imperfections. Market-based valuation formulas
are based on the risks that shareholders can diversify; only the non-diversiable risk is priced.
Therefore, the values I use in this study take shareholders' perspective and may have dierent values
from the manager's perspective, who cannot diversify her capital as shareholders do (Lambert,
Larcker, and Verrecchia (1991), Hall and Murphy (2000), Oyer and Schaefer (2005), and Murphy
11
(2013)).
1
Moreover, many companies pay annual bonuses partly in cash and partly in stock and
options. Consequently, the grant-date value of equity will still be a realization of the contract since
the number of shares will be a realization of CEO performance.
3 Major Trends
3.1 The Convergence of Executive Compensation Plans
I nd that the compensation packages for executives are becoming more homogeneous over time.
Figure 1 shows the time-series of the mean of compensation similarity. More formally, Table 1 shows
the results of a regression of compensation similarity on a time trend. The time trend coecient
is positive and statistically signicant (standard errors clustered by rm in parentheses), and it is
robust to including rm xed eects. Moreover, rms are not only getting closer to each other on
average but also there is less dispersion on the distance between them. As Figure 4 shows, the
standard deviation of similarity faced by each rm has a negative trend.
2
To get a sense of the statistical magnitude of this convergence, Table 2 presents summary
statistics of compensation similarity. Considering the whole sample of rms, the mean of CEO
compensation similarity is 0.56, and the standard deviation is 0.13. If we analyze the year 2007
{the lowest level of average compensation similarity{ and 2016 separately, from 2007 to 2016, the
similarity of CEO compensation increased from 0.50 to 0.624, which implies that 25% of the average
distance across rms disappeared in the last ten years. The increase in similarity corresponds to one
full standard deviation (and 1.6 standard deviations of 2007). If we consider the average standard
deviation of an industry {at SIC 3 level{, the convergence is even larger at two industry-standard
1
Similarly, option-pricing formulas are based on the assumption that the riskiness of the option's payo can be
perfectly hedged by continuously and costlessly revising a portfolio consisting of call options, shares of stock, and
riskless bonds over time. As a result, a manager's valuation of an executive stock option need not equal the Black
and Scholes (1973) option-pricing value of a \similar" call option, and his valuation of a share of restricted stock need
not equal the market price of a traded share.
2
Appendix A.2 presents a time series regression of variance of compensation similarity.
12
deviations.
Table 1: Cosine Similarity of Compensation Packages
This table presents the results of OLS panel regression of the cosine similarity on a time trend. Columns (1) and (2) correspond
to the similarity of CEO compensation, columns (3) and (4) of CFO compensation , and columns (5) and (6) of other executives
compensation. Odd columns include rm xed eects. Standard errors are clustered by rm and reported in parentheses.
Signicance levels are indicated: *=10%, **=5%, ***=1%.
CEO CFO OTH
Trend 0.009*** 0.013*** 0.006*** 0.010*** 0.006*** 0.009***
(0.000) (0.000) (0.000) (0.000) (0.000) (0.000)
Constant 0.438*** 0.386*** 0.537*** 0.494*** 0.556*** 0.522***
(0.003) (0.004) (0.003) (0.003) (0.003) (0.003)
Observations 16,747 16,747 16,628 16,628 16,787 16,787
R-squared 0.144 0.101 0.092
Firms 2,021 2,021 2,015 2,015 2,027 2,027
Firm FE NO YES NO YES NO YES
Figure 4: Average standard deviation of cosine similarity of CEO compensation plans
The gure shows the time-series of the average standard deviation of the cosine-similarity of CEO compensations plans faced
by each rm. The vector of compensation used to calculate the cosine similarity includes salary, bonus, stock awards, stock
options, non-equity incentives, and other compensation.
13
Table 2: Summary statistics of cosine similarity of CEO compensation
This table reports summary statistics of the measure of similarity of CEO compensation in 2007, 2016, and the period
2007-2016. The rst panel reports statistics when similarity of each rm is the average similarity with respect to all rms in
Execucomp. In the second panel, similarity is also the average similarity with respect to all rms in Execucomp but statistics
are calculated within industry (3-digit SIC). In the rest of the panels, the similarity of each rm is measured as the average
similarity only with respect to the rms that share the same industry (Fama French 48 or 3-digit SIC).
CEO Similarity within whole sample & stats within whole sample mean st. dev min max
2007 0.500 0.100 0.089 0.697
2016 0.624 0.163 0.069 0.789
2007-2016 0.560 0.134 0.069 0.789
CEO Similarity within whole sample & stats within SIC 3 mean st. dev min max
2007 0.499 0.046 0.116 0.683
2016 0.624 0.074 0.196 0.787
2007-2016 0.559 0.068 0.116 0.787
CEO Similarity within FF48 & stats within whole sample mean st. dev min max
2007 0.526 0.115 0.081 0.824
2016 0.644 0.166 0.089 1.000
2007-2016 0.584 0.141 0.055 0.787
CEO Similarity within FF48 & stats within FF48 mean st. dev min max
2007 0.525 0.050 0.456 0.808
2016 0.642 0.069 0.438 1.000
2007-2016 0.582 0.070 0.438 1.000
CEO Similarity within SIC 3 & stats within whole sample mean st. dev min max
2007 0.578 0.152 0.083 1.000
2016 0.686 0.179 0.105 1.000
2007-2016 0.630 0.164 0.055 1.000
CEO Similarity within SIC 3 & stats within SIC 3 mean st. dev min max
2007 0.578 0.115 0.372 1.000
2016 0.686 0.123 0.468 1.000
2007-2016 0.629 0.120 0.354 1.000
14
To understand the reasons for convergence, we need to get a sense of where it is happening. The
trend described above considers all rms together, regardless of their characteristics and industry.
One may wonder whether some specic type of rms drives this convergence. For example, Gabaix
and Landier (2008) suggest that CEO compensation is determined in a competitive talent market
and re
ects rms' size aected by talent. Specically, they suggest that the impact of CEO talent
is scaled by rm size, and thus the larger the rm, the more it will demand (and pay for) CEO's
talent. Following this reasoning, one might expect that rms of similar size will structure their
compensation plans alike.
To examine whether rm's size impacts the convergence in the structure of executive compen-
sation, I separate the sample into three tertiles based on their size: small, medium, and large. I
measure size as total assets.
3
Panel (a) in Figure 5 presents the time series of the average similarity
of each subsample and shows that similarity increases in all three subsamples.
Figure 5: Cosine similarity of CEO compensation and rm characteristics
The gure shows the time-series plot of the mean of cosine similarity of compensation plans after separating rms by size,
age, and protability. For each rm characteristic, I separate the sample in three tertiles and plot the time series of each
tertile. Size is measured as total assets; rm age is a listing vintage computed as the rst year the rm rst appears in
the CRSP/COMPUSTAT merged database; protability is the operating income before depreciation (OIBDP) divided by
assets. The vector of compensation used to calculate the cosine similarity includes salary, bonus, stock awards, stock options,
non-equity incentives, and other compensation.
(a) Size (b) Age (c) Protability
Additionally, one might think that age is a critical element in explaining the convergence of
compensation plans. Young rms dier from mature rms in several aspects. They exhibit higher
3
Firm-level data come from CRSP/COMPUSTAT.
15
growth rates (Haltiwanger, Jarmin, Kulick, and Miranda (2016), Loderer, Stulz, and Waelchli
(2017)), they are more likely to face nancial constraints (Hennessy and Whited (2007), Beck,
Demirg u c-Kunt, and Maksimovic (2008), and Hadlock and Pierce (2010)), and they tend to invest
more in innovative and risky projects (Galasso and Schankerman (2015), Acemoglu, Akcigit, Alp,
Bloom, and Kerr (2018), Hoberg and Maksimovic (2019)). It is reasonable to believe that young
rms face a wider variety of challenges and opportunities and, consequently, a higher dispersion in
their compensation structure.
To test whether the rate of convergence varies depending on rm age, I separate the sample into
three tertiles based on rms' age: young, medium, and old. Firm age is a listing vintage computed
as the rst year the rm rst appears in the CRSP/COMPUSTAT merged database. Panel (b) in
Figure 5 shows no dierence in the rate of convergence across the subsamples.
Since the purpose of executives' contracts is to improve rm performance, I examine whether
dierent levels can explain the convergence. Specically, I divide the sample into rms with low,
medium, and high protability. I dene protability as the operating income before depreciation
(OIBDP) divided by assets. Similar to when examining rm size and age, I do not nd signicant
dierences in convergence rate between rms with high and rms with low protability.
Given that the convergence is unlikely to be explained by rm characteristics, one might wonder
whether some specic industries are driving the phenomenon. Panel (a) and (b) of Figure 6 separate
the sample into ve and twelve industries, based on Fama French 5 and Fama French 12. The level
of similarity slightly varies depending on the industry. Moreover, all industries are converging
at similar rates. These ndings suggest that to understand the convergence, we need to look at
something that aects all industries at the same time, not something that industry-specic.
Additionally, the whole-economy convergence is similar to the within-industry convergence in
terms of both level and trend. Figure 7 shows the time series plot when compensation similarity
16
is only calculated between rms in the same industry. I use Fama French 48 and SIC 3. When
the similarity is measured within FF48, it increased from 0.53 in 2007 to 0.64 in 2016. When the
compensation similarity is measured within SIC 3, it increased from 0.58 to 0.69. In both cases, the
magnitude of the convergence is roughly the same as the whole-economy convergence. Again, all
these tests suggest that the convergence of executive compensation structures is an economy-wide
phenomenon.
Figure 6: Cosine similarity of CEO compensation by industry
The gure shows the time-series plot of the mean of cosine similarity of compensation plans by industry. Industries are dened
based on Fama French 5 and Fama French 12. The vector of compensation used to calculate the cosine similarity includes
salary, bonus, stock awards, stock options, non-equity incentives, and other compensation.
.45 .5 .55 .6 .65
Cosine Similarity of CEO Compensation
2006 2008 2010 2012 2014 2016
Year
Consumer Manuf
HiTech Health
Other
(a) FF 5
.5 .55 .6 .65 .7
Cosine Similarity of CEO Compensation
2006 2008 2010 2012 2014 2016
Year
NonDur Durbl Manuf Enrgy
Chems BusEq Telcm Utils
Shops Hlth Money Other
(b) FF 12
It is interesting to examine whether rms' compensation plans are becoming more similar due
to one specic pay element. To explore whether any particular element explains the convergence,
I calculate compensation similarity excluding one element from the vector at a time (importantly,
I also exclude it from the total compensation used to scale the vector). Figure 8 and Table 3
show that none of the elements can explain the convergence of CEO compensation by itself. The
coecient of the time trend is positive and signicant in every denition of the compensation vector.
However, the most signicant drop in the rate of convergence emerges when we exclude stock
awards. The latter nding is not surprising since stock awards account for the largest share of total
17
Figure 7: Cosine similarity of executive compensation plans within industry
The gure shows the time series plot of the cosine-similarity of compensation plans calculated between rms in the same
industry. Figure (a) uses Fama French 48 industy denition, and gure (b) uses three-digit SIC code. The vector of
compensation used to calculate the cosine similarity includes salary, bonus, stock awards, stock options, non-equity incentives,
and other compensation.
(a) Within Fama French 48 (b) Within SIC 3
executive compensation. One might think that convergence is a consequence of rms moving from
other compensation components to stock awards. However, this is unlikely to be true. As Figure 8
and Table 3 show, even excluding stock awards, the convergence is highly signicant and accounts
for a loss of 11% of the variation across rms.
Additionally, one may suspect that the compensation structures' heterogeneity moved to other
compensation types not included in the compensation vector v
it
. For example, rms may dieren-
tiate from each other on how they contribute to executives' pensions. Figure 9 shows that this is
not the case. The convergence is robust to including the change in pension value and non-qualied
deferred compensation earnings as a seventh element.
Alternatively, the variation across rms may have moved to within elements. Specically, it
may have moved to a dierent type of stock awards. We can think of dierent ways to classify stock
awards, although the most natural one is to distinguishing between restricted and performance-
based stock. I identify performance-based stocks as the market value of stocks awards that include
a target in the Grants of Plan-Based Awards Table and dene restricted stocks as the complement.
18
Figure 8: Cosine similarity of CEO compensation excluding one element at a time
The gure shows the time-series plot of the mean of cosine similarity of compensation plans after excluding one element
from the vector at a time. That is, gure (a) considers bonus, stock awards, stock options, non-equity incentives, and other
compensation. Figure (b) considers salary, stock awards, stock options, non-equity incentives, and other compensation. Figure
(c) considers salary, bonus, stock options, non-equity incentives, and other compensation. Figure (d) considers salary, bonus,
stock awards, non-equity incentives, and other compensation. Figure (e) considers salary, bonus, stock awards, stock options,
and other compensation. Figure (f) considers salary, bonus, stock awards, stock options, and non-equity incentives.
(a) Excluding salary (b) Excluding bonus (c) Excluding stock awards
(d) Excluding stock options (e) Excluding non equity awards (f) Excluding other compensation
Figure 10 shows that the convergence is also robust to distinguishing between restricted stocks and
performance-based stocks. Under this specication, the average similarity of compensation plans
increased by 13% between 2006 and 2016.
Another hypothesis to explain the convergence is the reduction of IPOs during the last decade.
New rms might have a higher variation of compensation structures than mature and established
rms. Thus, I compute the similarity of compensation plans only considering rms present in the
entire sample period. Figure 11 presents the time-series plot of this analysis and shows a similar
level and trend of convergence. This result suggests that new rms or rms exiting the market are
unlikely to explain this convergence.
Finally, I nd that this convergence is a recent phenomenon. I run a similar exercise using the
19
Table 3: Cosine Similarity of Compensation Packages
This table presents the results of OLS panel regression of the cosine similarity on a time trend. In each column, the similarity
is calculated after excluding one element of compensation. Firm xed eects are included. Standard errors are clustered by
rm and reported in parentheses. Signicance levels are indicated: *=10%, **=5%, ***=1%.
Element excluded
Salary Bonus Stocks Options Non eq Other
Trend 0.020*** 0.012*** 0.005*** 0.012*** 0.012*** 0.013***
(0.000) (0.000) (0.000) (0.000) (0.000) (0.000)
Constant 0.232*** 0.419*** 0.530*** 0.457*** 0.412*** 0.402***
(0.004) (0.003) (0.004) (0.004) (0.004) (0.003)
Observations 16,615 16,745 16,745 16,744 16,747 16,701
R-squared 0.213 0.124 0.027 0.115 0.121 0.168
Firms 2,019 2,021 2,021 2,020 2,021 2,018
Firm FE YES YES YES YES YES YES
Figure 9: Cosine similarity of CEO compensation including pension
The gure shows the time-series of the mean of cosine similarity of compensation plans including pensions as a seventh element.
That is, the vector of compensation used to calculate the cosine similarity between rms includes salary, bonus, stock awards,
stock options, non-equity incentives, other compensation, and change in pension values.
data on executive compensation available before 2006 and nd that similarity was not increasing
before 2006. The data available for executive compensation before 2006 is dierent from the data
available after 2006. Figure 12 shows the time-series of the mean similarity using a vector with
20
Figure 10: Cosine similarity of CEO compensation distinguishing restricted and performance-based
stock
The gure shows the time-series of the mean of cosine similarity of compensation plans after distinguishing between restricted
and performance-based stock. That is, the vector of compensation used to calculate the cosine similarity between rms includes
salary, bonus, restricted stock, performance-based stock, stock options, non-equity incentives, and other compensation.
Figure 11: Cosine similarity of CEO compensation excluding new and exiting rms
The gure shows the time-series of the mean of cosine similarity of compensation plans only considering rms that are present
in the entire sample period (2006-2016). The vector of compensation used to calculate the cosine similarity includes salary,
bonus, stock awards, stock options, non-equity incentives, and other compensation.
the elements of compensation available: salary, bonus, stock awards, option awards, long-term
21
incentives plan, and other compensation.
4
Figure 12: Cosine similarity of CEO compensation comparable before and after 2006
The gure shows the time-series of the mean of cosine similarity of CEO compensation plans. Before 2006, the vector used
to calculate the cosine similarity includes salary, (bonus + long-term incentive plans), stock awards, stock options, and other
compensation. After 2006, the vector includes salary, (bonus + non-equity incentives), stock awards, stock options, and other
compensation
(a) Compensation vector of 5 elements
In the gure, it can be noticed a downward trend in the early 2000s and the already discussed
convergence trend after 2006. Exploring further, I nd that the downward trend in the early
2000s is mainly explained by a movement from option awards to stock awards. The popularity of
stock awards began in the early 2000s, replacing option awards as the preferred equity payment.
Before 2006 companies were not mandated to expense options awards. Until 2001, only a couple
of rms voluntarily expensed options. In 2001, it became popular {probably in response to the
recent accounting scandals{ and, in 2006, rule FAS123R mandated all rms to expense their options
awards. Under this rule, the expense for options awards is similar to that of stock. As a result,
companies reduced the number of options awards and expanded stock awards (Murphy (2013)). If
4
The main dierence between the two periods is the denition of bonus and long-term incentives. Some of the
compensation that under the 2006 rules is considered \Bonus", was considered \Long-term incentives" under the
1992 rules. Some of the compensation that is considered \Non-equity" under the 2006 rules, was considered \bonus"
under the 1992 rules. In order to make both packages as similar as possible, I create a bonus component equal to
\Bonus" plus "Long-term incentives" prior to 2006 and \Bonus" plus \Non-equity" after 2006.
22
this movement occurred at dierent rates, it would explain the divergence that we observe in that
period.
Supporting this explanation, if I consider stock awards and options awards together as one
element of compensation {that is, without distinguishing between them{, the pre-2006 divergence
disappears, whereas the post-2006 convergence remains. Figure 13 shows the time series plot of
compensation similarity with a compensation vector that does not distinguish between stock and
option awards. The curve is
at until 2006, when it starts increasing.
Figure 13: Cosine similarity of CEO compensation considering stock and options awards together
The gure shows the time-series of the mean of cosine similarity of compensation plans considering stock and options awards
as the same type of compensation. That is, the vector of compensation used to calculate the cosine similarity between rms
includes salary, bonus, stock awards + stock options, non-equity incentives, and other compensation.
Overall, I nd that executive compensation packages' structure has become more similar year
after year after 2006. This study will focus on the after-2006 convergence. This convergence is a
recent phenomenon, is economically large, robust to dierent specications, unlikely to be explained
by rms' characteristics or industry-specic forces, and is consistent with a \one-size-ts-all" trend.
5
In the next section, I test the hypothesis that this convergence is an unintended consequence of
5
A valid concern is whether all these ndings are robust to alternative measures of similarity. Appendix A.3 shows
that the convergence is robust to using the Kullback-Leiber Divergence (KL) test and the Kolmogorov-Smirnov (KS)
test instead of the cosine-similarity measure.
23
recent regulations.
3.2 Discussion and Institutional Background
Regulatory pressure to involve shareholders in the design of compensation plans started at the
end of 2005. In November of that year, Representative Barney Frank introduced a bill to give
shareholders a veto power on executive pay. Even though the proposed bill did not win the House
approval, it was the rst time that a shareholder vote on executive compensation plans was seriously
discussed in the United States. The idea of involving shareholders in the design of compensation
plans became part of the public and political discussion, and the possibility of its implementation
became more real every year since then.
In March 2007, Representative Frank and Senator Obama introduced a Say-on-Pay bill in
the House and Senate simultaneously. Say-on-Pay is a regulation that requires all publicly traded
companies to submit their executive compensation plans to a non-binding advisory shareholder vote.
The bill passed in the House of Representatives but was stalled in the Senate Banking Committee.
In February 2009, a mandatory Say-on-Pay was included as a requirement for Treasury's Troubled
Asset Relief Program (TARP) recipients, and in July 2010, Say-on-Pay is added as part of the
Dodd-Frank Act. In January 2011, a mandatory Say-on-pay was adopted as part of the Dodd-
Frank Act. Parallel to the legislative movement, in the 2007 proxy season, about fty shareholder
proposals were calling for an advisory vote on executive compensation. In 2008, the number of
proposals increased to ninety. These proposals averaged support of 40%.
The existence of shareholders' vote on compensation plans might increase convergence in pay
structure if shareholders have homogenous preferences or are inadequately informed about optimal
variation. The reason is that management has to consider their preferences as a new element in
dening the rm's best compensation structure.
24
Figure 14: Cosine similarity of CEO compensation and the Discussion of Say-on-Pay
The gure shows the time-series of the mean of cosine similarity of compensation plans considering stock and options awards
as the same type of compensation. That is, the vector of compensation used to calculate the cosine similarity between rms
includes salary, bonus, stock awards + stock options, non-equity incentives, and other compensation.
Even though Say-on-Pay votes are non-binding, companies must also address in subsequent
years' CD&A (Compensation Disclosure and Analysis) how the companies considered the results
of their most recent Say-on-Pay vote and how that consideration aected their executive compen-
sation decisions and policies. Empirical research provides evidence that rms react to Say-on-Pay
outcomes.
6
For example, Ferri and Maber (2013) analyze Say-on-Pay's announcement in the UK
and nd that rms with substantial voting dissent respond by removing the controversial provisions
causing the adverse vote. Ertimur, Ferri, and Oesch (2013) nd similar results on American rms
after the implementation of the mandatory Say-on-Pay in 2011. Similarly, Correa and Lel (2016)
6
One reason to believe that non-binding votes matter is the fact the market for corporate control imposes dis-
cipline on managers and directors. Negative voting results may be interpreted as managers failing to act in the
best interest of shareholders. Admati and P
eiderer (2009) and Edmans (2009) show that large shareholders can
in
uence management's decisions through the threat of exit, even if they cannot intervene in a rm's operations. A
second reason is that a low voting result could foster negative recommendations by proxy advisory rms for future
management proposals, submission of binding bylaw amendments, or even lobbying for regulatory changes. For ex-
ample, Del Guercio and Hawkins (1999) nd that the frequency of a proxy contest attempt is signicantly higher
following majority-supported non-binding shareholder proposals. Fama (1980) and Fama and Jensen (1983) provide
a third reason, arguing that the labor market provides incentives for directors to develop their reputation as eective
monitors. Finally, Levit and Malenko (2011) show that, in the presence of an opportunistic activist, a non-binding
voting mechanism improves information aggregation relative to a binding mechanism.
25
use a sample of rms from 38 countries over the 2001{2012 period and nd evidence that CEO
pay growth rates decline, and the sensitivity of CEO pay to rm performance improves following
the adoption of Say-on-Pay. Denis, Jochem, and Rajamani (2020) show that rms even react to
the Say-on-pay results of their peers. They nd that rms whose compensation peers experience
Say-on-pay votes reduce CEO compensation following those votes.
To understand how shareholders decide their vote on Say-on-Pay, a crucial institutional in
uence
on their votes is proxy advisory rms' recommendations. Even though many of the major investors
make their own voting decisions, the empirical ndings suggest that shareholders routinely rely
on proxy-advisory rms for recommendations on how to vote and that rms do react to their
recommendations. McCahery, Sautner, and Starks (2016) survey institutional investors and nd
that most investors use proxy advisors and believe that the information provided by such advisors
improves their own voting decisions. Shu (2020) show that proxy advisors' activity has grown
signicantly in the last 15 years. Moreover, empirical studies show that their in
uence on executive
compensation schemes became stronger with Say-on-Pay's mandatory adoption. Ertimur, Ferri, and
Oesch (2013) analyze ISS and Glass Lewis & Co. (GL) voting recommendations for Say-on-Pay and
nd that negative ISS (GL) recommendations are associated with 24.7% (12.9%) more votes against
the compensation plan. Malenko and Shen (2016) exploit a cuto rule in ISS voting guidelines
and nd that a negative recommendation led to a 25% reduction in Say-on-Pay voting support.
Similarly, Larcker, McCall, and Ormazabal (2015) nd that rms change their compensation policies
to avoid proxy advisory rms' negative recommendations.
Some researchers have raised the concern that these recommendations are based on guidelines
that do not accurately take into account the dierent needs and goals of dierent companies (Gordon
(2009), Hou, Priem, and Goranova (2017), Murphy and Jensen (2018)). Some researchers point
out that the proxy advisors' data collection process relies on too few participants and is not a
26
good representation of the market. Others claim that proxy advisers do not update their policies
frequently enough(Larcker, McCall, and Tayan (2013) and GAO (2016)). The existence of a small
number of proxy advisors
7
and the limited time to provide recommendations on thousands of proxy
meetings has created a growing concern that a \best compensation practices" regime is pushing
towards a \one-size-ts-all" trend (Gordon (2009), Hou, Priem, and Goranova (2017), Murphy and
Jensen (2018)). Additionally, in a theoretical paper, Matsusaka and Shu (2020) show that proxy
advisory rms might have incentives to ignore rm-specic characteristics if the competition across
advisors is low. Through a eld study, Hayne and Vance (2019) report that boards feel pressure
to conform to proxy advisors' preferences despite their own preferred compensation philosophies.
They also highlight operational constraints faced by proxy advisors during busy seasons. Similarly,
Albuquerque, Carter, and Gallani (2020) show that ISS's ability to detect low-quality compensation
packages only occurs during the o-season.
The growing institutional investors' ownership and the increase in proxy advisory rms' activity
created the ideal setting for Say-on-pay to impact executive compensation design. If proxy-advisory
rms make a standard recommendation, and institutional investors follow that recommendation,
we would expect standardization of compensation plans, which would translate into a convergence
if the eect persists over time.
3.3 Suggestive Evidence
To test the hypothesis that institutional investors following proxy advisers' recommendations on
Say-on-pay voting fosters convergence, I run several tests. First, I show that institutional in-
vestors' ownership positively correlates with similarity. Then, I show suggestive evidence that
7
There are only ve proxy advisory rms in the United States: Institutional Shareholder Services (ISS), Glass
Lewis & Co. Glass Lewis (GL), Egan-Jones Proxy Services, Segal Marco Advisors, and ProxyVote Plus. Together,
ISS and GL provide proxy recommendations on more than 60,000 shareholder meetings. See Copland, Larcker, and
Tayan (2018) for an overview of the proxy advisory industry.
27
proxy advisory recommendations make compensation plans more homogenous. Finally, I use plau-
sible exogenous variation in Say-on-pay to show that shareholders' vote on executive pay increase
convergence.
Most of the empirical literature shows that passive institutional investors are the shareholders
most likely to follow proxy advisers' recommendations (Bushee and Noe (1999), Larcker, McCall,
and Ormazabal (2015) and Malenko and Shen (2016)). Thus, following Bushee and Noe (1999),
Larcker, McCall, and Ormazabal (2015) and Malenko and Shen (2016) in how to dene passive
institutional investors, I regress compensation similarity on the ratio of shares owned by institu-
tional investors. The data on institutional ownership comes from Thomson Reuters Institutional
(13F) Holdings database. Panel A of Table 4 presents the result of this regression. The rst two
columns show that rms with a higher ratio of shares owned by institutional investors converge in
compensation more than rms with a lower ratio. Columns (3) and (4) show that this eect is even
stronger when only considering passive institutional investors.
In a second test, I create a dummy variable that equals one if the rm received a negative
Say-on-pay recommendation from ISS. Then I regress that dummy variable on compensation sim-
ilarity lagged by one period. Panel B of Table 4 presents the results of this regression and shows
that rms with less similar compensation packages are more likely to receive a negative Say-on-pay
recommendation from ISS in the next period. This nding is robust to controlling for rm charac-
teristics and including rms and year xed eects. It suggests that ISS punishes rms that have a
compensation package that does not look like the others.
In a third test, I regress compensation similarity on a dummy variable that equals one if the rm
received a negative recommendation from ISS in the last two years. Panel C of Table 4 presents the
results of this regression. I nd that similarity increases when the rm received a negative Say-on-
pay recommendation from ISS in the last Say-on-pay voting. This nding is robust to controlling
28
for rm characteristics and including rms and year xed eects. These results suggest that rms
respond to negative ISS recommendations by making their compensation packages more similar to
the rest of the rms.
In a fourth exercise, I explore whether compensation plans are converging to what proxy ad-
visory rms believe is optimal. Because we do not know what the proxy advisory rms' preferred
compensation vector is, I create a simulated vector that mimics the implicitly preferred vector be-
hind ISS's recommendation on Say-on-pay. Specically, I randomly create 1,000,000 compensation
vectors for which each element is generated by a uniform distribution between zero and one. I
standardize the vector such that the sum of all elements equals one. I then estimate equation 4
using each of these 1,000,000 vectors and pick the vector that generates the highest adjusted R
2
.
ISS favor
it
=
0
+
X
k
h

1k
max(v
k
it
^ v
k
; 0) +
2k
min(v
k
it
^ v
k
; 0)
i
+
i
+
t
+
it
(4)
where ISS favor
it
is a dummy variable equal to one if the rm received a positive Say-on-pay
recommendation from ISS; v
k
it
is element k of compensation vector v of rm i in year t; ^ v
k
is the
simulated compensation element k preferred by ISS;
i
corresponds to industry xed eects and

t
to year xed eects. The intuition behind this equation is that the probability of receiving
a positive ISS recommendation on Say-on-pay depends on how close each element of the rm's
compensation package is to ISS's preferred compensation structure. Panel A of Table 5 reports the
simulated vector ^ v that maximizes R
2
of equation 4.
Finally, I calculate the cosine similarity of each rm's compensation package to this simulated
ISS vector. Figure 15 reports the time-series plot of that similarity, and Panel B of Table 5 reports
the same results in a formal regression. The compensation structure of all rms is converging to
the simulated vector that ISS most recommends to vote in favor of.
29
Figure 15: Cosine-similarity of rms' compensation plan and a simulated ISS's preferred compen-
sation
The gure shows the time-series plot of the average cosine-similarity of each rm's compensation plan and a simulated ISS's
preferred compensation plan. The gure uses a simulated vector that ISS most recommends to vote in favor of. Section ??
describes the methodology used to simulate these vectors.
It is dicult to measure the impact of adopting a mandatory Say-on-pay in compensation
similarity since it aected all rms at the same time. It is also dicult to measure the impact of
Say-on-pay's threat {before 2010{, for the same reason. However, the frequency with which rms
have to implement the mandatory Say-on-pay after 2011 is dierent for every rm. In the next
section, I exploit this variation in the Say-on-pay vote frequency to run a more exogenous analysis
of the eect of Say-on-pay on compensation similarity.
30
Table 4: CEO compensation similarity and the in
uence of Proxy Advisory Firms
Panel A of this table presents the results of the OLS panel regression of similarity on on the ratio of shares owned by institutional
investors and passive institutional investors. Panel B displays the results of the OLS panel regression of a dummy variable
that equals one if the rm received a negative recommendation in the next year on the measure of similarity. Panel C displays
the results of the OLS panel regression of similarity on a dummy variable that equals one if the rm received a negative
recommendation in previous years. Columns (1) and (2) consider a negative recommendation in the last year, whereas columns
(3) and (4) consider a negative recommendation in the last two years. All regressions include rm and year xed eects.
Standard errors are clustered by rm. Controls include log of assets in t-1, log of rm age in t-1, and protability in t-1. All
variables are winsorized at the 1-99% level. Standard errors are reported in parentheses and signicance levels are indicated:
*=10%, **=5%, ***=1%.
Panel A: CEO compensation similarity in t (1) (2) (3) (4)
institutional investors ownership 0.026*** 0.022**
(0.010) (0.011)
passive institutional investors ownership 0.038*** 0.031***
(0.010) (0.011)
Constant 0.492*** 0.481*** 0.484*** 0.485***
(0.008) (0.035) (0.008) (0.035)
Observations 11,863 11,382 11,693 11,227
R-squared 0.179 0.171 0.180 0.172
Number of gvkey 1,697 1,668 1,694 1,666
Controls NO YES NO YES
Firm FE YES YES YES YES
Year FE YES YES YES YES
Panel B: ISS negative recommendation in t (1) (2)
CEO Similarity in t-1 -0.084** -0.076*
(0.042) (0.043)
Constant 0.160*** -0.201
(0.025) (0.127)
Observations 8,294 8,263
R-squared 0.003 0.009
Number of gvkey 1,475 1,470
Controls NO YES
Firm FE YES YES
Year FE YES YES
Panel C: CEO compensation similarity in t (1) (2) (3) (4)
ISS against in t-1 0.009* 0.009*
(0.005) (0.005)
ISS against in t-1 or in t-2 0.016*** 0.015***
(0.004) (0.004)
Constant 0.563*** 0.586*** 0.561*** 0.568***
(0.003) (0.055) (0.003) (0.052)
Observations 8,179 8,177 8,323 8,288
R-squared 0.092 0.095 0.096 0.100
Number of gvkey 1,431 1,431 1,474 1,470
Controls NO YES NO YES
Firm FE YES YES YES YES
Year FE YES YES YES YES
31
Table 5: Similarity to ISS simulated preferred compensation scheme
Panel A of this table reports the simulated ^ v
k
that maximizes R
2
of equation 4. Panel B displays the results of OLS panel
regression of the cosine similarity compensation package to a simulated ISS vector on a time trend. Columns (1) to (3) use ISS
simulated vector based on positive recommendations, whereas columns (4) to (6) use ISS simulated vector based on negative
recommendations. Standard errors are clustered by rm and reported in parentheses. Signicance levels are indicated: *=10%,
**=5%, ***=1%.
Panel A: simulated ^ v
k
Salary/total Bonus/total Stocks/total Options/total Non eq/total Other/total adj R
2
ISS in favor 0.083 0.301 0.252 0.168 0.182 0.013 0.369
Panel B: Similarity to ISS simulated preferred compensation vector
ISS in Favor
Time trend 0.006*** 0.006*** 0.007***
(0.000) (0.000) (0.000)
Constant 0.483*** 0.542*** 0.470***
(0.004) (0.071) (0.005)
Observations 16,747 15,641 16,747
R-squared 0.031
Number of gvkey 2,021 1,892 2,021
Industry FE YES
Firm FE YES
32
4 Evidence from the frequency of mandatory Say-on-Pay
The Dodd-Frank Act mandated an advisory (non-binding) shareholder vote on a company's top
executives compensation {the CEO, the CFO, and at least three other named executive ocers.
This mandatory Say-on-pay took eect on the rst annual shareholder meeting on or after January
21, 2011,
8
as a non-binding yes or no vote.
Beginning with the rst annual shareholders' meeting in 2011{and every six years after that{
shareholders vote on the frequency of Say-on-pay to determine whether Say-on-pay votes will occur
every one, two, or three years. Even though this vote is also non-binding, 99.06% of the sample
rms follow the result of the voting. I use this frequency vote as the main instrument for increasing
external pressure on the design of compensation schemes. The intuition is that rms with a higher
frequency of Say-on-pay are exposed to shareholders' in
uence more frequently. The sole existence
of shareholders' vote on compensation plans may change contracts since management must consider
their preferences as a new element in determining the rm's compensation structure.
Because both treated and control rms implement Say-on-pay, by focusing on the frequency of
the vote, I do not measure the absolute eect of Say-on-pay but the dierence in Say-on-pay inten-
sity. Therefore, the right interpretation of the treatment is that treated rms are more frequently
exposed to the in
uence of shareholders votes on executive compensation than control rms. Table
6 reports the summary statistics of the results of the rst Say-on-pay frequency vote.
Table 6: Votes on the frequency of Say-on-Pay in the rst Say-on-Pay vote
SOP frequency results
Vote result Number of rms
One Year 1096
Two Years 3
Three Years 132
8
The amendments to the rules relating to the shareholder approval of executive compensation were rst proposed
on October 18, 2010, to implement Section 951 of the Dodd-Frank Wall Street Reform and Consumer Protection
Act. Link to the nal rule: https://www.sec.gov/rules/nal/2011/33-9178.pdf.
33
To test if an increase in shareholders' in
uence increases convergence, I use two strategies. First,
I estimate a dierence-in-dierence analysis. Second, I estimate a regression discontinuity design
using close elections between high-frequency and low-frequency Say-on-pay. I obtain Say-on-Pay
voting data and ISS recommendations from ISS Voting Analytics.
4.1 Dierence-in-dierence Analysis
I rst run a dierence-in-dierence analysis in which the treated rms are those with Say-on-pay
every year, and the control rms are those with Say-on-pay every three years. Equation (5) displays
the main specication for this analysis.
Similarity
it
=
0
+
1
POST2011xSOP1Y
it
+
1
CONTROLS
it1
+
i
+
t
+
it
(5)
where SOP1Y equals one if the rm has Say-on-Pay every year (based on the rst Say-on-pay
frequency vote) and zero if the rm has Say-on-Pay every three years. POST2011 is a dummy that
equals one for years after 2011. Thus, the post-treatment period considers the compensation plans
in 2011 (voted in shareholder meetings in 2012) and all years after that. TREATEDxPOST2011
is the interaction between TREATED and POST2011. Firm-level controls lagged one period are
included, as well as rm and year xed eects. Standard errors are clustered by rm. The coecient
of interest is
1
.
Table 7 shows the results of estimating equation (5). Firms in which more than 50% of share-
holders voted in favor of annual frequency of Say-on-pay experience a larger increase in similarity
than rms where more than 50% of shareholders voted in favor of a three-year frequency of Say-on-
pay.
9
This result is robust to dierent measures of similarity. Column (1) uses the baseline similarity
9
I exclude the three rms that voted in favor of two-year frequency. The results do not change if I include those
rms in either group.
34
described in section 2.1. Column (2) uses the measure of similarity that distinguishes restricted
stocks and performance-based stocks. Column (3) uses a measure of similarity in which \Bonus"
and \Non-equity compensation" are added together as one element of compensation. Many studies
consider them together since most of the compensation that is considered \Non-equity compensa-
tion" under the 2006 rules, was considered \bonus" under the 1992 rules.
10
Column (4) uses the
measure of similarity after including the change in pension value as an extra element. Column (5)
uses the measure of similarity within industry (Fama French 48).
Table 7: Eects of the frequency of Say-on-Pay on similarity of CEO compensation. Dierence-in-
dierence analysis
This table reports the results of the OLS panel regression of equation (5) using the whole sample of rms. Column (1) uses
the baseline similarity described in section 2.1. Column (2) uses the measure of similarity that distinguishes restricted stocks
and performance-based stocks. Column (3) uses a measure of similarity in which \Bonus" and "Non-equity compensation" are
added together as one element of compensation. Column (4) uses the measure of similarity with the change in pension value
as a seventh element. Column (5) uses the measure of similarity within industry (Fama French 48). All regressions include
rm and year xed eects, and standard errors are clustered by rm. All variables are winsorized at the 1-99% level. Standard
errors are reported in parentheses and signicance levels are indicated: *=10%, **=5%, ***=1%.
Dependent variable: CEO compensation similarity
(1) (2) (3) (4) (5)
baseline rest stock bon+noneq pension 48
post2011xSOP 0.044*** 0.037*** 0.048*** 0.044*** 0.039***
(0.011) (0.008) (0.010) (0.010) (0.011)
Log assets in t-1 -0.004 -0.015*** -0.009** -0.004 -0.006
(0.005) (0.004) (0.004) (0.005) (0.005)
Log age in t-1 0.007 0.006 0.005 0.007 -0.002
(0.005) (0.004) (0.005) (0.005) (0.005)
Protability in t-1 -0.014 -0.040*** -0.015 -0.022 -0.001
(0.018) (0.015) (0.017) (0.017) (0.019)
Constant 0.532*** 0.567*** 0.591*** 0.518*** 0.600***
(0.034) (0.028) (0.033) (0.034) (0.038)
Observations 11,800 11,800 11,800 11,800 11,800
R-squared 0.181 0.069 0.160 0.201 0.080
Firms 1,220 1,220 1,220 1,220 1,220
Firm FE YES YES YES YES YES
Year FE YES YES YES YES YES
10
They are dierent because \bonus" is a discretionary payout actually made, while \non-equity" is the target
payout based on an incentive plan.
35
The identifying assumption for this rst analysis is that treated rms and control rms only
dier in the frequency of Say-on-pay elected by the shareholders in the 2011 proxy voting. However,
shareholders voted for a one-year frequency of Say-on-pay instead of a three-year frequency for a
reason and, therefore, treatment may be a consequence of treated rms being substantially dierent
from control rms. To improve the identication, I restrict the sample to rms in which the election
between one-year-SOP and three-year-SOP was close. The intuition of the identication strategy
is that rms in which a one-year-SOP won against a three-year-SOP by a narrow margin can be a
proper counterfactual for those rms in which the opposite occurred (a three-year-SOP won against
a one-year-SOP by a narrow margin).
Specically, I restrict the sample such that in treated rms, a one-year-SOP won over a three-
year-SOP by less than 20% of the total votes. Similarly, in control rms, a three-years-SOP won
over one-year-SOP by less than 20%. This restriction leaves 111 treated rms and 57 control rms.
The identication relies on the idea that both treated and control rms face high levels of voting
in both one-year and three-year SOP frequency.
11
Thus, they should be similar regarding their
shareholders' voting preferences.
Table 8 reports the summary statistics of the treated and control group in 2011, when Say-on-
pay was implemented. Treated and control rms only dier in age {with treated rms being older
than control rms on average{ but they do not dier in terms of size (assets or sales), protability,
growth opportunities, tangibility, or innovation. Most importantly, before the SOP, they have
similar levels of compensation similarity.
Table 9 presents the results of the estimation of equation 5 for rms with close elections on
Say-on-pay frequency. On average, rms that are yearly treated by Say-on-pay increase their com-
pensation similarity in 0.038 more than rms that have Say-on-pay every three years. Considering
11
The literature suggests that a shareholder voting is high if it is greater than 20%. In my strategy I am considering
rms with at least 40% of support in both frequencies.
36
the compensation similarity level before the treatment, the magnitude of the local average treat-
ment eect is about 8%. Columns (2) to (5) report the same estimation using dierent measures
of similarity: distinguishing between restricted and performance-based stocks, using the pre-2006
denition of bonus, including pensions, and similarity within industry (Fama French 48). All esti-
mations have similar results. All these results are similar {both in magnitude and signicance{ if
I do not control for rm characteristics. Table A.4 in Appendix A.4 shows that all the results are
robust to an entropy balanced matching of the control group.
Figure 16 shows a graphical representation of these eects. The gure consists of a time-series
graph of compensation similarity, in which the blue line represents the treated rms (rms with
annual Say-on-pay) and the red line the control rms (rms with Say-on-pay every three years){
only for rms with close elections on the frequency of Say-on-pay. The vertical line points to the
year 2011, when shareholders voted on the frequency of Say-on-pay. Supporting the parallel trend
assumption, the treated rms do not change their level of compensation similarity dierently from
the control rms before the implementation of Say-on-pay.
Figure 16: Say-on-Pay: dierence-in-dierence analysis
The gure consists of a time-series graph of the average cosine-similarity of CEO compensation, in which the blue line
represents the treated rms (rms with annual Say-on-Pay) and the red line the control rms (rms with Say-on-Pay every
three years). Only for rms with close elections on the frequency of Say-on-Pay are considered (voting dierence lower than
20%). The vertical line points to the year 2011, when shareholders voted on the frequency of Say-on-Pay.
37
Table 8: Summary Statistics in 2011
Treatment Obs. Mean st. error Pr(jT j> jtj)
3-year SOP 57 6.899 0.202
Log asset in t 1-year SOP 111 7.256 0.168
di -0.357 0.276 0.197
3-year SOP 57 6.895 0.206
Log sales in t 1-year SOP 111 7.192 0.172
di -0.297 0.282 0.294
3-year SOP 57 2.652 0.105
Firm age in t 1-year SOP 111 2.996 0.064
di -0.344 0.117 0.004***
3-year SOP 57 0.152 0.016
OIBDP/asset in t 1-year SOP 111 0.156 0.009
di -0.006 0.017 0.723
3-year SOP 57 1.718 0.148
Market to book in t 1-year SOP 111 1.797 0.115
di -0.079 0.193 0.682
3-year SOP 57 0.279 0.029
Tangibility in t 1-year SOP 111 0.224 0.019
di 0.056 0.034 0.101
3-year SOP 57 0.043 0.011
R&D/asset in t 1-year SOP 111 0.042 0.006
di 0.001 0.012 0.949
3-year SOP 57 0.542 0.018
CEO Similarity in t 1-year SOP 111 0.559 0.011
di -0.017 0.020 0.398
38
Table 9: Eects of the frequency of Say-on-Pay on similarity of CEO compensation. Dierence-in-
dierence analysis
This table presents the results of the OLS panel regression of equation 5 for rms with a voting dierence between one-year
and three-year SOP frequency lower than 20%. Column (1) uses the baseline similarity described in section 2.1. Column (2)
uses the measure of similarity that distinguishes restricted stocks and performance-based stocks. Column (3) uses a measure of
similarity in which \Bonus" and "Non-equity compensation" are added together as one element of compensation. Column (4)
uses the measure of similarity with the change in pension value as a seventh element. Column (5) uses the measure of similarity
within industry (Fama French 48). All regressions include rm and year xed eects, and standard errors are clustered by rm.
All variables are winsorized at the 1-99% level. Standard errors are reported in parentheses and signicance levels are indicated:
*=10%, **=5%, ***=1%.
Dependent variable: CEO compensation similarity
(1) (2) (3) (4) (5)
baseline rest stock bon+noneq pension 48
post2011xSOP 0.038** 0.030** 0.051*** 0.036* 0.038*
(0.019) (0.015) (0.017) (0.019) (0.020)
Log assets in t-1 -0.001 -0.005 -0.011 -0.000 0.004
(0.010) (0.008) (0.011) (0.010) (0.012)
Log age in t-1 0.038 0.044** 0.040* 0.033 0.053**
(0.023) (0.019) (0.023) (0.023) (0.023)
Protability in t-1 -0.031 -0.039 -0.057 -0.035 -0.042
(0.047) (0.033) (0.047) (0.048) (0.051)
Constant 0.404*** 0.375*** 0.507*** 0.403*** 0.443***
(0.074) (0.056) (0.076) (0.074) (0.087)
Observations 1,607 1,607 1,607 1,607 1,607
R-squared 0.128 0.042 0.121 0.144 0.029
Firms 168 168 168 168 168
Firm FE YES YES YES YES YES
Year FE YES YES YES YES YES
39
4.2 Regression Discontinuity Design
In this section, I use the shareholders' votes on Say-on-pay frequency to run a sharp regression
discontinuity estimation. The intuition of the identication strategy is that rms in which a one-
year-SOP won against a three-year-SOP by a narrow margin can be a proper counterfactual for
those rms in which the opposite occurred (a three-year-SOP won against a one-year-SOP by a
narrow margin). Specically, I create a variable that measures the one-year-SOP margin of victory
dened as the vote share of the one-year-SOP minus the vote share of the three-year-SOP.
12
The
value of this variable goes from -1 to +1, with positive values meaning the victory of one-year SOP
frequency. At the zero-threshold, the frequency of Say-on-pay sharply changes from three to one.
I estimate this discontinuity model using local polynomial Regression Discontinuity (RDD) point
estimators with robust bias-corrected condence intervals and inference procedures developed in
Calonico, Cattaneo, and Titiunik (2014), Calonico, Cattaneo, Farrell, and Titiunik (2017), and
Calonico, Cattaneo, Farrell, and Titiunik (2019). Specically, since the object of interest is a
conditional expectation, the estimation follows the literature and uses a polynomial of order one.
The bandwidth is chosen by a data-driven model such that it minimizes an approximation to the
asymptotic mean squared error (MSE) of the RD point estimator (the MSE of an estimator is the
sum of its bias squared plus its variance). Also, following the literature, the estimation uses a
triangular kernel function to weight the observations (it gives more weight to an observation closer
to the cuto).
The RD estimates is dened asE[Similarity
i
(1)Similarity
i
(0)jx = 0]. WhereSimilarity
i
(1)
is compensation similarity of rm i with a one-year-SOP margin of victory greater than zero;
Similarity
i
(0) is compensation similarity of rm i with a one-year-SOP margin of victory lower
than zero; and x = 0 means margin of victory equal to zero.
12
As Table 6 shows, the two-year vote was immaterial.
40
Panel A of Table 10 reports the RDD estimation using the one-year frequency of Say-on-pay
margin of victory and the subsequent compensation similarity in the next period. The estimated
coecient has a magnitude of 0.047, similar to the eect found with the dierence-in-dierence anal-
ysis. This value corresponds to an increase in almost 10% of compensation similarity when a rm
has a one-year frequency Say-on-pay instead of a three-year frequency. This result is statistically
signicant, with a p-value of 2%.
Figure 17 presents the graphical representation of the discontinuous jump in the compensation
similarity level when a rm has a more frequent Say-on-pay. The gure shows a positive impact on
compensation similarity around the threshold of victory for the one-year-SOP. The plot presents
a global polynomial t and local sample means. The global polynomial t is simply the predicted
values from two fourth-order polynomials of compensation similarity on the voting dierence, tted
separately above and below the cuto. The local means are created by choosing disjoint intervals
or bins of the score, calculating the mean of the outcome within each bin, and then plotting the
binned outcomes against the midpoint of the bin. The number and length of the bins were chosen
by a data-driven model, following Calonico, Cattaneo, Farrell, and Titiunik (2017).
An essential assumption of a regression discontinuity analysis is that rms cannot precisely
manipulate the votes that they receive. Hence, the number of rms in which a three-year-SOP
closely defeats a one-year-SOP should be similar to the number of rms in which a one-year-SOP
closely defeat a three-year-SOP. Figure 18 shows a histogram of the vote dierence between a one-
year and three-year-SOP. A visual inspection of this gure supports the predictions of the density
hypothesis. The number of observations above and below the cuto is very similar.
In a formal density test, I use the local polynomial density estimators proposed by Cattaneo,
Jansson, and Ma (2015). This test estimates the density of observations near the cuto, separately
for observations above and below the cuto. The null hypothesis is that the density of the running
41
Table 10: Regression discontinuity design estimation: CEO similarity
This table displays the estimated discontinuities of rm characteristics at the threshold of zero margin of victory of the one-year
frequency of Say-on-Pay. Panel A uses CEO compensation similarity in t+1 as the dependent variable. Panel C uses size, age,
and protability. Panel D uses compensation similarity including pensions, restricted stocks, and measured at the industry
level. Robust standard errors are clustered by industry and reported in parentheses. Signicance levels are indicated: *=10%,
**=5%, ***=1%. Panel B presents the result of the local polynomial density test proposed by Cattaneo, Jansson, and Ma (2015).
Panel A: CEO compensation similarity
(1)
CEO Similarity in t+1
Local average eect of treatment at vote dierence equal zero 0.047**
(0.020)
Observations 1,350
Panel B: RD Manipulation Test using local polynomial density estimation
Method T P>T
Robust -0.0429 0.9658
Observations 1,350
Panel C: Covariates
(1) (2) (3)
Log asset Log age Protability
Local average eect of treatment at vote dierence equal zero 0.264 0.282 -0.010
(0.268) (0.240) (0.032)
Observations 1,347 1,350 1,347
Panel D: Alternative measures of similarity
(1) (2) (3)
Pension Restricted FF 48
Local average eect of treatment at vote dierence equal zero 0.036* 0.023* 0.061**
(0.019) (0.014) (0.026)
Observations 1,350 1,334 1,335
42
Figure 17: Say-on-Pay: RDD analysis
The gure presents the graphical representation of the discontinuous jump in the level of ASC when a rm has a higher
frequency of Say-on-Pay (SOP). The vertical axes shows the average cosine-similarity of compensation in the next period. The
horizontal axis shows the one-year frequency of SOP margin of victory (dened as the vote share of the one-year-SOP minus
the vote share of the three-year-SOP). The value of this variable goes from -1 to +1, with positive values meaning the victory
of one-year SOP frequency. At the zero-threshold, the frequency of SOP sharply changes from three to one. The plot presents
a global polynomial t and local sample means. The local means are created by choosing disjoint intervals or bins of the score.
The number and length of the bins were chosen by a data-driven model, following Calonico, Cattaneo, Farrell, and Titiunik
(2017). Figure (a) shows a lineal regression, and gure (b) shows a local polynomial regression of order 4.
(a) Local linear regression (b) local polynomial of order 4
Figure 18: Histogram of the vote dierence between 1-year and 3-year Say-on-Pay
The gure shows a histogram of the vote dierence between a one-year and three-year Say-on-Pay.
variable is continuous at the cuto. The results of this test are presented in Panel B of Table 10.
The resulting p-value is 0.966, meaning there is no evidence that the density is discontinuous at
the cuto.
Another underlying assumption of an RDD is that near the cuto, treated units are similar to
control units. To test this assumption, I estimate the RDD on rm characteristics. Specically, I
test if rms below and above the cuto {that is, rms with close SOP-frequency elections{ do not
43
dier in size, age, and protability. Panel C of Table 10 shows the results for each covariate. There
are no signicant dierences.
The results on similarity are robust to including pensions and to distinguishing restricted and
performance-based stocks. They are also robust to measuring similarity within Fama French 48.
Panel D of Table 10 reports all these estimations.
The identication strategy of both the dierence-in-dierence analysis and the RDD analysis
focuses on rms with close elections on Say-on-pay frequency. The eect recovered by the RD
design is the local average eect of treatment at a vote dierence of zero. The external validity
of this experiment would depend on how similar are cases in which the vote dierence increases.
Consequently, the ndings should be extended to other rms far from the cuto with caution. An
interesting result, however, is that I nd a coecient of similar magnitude when I run the dierence-
in-dierence estimation that considers all rms in the economy (see Table 7). This nding helps to
alleviate concerns related to the external validity of the experiment.
44
5 Economic Consequences of the Convergence of Compensation
Structures
In this section, I examine the relationship between compensation similarity and rm policies. A
standardization of compensation plans eliminates outlier compensation packages. It can be unde-
sirable if a rm would have otherwise set pay optimally. It can be benecial if the standardized plan
is closer to the optimum than the non-standardized plan. It is, therefore, an empirical question
whether the standardization in CEO pay is good or bad for rms.
In the rst part of this section, I examine potentially endogenous within-rm correlations. In
the second part, I propose an instrument for compensation convergence and explore changes in
similarity using a more exogenous framework.
Using compensation similarity as a right-hand-side variable, I rst examine its relationship with
the compensation level and pay sensitivities, as described in equation (6). Specically, I consider
the total level of pay, delta, and vega. Delta measures the pay-performance sensitivity of the CEO
and vega the risk-taking incentives. I obtain total pay from Execucomp and measures of delta and
vega from Coles, Daniel, and Naveen (2006).
13
Delta is measured as the dollar change in the CEO's
wealth (value of the CEO's stock and option portfolio) associated with a 1% change in the rm's
stock price (in $000s). Vega is the dollar change in the CEO's wealth associated with a 0.01 change
in the standard deviation of the rm's returns (in $000s). Table 11 presents the summary statistics
of all dependent variables examined in this section.
DEP
it
=
0
+
1
Similarity
it
+
1
CONTROLS
it
+
i
+
t
+
it
(6)
To facilitate the interpretation of the results, I standardize compensation similarity. Column
13
The calculations are based on the methodology described in Core and Guay (2002)
45
Table 11: Summary Statistics
This table presents the summary statistics of the dependent variables used in section 5.
Variable Obs Mean Std. Dev. Min Max P50
Log total CEO compensation 18,220 8.097 1.201 0 11.958 8.219
Delta 11,505 555.44 1,173.802 0.68 11,877.93 190.429
Vega 11,546 130.176 210.927 0 1,379.195 49.071
Tobin's Q 18,513 2.444 1.278 0.983 10.394 2.072
XRD/ assets 19,973 0.031 0.061 0 0.588 0
Patents/assets 19,740 0.015 0.032 0 0.832 0.005
(1) in Panel A of Table 12 shows that rms that increase similarity also increase the total CEO
compensation level. A one-standard-deviation increase in compensation similarity is associated
with a rise of 6.7% in total compensation. Column (2) and (3) show that rms that increase
similarity reduce delta and vega. Specically, a one-standard-deviation increase in compensation
similarity is associated with an 8.1% reduction in pay-performance sensitivity and a 7.7% reduction
in pay-risk-taking sensitivity. When a CEO compensation plan becomes more homogenous, that
CEO gets higher pay, and this payment is less sensitive to the rm performance and the risk taken.
The positive association between similarity and level of pay is in line with Murphy and Sandino
(2020). They nd that, when companies add new elements of compensation, they usually do not
change the other elements, and, as a consequence, the level of compensation increases. The positive
correlation between compensation similarity and level of pay suggests that rms standardize their
plans by increasing the low components rather than reducing the high components. The negative
association between compensation similarity and delta and vega is not surprising since there is the
convergence is associated with a move away from options, which have a big impact on delta and
vega.
The negative association with delta suggests that standardization may be pushing compensation
plans to a contract that is less linked to performance. Additionally, the negative association be-
tween similarity and vega suggests that rms are converging to a contract that does not incentivize
46
Table 12: CEO compensation similarity and economic consequences
Panel A of this table displays the results of the OLS panel regression of dierent rm policies on CEO compensation similarity
(standardized). Column (1) uses the log of CEO total compensation as the dependent variable. In column (2) the dependent
variable is delta; in column (3) it is vega. In column (4) the dependent variable is XRD/assets, in column (5) it is (Patents in
t+2)/assets, and in column (4) it is Tobin's Q. Firm and year xed eects are included. Controls include log of assets in t-1, log
of rm age in t-1, and protability in t-1. Panel B reports the results of the second stage of the 2SLS estimation. All variables
are winsorized at the 1-99% level. Standard errors are clustered by rm and reported in parentheses. Signicance levels are
indicated: *=10%, **=5%, ***=1%.
Panel A: Endogenous estimation
(1) (2) (3) (4) (5) (6)
Log(total pay)
t
Deltat Vega
t
XRDt=att Patentst+2=att Tobin's Q
t
CEO similarity in t 0.072*** -45.424** -10.088*** -0.001** -0.0005* -0.021**
(0.015) (18.251) (2.631) (0.000) (0.0002) (0.010)
Observations 16,263 10,901 10,934 16,774 16,774 16,120
R-squared 0.106 0.041 0.020 0.113 0.151 0.241
Number of rms 1,900 1,640 1,641 1,901 1,901 1,877
Controls YES YES YES YES YES YES
Firm FE YES YES YES YES YES YES
Year FE YES YES YES YES YES YES
Panel B: 2SLS estimation. Second Stage
(1) (2) (3) (4) (5) (6)
VARIABLES Log(total pay)
t
Deltat Vega
t
XRDt=att Patentst+2=att Tobin's Q
t
CEO similarity in t 0.238*** -115.639** -13.346** -0.002** -0.0014*** -0.048**
(0.031) (52.094) (6.174) (0.000) (0.0004) (0.022)
Observations 6,582 4,317 4,329 6,593 6,593 6,581
Number of rms 1,269 1,035 1,037 1,270 1,270 1,269
Controls YES YES YES YES YES YES
Firm FE YES YES YES YES YES YES
Year FE YES YES YES YES YES YES
47
executives to get involved in risk-taking activities. To explore further, I examine the relationship
between compensation similarity and innovation. Innovation is likely to be aected by lower risk-
taking incentives (Cohen, Dey, and Lys (2013)). In a theoretical study, Manso (2011) shows that
rms can motivate innovation using the right incentive scheme. Several empirical studies show
that rms use executive compensation to incentivize risk taking (Gormley, Matsa, and Milbourn
(2013), Shue and Townsend (2017), and Akins, Bitting, De Angelis, and Gaulin (2019)) and inno-
vation (Coles, Daniel, and Naveen (2006), Aghion, Van Reenen, and Zingales (2013), Baranchuk,
Kieschnick, and Moussawi (2014), Balsmeier, Fleming, and Manso (2017), Lin, Liu, and Manso
(2019)).
I rst examine the correlation between the convergence in the compensation structure and
investment in R&D. Column (4) in Panel A of Table 12 presents the regression of investment in R&D
(XRD scaled by assets)
14
on compensation similarity. The negative coecient of compensation
similarity shows that the more similar a rm becomes to the rest of the rms, the less it invests in
R&D.
Exploring further, I examine the relationship between compensation convergence and patenting
policies. Specically, I regress the number of patents in the next two years (scaled by assets) on
compensation similarity. I obtain patents data from The Global Corporate Patent Dataset that
links patents awarded by the US Patent and Trademark Oce (USPTO), between 1980 and 2017,
to publicly listed rms worldwide.
In line with the previous nding that convergence leads to less investment in R&D, column (5)
shows a negative correlation between compensation similarity and the number of patents reported
in the next two years. More specically, a one standard deviation rise in compensation similarity
is associated with a decrease equivalent to 2% of the mean of R&D/assets and a reduction equal
14
XRD is set to zero when missing.
48
to 4% of patents/assets. This evidence suggests that the standardization of compensation plans
sti
es innovation, and these results are in line with the negative impact on vega.
The standardization in CEO pay structure is associated with less innovation and less pay-
performance sensitivity. Whether this is good or bad depends on the optimal level of innovation
and delta of each company. The methodology of this paper does not allow to make such a claim.
However, I do nd evidence of possible value-destruction consequences.
Based on contracting theory, compensation contracts are chosen to align executives' incen-
tives with shareholders' preferences, such that the executive seeks to maximize the rm's value.
Ultimately, to test whether the standardization of compensation packages is ecient, we need to
examine whether it benets shareholders. Therefore, I examine the relationship between compensa-
tion similarity and Tobin's Q. Column (6) in Panel A of Table 12 presents the regression of Tobin's
Q on compensation similarity. The negative coecient of compensation similarity shows that the
more similar a rm becomes to the rest of the rms, the lower its value. A one-standard-deviation
rise in compensation similarity is associated with a 0.8% reduction in Tobin's Q.
5.1 Instrumental Variable Analysis
With the inclusion of rm xed eects, the previous analysis only considers within-rm variations,
and thus it controls for all time-invariant omitted variables. It also controls for size and age.
However, this does not control for endogeneity resulting from simultaneity or endogeneity relating
to omitted time-varying rm characteristics. We want to identify the eect of standardization
on a rm policy, but the correlation might show three eects at the same time: the eect of
standardization on the rm policy, the eect of the rm policy on standardization, and the eect
of an omitted variable in both standardization and rm policy. Furthermore, these eects can have
the same direction or opposite directions. Which eect are we observing? Does standardization
49
reduce innovation, or is it the case that its compensation becomes less homogeneous as the rm
innovates? Moreover, if the eect observed is, in fact, the eect of standardization, is it the full
impact or only what is left? Innovative rms could also be more prompt to increase similarity.
To overcome these endogeneity issues, I propose an instrument that is related to convergence
but is not related to the rm policy. There is evidence that directors can in
uence executive
compensation plans based on their experiences on the board of other rms. For example, Fernandes,
Ferreira, Matos, and Murphy (2013) show that for non-US rms with a high fraction of directors
who also sit on boards of US rms, the CEO pay is similar to that of the US CEOs. In line with the
idea that directors who share board rooms in
uence each other, I nd a positive correlation between
the board's ratio that serves on other boards and the convergence in compensation. Furthermore,
this correlation is more signicant if I consider the percentage of members in the compensation
committee that serves on other boards. Table 13 presents these correlations.
15
I take advantage of the potential existence of peer eects when directors serve on multiple boards
to build an instrument for compensation similarity. Specically, I consider the standardization of
the overlapping-board rm's compensation plan as an instrument for the standardization of the
focal rm's compensation plan. I dene an overlapping-board rm as a rm with which the focal
rm shares a director. This instrument's idea is that if the director of a rm participates on the
board of another rm that has a very standard compensation structure, she might in
uence the
rm to mimic that structure. Moreover, I only consider overlapping-board rms that belong to
a dierent industry (dened at SIC 2 level). In other words, the instrument only considers the
variation of compensation similarity that is explained by the convergence of a rm in a dierent
industry. The exclusion restriction relies on the assumption that the convergence of a dierent
15
Consistent with prior literature (Core, Holthausen, and Larcker (1999), Ferris, Jagannathan, and Pritchard
(2003), Fich and Shivdasani (2006), Field, Lowry, and Mkrtchyan (2013)), I nd similar results if I dene multi-
board directors as directors who sits on the boards of three or more rms or if I dene it as the average number of
seats per director.
50
Table 13: CEO compensation similarity and directors serving on the board of other rms
Columns (1) to (3) of this table display the results of the OLS panel regression of similarity on the percentage of all directors
that serves in other boards. Columns (4) to (6) uses the percentage of directors in the compensation committee that serves in
other boards. Column (1), (2), (4), and (5) include industry xed eects at SIC 3-digit level. Columns (3) and (6) include
rm xed eects. Firms characteristics include size, age and protability. Board characteristics include size of the board,
independence of the board, and monitoring intensity of the board (dene as the percentage of independent directors serving
on monitoring committees (Faleye, Hoitash, and Hoitash (2011))). Standard errors are clustered by rm and reported in
parentheses. Signicance levels are indicated: *=10%, **=5%, ***=1%.
CEO similarity in t
(1) (2) (3) (4) (5) (6)
% board serving in other board 0.033*** 0.028** 0.015
(0.010) (0.011) (0.013)
% comp committee serving in other board 0.020*** 0.019*** 0.013*
(0.006) (0.006) (0.007)
Constant 0.559*** 0.457*** 0.515*** 0.559*** 0.451*** 0.516***
(0.004) (0.032) (0.057) (0.004) (0.032) (0.057)
Observations 9,798 9,775 9,778 9,792 9,769 9,772
R-squared 0.172 0.173
Number of Firms 1,476 1,473 1,474 1,476 1,473 1,474
Firm characteristics YES YES YES YES
Board characteristics YES YES YES YES
Industry FE YES YES YES YES
Firm FE YES YES
Year FE YES YES YES YES YES YES
51
rm's compensation plan is unlikely to be related to the focal rm's policy, especially if that other
rm belongs to a dierent industry.
More specically, the instrument is dened as the similarity between the focal rm's com-
pensation plan and the overlapping-board rm's compensation plan. If there is more than one
overlapping-board rm, I consider the average similarity across all overlapping-board rms. Figure
19 shows a representation of the instrument in a world of two dimensions. Point F is the compen-
sation plan of the focal rm. Point E is the mean compensation plan of the economy. The closer
to E, the more homogeneous a compensation plan is. Point P is the compensation plan of a rm
that (i) shares a director with rm F, and (ii) belongs to a dierent industry. Thus, I exclude all
rms that do not share a director with rm F and all rms that are in the same industry of rm
F. The instrument is dened as the distance between F and P.
Figure 19: Representation of the instrumental variable
The gure shows a representation of the instrument in a world of two dimensions. Point F is the compensation plan of the
focal rm. Point E is the mean compensation plan of the economy. Point P is the compensation plan of a rm that (i) shares
a director with rm F, and (ii) belongs to a dierent industry. The instrument is dened as the distance between F and P.
E = Mean compensation plan
of the Economy
Focal firm’s
compensation plan
P = Peer’s compensation plan:
- shared director
- different industry
F
IV
1
I run a Two-Stage least squares (2SLS) analysis with rm and year xed eects using this
52
instrument. Column (1) in Table 16 in Appendix A.5 reports the results of the rst-stage estimation.
The coecient estimate of the instrument is signicant at the 1% level with F-test of 199.03. As
placebo tests, columns (2) to (4) show that the instrument does not correlate with the rm size,
age, or protability.
Panel B of Table 12 presents the second-stage results for each variable described in the previous
section. I nd a positive eect of similarity on total CEO compensation. Similarly, I nd a
negative impact on delta, vega, R&D investment, number of patents, and Tobin's Q. These results
are stronger both in magnitude and statistical power than those obtained without instrumentation.
In the last decade, compensation similarity increased in one standard deviation. Based on the
IV analysis, a one standard deviation rise in compensation similarity causes a 24% increase in
total pay, a 21% decrease in delta, a 10% in vega, a 5% decrease in R&D/assets, a 9% decrease in
patents/assets, and a 2% decrease in Tobin's Q.
Even though this IV analysis aims to overcome endogeneity, it should be interpreted with
caution. The most relevant concern is the fact that rms sharing a director are not randomly
assigned. However, since they are in dierent industries, it is reasonable to believe that they share
a director because of her general knowledge instead of her rm-specic knowledge. A second concern
is that omitted variables may aect the compensation similarity of the overlapping-board rm and
the focal rm's policy (e.g., managerial talent). My identication relies on the assumption that
these omitted variables are time-invariant, and thus the rm xed eects control for them.
53
6 Conclusion
There exists a growing concern across academic researchers and practitioners that in
uences from
institutional shareholders, advisory services, and regulators might have contributed to standard-
ization in CEO pay and the prevalence of a \one-size-ts-all" trend. In this paper, I report that
the structure of executive compensation in public rms is converging. Moreover, I show that the
in
uence of shareholders on compensation packages' design has an important role in explaining
this convergence. Indeed, I nd that rms' compensation structures with Say-on-Pay every year
converge faster than rms with Say-on-Pay every three years.
Exploring further, I nd evidence suggesting that proxy advisory rms' recommendations ex-
plain, in part, why shareholders' in
uence pushes towards convergence. I also nd evidence sug-
gesting that the convergence is unlikely to be optimal. The more similar a rm's compensation
structure becomes to the others, the CEO gets higher pay, and this payment is less sensitive to
the rm performance and the risk taken. Simultaneously, the rm innovates less {invests less in
R&D and is less likely to patent{ and reduces its market value. These ndings are robust both
in correlations and to using controls for endogeneity. Under the \shareholder-value" view, these
negative eects of a \one-size-ts-all" trend imply that rms are being pushed away from optimal
contracts. Under the \rent-extraction" view, they imply that standardization makes rent extraction
easier. In both cases, the ndings suggest that institutional pressure for uniformity might come at
the expense of optimal incentives.
Overall, this paper supports the hypothesis that the external in
uence of shareholders and
proxy advisory rms has fostered standardization in the structure of executive compensation plans.
However, this hypothesis is unlikely to be the only explanation for the convergence. Future research
might explore other economic forces. For example, is the convergence a consequence of regulations
other than Say-on-Pay? In 2006 the SEC implemented new rules on the disclosure of executive
54
compensation with the primary goal of facilitating comparison across rms. Better comparison
across rms may foster convergence by facilitating mimicking between rms. It can also increase
convergence by incentivizing strategic behaviors (Bizjak, Lemmon, and Nguyen (2011), Faulkender
and Yang (2013), Kalpathy, Nanda, and Zhao (2019)) that can create a pooling equilibrium with
rms having similar compensation structures. Alternatively, the 2006 regulation could foster con-
vergence by in
uencing rms to design their compensation packages based on what is required to
report. Overall, the 2006 regulation eects on the \one-size-ts-all" trend is still an open question.
Furthermore, this paper nds that the standardization of compensation plans sti
es innovation.
It also nds evidence of possible value-destruction. However, the latter result is smaller in magni-
tude. More research is required to identify the potential benets of the standardization of executive
compensation plans and whether they compensate for the loss in market value and innovation.
Finally, the convergence documented in this paper may also be part of convergence in gov-
ernance more broadly. Regulation dramatically altered the path of governance over the last 20
years, and more research is required to explore its consequences in other aspects besides executive
compensation plans.
55
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Appendix A Appendices
A.1 Variable denitions
Firm size: log ( 1 + at)
Firm age: log (1 + (year - link year))
Protability: oibdp/at
Tobin's Q: (at-uceq-txdb+(csho*prcc f))/at
Tangibility: ppent/at (if ppent is not reported, then ppent=0)
SOP-frequency voting share: number of votes / number of outstanding shares
Institutional investor ownership: institutional ownership shares/(shrout1*1000000)
Size of the board: log(number of directors)
Independence ratio: independent directors / number of directors
% of board serving on other board: number of directors seating on the board of other rm / number
of directors
% of compensation committee serving on other board: number of members of compensation com-
mittee seating on the board of other rm / number of members of compensation committee
Independent committees: number of independent directors serving on a monitoring committee (au-
diting, compensation, or nominating) / number of independent directors
Total Pay: log (1+ salary+bonus+stock awards fv+option awards fv+noneq incent+othcomp)
Delta: the dollar change in the CEO's wealth (value of the CEO's stock and option portfolio)
associated with a 1% change in the rm's stock price (in $000s).
Vega: the dollar change in the CEO's wealth associated with a 0.01 change in the standard deviation
of the rm's returns (in $000s).
63
A.2 Variance of Similarity
Table 14: Cosine Similarity of Compensation Packages
This table displays the results of OLS panel regression of the standard deviation of cosine similarity on a time trend. Columns
(1) and (2) correspond to the similarity of CEO compensation, columns (3) and (4) of CFO compensation , and columns (5)
and (6) of other executives compensation. Odd columns include rm xed eects. Firm xed eects are included. Standard
errors are clustered by rm and reported in parentheses. Signicance levels are indicated: *=10%, **=5%, ***=1%.
Panel A: Variance of cosine similarity on a time trend
CEO CFO OTH
Time trend -0.001*** -0.001*** -0.001*** -0.002*** -0.001*** -0.001***
(0.000) (0.000) (0.000) (0.000) (0.000) (0.000)
Constant 0.262*** 0.271*** 0.236*** 0.247*** 0.219*** 0.225***
(0.001) (0.001) (0.001) (0.001) (0.001) (0.001)
Observations 16,747 16,747 16,628 16,628 16,787 16,787
R-squared 0.144 0.101 0.092
Firms 2,021 2,021 2,015 2,015 2,027 2,027
Firm FE NO YES NO YES NO YES
64
A.3 Alternative Measures of Similarity
As a robustness test, I follow the same methodology described in Section 2.1 but using the Kullback-
Leiber Divergence (KL) test instead of the cosine-similarity measure. In this exercise, I treat each
vector of compensation as a statistical distribution and use the KL test to examine how similar
they look. The KL divergence is the expectation of the log dierence between the probability of
data in one distribution with the other distribution, called statistic D. Basically, KL divergence
calculates how much information is lost when we approximate one distribution with another.
Panel A of Figure 20 plots the time series of the average D between each pair of rms. It is
decreasing over time. Columns (1) and (2) in Table 15 in Appendix A.3 show the formal estimation
with a negative trend signicant at 1%. The statistical interpretation of this test is simple: on
average, the \loss of information" from moving from one compensation plan to another is decreasing
over time. This nding is evidence of convergence. If each compensation plan was a statistical
distribution, those distributions are becoming more similar over time.
Similarly, I run the same exercise using the Kolmogorov-Smirnov (KS) test. The KS test
compares the cumulative fraction function of two distribution and reports the maximum vertical
deviation between the two curves as the statistic D. Panel B of Figure 20 plots the time series of
the average D. Columns (3) and (4) in Table 15 in Appendix A.3 show the formal estimation. Both
show a negative trend, showing that the structures of compensations are less statistically dierent.
The economic interpretation of these two tests, however, is less informative than the cosine
similarity measure. The reason is that both tests sort the elements of the vector and then compares
the distribution. Hence, it does not take into account the type of each element. For example,
according to them, a rm with an 80% salary and 20% stock has the same distribution as a rm
with a 20% salary and 80% stock. This is not the case with the cosine similarity, which measures
location considering each element as a dierent axis. Also, even if we do not care about the type
65
of each element of the vector {something that is essential for this project{ and we only care about
its distribution, neither KL Divergence test nor KS test are usually used as a measure of distance.
The reason is that the magnitude of D can vary depending on which distribution is used as the
point of reference, and thus, they are not symmetric. Regardless of these caveats, the ndings are
in line with an increase in standardization over time.
Figure 20: Statistical distribution similarity of executive compensation plans
Figure (a) shows the time-series plot of the average statistic D from the Kullback-Leiber Divergence test between each pair
of rms. Figure (b) the time-series plot of the average statistic D from the Kolmogorov-Smirnov (KS) test. The vector of
compensation used to calculate each test includes salary, bonus, stock awards, stock options, non-equity incentives, and other
compensation.
(a) Kullback-Leibler Divergence (b) Kolmogorov-Smirnov test
66
Table 15: KL Divergence test and KS test of Compensation Packages
This table displays the results of OLS panel regression of the Statistic D (average Statistic D between the compensation
structure of a given rm and each of all other rms in Execucomp in a given year) on a time trend. Columns (1) and (2)
correspond to the Kullback-Leibler Divergence test, and columns (3) and (4) to Kolmogorov-Smirnov test. Odd columns
include rm xed eects. Standard errors are clustered by rm and reported in parentheses. Signicance levels are indicated:
*=10%, **=5%, ***=1%.
(1) (2) (3) (4)
KL divergence test KS test
Statistic D Statistic D Statistic D Statistic D
Time trend -0.080*** -0.135*** -0.001*** -0.001***
(0.002) (0.003) (0.000) (0.000)
Constant 5.559*** 6.333*** 0.321*** 0.332***
(0.038) (0.041) (0.001) (0.002)
Observations 16,743 16,743 16,743 16,743
R-squared 0.119 0.009
Number of gvkey 2,021 2,021 2,021 2,021
Firm FE NO YES NO YES
67
A.4 SOP: Di-in-di with entropy balanced matching
This table presents the results of the OLS panel regression of equation 5 after an entropy balanced matching. I follow the
methodology of Hainmueller (2012) and balance the rst and second moments of six observable characteristics|the log of asets,
the log of rm age, protability, tangibility, and market to book ratio. Each observation is weighted in order to maximize the
probability of being treated. The balancing is based on those observable characteristics in 2011. The purpose of the entropy
balancing is to make the treated and the control group as similar as possible in the probability of being treated, regarding
mean and variance of size, age, protability, the ratio of tangible assets, and the growth opportunities they had just before
SOP-frequency voting.
Panel A present the result for the whole sample of rms and Panel B for rms with a voting dierence between one-year and
three-year SOP frequency lower than 20%. Column (1) uses the baseline similarity described in section 2.1. Column (2) uses
the measure of similarity that distinguishes restricted stocks and performance-based stocks. Column (3) uses a measure of
similarity in which \Bonus" and "Non-equity compensation" are added together as one element of compensation. Column (4)
uses the measure of similarity with the change in pension value as a seventh element. Column (5) uses the measure of similarity
within industry (Fama French 48). All regressions include rm and year xed eects, and standard errors are clustered by rm.
All variables are winsorized at the 1-99% level. Standard errors are reported in parentheses and signicance levels are indicated:
*=10%, **=5%, ***=1%.
Dependent variable: CEO compensation similarity
Panel A: whole sample
(1) (2) (3) (4) (5)
baseline rest stock bon+noneq pension 48
post2011xSOP 0.042*** 0.033*** 0.046*** 0.044*** 0.037***
(0.011) (0.009) (0.010) (0.011) (0.012)
Observations 11,800 11,800 11,954 11,800 11,676
R-squared 0.119 0.039 0.107 0.132 0.097
Firms 1,220 1,220 1,220 1,220 1,206
Firm FE YES YES YES YES YES
Year FE YES YES YES YES YES
Panel B: rms with a voting dierence lower than 20%
(1) (2) (3) (4) (5)
baseline rest stock bon+noneq pension 48
post2011xSOP 0.042** 0.033** 0.055*** 0.043** 0.041*
(0.020) (0.015) (0.018) (0.021) (0.024)
Observations 1,607 1,607 1,629 1,607 1,607
R-squared 0.104 0.035 0.106 0.115 0.064
Firms 168 168 168 168 168
Firm FE YES YES YES YES YES
Year FE YES YES YES YES YES
68
A.5 IV Estimation: First Stage
Table 16: Instrumental Variable Estimation: First Stage
This table displays the results of the OLS panel regression of CEO compensation similarity and the instrument proposed in
section 5.5.1. The instrument is dened as the similarity between the compensation plan of the focal rm and the compensation
plan of a rm that shares a directors with the focal rm and it is in a dierent industry. Firm and year xed eects are included.
Standard errors are clustered by rm and reported in parentheses. Signicance levels are indicated: *=10%, **=5%, ***=1%.
(1) (2) (3) (4)
VARIABLES CEO Similarity
t
Log(Assets)
t
Log(Age)
t
Protability
t
Instrument in t 0.305*** 0.010 0.038 -0.003
(0.008) (0.026) (0.026) (0.004)
Log assets in t-1 -0.007
(0.005)
Log age in t-1 0.007
(0.007)
Protability in t-1 0.014
(0.021)
Constant 0.332*** 7.946*** 2.811*** 0.155***
(0.041) (0.026) (0.020) (0.004)
Observations 6,582 7,325 7,326 7,324
R-squared 0.527 0.314 0.335 0.021
Number of rms 1,269 1,337 1,337 1,337
F-test 199.03***
Firm FE YES YES YES YES
Year FE YES YES YES YES
69

Abstract (if available)

Abstract This paper reports the prevalence of a “one-size-fits-all” trend in the structure of executive compensation plans. The way firms distribute total compensation across different components of pay—salary, bonus, stock awards, option awards, non-equity incentives, pensions, and perquisites—is becoming more similar since 2006. In particular, 25% of the variation across firms disappeared in the last ten years. Using close votes surrounding Say-on-Pay’s implementation, I find that shareholders’ influence on management decisions causes part of this convergence. This finding is robust in both difference-in-difference and RDD estimations. Additional evidence suggests that proxy advisors play a role by pushing towards standardization. The convergence has economic consequences. The more similar a firm’s compensation structure becomes to the others, the higher the pay and the lower its sensitivity to the firm performance and the risk taken. Additionally, the firm innovates less—invests less in R&D and is less likely to patent—and reduces its market value.

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Asset Metadata

Creator Cabezón, Felipe (Luis Felipe) (author)

Core Title Executive compensation: the trend toward one size fits all

School Marshall School of Business

Degree Doctor of Philosophy

Degree Program Business Administration

Publication Date 03/25/2021

Defense Date 03/11/2021

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag corporate governance,corporate regulation,corporate voting,executive compensation,OAI-PMH Harvest,proxy advisors,shareholders

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Hoberg, Gerard (committee chair), Matsusaka, John (committee chair), Murphy, Kevin J. (committee member), Sloan, Richard (committee member)

Creator Email cabezon@usc.edu,lfcabezon@gmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c89-431436

Unique identifier UC11666514

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Legacy Identifier etd-CabezonFel-9351.pdf

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Document Type Dissertation

Rights Cabezón, Felipe (Luis Felipe)

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...

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