Voting Efficiency and the Even-Odd Effects of Corporate Board:
Theory and Evidence
Xin Deng, Huasheng Gao, Wei-Lin Liu*
This Version: April 2012
Abstract: We analyze a simple model of board voting and find that in comparison to boards
with an even number of directors (even boards), those with an odd number of directors
(odd boards) improve voting efficiency by better aggregating directors’ information.
Consistent with the model’s implications, we empirically find that firms with an odd board
derive higher Tobin’s q, deliver better operating performance, exhibit stronger CEO
turnover-performance sensitivity, and have lower levels of CEO compensation but higher
CEO pay-performance sensitivity, than do firms with an even board. Furthermore, these
even-odd effects diminish as board size increases. Overall, our findings are consistent with
the even-odd characteristic of board playing an important role in influencing board voting
efficiency and thus the quality of board decisions.
Keywords: Voting Efficiency, Odd Boards, Even Boards, Firm Performance, Corporate
Governance
JEL Classification: G32; G34; K22
*
Xin Deng (deng0021@e.ntu.edu.sg), Huasheng Gao (hsgao@ntu.edu.sg), and Wei-Lin Liu (wlliu@ntu.edu.sg) are
from the Nanyang Technological University. We thank Chishen Wei, Chuan Yang Hwang, and seminar participants
at the Nanyang Technological University (NTU), National University of Singapore (NUS), University of Hong
Kong, and 24th Australasian Banking and Finance conference, for helpful comments. We also thank Zheng Qiao for
excellent research assistance. All remaining errors are our own.
1. Introduction
Understanding the relation between board characteristics and the efficacy of board
decisions is an important issue that has attracted considerable research interests. Extant finance
literature has put under scrutiny the effects of key board characteristics, including board size,
fraction of independent directors, CEO-chairman duality, etc., on boards’ role in advising CEOs
on major corporate strategy, monitoring CEO conduct, and, when circumstances necessitate,
disciplining CEOs.1 This paper extends the existing literature by examining the link between
board characteristics and board voting efficiency – the extent to which voting outcomes
aggregate directors’ information. Since major board decisions are generally preceded by a voting
process, voting efficiency is of critical importance to the quality of such decisions.
The board characteristic we focus on relates to the even-odd nature of the number of
directors. This focus is motivated in part by anecdotal evidence suggesting that the even-odd
characteristic of a board may significantly influence the board’s voting process. For example,
the 2003 proxy filing of Del Global Technologies Corp., a manufacturer of medical devices,
described how the company, in an effort to improve board voting outcomes, switched to an odd
board by expanding its board members from four to five.2 As another example, the corporate
governance guidelines of Enliven Corporation (Nasdaq: ENLV), in addition to prescribing the
range of board size, explicitly states that an odd number of directors is desirable, though not
1
A partial list of the previous studies include Weisbach (1988), Byrd and Hickman (1992), Brickley et al. (1994),
Yermack (1996), Baliga et al (1996), Brickley et al. (1997), Eisenberg et al. (1998), Adams and Ferreira (2007), and
Linck et al. (2008). Also see Adams, Hermalin, and Weisbach (2010) for an excellent survey of the recent research
on corporate boards.
2
http://findarticles.com/p/articles/mi_m0EIN/is_2003_May_13/ai_101653816/
1
required.3 A similar statement appears in the corporate governance guidelines of Gleacher &
Company, Inc. (Nasdaq: GLCH).4
Our focus on the even-odd characteristic of board is also motivated by Yermack’s (1996)
classical study on corporate board. While Yermack (1996) focuses on the effects of board size,
his findings also reveal a possible relation between the even-odd characteristic of boards and firm
values. In particular, Figure 1, which is reproduced from Yermack (1996), shows that odd
boards tend to be associated with a higher Tobin’s q relative to even boards, especially among
small boards. Reading from the figure, for instance the average Tobin’s Q is 2.1 for five-member
boards, whereas for four-member and six-member boards the averages of Tobin’s Q assume
much smaller values of 1.6 and 1.55, respectively. Surprisingly, this empirical pattern appears to
have so far eluded the attention of finance researchers. As a result, there remains a lack of
understanding of the potentially distinctive role of the even-odd characteristic of boards in
determining firm values.
To explore the relation between the even-odd characteristic of board and voting
efficiency, we first analyze a simple model of board voting, which is inspired by the previous
studies on group voting in economics and political science. The key element of our model is that
each director has both a performance preference and a conformity preference. The performance
preference aligns a director’s incentive with ensuring high quality board decision, and thus
motivates the director to vote based on his own information. The conformity preference, on the
3
http://www.enliven.com/downloads/CorporateGovornanceGuidlines.pdf
http://www.gleacher.com/investorrelations/corporategovernance/Documents/Gleacher%20%20Company%20%20Amended%20and%20Restated%20Corporate%20Goverance%20Guidelines%20_5-9-11_.pdf
4
2
other hand, induces an incentive for the director to vote for the decision favored by a majority of
other directors.5
The analysis of our model reveals that because of the conformity preference, voting in
odd boards may better aggregate directors’ information than that in even boards. The intuition
behind this finding is as follows. Because of the conformity preference, in deciding what
decision to vote for each director considers not only his own information but also how the other
directors vote. In an odd board, each director faces an even number of other directors. Since, on
average, opposing votes among an even number of directors tend to balance out one another, in
an odd board the conformity preference becomes moot, and the performance preference causes
each director to vote based on own information. In contrast, in an even board each director faces
an odd number of other directors, among whom opposing votes generally do not balance out one
another. Consequently, a strong conformity preference can cause a director to vote in accordance
to the anticipated net vote by the other directors, even if his own information suggests otherwise.
To empirically examine the implications of our model, we analyze a large sample of
corporate boards over the period 1999-2009. Directly testing our model, however, requires an
accurate measurement of voting efficiency, which appears to be quite challenging.
To
circumvent this problem, we follow most of the previous studies on corporate boards by
assuming that higher quality of board decisions should manifest in improved firm performance
and strengthened corporate governance. Our tests, therefore, focus on the implications of the
even-odd characteristic of boards on firm performance and corporate governance.
5
Director conformity preference has previously been employed by several theoretical studies to provide
explanations to a multitude of empirical regularities of corporate boards (Gillette, Noe, and Rebello, 2003;
Chemmanur and Fedaseyeu, 2010; Malenko, 2011).
3
Our empirical analysis yields several important findings. First, we find that firms with an
odd board are associated with significantly higher firm values, as measured by Tobin’s Q, than
do firms with an even board. In terms of economic significance, the firm fixed-effect regression
shows that odd boards on average derive 2.7% higher Tobin’s Q relative to even boards. To put
this number in perspective, Yermack (1996) finds that in the firm fixed-effect regression,
expanding an eight-person board by one member results in a reduction in Tobin’s Q by 4%.
Thus, in terms of firm value, the even-odd effect we document represents close to 70% of the
above size effect in Yermack (1996), suggesting that the former effect provides an important
modification to the latter effect. Moreover, we show that firms with an odd board are associated
with significantly better operating performance, as measured by return-on-asset (ROA), than do
firms with an even board.
In sum, consistent with our model implications, odd boards
significantly improve firm values and operating performance relative to even boards.
Second, we find that the benefits of odd boards exhibit patterns of cross-sectional
variations that are consistent with improved voting efficiency being the source of these benefits.
In particular, we find that the differences in firm value and operating performance between firms
with even and odd boards are especially evident when directors have a strong conformity
preference but weak performance preference. Furthermore, since the extent to which board
decisions aggregate directors’ information is likely to be of critical importance to firms that
actively make informationally intensive investments (e.g., R&D expenditure), the difference in
firm value and operating performance between even and odd boards should be particularly
pronounced among firms that have high R&D expenditures.
observation.
4
Our result also confirms this
Third, we find significant differences in the occurrences of CEO turnovers and CEO
compensation practice between firms with an odd board and those with an even board. In
particular, firms with an odd board show higher CEO turnover-performance sensitivity, and have
lower levels of CEO compensation but higher pay-to-performance sensitivity, than do firms with
an even board. Moreover, both of the differences in CEO turnover and CEO compensation
between firms with an odd board and those with an even board are generally more pronounced
when directors have strong conformity preference but weak performance preference, and when
firms actively make R&D investments. Prior studies suggest that the settings of CEO turnover
policy and CEO pay are important governance mechanisms that align a CEO’s incentive with
that of shareholders’ (e.g., Weisbach,1988; Hartzell and Starks,2003; Core et al. 1999). Our
findings, therefore, indicate that odd boards enhance the boards’ effectiveness in corporate
governance relative to even boards, and the enhanced effectiveness is likely to arise from
improved board voting efficiency.
Finally, as an extension of our model, we consider the possibility that directors may face
varying costs in acquiring information critical to board decisions or in participating in board
voting. We argue that because of these costs, the even-odd effects tend to diminish as board size
increases. The results from additional analyses on Tobin’s q, operating performance, CEO
turnover, and CEO compensation, strongly confirm this argument.
There may be two concerns with our findings. First, as with any study on board structure,
our results may also suffer from endogeneity problems. To alleviate these problems, we control
for an extensive list of firm characteristics in our regression analysis. In addition, we explicitly
control for other board characteristics, including board size, proportion of independent directors,
and CEO-chairman duality, so as to mitigate the concern that the differences between even and
5
odd boards are a mere reflection of the effects associated with these other characteristics. To
further mitigate possible endogeneity problems, we conduct two additional robustness tests. In
the first test, we use firm fixed effect to control for firm-specific and time-invariant factors that
potentially correlate with firm propensity of having an odd board, and also affect firm
performance and corporate governance. Next, we perform a two-stage treatment regression,
using as instrumental variables the prevalence of odd boards in the firm’s industry and that in the
state in which the firm is located. We find that our key results on the difference between firms
with even and odd boards survive both tests.
Second, if our findings suggest genuine benefits of odd boards, it might appear that firms
should invariably opt for odd boards. Yet, many firms in our sample have even boards. Our
response to the seemingly conflicting evidence follows from the views in Adams et al. (2010)
and Coles et al. (2010).
Specifically, since each firm operates within the confines of its
exogeneously given environment, a firm’s choice between an even and odd board represents the
firm’s best solution to the constrained optimization problem relating to the design of the board.
If changing the exogenous environment is costly and takes time, the firm may optimally adopt an
even board, even if an odd board is more desirable when the firm can freely choose its exogenous
environment.6 Such reasoning also explains why we are able to empirically find the significant
effects of odd boards in the first place.
This paper makes two important contributions to the literature. First, while there is a
voluminous literature on group voting in economics and political science, the finance literature
on board voting remains small and mostly theoretical in nature (e.g., Warther, 1998; Gillette et al,
6
For instance, a firm wishing to switch from an even board to an odd board may be constrained from doing so when
the supply of competent directors is limited. Since the firm cannot freely change the availability of competent
directors, staying with an even board may be the firm’s solution to the constrained optimization problem.
6
2003; Harris and Raviv, 2006; Baranchuck and Dybvig, 2008; Chemmanur and Fedaseyeu, 2010;
Malenko, 2011). Lack of sufficiently detailed data on the process and outcome of board voting
renders challenging direct tests of these theories, which typically involve subtle assumptions on
board composition and director preference. Perhaps for this reason, empirical analysis on board
voting remains scarce. Our model and empirical analysis focus on an easily measurable board
characteristic, the even-odd nature of the number of directors. Our findings help empirically
establish a link between board characteristics and board voting efficiency.
Second, we complement the existing literature on corporate board by identifying the
even-odd characteristic of boards as a new measure of the boards’ effectiveness in improving
firm performance and strengthening corporate governance. Our analysis suggests that this new
measure represents an economically significant yet under-explored aspect of boards that is
distinct from those captured by the conventional measures. As such, our results complement the
existing studies by Yermack (1996) and Coles et al (2008) in providing a precise characterization
of the relation between firm value and the number of directors.
The rest of the paper is organized as follows. Section 2 presents a simple model of board
voting and develops the empirical implications of the model. Section 3 describes the data and the
summary statistics of the key variables. Section 4 presents the main empirical findings. We
describe the results of additional tests in Section 5. Section 6 concludes the paper.
2. A simple model of voting and model implications
2.1. A simple model of board voting
2.1.1. Model setup
7
A firm can undertake one of two actions: sticking to the status quo, which is denoted as
a=0, and adopting a new strategy, which is denoted as a=1. The new strategy can be a decision
to change CEO compensation scheme, replace the current CEO, adapt key firm policies, etc. The
firm’s performance improvement
depends on the suitability of the new strategy
firm, which can be either high
or low
to the
, and the action undertaken:
;
,
(1)
.
(2)
From Eq. (1), if the status quo is maintained the performance improvement is invariably 0.
On the other hand, from Eq. (2) adopting the new strategy enhances the firm’s performance if it
is highly suitable to the firm, but leads to a decline in performance if its suitability is low. In the
example of CEO replacement decision (a=1 if the current CEO is replaced, and a=0 if the current
CEO is retained), suitability is determined by the difference in the overall abilities between a
new CEO candidate and the current CEO. If the new CEO candidate is more (less) competent
than the current CEO, replacing the current CEO is a highly suitable (unsuitable) strategy, and it
improves (reduces) firm performance.
The firm’s choice of action is determined by the firm’s board through voting. The board
has n>2directors. 7 Prior to casting their votes, the directors learn aspects of the new strategy.
Specifically, director i, i=1, 2, …, n, can privately learn the ith aspect of the new strategy
which can be either good,
, or bad,
they share a common prior belief that each
. Before the directors learn about the
s,
is equally likely to be good or bad. Since
s
represent distinct aspects of the new strategy, they are independently distributed.
7
,
The smallest board in our sample has three directors.
8
Collectively, the various aspects of the new strategy stochastically determine its
suitability. Specifically, let
=(
,…,
) be the set of the directors’ information, and
be the n directors’ collective information about the new strategy. The probabilities of
high and low suitability conditional on
are:
,
(3)
.
(4)
Eqs. (3) and (4) suggest that positive (negative) collective information, i.e.
(
), is indicative of high (low) suitability. Moreover, as
increases, high suitability
becomes increasingly more likely. In the limit when all the directors get positive (negative)
information, i.e.
(
for all i, suitability
(
with certainty. Note that
before the directors obtain their information, according to the common prior belief
and
are equally likely.
In the running example of CEO replacement, suitability
is likely to reflect the aggregate
of the differences between the two individuals in multiple aspects. These aspects may include
knowledge and understanding about the firm’s business, creative ideas about how to grow the
firm, the abilities to work with the firm’s other senior executives and provide leadership,
personal charisma, etc. Collectively, the differences in these aspects determine which one of the
two individuals is likely to be the more competent CEO.
Upon obtaining information about , each director votes for either
or
.8 In
casting his vote, a director does not know the information that other directors have and how each
8
Implicitly, we are assuming that the directors cannot choose to abstain. In our model, this is without loss of
generality as directors will either vote based on own information when performance preference dominates
conformity preference, or vote to conform to the majority opinion. Thus, even if abstention is allowed, directors will
not invoke that option.
9
of the other directors votes, but holds rational expectations about others’ information and voting
strategies. After the directors cast their votes, each director’s vote is revealed, and the board
chooses the action to implement based on the pre-specified voting rule
strategy is adopted, i.e.,
.
part,
, if the number of directors voting for
, so that the new
is greater or equal to
All of the directors have the same utility function, which consists of two parts. The first
, produces a performance preference that is perfectly aligned with maximizing the
firm’s expected performance improvement.
performance improvement
Specifically,
, so that
is proportional to the
, where constant
and
measures the strength of the directors’ preference for performance maximization. The directors’
performance preference may arise directly from their share ownership, as greater ownership
benefit directors more when firm performance improves. Performance preference can also arise
from directors’ reputational concerns: Poor firm performance may be seen by the director labor
market as a sign of the directors’ inability in providing quality monitoring and advising services,
thereby jeopardizing the directors’ pursuit of retaining their incumbent directorships or obtaining
new directorships.
The basic setup outlined so far parallels the standard setup widely used in the previous
studies on common value voting (e.g., Austen-Smith and Banks, 1996; Feddersen and
Pesendorfer, 1996). We enrich the basic setup by considering a second part of the director’s
utility function that gives rise to a conformity preference – that to vote for the same action as the
one that the board ends up adopting (Gillette et al, 2003; Chemmanur and Fedaseyeu, 2010;
Malenko, 2011). Specifically, we assume that each director faces a personal cost
if the
action he votes for turns out to disagree with the action that the board chooses. Thus, the total
utility for director i
10
,
(5)
is an indicator function that takes the value of one if director i’s vote disagrees with
where
the board’s decision, and zero otherwise.
Cost
measures the strength of the directors’
conformity preference.
2.1.2. The analysis of the model
Before examining the voting equilibrium, consider the optimal decision that utilizes the
directors’ collective information to maximize the expected performance improvement. Since
based on the prior belief the two actions yield the same expected performance improvement, one
good (bad) aspect of the new strategy tips the balance toward favoring action a=1 (a=0). Thus,
the optimal decision is determined by the difference between the numbers of the good and bad
aspects that the directors observe.
Given a set of the directors’ observations
aspects is
let
, the total number of the good
, while that of the bad aspects is
. If
(
. When n is an odd number,
, the directors observe a strictly greater (smaller)
number of good aspects than that of bad aspects, so the optimal decision chooses
When n is an even number, we set
. If
(
(
).
, the directors
observe a strictly greater (smaller) number of good aspects than that of bad aspects, so the
optimal decision chooses
(
). If
, there is an equal number of good
and bad aspects. In this case, the two alternative actions provide the same expected performance
improvement, and without loss of generality, we assume that the optimal decision chooses
.
To achieve the optimal decision through board voting, it is essential that in equilibrium
each director follows an informative voting strategy, according to which a director votes for
11
action
(
) upon observing a good (bad) aspect. It follows from the above discussion
on the optimal decision that the appropriate voting rule is a simple majority voting rule with
(the proof of Proposition 1 shows that this is indeed the optimal rule). The following
proposition describes the respective voting equilibrium for an odd board (n is odd) and an even
board (n is even). The proof of the proposition is in Appendix B.
Proposition 1: For an odd board, informative voting is an equilibrium strategy for the directors.
Thus, voting fully aggregates the directors’ information, and board decision coincides with the
optimal decision. For an even board, if
strategy. However, when
, informative voting is also an equilibrium
, informative voting is not an equilibrium strategy, so board
voting fails to aggregate directors’ information. In this case, the board’s decision does not
coincide with the optimal decision.
Since the performance preference is aligned with maximizing the firm’s expected
performance improvement, this preference produces an incentive for the directors to vote
informatively. However, as Proposition 1 indicates, for an even board the conformity preference
can conflict with the performance preference, and when the former is stronger than the latter, in
equilibrium the directors no longer vote informatively. In particular, even after observing a good
(bad) aspect of the new strategy, a director may vote for
(
) if he expects that other
directors’ votes are likely to lead the board to stick to the status quo (adopt the new strategy). In
other words, in an even board when the directors’ conformity preference dominates the
performance preference, they tend to vote based on their conjectures about how the other
directors will vote instead of on their own information.
To illustrate the differential effects of the conformity preference on voting in even and
odd boards, consider an odd board with n=5, and the voting decision by one of the directors, say
director 1, when all the other directors vote informatively. Because director 1 does not know the
12
other directors’ information, he thinks that the other directors’ possible voting profile can be (4,
0), (3, 1), (2, 2), (1, 3), or (0, 4), where the first (second) component in each binary is the number
of other directors who vote for a=0 (a=1). Given voting rule
, profile (2, 2)
represents a pivotal case in which director 1’s vote determines the board’s choice of action. In
this case, director 1 can always ensure his vote to be in line with the board’s decision, so the
conformity preference does not bias director 1’s choice between the two alternative actions.
For the four (even number of) remaining non-pivotal cases, the board’s choice of action is
independent of director 1’s vote. However, because these non-pivotal cases are paired, on net
conformity preference does not bias director 1’s choice between the two actions, either.
Specifically, when the other directors’ voting profile is (1, 3), the board chooses action a=1
regardless of director 1’s vote, so the conformity preference causes director 1 to bias toward
voting for a=1. But, in the case of voting profile being (3, 1), the board chooses a=0 regardless
of director 1’s vote, so director 1 is biased toward voting for a=0.
Since the directors’
information is statistically independent, director 1 views (1, 3) and (3, 1) as equally likely. 9
Thus, for the paired equal probable profiles (1, 3) and (3, 1), the conformity preference creates
exactly offsetting biases between the two actions. The same logic applies to the pair (4, 0) and (0,
4). Consequently, in an odd board conformity preference does not bias directors’ voting decision,
which will be based on their own information, and board voting fully aggregates directors’
information.
Consider next director 1’s voting decision in an even board with n=4. To director 1, the
other directors’ possible voting profiles include (3, 0), (2, 1), (1, 2), and (0, 3). Given voting rule
9
The probability for profile (3, 1) is
, while the probability for profile (1, 3) is
.
13
, profile (1, 2) is the pivotal case, for which the conformity preference does not
bias director 1’s choice between the two actions. However, among the three (odd number of)
remaining non-pivotal profiles, one profile must be unpaired, thereby creating a net bias in
director 1’s preference between the two actions. Specifically, it is clear that (3, 0) and (0, 3) are
paired equal probable profiles for which the conformity preference creates exactly offsetting
biases between the two actions. In the case of the unpaired profile (2, 1), the board adopts action
a=0 regardless of director 1’s vote, so the conformity preference biases director 1’s decision
towards voting for a=0.
When this bias is stronger than the incentive that performance
preference creates to vote informatively, director 1 votes for a=0 even after observing a good
aspect of the new strategy, rendering an equilibrium with informative voting infeasible. Thus, in
an even board, conformity preference creates systematical biases in directors’ voting decisions,
and may prevent board voting from fully aggregating directors’ information.
2.1.3. Discussion
The main intent of our model is to provide a simple and focused illustration of the
difference in information aggregation between voting in odd and even boards. Our model can be
extended in a variety of ways. For example, in our model directors can both costlessly acquire
private information about the relative merits of the two actions and costlessly participate in
voting.
It is conceivable that information acquisition may be costly as in Fedderson and
Pensendorfer (1997) and Persico (2004), and directors may have to incur private costs in
attending board meetings and participating in voting as in Borgers (2004). Furthermore, in our
model, directors proceed directly to the formal voting after they obtain information about the
performance consequences of the actions. In practice, directors may take part in pre-voting
14
communication that can be modeled as directors taking a straw poll (e.g.,Coughlan, 2000) or
engaging in cheap talk (e.g., Gerardi and Yariv, 2007; Lizzeri and Yariv, 2011).
Making the above and other extensions to our model undoubtedly will enrich the
characterization of board voting. However, these enrichments will necessarily bring into the
model additional key variables that are likely to be hard to measure empirically. The main
implications from our simple model revolve around the even-odd characteristic of boards, which
can be easily and unambiguously measured.
Ultimately, whether, on average, our model
provides a useful abstraction of board voting process and the revealed difference between odd
and even boards bears a first-order effect on the quality of board decisions are empirical issues.
Consequently, rather than seeking to provide a comprehensive model of board voting, we believe
that it is more fruitful to take our model to the data.
2.2. Model implications
Our model indicates that odd boards enhance the quality of board decision by better
aggregating directors’ information than do even boards.
Previous studies show that better
decision making by the board generally leads to increased firm value and operating performance.
For example, supporting the arguments by Lipton and Lorsch (1992) and Jensen (1993) that
small boards improve board decision by affording efficient communication, Yermack (1996)
finds that small boards are associated with greater firm value and better operating performance.
Following the previous studies, we measure firm value by Tobin’s Q and operating performance
by return-on-asset (ROA). Our model, thus, implies that firms with an odd board, on average,
derive higher Tobin’s Q and ROA than do firms with an even board.
15
Furthermore, our model suggests that directors’ conformity preference is the culprit of the
low voting efficiency of even boards.
In our empirical analysis, we measure conformity
preference by CEO tenure. The idea here is that a CEO with a longer tenure tends to have
greater influence over the board (e.g. Hermalin and Weisbach, 1998, and Coles et al, 2010).
With a more influential CEO, the directors are likely to try harder to anticipate the board’s final
decision and vote in support of that decision for two reasons. First, in instances when the board
sides with the CEO in its final decision, a dissident director can be denied future nomination for
reelection, as the influential CEO can exercise significant control over the selection of directors
(Mace, 1971; Lorsch and MacIver, 1994; Tejada 1997). Second, when the board decides against
an influential CEO, a director may also suffer a significant personal cost from dissenting from
the majority. For example, Farrell and Whidbee (2000) examine forced CEO succession, a
process that can get rather contentious especially if the CEO has normally been quite influential.
Farrell and Whidbee find that outside directors that are closely aligned with the outgoing CEO
face increased likelihood of leaving the board subsequent to the departure of the CEO. Thus,
longer CEO tenure is likely to be associated with strengthened director conformity preference.
Directors’ performance preference, on the other hand, provides a countervailing force that
mitigates the effect of conformity preference. In our empirical analysis, we use the average
director ownership as the proxy for directors’ performance preference.
This is reasonable
because directors receive more benefits from improvements in firm performance when they hold
larger financial stakes in the firms.10
10
Directors’ reputational concerns can also provide strong performance preference (Fama and Jensen, 1983).
However, it is not clear how the average reputational concern for directors can be empirically measured in a
meaningful way.
16
Taken together, our model implies that the differences in Tobin’s Q and ROA between
firms with an even board and those with an odd board increase as CEO tenure increases, and as
average director ownership decreases. In stating the above implication, we fully recognize that
CEO tenure and director ownership may influence Tobin’s Q and ROA through other effects.
For example, the larger CEO influence over the board that comes with longer CEO tenure may
lead to greater CEO entrenchment and thus managerial agency problems, which can negatively
affect Tobin’s Q and ROA. On the other hand, by better aligning directors’ interest with those of
shareholders larger director ownership can have a positive effect on Tobin’s Q and ROA.
However, there are no obvious reasons why these other effects should operate differently
between even and odd boards. The unique aspect of our model implication is that because of the
disparate influences on board voting in even and odd boards, CEO tenure and director ownership
affect Tobin’s Q and ROA differently between the two types of boards.
Finally, board voting efficiency is likely to have varying benefits to different firms. In
particular, board decision making that better aggregates directors’ information should be
especially beneficial to firms that more actively make investments whose payoffs are highly
uncertain and informationally sensitive. A primary example of such type of investments is R&D
investment.
Consequently, our model implies that the differences in Tobin’s Q and ROA
between firms with an even board and an odd board are particularly pronounced when firms
make large amounts of R&D investments. These arguments lead to the following implication.
Implication 1: All else equal, firms with an odd board are associated with higher Tobin’s Q and
ROA than are firms with an even board. These differences tend to be larger among firms with
longer CEO tenure and lower average director ownership, and among those that more heavily
engage in R&D investments.
17
Better board decision making should also improve boards’ effectiveness in corporate
governance. A key governance function of boards involves properly evaluating CEOs and acting
promptly to replace those who are performing poorly.
Prior studies show that poor CEO
performance is associated with high likelihood of CEO turnover (Coughlan and Schmidt,1985;
Warner et al,1988; Huson et al, 2001). Moreover, evidence shows that more effective boards
tend to be timelier in taking actions against under-performing CEOs, elevating the turnoverperformance sensitivity. For example, Weisbach (1988) finds that boards with more independent
directors are more likely to promptly remove poorly-performing CEOs. On the other hand,
Goyal and Park (2002) find that captured boards are slower in replacing poorly performing CEOs.
Thus, in parallel with Implication 1, our model provides the following implication regarding
CEO turnover decision.
Implication 2: All else equal, firms with an odd board show higher sensitivity of CEO turnover to
performance than do firms with an even board. This difference tends to be larger among firms
with longer CEO tenure and lower average director ownership, and among those that more
heavily engage in R&D investments.
Another important governance function of boards is to set appropriate managerial
incentives through well-designed CEO compensation. A large number of previous studies show
a close link between the quality of corporate governance and CEO pay. For example, Core et al.
(1999) and Faleye (2007) find that in firms where boards are less capable of providing effective
corporate governance, CEOs tend to receive higher compensation, and their pay tends to be less
sensitive to firm performance. Thus, in parallel with the previous implications, our model
provides the following implication.
Implication 3: All else equal, firms with an odd board are associated with lower level of CEO
compensation and higher pay-for-performance sensitivity than are firms with an even board.
18
This difference tends to be larger among firms with longer CEO tenure and lower average
director ownership, and among those that more heavily engage in R&D investments.
3. Data and Summary Statistics
Our starting point is the RiskMetrics database, which covers directors of S&P 1500
companies. We obtain CEO turnover and compensation data from Execucomp, accounting
information from Compustat, and stock price data from CRSP. Our final sample consists of 12,
075 firm-year observations from 1999 to 2009.11
[Insert Table 1 Here]
Table 1 presents descriptive statistics of sample firms. All dollar values are in 2009
dollars, and all continuous variables are winsorized at the 1st and 99th percentiles. The median
board of our sample firms has around 9 directors, 71.4% of which are outside directors. In a
median firm, the median dollar-value director ownership is 6.4 million.
The median firm is quite large with market value of equity of $1,685 million. The sample
firms have a median ROA of 8.9%, and annual stock return of 5.1%. Moreover, the median firm
has a leverage of 56.1%, and makes considerable investment with Capex at 3.9% of the total
sales. On average, about 80% of the CEOs are also the chairman of the board, and their median
tenure is 5 years. The median firm has a Tobin’s Q of 1.5 and pays $3.3 million annual
compensation to the CEO.
We also split the sample into subsamples of firms that respectively have an even board
and an odd board. There are 6,462 (54%) odd boards and 5,613 (46%) even boards. These
11
We start from 1999 because the director ownership information is available in RiskMetrics from 1998 and control
variables are lagged by one year.
19
numbers indicate a greater but not significantly larger likelihood of odd boards, and, thus, might
appear to be inconsistent with the hypothesized benefits of odd boards. Caution needs be
exercised in jumping to this conclusion, however. As we pointed out earlier, a firm’s choice
between an even and odd board represents the solution to the constrained optimization problem
relating to the design of board structure (Cole et al, 2010; Adams et al, 2010). To the extent a
firm cannot freely and instantly change the external environment it resides in, an even board may
indeed be the firm’s best solution to the constrained optimization problem it faces.
Comparisons between the subsamples of firms with even and odd boards show several
differences between the two types of firms. Specifically, in comparison to firms with an even
board, those with an odd board have smaller boards, fewer independent directors, are younger,
have simpler corporate structure with a smaller number of business segments, use less leverage,
and have slightly longer CEO tenure. Comparisons based on median show that firms with an odd
board are smaller in size, as measured by the market value of equity. Furthermore, consistent
with our model implications, firms with an odd board have higher Tobin’s Q and ROA, and pay
less to their CEOs, than do firms with an even board.
4. Empirical Results
4.1. Firm Value
We begin our investigation of the ramifications of odd boards by examining firm value, as
measured by Tobin’s Q. The results are reported in Table 2. In all of the regression models we
control for an extensive set of board, firm, and CEO characteristics. We also control for year
fixed effects and, except for firm fixed effects regression, industry fixed effects. Here and
throughout our analysis, all standard errors are adjusted for heteroscedasticity and firm clustering.
20
[Insert Table 2 Here]
In the baseline regression model, we focus on Odd , which is a dummy variable that takes
a value of one if the firm has an odd board and zero otherwise. We calculate Odd dummy based
on the board structure at the end of the previous fiscal year, since the impact of board decisions
are likely to take some time to show up in firm performance. Likewise, we use lagged values for
all the other independent variables. In unreported tests, we have also experimented with using
the contemporaneous variables, and find that results remain unchanged.
Column (1) of Table 2 shows that the coefficient of the Odd dummy is positive at 0.060
and significant at the 1% level. Thus, in consistency with Implication 1 of our model, firms with
an odd board have on average a significantly higher Tobin’s Q than do firms with an even board.
Column (1) also shows that the coefficient of big board dummy, which takes a value of one if
board size is above sample median size and zero otherwise, is negative at -0.17 and significant at
the 1% level. Thus, consistent with Yermack (1996), board size bears a negative effect on firm
value. Similar to Hermalin and Weisbach (1991), Column (1) shows that the proportion of
independent directors does not have a significant effect on Tobin’s Q.
Our theoretical arguments suggest that the difference in Tobin’s Q between firms with an
odd board and those with an even board increases as CEO tenure (the proxy for directors’
conformity preference) increases. To test this prediction, in the second regression model we
include the interaction term between the Odd dummy and CEO tenure.
Consistent with
Implication 1, Column (2) shows that the coefficient of the interaction term is positive and
significant at the 1% level.
21
Furthermore, our theoretical arguments suggest that the difference in Tobin’s Q between
firms with an odd board and those with an even board narrows when the directors’ average
ownership (the proxy for directors’ performance preference) increases. In Column (3), we
include the interaction between the Odd dummy and average director ownership. The coefficient
of the interaction term is negative and significant at the 5% level.
Thus, consistent with
Implication 1 of our model, this result indicates that the contrast in Tobin’s Q between even and
odd boards is more evident when directors have lower ownerships.
Finally, our theoretical arguments suggest that improved board voting efficiency is likely
to be especially beneficial to firms that heavily engage in R&D investments. To test for this
prediction, we interact the Odd dummy with R&D expenditure in Column (4).12 Consistent with
Implication 1, the interaction term is positive and significant at the 1% level.
The last two regressions in Table 2 provide additional tests of the findings. First, to
account for possible biases due to omitted variables that are associated with firm-specific and
time-invariant characteristics, we perform a firm fixed-effect regression by including fixed-effect
dummies in the baseline regression. The result in column (5) shows that the Odd dummy
remains positive and significant.
Second, the univariate comparison in Table 1 shows that odd boards are generally smaller
in size than are even boards. While we have tried to control for board size using the big board
dummy, this control may nevertheless be imperfect. In light of the findings in Yermack (1996),
it is important to further verify that the even-odd effect we document is not simply a reflection of
the board-size effect. To more precisely control for board size, we select boards with 6, 7, 8
12
To address the concern that firms in financial and utility industries tend to have very small R&D intensities, we
exclude all the financial and utility firms from our sample and re-do all the regressions. The results are largely the
same.
22
directors, with 10, 11, 12 directors, with 14, 15,16, and so on. The idea here is that in the group
of boards with 6, 7, and 8 directors, the even boards (with 6 and 8 directors) have a weighted
average board size close to 7, so the comparison between even and odd boards within the group
is conducted with closely matched board size. Similar logic applies to the comparison in the
group of boards with 10, 11, and 12 directors, and to those in the other groups.
We then rerun the baseline regression in the sample of the selected firms. To account for
the differences in the average sizes of the groups of boards, we also include a set of group
dummies in the regression. The Odd dummy in this size-matched regression, therefore, measures
the average difference between odd and even boards across the groups. The regression result is
reported in Column (6) of Table 1. As Column (6) shows, the Odd dummy remains significant at
5% level and positive at 0.046, suggesting a marginal effect of over 4% increase in market value
when a firm switches from an even board to an odd board.
In an unreported test, we repeat the above size-matched regression by selecting boards
with 4, 5, 6 directors, with 8, 9, 10 directors, and so on. We find that the Odd dummy remains
significant and is positive at 0.041. Note that we cannot combine the two regressions as boards
with 6 directors will belong to both the group with 4, 5, 6 directors and the group with 6, 7, 8
directors, cofounding the interpretation of the Odd dummy. The same problem applies to boards
with 8 directors, and so on. In the rest of the paper, when referring to size-matched regression,
we report the one where the boards are selected as in the previous regression. However, each
time in the unreported test we also verify that the result remains similar when the boards are
selected as in the second regression.
23
Taken together, our findings show a pronounced and robust difference in Tobin’s Q
between firms with an even board and those with an odd board, and this difference exhibits
cross-sectional variations that are consistent with Implication 1 of our model.
4.2. Firm Operating Performance
We compare ROA between firms with an even board and those with an odd board. Table
3 presents the regression results. We include in the regressions the same set of control variables
as in Table 2.
[Insert Table 3 Here]
Column (1) of Table 3 shows that the coefficient of the Odd dummy is 0.251 and
significant at the 1% level. Thus, in comparison to firms with an even board, those with an odd
board deliver significantly better operating performance.
Next, we respectively include the interaction term between the Odd dummy with CEO
tenure and with director ownership in Columns (2) and (3). We find that the coefficient of Odd
× (CEO tenure) is significantly positive in Column (2), while the coefficient of Odd × (Director
ownership) is significantly negative in Column (3). When we include the interaction term
between the Odd dummy with R&D expenditure in Column (4) we find that the interaction term
is positive and significant at the 1% level. Finally, we perform the fixed-effect and size-matched
regressions respectively in Columns (5) and (6). We find that in each of the regressions, the
coefficient on the Odd dummy remains positive and significant.
In sum, the analysis of firm operating performance provides results that are consistent
with Implication 1 of our model.
24
4.3. CEO Turnover
In this subsection, we compare CEO turnover decision and, in particular, CEO turnoverperformance sensitivity between firms with an even board and those with an odd board. We
estimate the probability of CEO turnover using logit regression, where the dependent variable is
the CEO turnover indicator, which equals one if the CEO is in his last year in office, and zero
otherwise. Based on the recent findings by Kaplan and Minton (2010) and Jenter and Lewellen
(2010), we do not separate turnover events into forced and unforced ones. Kaplan and Minton
(2010) show that the determinants of forced turnovers are similar to those of voluntary turnovers,
because turnovers labeled as unforced using the algorithms in, for example, Parrino (1997), may
not be de facto voluntary. Furthermore, Jenter and Lewellen (2010) suggest that treating all
turnovers equally can avoid the bias caused by misclassifying forced ones as voluntary ones.13
[Insert Table 4 Here]
Table 4 presents the results of the logit estimation. The key explanatory variables are the
Odd dummy and firm stock return over the previous three years. We use past three-year
performance because using short-term performance (e.g., performance in the previous 12 or 24
months) tends to under-estimate turnover-performance sensitivity (Jenter and Lewellen (2010)).
Looking at Panel A of Table 4, Column (1) shows that the coefficient of Odd dummy is
0.170 and significant at the 1% level, indicating that firms with an odd board are more likely to
experience CEO turnover relative to firms with an even board. Moreover, consistent with
findings in the prior studies, the coefficients of the firm’s stock return performance is negative
and significant at the 5% level, indicating that CEO turnover becomes more likely subsequent to
poor firm performance.
13
As a robustness check, we delete events where CEO departures are likely to be due to retirements, namely CEOs
who are either over 60 or over 65. We find similar results as in the full sample.
25
To examine the difference in the performance sensitivity of CEO turnover between firms
with an even board and those with an odd board, in the second regression we include the
interaction between the Odd dummy with past stock performance. Column (2) shows that the
coefficient on the interaction term is negative and significant. This result indicates that firms
with an odd board are more likely to fire CEO in response to poor firm performance than do
firms with an even board, in consistency with Implication 2 of our model.
We control for firm fixed effects in Column (3) and run size-matched regression in Column
(4), and find that in both instances the coefficient of Odd ×(past 3-year return) remains negative
and significant.14
In Panel B of Table 4, we conduct sub-sample analysis on CEO turnover-performance
sensitivity. In the first two columns of Panel B, we divide the sample based on the sample
median CEO tenure. We find that the coefficient on Odd × (past 3-year return) is -0.112 (-0.196)
for the subsample with short (long) CEO tenure, and is insignificant (significant at the 1% level).
Thus, in terms of both economic magnitude and statistical significance, the effect of odd boards
in strengthening turnover-performance sensitivity is greater for firms with longer CEO tenure,
consistent with Implication 2 of our model.
In Columns (3) and (4) of Panel B, we split our full sample into two subsamples based on
the sample median director ownership. The coefficient of the interaction term, Odd × (past 3year return), is -0.178 in the low director ownership subsample, and -0.091 in the high director
ownership subsample. Thus, in terms of the economic significance, the difference in turnover-
14
Given that we are using 3-year past stock performance, we conduct robustness checks by focusing on the
subsample of CEOs who stay in office for at least three years, and our results are largely the same.
26
performance sensitivity between firms with an odd board and those with an even board is more
pronounced when director ownership is lower, consistent with Implication 2 of our model.
In the last two columns of Panel B, we conduct subsample analysis based on R&D expense.
The coefficient on Odd × (3-year return) is -0.177 (-0.166) for the high (low) R&D subsample,
and is significant at the 5% (10%) level. Thus, in terms of both economic magnitude and
statistical significance, the effect of odd board in enhancing CEO turnover-performance
sensitivity is more pronounced for the high R&D firms, consistent with Implication 2 of our
model.
4.4. CEO Compensation
In this subsection, we compare both the level of CEO pay and the pay-for-performance
sensitivities between firms with an odd board and those with an even board. Table 5 contains the
results of this analysis. To alleviate the influence of extreme observations, we use the natural
logarithm of total compensation as the dependent variable in the regressions.15
[Insert Table 5 Here]
The first regression model examines the total CEO compensation (Execucomp item
TDC1). Column (1) of Panel A in Table 5 shows that the coefficient on the Odd dummy is 0.042 and is significant at the 5% level, indicating that CEOs of firms with an odd board tend to
receive around 4% less total compensation. On the other hand, the coefficient on past 3-year
stock return is positive and significant, indicating that good past performance leads to high
compensation to CEO.
15
We conduct robustness check by focusing on the subsample of CEOs who stay in office for at least three years;
our results are the same.
27
A possible reason behind the lower total compensation might be that CEO compensation
for firms with an odd board has lower performance sensitivity so that less pay is needed to
compensate CEOs for bearing the compensation risk. To examine this possibility, in Column (2)
we look at the pay-for-performance sensitivity. Column (2) shows that the coefficient of the
interaction between the Odd dummy and past 3-year stock return is positive and significant.
Thus, in comparison to firms with an even board, CEO compensation of firms with an odd board
is more closely tied to firm performance. In sum, in consistency with Implication 3 of our model
firms with an odd board have lower total CEO compensation but higher pay-for-performance
sensitivity.
We control for firm fixed effects in Column (3) and run size-matched regression in
Column (4). In both instances, we continue to find that firms with an odd board pay less to their
CEOs (though the Odd dummy loses significance in the firm-fixed effect regression) and have
stronger CEO pay-for-performance sensitivity than do firms with an even board.
In Panel B of Table 5, we conduct subsample analysis on CEO compensation, and the
results are generally consistent with Implication 3 of our model. In Columns (1) and (2), we find
that the coefficient on Odd× (past 3-year return) is -0.004 (0.045) and is insignificant
(significant) for the subsample with short (long) CEO tenure. In Columns (3) and (4), we divide
the sample based on the median director ownership. The coefficient on the interaction term
Odd× (past 3-year return) is significantly positive in the low director ownership subsample, but
is negative and insignificant in the high director ownership subsample. Finally, in Columns (5)
and (6), we divide the sample based on the median R&D expenditure. The coefficient on Odd×
(past 3-year return) is significantly positive in the high R&D subsample, but is close to zero and
insignificant in the low R&D subsample.
28
Taken together, the results in this subsection show that consistent with Implication 3, odd
boards are associated with lower CEO compensation and higher pay-for-performance sensitivity.
Furthermore, the higher pay-for-performance sensitivity of firms with an odd board is especially
evident when CEOs have long tenures but directors have low ownerships, and when firms
actively engage in R&D investments.
5. Additional Tests
5.1. The dependence of even-odd effects on board size
In the regression analysis so far, we have focused on the Odd dummy variable as the
measure of the average even-odd effects and used the big board dummy to control for board size.
Intuitions suggest that the significance of the even-odd effects is likely to diminish as board size
increases. Specifically, extending our model of voting in Section 2, suppose that directors face
varying costs to obtain information about the suitability of the new strategy or to participate in
board voting.
Since a director’s chance of being pivotal in voting declines as board size
increases, in large boards directors facing high costs of information acquisition or voting have
reduced incentives to acquire information (e.g., Persico, 2004), or show up for voting (Adams and
Ferreira, 2008a, b). Thus, with odd boards voting outcomes may still fail to capture sufficient
information. As a result, the difference in the voting efficiency between even and odd boards
narrows when board size increases.
[Insert Table 6 Here]
We formally test the above prediction in Table 6. In Columns (1) and (2), the dependent
variables are Tobin’s Q and ROA, respectively.
In both columns, the coefficient on the
interaction term, Odd×(Bigboard dummy), is negative and significant, indicating that the
29
differences in Tobin’s Q and ROA between firms with an odd board and those with an even
board abate when board size increases. These results are consistent with Figure 1 of Yermack
(1996).
Next, we divide the sample based on the median of board size and examine CEO turnover
and CEO compensation in the respective subsamples. The results on CEO turnover are in
Columns (3) and (4). We find that the interaction between Odd dummy and firm’s past stock
performance is significantly negative in the subsample of firms with small boards, but is not
significant in the subsample of firms with large boards. Similarly, from the results on CEO
compensation in Columns (5) and (6), the coefficient on Odd dummy is significantly negative,
and that on the interaction between Odd dummy and past stock performance is significantly
positive, only in the subsample of firms with below median board size. These results reveal that
the difference in CEO turnover and CEO compensation between firms with even and odd boards
declines as board size increases.
Overall, the results in Table 6 reveal that the even-odd effects of board are most
pronounced in small boards. In addition, these results are consistent with directors’ costs of
information acquisition and voting presenting a significantly negative effect on the voting
efficiency of large boards.
5.2. The treatment regression
In the previous regression models, we have tried to mitigate potential endogeneity
problems by explicitly including in the models a comprehensive list of control variables and by
running firm fixed-effect regressions. To further substantiate our results, we conduct a treatment
regression analysis.
30
According to Table 1, a firm’s decision to have an odd board has its own determinants. It is
well known that if self-selecting firms are not random subsets of population, the usual OLS
estimators will not be consistent (Heckman (1979)). To correct for the potential selection effect,
the odd board effect can be modeled as follows:
In the equation above, X is a list of control variables. The coefficient of key interest is
.
indicates the latent propensity of a firm having odd board. For the purpose of
identification, we include instruments variables
that affect a firm’s propensity of having odd
board, but do not directly affect firm performance and corporate governance. The odd dummy is
allowed to be endogenous in the sense that corr(
. The positive (negative) correlation
suggests that the firm performance and corporate governance practice are better (worse) based on
the unobservable heterogeneity. Therefore, the coefficient estimate on odd dummy or on the
interaction of odd dummy × 3 year return in OLS or logit regression is upward (downward)
biased where the endogeneity is not properly controlled.
To allow for time-varying unobserved heterogeneity across firms, we employ the treatment
regression using the maximum likelihood estimator developed by Maddala (1983, Chapter 5),
where the Odd dummy is considered endogenous.
We use two instrumental variables. The first is the prevalence of odd boards in the firm’s
industry, which is computed as the ratio of the number of companies with an odd board to the
31
total number of companies in the firm’s industry. The second is the prevalence of odd boards in
the state in which the firm is located, which is measured as the ratio of the number of companies
with an odd board to the total number of companies in the firm’s state. Since peer firms in the
same industry or geographic region tend to face similar product market, factor market, and legal
environment, an individual firm is likely to share a similar propensity to have an odd board as the
peer firms. Supporting this view, Knyazeva, Knyazeva, and Masulis (2009) provide evidence
that a firm’s board structure is significantly influenced by the same-industry firms in the same
state. Thus, the instruments are likely to satisfy the relevance condition. Furthermore due to the
exogeneity of industry(state)-level variables, there are no clear reasons to believe that the
instruments directly affect firm performance and corporate governance practice after controlling
for various firm characteristics. Thus, the instruments are also likely to satisfy the exogeneity
condition.
[Insert Table 7 Here]
The results are reported in Table 7. We find that in the first-stage probit regression, the
coefficient estimates on industry odd board prevalence and state odd board prevalence are 2.549
and 2.695, respectively, and are significant at the 1% level. In the second-stage OLS regression
of Tobin’s Q, we find that the coefficient on the odd dummy is 0.351 and is significant at the 5%
level, indicating that after controlling for self-selection bias, the effect of the odd board on the
firm value is still positive. In Column (3) we report the second-stage OLS regression ROA and
find that, after controlling for self-selection bias, the coefficient of Odd dummy is still positive
and significant at the 1% level. In Columns (4) and (5), we report the results of the second-stage
logit regressions of CEO turnover and compensation, respectively. The coefficients on the
interaction Odd×3-year return are significantly negative in the turnover regression, and
significantly positive in the compensation analysis.
32
In conclusion, the results of treatment regression are generally consistent with those of
OLS and logit regression, suggesting that our results are robust to controlling for the endogeneity
problem.
5.3. The choices of switching to an odd board
In evaluating the even-odd effects of board, we have so far used pooled regressions. To
gain further insights about the effects, we explore the time-series aspect of our sample, focusing
in particular on instances when firms switch from even boards to odd boards. Given that the
advantage of odd boards over even boards in aggregating directors’ information is particularly
pronounced when CEO tenure is longer, director ownership is lower, and R&D expenditure is
higher, we expect that firms are more likely to switch to an odd board in response to increase in
CEO tenure and R&D expenditure, and decrease in director ownership.
[Insert Table 8 Here]
In our sample, there are 2,187 firm-year observations where an even board changes to an
odd board. In Table 8, we apply propensity score matching method to investigate what drive
these changes. The matching procedure that we employ is a one-to-one nearest neighbor
matching with replacement (Heckman, et al. (1997)). In particular, we start with a probit
regression, using board size, prior-year stock return, prior-year ROA, Ln(MV), leverage, and
return volatility as the independent variables, and the indicator variable on whether a firm
switches to an odd board as the dependent variable. Then using the predicted probabilities,
propensity scores, from the estimated probit regressions, we match to each firm that switches to
an odd board, a firm without such changes that minimizes the absolute value of the difference
between propensity scores. Column (3) of Table 8 indicates that, compared to the matched
sample, firms that switch to odd boards are associated with greater increase in CEO tenure and
R&D expenditure, and greater decrease in average director ownership.
33
In sum, Table 8 shows that firms have a tendency to switch to odd boards when the
benefits associated with odd boards are larger.
6. Conclusions
This paper examines the voting efficiency of corporate boards. We develop a simple
model of board voting that predicts that odd boards enhance voting efficiency by enabling better
aggregation of directors’ information relative to even boards. Our empirical analysis provides
evidence supporting the implications of the model. In particular, we find that in comparison to
firms with an even board, those with an odd board have higher firm values and better operating
performance. Moreover, our analysis reveals that odd boards strengthen corporate governance
by increasing both CEO turnover-performance sensitivity and CEO pay-for-performance
sensitivity. Finally, the cross-sectional variations in the differences in firm value, operating
performance, and the corporate governance measures, between the two types of boards display
patterns that are consistent with greater voting efficiency of odd boards being the source of these
differences. Taken together, our findings help establish a link between board composition and
board voting efficiency.
34
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37
Appendix A: Variable Definitions
This appendix provides a detailed description of the construction of all the variables used in the tables.
Variable
Definitions
Odd dummy
One if an odd number of directors are on board, and zero otherwise.
Big board dummy
One if the number of directors is greater than the sample median and zero
otherwise.
Independent director proportion
The ratio of the number of independent directors over the total number of
directors.
Director ownership
The average number of shares owned by directors times the stock price at
the end of fiscal year.
Tobin’s Q
ROA
Return
Market value of assets (total book value of assets minus book value of
equity plus market value of equity) over book value of assets.
Return on total assets, calculated as (Operating income before depreciation
– Net interest expense – Cash taxes – Change in net working capital) /
Total assets.
The buy-and-hold return on the firm’s stock for the prior twelve months.
3-year return
The buy-and-hold return on the firm’s stock for the prior thirty-six months.
Sale growth
The ratio of sales over previous year sales.
Capx/sale
Capital expenditure divided by sale.
R&D/sale
Research and development expense divided by sale.
MV
Leverage
The number of shares outstanding times the stock price at the end of fiscal
year.
The book value of total asset minus book value of equity divided by the
book value of total assets.
No. of segments
Firm age
Return volatility
CEO duality dummy
CEO tenure
CEO total pay
Turnover dummy
The number of segments the firm has.
The number of years since the firm first appears in CRSP.
The standard deviation of monthly stock return for the prior sixty months.
One if the CEO is also the chairman of the board and zero otherwise.
The number of years since the person became CEO.
The variable TDC1 in Execucomp, which consists of salary, bonus, value
of restricted stock granted, value of options granted (using Black-Scholes),
long-term incentive payouts, and other compensation.
One if the CEO is in his last year in office, and zero otherwise
Industry odd-number board prevalence
The ratio of the number of firms with the odd board in the same industry to
the total number of firms in that industry.
State odd-number board prevalence
The ratio of the number of firms with the odd board in the same state to the
total number of firms in that state.
38
Appendix B
Proof of Proposition 1: To examine if informative voting is an equilibrium strategy, consider
director 1’s voting decision when all the other directors follow the informative voting strategy.
In the following, we define a voting profile
as an outcome in which among directors
other than director 1, a
vote for a=1.
number vote for a=0 and
Suppose first that n is an odd number. Given voting rule
, director 1’s
voting strategy is determined by considering the pivotal case ((n-1)/2, (n-1)/2), i.e., the case in
which his vote changes the board’s choice of action. Since the other directors follow the
informative voting strategy, in this pivotal case the other directors’ collective information
. Thus, when
(
, director 1 views the new strategy as providing a
strictly positive (negative) expected performance improvement. Consequently, based on the
performance preference, director 1 strictly prefers to follow the informative voting strategy.
To see the effect of conformity preference on director 1’s voting decision, note first that
in the pivotal case director 1 can always ensure himself to be in conformity with the board’s
decision irrespective of which action he votes for. Thus, in the pivotal case the conformity
preference leaves director 1 indifferent between voting for a=1 and for a=0. Consider next a
non-pivotal case
, where
. If
, the board will choose a=1 independent of
director 1’s vote. In this case, by voting for a=1 director 1 avoid the disconformity cost.
However, by voting for a=1, director 1 will incur the disconformity cost if the voting profile for
the other directors is
, in which case the board chooses action a=0. Conversely, by
voting for a=0, director 1 avoids the disconformity cost in the case of
in the case of
. Since the
, but incurs the cost
s are uncorrelated, director 1 view the profiles
39
and
as equally likely irrespective of what
he observes. Thus, these two paring non-
pivotal case leaves director 1 indifferent between voting for a=1 and for a=0. When n is an odd
number, there are n-1 directors other than director 1. These n-1 directors produce a total of n
possible voting profile, namely, (n-1, 0),…, (0, n-1). Excluding the pivotal case, there is an even
number ((n-1)) of non-pivotal cases. Thus, each non-pivotal case
be uniquely paired with an equally likely non-pivotal case
, where
, can
. Consequently, in all the
non-pivotal cases, conformity preference also leaves director 1 indifferent between voting for
a=1 and for a=0. In sum, for an odd board, the conformity preference does not produce a strict
preference for director 1 between the two actions.
Taken together, the above discussions suggest that when other directors follow
informative voting strategy, Director 1 also prefers to adopt the same strategy. Thus, in an odd
board, informative voting strategy is an equilibrium strategy for the directors.
Suppose next that n is an even number. If the voting rule
director 1 is
pivotal when the voting profile for the other directors is ((n/2)-1, n/2). Since the other directors
follow the informative voting strategy, in this pivotal case the other directors’ collective
information
. Thus, if
(
), director 1 views the new strategy as
providing a strictly positive (zero) expected performance improvement, and based on
performance preference director 1 strictly (weakly) prefers to vote for a=1 (a=0).
Consider next the effect of conformity preference on director 1’s voting decision. In the
pivotal case, the conformity preference leaves director 1 indifferent between the two actions.
Consider the (n-1) non-pivotal cases. Since n is even, there is an odd number of non-pivotal
cases. Consequently, there is one non-pivotal case that does not have an equally probable paring
40
non-pivotal case. It is easy to see that this unpaired non-pivotal case corresponds to the profile
(n/2, (n/2)-1). Given this profile, the board will adopt action a=0, so director 1 strictly prefers to
vote for a=0. Combining the pivotal and the non-pivotal cases, the conformity preference
produces a strict preference for director 1 to vote for a=0.
The discussion indicates that when n is even, the conformity preference reinforces the
performance preference, so that upon observing
a=-1. However, when director 1 observes
director 1 strictly prefers to vote for
conformity preference conflicts with the
performance preference. In this case, by voting for a=1 and ensuring that the board adopts a=1
in the pivotal case ((n/2)-1, n/2), director 1 derives an expected gain of
However, voting for a=1 imposes an expected discomformity cost due to non-pivotal case ((n/2)1, n/2) of
. If
, director 1 is better off voting for a=1 after getting
, so informative voting is an equilibrium strategy.
In contrast, if
, the
discomformity cost dominates the gain from enabling better board decision, so director 1 strictly
prefers to vote for a=1 upon observing
. It follows therefore that if
voting cannot be an equilibrium strategy.
41
informative
Table 1. Summary Statistics
The sample consists of 6,462 firm-year observations with an odd number of directors and 5,613 firm-year observations with an
even number of directors from 1999 to 2009. We collect the information of the board of director from RiskMetrics, accounting
information from Compustat, stock price data from CRSP, and CEO compensation and turnover information from ExecuComp.
Definitions of all variables are provided in the appendix. All dollar values are in 2009 dollars. All continuous variables are
winsorized at the 1st and 99th percentiles. Superscripts ***, ** and * denote statistical significance at the 1%, 5% and 10%
levels, respectively.
Full sample
(N=12,075)
Number of director
Mean
9.3
Median
9.0
Odd-number
subsample (A)
(N=6,462)
Mean
Median
9.2
9.0
Independent director proportion (%)
68.7%
71.4%
68.4%
71.4%
69.0%
71.4%
-0.60%**
0.00%**
Director ownership ($M)
27.6
6.4
26.9
6.3
28.4
6.4
-1.425
-0.122
Stock return (%)
8.2%
5.1%
8.4%
5.1%
8.1%
5.2%
0.30%
-0.10%
Sale growth (%)
111.3%
108.4%
111.1%
108.4%
111.4%
108.3%
-0.33%
0.10%
Capex (%)
7.2%
3.9%
7.2%
3.9%
7.3%
4.0%
-0.08%
-0.08%
R&D (%)
4.1%
0.0%
4.1%
0.0%
4.1%
0.0%
-0.04%
0.00%
MV($M)
7,381.6
1,685.3
7,265.3
1,612.0
7,515.6
1,773.8
-250.3
-161.8***
Leverage (%)
55.1%
56.1%
54.8%
56.0%
55.5%
56.1%
-0.69%*
-0.07%
No. of segments
2.5
2.0
2.5
2.0
2.5
2.0
-0.053*
0.000*
Firm age
24.3
18.0
23.9
17.0
24.8
19.0
-0.809**
-2.000**
Return volatility (%)
12.1%
10.7%
12.1%
10.7%
12.1%
10.7%
-0.01%
0.07%
CEO duality
0.8
1.0
0.8
1.0
0.8
1.0
-0.002
0.000
CEO tenure
6.8
5.0
6.9
5.0
6.7
5.0
0.215*
0.000**
Tobin's Q
1.9
1.5
1.9
1.5
1.8
1.5
0.043**
0.005
ROA (%)
8.8%
8.9%
8.9%
9.0%
8.7%
8.8%
0.2%
0.2%*
CEO turnover
0.112
0.000
0.122
0.000
0.101
0.000
0.021***
0.000***
CEO total pay ($K)
5,636
3,284
5,537
3,175
5,752
3,372
-215.7
-196.9***
42
Even-number
subsample (B)
(5,613)
Mean
Median
9.4
10.0
Mean
-0.162***
Median
-1.000***
Test of difference:
(A)-(B)
Table 2. Firm Value and Odd Board
The sample consists of 6,462 firm-year observations with an odd number of directors and 5,613 firm-year observations
with an even number of directors from 1999 to 2009. The dependent variable is Tobin’s Q, calculated as market value
of assets (total book value of assets minus book value of equity plus market value of equity) over book value of assets.
Odd dummy is equal to 1 if the number of directors on the board is an odd number and 0 otherwise. All other controls
are defined in Appendix A. Two-digit SIC code dummies are used to control for industry fixed effects. In Columns (1)(4), we control for industry fixed effects. In Column (5) we control for the firm fixed effects. In Column (6) we control
for the board size dummies. The p-values in parentheses are based on standard errors adjusted for heteroscedasticity
and firm clustering. Superscripts ***, ** and * denote statistical significance at the 1%, 5% and 10% levels,
respectively.
Oddt-1
(1)
(2)
(3)
(4)
(5)
(6)
0.060***
(0.001)
0.010
(0.667)
0.007***
(0.006)
0.074***
(0.000)
-0.030
(0.155)
0.027*
(0.088)
0.046**
(0.048)
2.233***
(0.000)
-0.194***
(0.000)
0.000
(0.901)
1.676***
(0.000)
0.250***
(0.000)
5.409***
(0.000)
0.038
(0.520)
-0.141
(0.469)
0.214***
(0.000)
0.165***
(0.000)
-0.255**
(0.043)
-0.058***
(0.000)
-0.033
(0.139)
2.243***
(0.000)
-0.073**
(0.019)
0.004*
(0.097)
0.519***
(0.001)
-0.084**
(0.016)
-0.001
(0.548)
1.548***
(0.000)
0.268***
(0.000)
1.123***
(0.005)
0.026
(0.575)
-0.079
(0.113)
-0.417
(0.439)
0.012
(0.682)
-0.173
(0.232)
-0.027**
(0.011)
-0.305***
(0.000)
1.075**
(0.029)
0.017
(0.570)
-0.001
(0.687)
2.652***
(0.000)
-0.001
(0.260)
1.904***
(0.000)
0.254***
(0.000)
3.863***
(0.000)
0.107
(0.191)
-0.194
(0.368)
3.814***
(0.000)
0.160***
(0.000)
-0.154
(0.296)
-0.055***
(0.000)
-0.024
(0.335)
0.549
(0.221)
-0.074**
(0.028)
0.002
(0.413)
1.095***
(0.000)
Odd t-1×CEO tenure t-1
Odd t-1× Director ownership t-1
-0.110**
(0.034)
Odd t-1×R&D t-1
Big board dummy t-1
Independent director proportion t-1
Director ownership t-1
Return t-1
ROA t-1
Sale growth t-1
Capex t-1
R&D t-1
Ln(MV) t-1
Leverage t-1
Segment number t-1
Ln(firmage) t-1
Volatility t-1
Duality t-1
CEO tenure t-1
Constant t-1
-0.170***
(0.000)
-0.000
(0.629)
1.819***
(0.000)
0.269***
(0.000)
6.125***
(0.000)
0.035
(0.549)
-0.186
(0.332)
3.923***
(0.000)
0.133***
(0.000)
-0.042
(0.743)
-0.049***
(0.000)
-0.029
(0.177)
1.080**
(0.010)
-0.055*
(0.065)
0.003
(0.151)
0.530***
(0.000)
-0.169***
(0.000)
-0.000
(0.631)
1.802***
(0.000)
0.270***
(0.000)
6.118***
(0.000)
0.036
(0.539)
-0.181
(0.345)
3.921***
(0.000)
0.132***
(0.000)
-0.044
(0.736)
-0.049***
(0.000)
-0.029
(0.178)
1.075**
(0.011)
-0.055*
(0.063)
-0.000
(0.848)
0.559***
(0.000)
43
-0.217***
(0.000)
-0.001
(0.434)
0.203***
(0.002)
0.258***
(0.000)
3.363***
(0.000)
0.154**
(0.031)
-0.064
(0.752)
0.367***
(0.000)
0.216***
(0.000)
-0.435***
(0.001)
-0.067***
(0.000)
-0.037
(0.127)
2.270***
(0.000)
-0.096***
(0.003)
0.005**
(0.046)
0.453***
(0.007)
Year FE
Industry FE
Firm FE
Board size dummies
Observations
Adj R2
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
12075
45%
12075
45%
44
12075
44%
12075
43%
12075
76%
8882
41%
Table 3. Operating Performance and Odd Board
The sample consists of 6,462 firm-year observations with an odd number of directors and 5,613 firm-year observations
with an even number of directors from 1999 to 2009. The dependent variable is ROA, where ROA is calculated as
(Operating income before depreciation – Net interest expense – Cash taxes – Change in net working capital) deflated
by total asset. Odd dummy is equal to 1 if the number of directors on the board isan odd number and 0 otherwise. All
other controls are defined in Appendix A. Two-digit SIC code dummies are used to control for industry fixed effects.
In Columns (1)-(4), we control for industry fixed effects. In Column (5) we control for the firm fixed effects. In
Column (6) we control for the board size dummies. The p-values in parentheses are based on standard errors adjusted
for heteroscedasticity and firm clustering. Superscripts ***, ** and * denote statistical significance at the 1%, 5% and
10% levels, respectively.
Odd t-1
(1)
(2)
(3)
(4)
(5)
(6)
0.251***
(0.007)
-0.102
(0.729)
0.049*
(0.098)
0.459
(0.164)
0.294
(0.261)
0.240*
(0.086)
0.179*
(0.090)
1.915***
(0.000)
-0.575
(0.230)
0.012
(0.341)
-0.578
(0.303)
2.106***
(0.000)
0.852***
(0.000)
-4.686*
(0.096)
0.785
(0.773)
-6.473***
(0.000)
0.445***
(0.004)
-0.672
(0.664)
0.068
(0.461)
-0.287
(0.120)
-9.066**
(0.039)
-0.519***
(0.001)
0.012
(0.579)
4.344*
(0.077)
-0.592
(0.332)
-0.015
(0.249)
-0.177
(0.231)
2.319***
(0.000)
0.300***
(0.000)
-5.692
(0.354)
-0.780
(0.769)
-11.075*
(0.053)
0.913
(0.285)
-3.141*
(0.061)
-0.014
(0.884)
-0.815
(0.295)
-0.511
(0.928)
-0.017
(0.941)
-0.016
(0.415)
10.590**
(0.027)
-0.002
(0.678)
0.936
(0.213)
1.894***
(0.000)
0.530***
(0.000)
-0.370
(0.358)
2.843*
(0.057)
-3.744*
(0.056)
0.416***
(0.000)
-0.126
(0.815)
-0.147***
(0.001)
0.005
(0.960)
-7.691***
(0.000)
-0.398**
(0.010)
0.009
(0.381)
1.973
(0.154)
Odd t-1×CEO tenure t-1
Odd t-1× Director ownership t-1
-2.698**
(0.049)
Odd t-1×R&D t-1
Bigboard dummy t-1
Independent director proportion t-1
Director ownership t-1
Return t-1
ROA t-1
Sale growth t-1
Capex t-1
R&D t-1
Ln(MV) t-1
Leverage t-1
Segment number t-1
Ln(firmage) t-1
Volatilityt-1
Dualityt-1
CEO tenuret-1
Constant
-0.323**
(0.025)
-0.003
(0.427)
0.209
(0.797)
1.821***
(0.000)
0.520***
(0.000)
-0.605*
(0.094)
3.264**
(0.011)
-4.013**
(0.021)
0.395***
(0.000)
-0.300
(0.513)
-0.140***
(0.000)
-0.018
(0.832)
-9.007***
(0.000)
-0.430***
(0.002)
0.016*
(0.076)
3.689***
(0.000)
-0.793***
(0.002)
0.010
(0.171)
-0.469
(0.771)
1.837***
(0.000)
0.862***
(0.000)
-4.581***
(0.000)
1.300
(0.352)
-10.625***
(0.000)
0.435***
(0.000)
-0.129
(0.887)
0.058
(0.405)
-0.243
(0.102)
-1.457
(0.577)
-0.520**
(0.047)
-0.019
(0.375)
3.689***
(0.001)
45
-0.806
(0.199)
0.016
(0.377)
0.026
(0.765)
1.669***
(0.000)
0.840***
(0.000)
-4.548*
(0.089)
-2.755
(0.330)
-24.354**
(0.032)
0.710**
(0.021)
-2.440
(0.368)
0.032
(0.633)
-0.375*
(0.079)
-2.355
(0.266)
-0.647***
(0.009)
0.016
(0.493)
3.648*
(0.064)
Year FE
Industry FE
Firm FE
Board size dummies
Observations
2
Adj R
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
11968
60%
11968
63%
46
11968
64%
11968
63%
11968
74%
8806
60%
Table 4. CEO Turnover and Odd Board
The sample consists of 6,462 firm-year observations with an odd number of directors and 5,613 firm-year observations
with an even number of directors from 1999 to 2009. Turnover is a dummy variable defined as 1 if the CEO is in his
last year in office, and zero otherwise. Odd dummy is equal to 1 if the number of directors on the board is an odd
number and 0 otherwise. All other controls are defined in Appendix A. Two-digit SIC code dummies are used to
control for industry fixed effects. Panel A presents the full sample analysis and Panel B presents the subsample
analysis. The p-values in parentheses are based on standard errors adjusted for heteroscedasticity and firm clustering.
Superscripts ***, ** and * denote statistical significance at the 1%, 5% and 10% levels, respectively.
47
Panel A Full Sample Analysis
Odd dummy t-1
(1)
(2)
(3)
(4)
0.170***
(0.006)
-0.087**
(0.033)
-0.766
(0.158)
0.260***
(0.000)
0.005**
(0.024)
-0.125
(0.838)
-0.316**
(0.037)
0.235
(0.542)
-0.077
(0.881)
0.031
(0.219)
-0.178
(0.324)
0.021
(0.285)
0.019
(0.650)
1.592**
(0.043)
0.184**
(0.014)
0.011**
(0.014)
-34.711
0.242***
(0.000)
-0.179***
(0.002)
0.030
(0.175)
-0.780
(0.147)
0.262***
(0.000)
0.005**
(0.024)
-0.117
(0.848)
-0.362**
(0.018)
0.211
(0.586)
-0.049
(0.924)
0.028
(0.280)
-0.164
(0.365)
0.021
(0.281)
0.020
(0.634)
1.470*
(0.061)
0.183**
(0.014)
0.011**
(0.015)
-35.529***
0.020**
(0.017)
-0.017**
(0.011)
0.003
(0.395)
-0.102
(0.276)
0.031**
(0.021)
0.001**
(0.021)
0.092
(0.546)
-0.011
(0.557)
-0.126
(0.132)
0.152
(0.263)
0.009
(0.382)
-0.064
(0.139)
-0.000
(0.916)
-0.034
(0.134)
-0.295*
(0.068)
0.029***
(0.004)
0.015***
(0.000)
-0.129
0.333***
(0.000)
-0.227***
(0.004)
0.035
(0.212)
-0.881
(0.147)
Yes
Yes
Yes
Yes
Yes
Odd t-1×3-year return
3-year return
ROA t-1
Bigboard dummy t-1
Independent director proportion t-1
Director ownership t-1
Sale growth t-1
Capex t-1
R&D t-1
Ln(MV) t-1
Leverage t-1
Segment number t-1
Ln(firm age) t-1
Volatility t-1
Duality t-1
Tenure t-1
Constant
Year FE
Industry FE
Firm FE
Board size dummies
Observations
Pseudo R2
0.004
(0.106)
0.039
(0.953)
-0.414**
(0.020)
0.475
(0.321)
-0.564
(0.373)
0.021
(0.497)
-0.195
(0.378)
0.015
(0.518)
0.043
(0.407)
1.463
(0.119)
0.161*
(0.070)
0.009*
(0.078)
-34.348***
Yes
Yes
Yes
Yes
11252
2.5%
48
11252
2.6%
11252
19.6%
8208
3.0%
Panel B Subsample Analysis
Short CEO
tenure
subsample
(1)
Long CEO
tenure
subsample
(2)
0.080
(0.439)
-0.112
(0.307)
-0.090
(0.235)
-0.835
(0.333)
0.162
(0.157)
0.003
0.346***
(0.000)
-0.196***
(0.007)
0.063**
(0.023)
-0.461
(0.548)
0.324***
(0.001)
0.006**
0.213**
(0.019)
-0.178*
(0.095)
-0.014
(0.847)
0.352
(0.529)
0.364***
(0.001)
0.004
(0.444)
0.897
(0.319)
-0.150
(0.522)
0.170***
(0.002)
-0.447
(0.560)
-0.024
(0.553)
-0.642**
(0.019)
-0.033
(0.281)
0.013
(0.833)
2.084*
(0.090)
0.217**
(0.042)
(0.027)
-1.122
(0.242)
-0.655***
(0.001)
0.302
(0.389)
0.129
(0.839)
0.063*
(0.066)
0.248
(0.326)
0.074***
(0.006)
0.014
(0.832)
0.276
(0.722)
0.180
(0.124)
-18.894
Year FE
Industry FE
Observations
Odd dummy t-1
Odd t-1×3-year return
3-year return
ROA t-1
Bigboard dummy t-1
Independent director
proportion t-1
Director ownership t-1
Sale growth t-1
Capex t-1
R&D t-1
Ln(MV) t-1
Leverage t-1
Segment number t-1
Ln(firm age) t-1
Volatility t-1
Duality t-1
Low R&D
subsample
(5)
High R&D
subsample
(6)
0.241**
(0.012)
-0.091*
(0.086)
0.042
(0.152)
-0.527
(0.413)
0.180
(0.104)
0.002
0.230**
(0.018)
-0.166*
(0.093)
0.003
(0.969)
-0.856
(0.228)
0.312***
(0.003)
0.002
0.235**
(0.015)
-0.177**
(0.020)
0.029
(0.226)
-0.437
(0.325)
0.218**
(0.040)
0.006*
(0.190)
(0.503)
-0.335
(0.128)
-0.519
(0.306)
-0.130
(0.869)
0.088**
(0.021)
-0.043
(0.872)
0.048*
(0.094)
0.004
(0.954)
1.431*
(0.092)
0.223**
(0.039)
0.004
(0.469)
-17.890
(0.075)
-1.410
(0.218)
-0.345**
(0.031)
0.195***
(0.000)
-20.291
-0.361*
(0.085)
0.289
(0.158)
0.938
(0.140)
-0.073*
(0.085)
-0.168
(0.500)
-0.001
(0.971)
0.011
(0.850)
0.549
(0.531)
0.243**
(0.029)
0.021***
(0.005)
-2.450***
(0.443)
0.747
(0.318)
-0.259
(0.250)
0.599
(0.184)
0.033
(0.393)
-0.151
(0.548)
0.012
(0.671)
0.006
(0.924)
3.609***
(0.001)
0.272***
(0.010)
0.017***
(0.007)
-3.247***
0.016
(0.649)
-0.210
(0.395)
0.030
(0.261)
0.037
(0.523)
0.384
(0.691)
0.120
(0.257)
0.004
(0.511)
-36.337***
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
5407
3.9%
5845
3.8%
5626
3.5%
5626
3.5%
6202
3.8%
5050
3.0%
Tenure t-1
Constant
Pseudo R2
Low director High director
ownership
ownership
subsample
subsample
(3)
(4)
49
Table 5. CEO Compensation and Odd Board
The sample consists of 6,462 firm-year observations with an odd number of directors and 5,613 firm-year observations
with an even number of directors from 1999 to 2009. The dependent variable is Ln(CEO total compensation), where total
compensation is Item TDC1 in Execucomp, which consists of salary, bonus, value of restricted stock granted, value of
options granted (using Black-Scholes), long-term incentive payouts, and other compensation. Odd dummy is equal to 1 if
the number of directors on the board is an odd number and 0 otherwise. All other controls are defined in Appendix A. Twodigit SIC code dummies are used to control for industry fixed effects. Panel A presents the full sample analysis and Panel B
presents the subsample analysis. The p-values in parentheses are based on standard errors adjusted for heteroscedasticity
and firm clustering. Superscripts ***, ** and * denote statistical significance at the 1%, 5% and 10% levels, respectively.
50
Panel A Full Sample Analysis
Odd t-1
(1)
(2)
(3)
(4)
-0.042**
(0.011)
0.129***
(0.000)
-0.575***
(0.008)
0.051*
(0.061)
0.005***
(0.000)
-1.521***
(0.000)
-0.108***
(0.010)
-0.227
(0.147)
0.051
(0.797)
0.465***
(0.000)
0.641***
(0.000)
0.007
(0.386)
-0.032*
(0.055)
1.870***
(0.000)
0.103***
(0.000)
-0.005**
(0.025)
3.984***
(0.000)
-0.066***
(0.000)
0.075**
(0.010)
0.027
(0.321)
-0.446**
(0.046)
0.046*
(0.091)
0.005***
(0.000)
-1.549***
(0.000)
-0.070*
(0.093)
-0.237
(0.134)
0.036
(0.853)
0.469***
(0.000)
0.639***
(0.000)
0.007
(0.393)
-0.033*
(0.053)
1.868***
(0.000)
0.097***
(0.000)
-0.005**
(0.032)
3.923***
(0.000)
-0.025
(0.125)
0.072***
(0.002)
0.042**
(0.050)
-0.085
(0.711)
-0.005
(0.847)
0.002*
(0.095)
0.078
(0.762)
-0.069
(0.106)
-0.012
(0.942)
-0.495
(0.139)
0.291***
(0.000)
0.050
(0.623)
0.019*
(0.077)
-0.011
(0.838)
0.659
(0.130)
0.008
(0.751)
-0.001
(0.798)
5.885***
(0.000)
-0.039*
(0.061)
0.047*
(0.078)
0.061***
(0.005)
-0.323
(0.151)
Yes
Yes
Yes
Yes
Yes
Odd t-1×3-year return
3-year return
ROA t-1
Bigboard dummy t-1
Independent director proportion t-1
Director ownership t-1
Sale growth t-1
Capex t-1
R&D t-1
Ln(MV) t-1
Leverage t-1
Segment number t-1
Ln(firm age) t-1
Volatility t-1
Duality t-1
Tenure t-1
Constant
Year FE
Industry FE
Firm FE
Board size dummies
Observations
2
Adj R
0.006***
(0.000)
-1.381***
(0.001)
-0.110**
(0.019)
-0.308*
(0.090)
0.063
(0.774)
0.462***
(0.000)
0.600***
(0.000)
0.011
(0.208)
-0.052***
(0.005)
2.006***
(0.000)
0.094***
(0.000)
-0.004
(0.137)
3.529***
(0.000)
Yes
Yes
Yes
Yes
10520
53%
51
10520
52%
10520
76%
7731
53%
Panel B Subsample Analysis
Short CEO
tenure
subsample
(1)
Long CEO
tenure
subsample
(2)
-0.033
(0.109)
-0.004
(0.901)
0.149***
(0.000)
-0.691***
(0.005)
0.059*
(0.054)
0.004***
-0.062**
(0.015)
0.045*
(0.071)
0.037**
(0.037)
-0.327
(0.313)
0.055
(0.135)
0.008***
-0.025
(0.158)
0.030*
(0.091)
0.079***
(0.000)
-0.444***
(0.002)
0.038*
(0.067)
0.004***
(0.000)
-0.606
(0.137)
-0.162***
(0.004)
-0.340**
(0.039)
-0.108
(0.663)
0.454***
(0.000)
0.551***
(0.000)
0.021**
(0.019)
-0.050***
(0.005)
2.223***
(0.000)
0.088***
(0.001)
(0.000)
-0.688***
(0.000)
-0.048
(0.411)
-0.178
(0.405)
0.179
(0.509)
0.466***
(0.000)
0.742***
(0.000)
0.001
(0.909)
-0.020
(0.408)
1.407***
(0.001)
0.085**
(0.030)
4.214***
(0.000)
Year FE
Industry FE
Observations
2
Adj R
Odd dummy t-1
Odd t-1×3-year return
3-year return
ROA t-1
Bigboard dummy t-1
Independent director
proportion t-1
Director ownership t-1
Sale growth t-1
Capex t-1
R&D t-1
Ln(MV) t-1
Leverage t-1
Segment number t-1
Ln(firm age) t-1
Volatility t-1
Duality t-1
Low R&D
subsample
(5)
High R&D
subsample
(6)
-0.048*
(0.060)
-0.030
(0.220)
0.144***
(0.000)
-0.648***
(0.001)
0.076***
(0.007)
0.007***
-0.039
(0.121)
-0.000
(0.998)
0.109***
(0.000)
-0.370
(0.210)
0.071*
(0.061)
0.005***
-0.058**
(0.019)
0.068*
(0.069)
0.035
(0.248)
-0.728***
(0.004)
0.007
(0.856)
0.005***
(0.000)
(0.000)
-0.040
(0.346)
-0.135
(0.380)
-0.055
(0.413)
0.432***
(0.000)
0.767***
(0.000)
-0.023***
(0.002)
0.004
(0.814)
1.639***
(0.000)
0.091***
(0.001)
-0.006***
(0.000)
3.140***
(0.000)
(0.000)
-1.614***
(0.010)
-0.069
(0.242)
-0.486**
(0.047)
3.645***
(0.000)
-0.141***
(0.000)
-0.038
(0.732)
-0.023**
(0.048)
0.468***
(0.000)
0.512***
(0.000)
0.031***
(0.000)
-0.045***
(0.000)
2.013***
(0.000)
0.108***
(0.000)
0.000
(0.973)
3.758***
(0.000)
(0.000)
-1.366***
(0.004)
-0.093
(0.103)
-0.152
(0.435)
0.461***
(0.000)
0.953***
(0.000)
0.018
(0.110)
-0.031
(0.232)
3.079***
(0.000)
0.129***
(0.000)
-0.003
(0.375)
3.548***
(0.000)
0.469***
(0.000)
0.349***
(0.000)
-0.003
(0.779)
-0.011
(0.625)
0.925**
(0.033)
0.067*
(0.059)
-0.006**
(0.038)
4.247***
(0.000)
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
5005
58%
5515
51%
5260
57%
5260
47%
5608
52%
4912
55%
Tenure t-1
Constant
Low director High director
ownership
ownership
subsample
subsample
(3)
(4)
52
Table 6. Board Size and Odd Board
The sample consists of 6,462 firm-year observations with an odd number of directors and 5,613 firm-year observations
with an even number of directors from 1999 to 2009. Tobin’s Q is calculated as market value of assets (total book value of
assets minus book value of equity plus market value of equity) over book value of assets. ROA is calculated as (Operating
income before depreciation – Net interest expense – Cash taxes – Change in net working capital) deflated by total asset.
Turnover is a dummy variable defined as 1 if the CEO is in his last year in office, and zero otherwise. CEO total
compensation is Item TDC1 in Execucomp, which consists of salary, bonus, value of restricted stock granted, value of
options granted (using Black-Scholes), long-term incentive payouts, and other compensation. Odd dummy is equal to 1 if
the number of directors on the board is an odd number and 0 otherwise. All other controls are defined in Appendix A. Twodigit SIC code dummies are used to control for industry fixed effects. The p-values in parentheses are based on standard
errors adjusted for heteroscedasticity and firm clustering. Superscripts ***, ** and * denote statistical significance at the
1%, 5% and 10% levels, respectively.
VARIABLES
Odd t-1
Odd t-1×Bigboard dummy t-1
Tobin’s q
(1)
0.093***
(0.007)
-0.124***
(0.001)
ROA
(2)
0.353***
(0.002)
-0.314**
(0.015)
Odd t-1×3-year return
3-year return
Bigboard dummy t-1
Independent director
proportion t-1
Director ownership t-1
Return t-1
ROA t-1
Sale growth t-1
Capex t-1
R&D t-1
Ln(MV) t-1
Leverage t-1
Segment number t-1
Ln(firmage) t-1
Volatilityt-1
-0.140***
(0.000)
-0.000
-0.279*
(0.052)
-0.003
(0.639)
1.802***
(0.000)
0.265***
(0.000)
6.103***
(0.000)
0.031
(0.592)
-0.180
(0.354)
3.899***
(0.000)
0.138***
(0.000)
-0.038
(0.770)
-0.049***
(0.000)
-0.026
(0.226)
1.086***
(0.010)
(0.429)
0.163
(0.840)
1.810***
(0.000)
51.967***
(0.000)
-0.617*
(0.088)
3.275**
(0.011)
-4.077**
(0.019)
0.410***
(0.000)
-0.277
(0.546)
-0.138***
(0.000)
-0.008
(0.926)
-9.041***
(0.000)
Turnover
Ln(CEO total pay)
Small board
subsample
(3)
Big board
subsample
(4)
0.316***
(0.001)
0.290***
(0.004)
-0.045*
(0.054)
-0.018
(0.472)
-0.144*
(0.090)
0.061
(0.383)
-0.191
(0.114)
-0.107
(0.228)
0.088***
(0.004)
0.010
(0.708)
-0.016
(0.618)
0.133***
(0.000)
0.005*
0.005
0.005***
0.006***
(0.092)
0.332
(0.748)
(0.129)
-0.285
(0.717)
(0.000)
-2.719***
(0.000)
(0.000)
-0.755**
(0.031)
-0.071
(0.915)
-0.584***
(0.004)
-0.235
(0.673)
0.713
(0.241)
-0.032
(0.414)
-0.009
(0.970)
0.028
(0.340)
0.016
(0.789)
0.965
(0.328)
-1.715*
(0.085)
0.033
(0.894)
0.723
(0.178)
-1.417
(0.130)
0.091**
(0.011)
-0.432
(0.145)
0.023
(0.409)
0.078
(0.241)
2.108
(0.150)
-0.387
(0.131)
-0.081
(0.137)
0.006
(0.971)
0.008
(0.972)
0.492***
(0.000)
0.575***
(0.000)
0.003
(0.766)
-0.025
(0.222)
1.456***
(0.000)
-0.488*
(0.097)
-0.107*
(0.089)
-0.870***
(0.002)
0.162
(0.628)
0.449***
(0.000)
0.748***
(0.000)
0.015
(0.158)
-0.023
(0.331)
2.970***
(0.000)
53
Small board
subsample
(5)
Big board
subsample
(6)
Dualityt-1
CEO tenuret-1
Constant
Year FE
Industry FE
Observations
2
2
Adj R /Pseudo R
-0.055*
(0.061)
0.004
(0.142)
0.469***
(0.002)
-0.432***
(0.001)
0.016*
(0.076)
3.524***
(0.000)
0.186*
(0.053)
0.003
(0.626)
-34.867
0.217*
(0.089)
0.022***
(0.001)
-35.422
0.104***
(0.001)
-0.008***
(0.002)
3.896***
(0.000)
0.076**
(0.038)
0.002
(0.397)
3.868***
(0.000)
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
12075
45%
11968
60%
6541
3.8%
4711
4.3%
6307
45%
4213
58%
54
Table 7. Controlling for Self-Selection Bias
The sample consists of 12,075 firm-year observations based on RiskMetrics/CRSP/Compustat merged data from
1999 to 2009. Tobin’s Q is calculated as market value of assets (total book value of assets minus book value of
equity plus market value of equity) over book value of assets. ROA is the return on asset, calculated as
(Operating income before depreciation – Net interest expense – Cash taxes – Change in net working capital)
deflated by total asset. Turnover is a dummy variable defined as 1 if the CEO is in his last year in office, and
zero otherwise. CEO total compensation is Item TDC1 in Execucomp, which consists of salary, bonus, value of
restricted stock granted, value of options granted (using Black-Scholes), long-term incentive payouts, and other
compensation. Odd dummy is equal to 1 if an odd number of directors are on board and 0 otherwise. Industry
odd-number board prevalence is measured as the ratio of the number of firms with the odd board in the same
industry to the total number of firms in that industry. State odd-number board prevalence is measured as the ratio
of the number of firms with the odd board in the same state to the total number of firms in that state. All other
controls are defined in Appendix. Two-digit SIC code dummies are used to control for industry fixed effects. The
p-values in parentheses are based on standard errors adjusted for heteroscedasticity and firm clustering.
Superscripts ***, ** and * denote statistical significance at the 1%, 5% and 10% levels, respectively.
VARIABLES
1st stage
Odd dummy
(1)
Odd dummy t-1
2nd stage
Tobin’s Q
2nd stage
ROA
2nd stage
Turnover
(2)
(3)
(4)
2nd stage
Ln(CEO total
pay)
(5)
0.351**
(0.012)
5.054***
(0.000)
0.098
(0.874)
-0.091***
(0.001)
0.017
(0.191)
0.087
(0.998)
0.075***
(0.000)
0.025***
(0.000)
-0.076*
(0.053)
-0.000
(0.673)
1.846***
(0.000)
0.268***
(0.000)
6.128***
(0.000)
0.047
(0.223)
-0.193*
(0.070)
3.883***
(0.000)
0.131***
(0.000)
-0.085*
-1.475***
(0.000)
-0.001
(0.746)
0.300
(0.689)
1.756***
(0.000)
49.006***
(0.000)
-0.508**
(0.029)
2.768***
(0.000)
-5.612***
(0.000)
0.553***
(0.000)
-0.374
0.143
(0.335)
0.003**
(0.035)
-0.080
(0.820)
0.010
(0.567)
0.005***
(0.000)
-1.549***
(0.000)
-0.366
(0.243)
-0.198**
(0.013)
0.117
(0.147)
-0.046
(0.864)
0.015
(0.504)
-0.076
-0.469***
(0.000)
-0.070**
(0.035)
-0.243***
(0.008)
0.016
(0.893)
0.473***
(0.000)
0.650***
Odd t-1×3-year return
3-year return
Instrument variables:
Industry odd-number board
prevalence t-1
State odd-number board
prevalence t-1
2.549***
(0.000)
2.695***
(0.000)
Control variables:
Big board dummy t-1
Independent director proportion t-1
Director ownership t-1
Stock Return t-1
ROA t-1
Sale growth t-1
Capex t-1
R&D t-1
Ln(MV) t-1
Leverage t-1
-0.628***
(0.000)
-0.002**
(0.028)
-0.181
(0.305)
-0.013
(0.664)
-0.040
(0.828)
-0.086
(0.122)
0.099
(0.388)
0.058**
(0.021)
0.038***
(0.000)
0.243***
55
Number of segments t-1
Ln(firm age) t-1
Return volatility t-1
Duality dummy t-1
Tenure t-1
Constant t-1
Year fixed effect
Industry fixed effect
Observations
Rho
Chi-2 statistic
(0.000)
0.009
(0.226)
0.027*
(0.094)
-1.652***
(0.000)
0.022
(0.454)
-0.001
(0.705)
-2.604***
(0.000)
(0.099)
-0.051***
(0.000)
-0.034***
(0.003)
1.366***
(0.000)
-0.058***
(0.004)
0.004***
(0.001)
-0.644
(0.307)
(0.207)
-0.130***
(0.000)
0.155**
(0.028)
-9.804***
(0.000)
-0.426***
(0.001)
0.009
(0.220)
-0.667
(0.855)
(0.472)
0.012
(0.284)
0.008
(0.777)
0.818*
(0.060)
0.095**
(0.023)
0.006**
(0.014)
-11.098
(0.000)
0.009*
(0.085)
-0.028***
(0.005)
1.857***
(0.000)
0.096***
(0.000)
-0.005***
(0.000)
3.722***
(0.000)
Yes
No
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
12,075
12,075
-0.373
6.19**
11,968
-0.568
64.28***
11,252
0.018
0.078
10,520
-0.133
0.250
56
Table 8. Firms that Change from an Even Board to an Odd board, Propensity Score Matching
The sample consists of 2,187 firm-year observations that an even board changes to an odd board from 1999 to 2009. We
match each observation to a firm-year observation without such changes using the nearest neighborhood matching approach.
The variables used in the matching are number of directors, prior-year stock return, prior-year ROA, Ln(MV), leverage,
return volatility, industry (two-digit SIC code) indicators, and year indicators. All continuous variables are winsorized at the
1st and 99th percentiles. P-values based on bootstrapped standard errors of 50 replications with replacement are reported in
parentheses. Superscripts ***, ** and * denote statistical significance at the 1%, 5% and 10% levels, respectively.
Δ CEO tenure
Δ Director ownership ($M)
Δ R&D
Firms that change from an
even board to an odd board
(1)
-0.05
Matched firms
(2)
Test the difference:
(1) - (2)
-0.26***
0.21*
(0.534)
(0.002)
(0.065)
-1.32***
0.13
-1.45**
(0.008)
(0.760)
(0.043)
0.8%
-1.6%
2.4%*
(0.246)
(0.167)
(0.075)
57
Figure 1. Board Size and Tobin’s Q
This graph is extracted from Figure 1 of Yermack (1996) and illustrates sample means and medians of Tobin’s Q for different
sizes of boards of directors. Yermack’s sample consists of 3,438 annual observations from 452 firms between 1984 and 1991.
Figure 1
58