paper board structure and price informativeness

Thus, stock markets play an important monitoring role.The trade-off between board structure and price informativeness is stronger for firmsexposed to external governance mechanisms i.e..

Board Structure and Price Informativeness

Daniel Ferreira∗London School of Economics,

CEPR and ECGI

Miguel A Ferreira†ISCTE Business School

1 Introduction

Empirical evidence that firm- and industry-specific characteristics affect board structuresupports the view that corporate boards are endogenously-determined institutions (see Her-malin and Weisbach (2003)) In this paper, we develop a theory of endogenously-determinedboards in which the link between stock price informativeness and board structure plays acentral role We also provide new evidence that is consistent with the main implications ofthe theory

Whenever a stock is subject to intense informed trading, its price incorporates part ofthe private information that motivates speculative trading We argue that the informationembedded in stock prices performs two useful roles Firstly, it allows managers to revisetheir corporate investment decisions in light of the new information revealed by stock prices.This is the advisory role of stock markets Secondly, information revealed by prices allowsexternal monitoring mechanisms to operate more efficiently For example, if prices fall due

to the announcement of value-decreasing investments, the firm becomes a cheaper takeovertarget Managers who enjoy private benefits of control would thus avoid undertaking value-destroying projects if prices react adversely to such events Thus, stock markets also play

an important monitoring role

The information contained in stock prices works as an external governance mechanism.When prices are not too informative, internal mechanisms can substitute for the stock mar-ket In particular, corporate boards are known for their advising and monitoring roles Theeffectiveness of a board in performing these two tasks depends on its characteristics Inpractice, the literature focuses on two main features: board size and director independence.Due to coordination problems and free-riding, larger boards tend to be less effective monitorsthan small ones (Lipton and Lorsch (1992) and Jensen (1993)), and the evidence suggeststhat larger boards are associated with lower market valuations (Yermack (1996)) Moreindependent boards are likely to perform their monitoring role more effectively and there

is evidence that outside directors affect crucial decisions such as hiring and firing the CEO

(Weisbach (1988)) However, recent papers emphasize the idea that the optimal board ture varies with firm characteristics and that “one size” does not fit all firms In particular,there is some evidence consistent with the idea that the board structure depends on thedegree of complexity of firms’ operations and on the trade-off between the costs and benefits

struc-of advising and monitoring (Boone, Field, Karpoff, and Raheja (2006), Coles, Daniel, andNaveen (2006), Gillan, Hartzell, and Starks (2006), and Linck, Netter, and Yang (2007)).Consistent with the existence of such trade-offs, Chhaochharia and Grinstein (2007) findevidence that large firms have benefited from the stronger board independence requirementsmandated by the 2002 governance rules, while small firms have been negatively affected bythe same rules

Consistent with the empirical literature, our model allows board size and independence tohave both costs and benefits We make the intuitive assumptions that larger boards providebetter advice to managers, because a larger board yields a large pool of director expertise,and that more independent boards are tougher monitors, because directors are less alignedwith managers Under these assumptions, our model implies the existence of a substitutioneffect between corporate boards and stock price informativeness (i.e the amount of privateinformation incorporated into stock prices) That is, the model’s main prediction is thatboard size and board independence are both negatively related to price informativeness.Our theory builds upon the natural assumption that the amount of information incor-porated into stock prices varies across stocks It is widely accepted that one of the mainroles of stock markets is the production and aggregation of information via trading betweenspeculators and other types of investors (e.g Grossman and Stiglitz (1980) and Kyle (1985)).The amount of private information incorporated into stock prices can vary due to differentcosts of collecting and producing private information In fact, Grossman and Stiglitz (1980)predict that improving the cost-benefit trade-off on private information collection leads tomore extensive informed trading and more informative pricing They suggest that in a mar-ket with many risky stocks, the ones with cheaper information about their fundamental

values are more attractive to traders Accordingly, traders acquire more information aboutthese stocks and their prices are more informative than the prices of stocks with more costlyinformation.

In order to test the main implications of our model, we need an empirical proxy for stockprice informativeness Our measure of price informativeness, the “probability of informedtrading” (PIN), has been developed in a series of papers by Easley, Kiefer, and O’Hara(1996), Easley, Kiefer, and O’Hara (1997a), and Easley, Kiefer, and O’Hara (1997b) It has

a strong theoretical foundation, since it comes from a structural microstructure model Theinterpretation is that the information incorporated into a stock with high PIN is coming morefrom private sources than public ones Some recent papers adopt this measure to assess theimpact of price informativeness on corporate investment (e.g Chen, Goldstein, and Jiang(2006)) Our empirical work naturally complements this literature, by focusing on the effects

of price informativeness on governance mechanisms, which ultimately determine corporateinvestment decisions

We find that the probability of informed trading is negatively related to both board sizeand board independence These findings are consistent with our model’s prediction that priceinformativeness can substitute for the advising and monitoring roles of corporate boards.Consistent with our interpretation, we find that these negative relationships are stronger formore complex firms (such as diversified firms) and for firms in which firm-specific knowledge

is less important (or firms with low levels of R&D investments)

The negative impact of price informativeness on corporate boards is stronger for firmswith few takeover defenses, confirming our conjecture that stock price informativeness is moreeffective as a substitute for the board in its monitoring role when firms are more exposed tothe market for corporate control (Jensen (1986))

We also find that the negative relation between price informativeness and corporateboards is stronger for firms with higher concentration of institutional investors This findingsuggests that price informativeness can only be an effective substitute for the internal mon-

itoring role of corporate boards when there are large shareholders, who supervise the boardthemselves (Shleifer and Vishny (1986)).

We perform several robustness checks of our main empirical findings and also addressendogeneity concerns by means of instrumental variables methods We confirm that theempirical findings are robust and generally consistent with a causal link running from priceinformativeness to board structure

On the theoretical side, our paper integrates the literature that explains board structure

as the result of optimal shareholder choices when contracts are incomplete (Hermalin andWeisbach (1998), Raheja (2005), Song and Thakor (2006), Adams and Ferreira (2007), andHarris and Raviv (2007)) with the theoretical literature on the role of stock prices in dis-ciplining managers (Holmstrom and Tirole (1993), Faure-Grimaud and Gromb (2004), andAlmazan, Banerji, and Motta (2006)) To the best of our knowledge, these two strands ofthe literature have not yet been integrated Furthermore, our paper is also related to theliterature on incentives and strategic change (Dow and Raposo (2005)), and also to the liter-ature on the role of stock prices in guiding corporate investment decisions (Dow and Gorton(1997), Subrahmanyam and Titman (1999), and Dow, Goldstein, and Guembel (2006))

On the empirical side, our contribution is the examination of the role of stock prices andtrading as determinants of board structure We add a new and important dimension – priceinformativeness – to the literature on the determinants of board structure Our findingsunderscore the dual role of the stock trading process as both a provider of informationand a monitor of management Our findings are also consistent with the recent boardliterature that challenges the conventional wisdom that small and highly independent boardsare always optimal Finally, our paper is also related to a recent literature that investigateswhat corporate directors know and the impact of their expertise on firm outcomes (Guner,Malmendier, and Tate (2006) and Ravina and Sapienza (2006))

The remainder of the paper is organized as follows In Section 2 we develop a model inwhich the optimal structure of corporate boards depends on the degree of price informative-

ness We use the model to derive the testable hypotheses for the empirical part of the paper.Section 3 describes the sample, data, and the variables construction In Section 4 we presentour core evidence on the relation between board structure and price informativeness In Sec-tion 5 we examine whether firm complexity, firm-specific knowledge, takeover defenses, andlarge shareholders affect the relation between corporate boards and price informativeness.

In Section 6 we perform additional robustness checks Section 7 concludes

an independent board (via firing and replacement) can impose on him As it is common inthe board literature, for the problem to be meaningful, we assume that the interests of theCEO are not completely aligned with those of the shareholders (see Hermalin and Weisbach(1998), Raheja (2005), Song and Thakor (2006), Adams and Ferreira (2007), and Harris andRaviv (2007))

The model includes four types of agents Intuitively, the role played by each type can

be summarized as follows: (1) Shareholders are risk neutral agents, who care about themarket value of the firm and have delegated management to a CEO and a board of directors

In this model the shareholders will choose the optimal board structure, in terms of sizeand independence (2) The CEO, who holds some shares of the firm, and will make aninvestment decision (3) The Market, which may be informed about the prospects of thefirm, in which case it can provide influential information to the board and the CEO (external

advisory role) An informed market can also directly discipline a misbehaving firm/CEO viatakeovers (external monitoring role) Finally, (4) the Board of Directors, which may beinformed either because it learns information from the market, or because it independentlyacquires information (internal advisory role) An informed board may also directly discipline

a misbehaving CEO by firing and replacing him (internal monitoring role)

We now present the structure and timing of the model Consider a firm run by a CEOwho owns a fraction α of its shares The CEO must decide whether or not to undertake aproject y The payoff of the project depends on the underlying state of nature (i.e firm-specific conditions) There are three possible states: ω ∈ {H, M, L} These states of natureare not affected by any of the CEO’s decisions and are initially unobservable by all agents.The ex ante probability of each state is 13 At the end of the game, the realized state isrevealed to everyone

Let Vy

ω denote the end-of-the-game value of the firm given the realized state ω and thedecision on the project y ∈ {0, 1}, where y = 1 if the project is implemented, and zerootherwise We assume that

The CEO’s Problem: The CEO derives positive private benefits, b , from adoptingthe project, regardless of the underlying state, plus security benefits through his share-holdings (see Burkart, Gromb, and Panunzi (1997), Benos and Weisbach (2004), and Dyckand Zingales (2004); Dow and Raposo (2005) also model CEOs’ biased preferences for such

strategies) Formally, we assume that the manager’s utility function is given by:1

U (ω, y) = αVωy+ by (4)

In alternative, we could have formulated the agency problem as an adverse selection problem(as in Hermalin and Weisbach (1998)) or as a moral hazard problem (as in Adams andFerreira (2007)), with qualitatively similar results For the sake of simplicity and clarity ofexposition, we choose this moral hazard formulation with private benefits In order to have

a meaningful agency problem, we make the following parametric assumption:

b∈¡

α¡

VM0 − VM1

¢, α¡

1 In the end of this section we provide a brief discussion of our main assumptions, including the restrictions

on the contracting space.

2 Endogenizing this assumption is straightforward; it is sufficient to assume that the CEO has zero initial wealth and is protected by limited liability Intuitively, in an extreme scenario, one can think of α being arbitrarily large, i.e very close to one In such a case, the CEO would no longer take his private benefits into consideration, but the shareholders would give him the firm.

some probability of revealing information about the underlying conditions facing the firm.One could model the price formation process explicitly, but we choose this simpler approachbecause the specifics of the trading process are not relevant for our model In the empiricalpart of the paper, our proxy for p is the probability of informed trading (PIN) developed byEasley, Kiefer, and O’Hara (1996).

Because our interpretation is such that information is revealed by stock prices, this formation can be used by anyone inside or outside the firm In particular, it is rational forthe CEO to condition his actions on the information revealed by prices: clearly, if pricesreveal that ω = L he would rather choose not to invest Thus, in this sense the stock marketperforms a valuable advisory role: it is a source of important additional information thathelps guiding corporate investments decision-making (see Dow and Gorton (1997) and Chen,Goldstein, and Jiang (2006)).3

in-Investors in the market can also condition their decisions on the information revealed

by stock prices For example, suppose that prices reveal that the state is M, but the CEOchooses to invest; if this decision can be (at least partially) reversed, a firm in state M thathas invested becomes an attractive takeover target Thus, we assume that if the CEO makes

a value-decreasing decision, and if this decision is public information, external monitoringforces (such as hostile takeovers) will force the resignation of the CEO with some positiveprobability This is the monitoring role of stock price informativeness

For simplicity, we assume that the CEO is fired with probability 1 (we relax this tion in the next subsection) in case the market learns that he has undertaken the projectwhen it is common knowledge that the state is either L or M If fired, the CEO is compen-sated according to his shares α at the current value that corresponds to his “bad” decision(i.e V1

not to invest Thus, price informativeness increases firm value not only by providing betterinformation that is useful for corporate investment decisions, but also by allowing externalmonitors to become informed and to punish managers who misbehave.

The Role of the Board: Boards perform valuable advisory and monitoring functions(see Song and Thakor (2006), Adams and Ferreira (2007), and Harris and Raviv (2007); forempirical evidence on the multiple roles of boards, see for example Coles, Daniel, and Naveen(2006) and Linck, Netter, and Yang (2007)) We assume that there is a board of directorsthat is characterized by two parameters, n and i, which we assume to lie between zero andone for simplicity

Parameter n is a measure of the advisory capacity of the board, which in our model issimply the probability that the board learns the underlying state ω when prices are notinformative Thus, the probability that the board learns ω before the investment decision is

p + (1− p) n Empirically, our proxy for n is board size A larger board brings together alarger pool of individual experiences and expertise Although it is unrealistic to assume thatlarger boards are better monitors (in fact, the opposite is likely to be true), it is plausiblethat larger boards can bring more information that is unrelated to managers’ actions andabilities to the table, because of the diversity of directors’ backgrounds (see Coles, Daniel,and Naveen (2006)) The assumption that n is bounded above by one is made for simplicity,but can be also interpreted as consistent with the view that the quality of the board’s advicecannot increase indefinitely with size

Parameter i is a measure of the board’s monitoring intensity In our model, parameter iamounts to the probability that the board punishes (i.e fires) the CEO if it learns that theCEO has made a value-decreasing decision without being punished by the market (becauseprices were not informative) That is, boards will fire the CEO when they learn that ω equals

Lor M through their private investigations but the CEO still chooses to invest Empirically,our proxy for i is the proportion of independent directors, which is a natural one (e.g., Adamsand Ferreira (2007) argue that it is less costly for independent board members to monitor

the CEO since their careers and personal interests are not so closely tied to his.)

Both board size and board independence are costly characteristics A larger board leads

to free-riding problems and may reduce the quality of monitoring (see Yermack (1996)) Toomuch independence may lead to less information sharing between managers and directors,compromising both advising and monitoring functions of the board (see Adams and Ferreira(2007)) There are also direct costs, since outside directors must be compensated Weabstract from these issues and simply assume here a convex cost function:

Timing of the Model: There are four periods

Period 0 Shareholders set up a firm, hire a CEO, and all types of agents observe (i.e.,predict) an exogenous measure of price informativeness p Shareholders also hire a boardwith characteristics (n, i)

Period 1 The market observes ω with probability p The board observes ω withprobability one if prices are informative and with probability n otherwise The CEO makesthe investment decision after learning what the board knows

Period 2 The CEO is fired with probability one if the market learns that he hasmade the value-decreasing decision or with probability i if only the board learns about avalue-decreasing decision If fired, the CEO is compensated and loses his private benefit.Period 3 The state of nature ω is revealed to everyone Shareholders receive (1 − α) Vy

ω.The CEO receives αVy

ω + by if still in charge

2.1 Choice of Board Structure

To solve the model we start by examining the investment decision of the CEO in period 1.This decision will be conditional on the degree of independence of the board, i

CEO Behavior in Period 1 Because we are assuming that (VH1 − VH0) > (VM0 − VM1) +(VL0− VL1), it is optimal for the CEO to choose y = 1 when neither the market nor the boardare informed If the market and/or the board are informed that ω = H, there is no conflict

of interests between the CEO and the shareholders, and the CEO chooses y = 1 Likewise, if

it is known that ω = L, the CEO will make the uncontroversial choice y = 0 The interestingcase arises when ω = M If the market is aware of this, the CEO will end up choosing y = 0,because otherwise he would be subjected to replacement via takeover with probability one

If only the board (and not outside investors) is aware of state M , then the CEO will prefer

to choose y = 0 only if:

αVM0 ≥ i¡

αVM1¢+ (1− i)¡

intensity should be:4

L will be useful, but not in state M In contrast, if the board is structured according to(i∗, n∗), its advisory role in both states L and M will be influential in the CEO’s decision.Therefore, a higher i goes hand in hand with a higher n

The circumstances in which solution (i∗, n∗) is preferable to (i∗∗, n∗∗) are characterized

4 It is easy to check that i ∗ ∈ (0, 1), given assumption (5).

5 Empirically, it is usually the case that board size and independence are positively correlated.

by (following the comparison of shareholder expected value in period 0, conditional on case(1) or case (2)):

be higher than the right-hand side for all b ≤ bb

Proposition 1 Board size decreases with price informativeness

Proof Suppose we start from parameters such that condition (14) holds, so that (i∗, n∗)

is optimal If inequality (14) remains valid while p increases, we have that

Proposition 2 Board independence decreases with price informativeness.

The result with respect to board independence is straightforward There are only twooptimal values, i∗ > 0 and i∗∗ = 0 Starting from condition (14), board independence is at

i∗ and will eventually fall down to zero as p becomes large

Overall, we find that higher price informativeness (i.e higher p) implies a less relevantrole for the board, both in terms of advice (i.e lower n) and in terms of monitoring.(i.e.lower i)

We can also derive some additional empirical implications with respect to variables thataffect the total and marginal costs of board size and independence Intuitively, any variablethat increases the marginal costs of board size and independence will make the trade-off be-tween price informativeness and board structure less pronounced The following propositionformalizes this intuition

Proposition 3 The trade-off between board structure and price informativeness is weakerwhen the marginal cost of board size and independence is high:

∂2(π∗− π∗∗)

∂p∂k > 0The proof follows from straightforward algebra Because increases in price informative-ness have a negative effect on the value difference between the two possible board structures(∂ (π∗− π∗∗) /∂p < 0), the trade-off becomes weaker if the cross-derivative above is positive(i.e the effect becomes “less negative” if k is higher)

We have chosen a parsimonious model to guide our empirical work In order to keep theanalysis simple, we do not fully model all costs and benefits of board size and independence.However, it is straightforward to extrapolate some of the implications of the model to slightlymore sophisticated environments, as long as one is willing to make further assumptions Forexample, any variable that is believed to affect k could be used in a test of Proposition 3 Inthe empirical part of the paper, we consider some proxies for k One should keep in mind,

however, that testing Proposition 3 with informal proxies for k is a joint test of both ourtheory and other complementary theories that are used to motivate the proxies for k (themarginal cost of board size and independence such as firm-specific knowledge).

2.2 The Role of the Market as an External Monitor

Our model illustrates the substitution effect between board structure and price ness when there is an active market for corporate control Here we consider the other polarcase in which the firm is insulated from the market for corporate control

informative-Let us assume that the market never disciplines the CEO, even when informed Forexample, when a firm has many anti-takeover charter provisions Intuitively, the monitoringrole of the board is now more important, because the board is the only monitoring mecha-nism available As a consequence, the substitution effect between board structure and priceinformativeness is weaker It is straightforward to use our model to confirm this intuitionformally

If the probability of takeover is zero, inequality (14) becomes

p Thus now price informativeness and board independence are not necessarily substitutes;this term represents a complementarity effect between the two Due to this effect, as pricesbecome more informative, shareholders gain more by having a board that monitors moreintensively, because informed monitoring is more valuable However, the original substitution

effect is still present (the first term of the left-hand side of (17)), thus the net effect of a rise

in p on the choice between (i∗, n∗) and (i∗∗, n∗∗) is ambiguous

Thus, we expect that the trade-off between price informativeness and board size and pendence should be weaker in this case (perhaps even inexistent) The following propositionmakes this point formally

inde-Proposition 4 The trade-off between board structure and price informativeness is weakerwhen takeovers are not possible:

The proof follows from straightforward algebra Proposition 4 says that the effect of p

on the profit difference π∗− π∗∗ is always “more negative” when takeovers are possible thanwhen they are not possible (the effect could even be positive)

In practice, Proposition 4 implies that the negative effect of price informativeness onboard size and independence is stronger (in absolute value) when firms are not insulatedfrom the market for corporate control This implication can be tested by using takeoverdefenses as a proxy for the likelihood of takeovers (Ambrose and Megginson (1992))

2.3 Discussion of the Main Assumptions

For the sake of presenting our ideas in an intuitive and simple way, we choose a particularsetting for the model in which generality (and some elegance as well) is sacrificed Webelieve that most of the ingredients that are relevant for understanding the relation betweencorporate boards and stock price informativeness are present, but in some instances they areoversimplified, which we acknowledge

One of our main simplifications is the way in which we model the formation of prices Wetreat the process by which prices reveal information as a black box, whereas we could havedeveloped a much more detailed market microstructure model with different prices being

formed under different informational conditions However, for the purposes of our paper

we are simply interested in establishing a link between a more knowledgeable market andthe characteristics of the board, which we believe to have achieved with the current simplestructure

The way in which we model the board of directors is also simplified We focus on twoboard characteristics: size (or capability of advising) and independence (or monitoring in-tensity) We could have modeled these characteristics, along with their costs and benefits, in

a much more complex way In particular, we could have endogenized all costs and benefits

of advising and monitoring, as is the case in some of the board literature However, most ofthe results from the literature are well known, and it is unclear what is gained by replicatingsuch results

A limitation of our analysis is the way in which we model the contracting process betweenthe firm and the CEO We assume that the CEO simply holds some shares, and that such

an arrangement is not a consequence of an optimal compensation scheme There is a vastliterature that deals with the issue of how to provide an agent with the right incentives Inthis literature, there are always some limitations on the contracting possibilities that preventfull alignment of interests between CEOs and owners at a reasonable cost Some of theusual assumptions used to justify less-than-full alignment of interests include limited liability,limited CEO wealth, risk aversion, unverifiable actions, or simple contractual incompleteness.For our purposes, as long as interests are not fully aligned, our results go through Hence, wesimply consider a setup in which the CEO is exogenously awarded a percentage of the shares

of the company We could have another round or period in the model in which shareholderswould optimize this contract, but this modification should not affect in any meaningful waythe relationship between board structure and price informativeness, which is the core of ouranalysis

In particular, in our setup, without ad hoc restrictions on the contracting space, it isvery easy to attain the first-best outcome The support for the value of the firm involves

six different values, which are just enough to allow for an unrestricted optimal contract toachieve the first-best This is so because firm value is fully informative about the state ofnature If we were to allow for optimal contracting, we would have to modify the setup

so that firm value would not be completely informative about the underlying state.6 Thiswould unnecessarily complicate the model without yielding further insights

Finally, we have compared only two polar cases: the one in which the probability oftakeover is one and the one in which it is zero The results can be easily extended to the case

in which the probability of takeover is any value τ ∈ [0, 1] When τ < 1 there is a third boardstructure that may be optimal and needs to be considered It corresponds to the situation

in which the market is informed (with probability p), not just the board In such a case, themarket will discipline the CEO with probability τ and, in case the market fails to replacethe CEO, the board fires the CEO with probability i That is, the probability that the CEO

is fired in case Im = Id={M} is τ + (1 − τ) i The firm can choose having an intermediatelevel of board independence, i∗∗∗, such that the CEO prefers to drop the project when state

M is revealed to everyone in order to avoid both external monitoring with probability τ andinternal monitoring with probability (1 − τ)i∗∗∗:

cumber-6 This is a standard assumption in moral hazard models with unobservable actions and complete ing.

contract-3 Sample and Variables

Our sample is based on the Investor Responsibility Research Center (IRRC) database from

1996 to 2001 The IRRC database contains detailed data on board and director istics for a large number of firms We exclude financial firms (SIC codes 6000-6999) andfirm-year observations with fewer than three directors After these adjustments the number

character-of firms in the sample is 2,188 Next we merge the IRRC database with the probability character-ofinformation-based trading (PIN) dataset The final sample consists of 1,358 firms and 5,485firm-year observations We obtain additional board characteristics such as CEO ownershipand tenure from ExecuComp We obtain financial and segment data from Compustat andstock price and turnover data from CRSP The governance index of Gompers, Ishii, andMetrick (2003) (GIM) is also available from the IRRC database Finally, we obtain data onthe number of analysts covering a firm and institutional holdings from IBES and ThomsonCDA/Spectrum Institutional 13f Holdings We winsorize variables at the bottom and top1% levels.7 Table 1 describes in detail the definition and sources of the variables used in thisstudy

3.1 Measures and Determinants of Board Structure

Our dependent variables are board size and board independence Board size is defined asthe number of directors on the board Board independence is proxied by the fraction ofindependent directors In order for a director to qualify as independent, he or she must not

be an employee, a former executive, or a relative of a current corporate executive of thecompany, and must not have any business relations with the company

In order to identify the effect of price informativeness on the structure of corporate boards,

we need to control for other determinants of board structure The literature on corporateboards provides many suggestions with respect to the determinants of board structure Onehypothesis is that the scope and complexity of firms’ operations affect board structure (Fama

and Jensen (1983) and Coles, Daniel, and Naveen (2006)) According to this hypothesis,larger and more complex firms require larger boards For example, as a firm grows anddiversifies there is an increasing demand for specialized board members to perform taskssuch as managerial compensation and auditing Furthermore, the scope and complexity ofoperations can also have an effect on board independence For example, more complex firmsface larger agency costs and thus require added board monitoring.

We consider three proxies to capture firms’ operational complexity: firm size (as measured

by equity market capitalization), firm age (as measured by the number of years since thefirm’s stock appeared in the CRSP database), and the number of business segments Weexpect larger, older, and more diversified firms to have larger boards and a higher fraction

of independent directors

Many theories of the determinants of boards emphasize the importance of the firm’sbusiness and information environment (Demsetz and Lehn (1985), Raheja (2005), Adamsand Ferreira (2007), and Harris and Raviv (2007)), while others emphasize the negotiationbetween the CEO and the outside board members (Hermalin and Weisbach (1998)) We useseveral control variables that capture some of the elements of these theories To control forthe cost of outside monitoring, we consider growth opportunities as proxied by the market-to-book ratio and R&D expenditures, stock price volatility as proxied by total stock returnvariance, and CEO stock ownership and tenure We consider free cash flow, leverage andprofitability (return-on-assets) because these variables could be related to agency conflictsand to opportunities to extract private benefits We include the governance index (GIM) as ameasure of the number of takeover defenses in the firm’s charter For a more comprehensivediscussion of some of these variables and their relationships with board structures, see Boone,Field, Karpoff, and Raheja (2006), Coles, Daniel, and Naveen (2006), Gillan, Hartzell, andStarks (2006), and Linck, Netter, and Yang (2007)

We also introduce institutional ownership variables as additional controls in our empiricalspecifications Because the trading activity of large institutional investors may have a direct

effect on the amount of private information revealed by stock prices, we expect institutionalownership to be correlated with PIN Because there is evidence that many institutional in-vestors perform an active role in corporate governance (e.g., Hartzell and Starks (2003)),

an omission of institutional ownership variables may lead to spurious correlations betweenprice informativeness and board structure.8 In addition, institutional investors are expected

to have more influence when they are large shareholders, because they have easier access

to board members (Carleton, Nelson, and Weisbach (1998)) and benefit from economies ofscale in monitoring activities Thus, we consider two measures of concentrated holdings: in-stitutional blockholder ownership (defined as holdings by institutional investors with at least5% of the shares outstanding), and the concentration of institutional ownership (measured

by the Herfindahl index) We also control for the total institutional ownership (defined astotal holdings by institutions as percentage of shares outstanding).9

Table 2 presents the descriptive statistics of our data Board size ranges from 3 to 30directors, with a median of 9 directors The median fraction of independent directors is0.813 The median firm in our sample has market capitalization of $1.4 billion, age of 41.1years, and leverage of 29.4% The mean number of business segments is 2.3, the mean R&Dexpenditures-to-assets ratio is 1.5%, and the mean CEO ownership is 1.9% The median firmhas 10 takeover defenses (out of a maximum of 24) The mean total institutional ownership is51.5% and the mean institutional blockholder ownership is 13.9% The descriptive statisticsare comparable to other studies that use a similar sample of firms, such as Coles, Daniel,and Naveen (2006) and Gillan, Hartzell, and Starks (2006)

8 There is some controversy in the literature whether some types of institutions specialize in monitoring and activism rather than trading Research by Brickley, Lease, and Smith (1988) and Almazan, Hartzell, and Starks (2005) show that only “independent institutions” (mutual fund managers and investment advisors) are effective monitors, while “grey” institutions (bank trusts, insurance companies, and other institutions) are not.

9 We obtain similar results using alternative measures of concentrated holdings: ownership by the five largest institutional investors, ownership by the single largest institutional investor, and ownership by out- side blockholders taken from Dlugosz, Fahlenbrach, Gompers, and Metrick (2006) Similar results are also obtained when we only include total institutional ownership or institutional ownership concentration as explanatory variables.

3.2 Measuring Price Informativeness

Our measure of stock price informativeness is the probability of information-based trading(PIN) developed by Easley, Kiefer, and O’Hara (1996) This measure is based on a structuralmarket microstructure model in which trades come from noise traders or from informedtraders Easley, Hvidkjaer, and O’Hara (2002) provide a detailed and intuitive description

of the theoretical foundations of PIN Here we simply explains its intuition

The trading process is modeled in the following way At the beginning of each day, there

is a probability λ that some traders acquire new information about the fundamental value

of the firm Trading orders arrive throughout the day according to Poisson distributions, at

a rate of μ for informed trade orders, b for uninformed buy orders, and s for uninformedsell orders The probability that the opening trade of the day is information-based is:

Easley, Hvidkjaer, and O’Hara (2002) use intra-day transaction data over a given period

to estimate the parameters above and, consequently, the probability of informed trading in

a stock Notice that PIN should be low for stocks with less fluctuation of daily buy and sellorders, as these orders are more likely to come from liquidity or noise trading Furthermore,PIN should be high for stocks that display frequent large deviations from their normal orderflows

Our sample includes all stock-year observations that have PIN estimates (and boarddata) in the 1996-2001 sample period, based on the data from Easley, Hvidkjaer, and O’Hara(2002).10

Previous empirical work generally supports the use of PIN as a valid measure of the

(http://www.smith.umd.edu/faculty/hvidkjaer/data.htm).

probability of informed trading and stock price informativeness Easley, Hvidkjaer, andO’Hara (2002) find that the risk of private information trading is priced and carries a pos-itive risk premium, i.e stocks with higher PIN have higher expected returns Vega (2006)shows that stocks with higher PIN have smaller reactions following earnings announcements,which is consistent with these stocks incorporating more private information and trackingmore closely their fundamental value PIN also seems to be related to managerial decisions.Chen, Goldstein, and Jiang (2006) find a positive relation between PIN and the sensitivity

of investment to stock prices, which supports the hypothesis that managers learn from theprivate information incorporated into stock prices Ferreira and Laux (2007) find a positiverelation between strong corporate governance (few takeover defenses) and PIN, suggestingthat strong shareholder protection induces private information collection and trading byinformed market participants Overall, the available empirical evidence supports the inter-pretation of PIN as a valid measure of stock price informativeness

Table 2 presents descriptive statistics of PIN The mean (median) PIN is our sample is0.142 (0.133) with standard deviation of 0.05 The descriptive statistics of PIN are compa-rable to those reported in Easley, Hvidkjaer, and O’Hara (2002)

4 Main Empirical Results

In this section we present the main results on the relation between board structure and priceinformativeness Specifically, we test the empirical predictions of our model (see Propositions

1 and 2) In the next two sections we provide additional evidence that is consistent with ourhypotheses and perform several robustness checks

4.1 Board Size and Price Informativeness

In Table 3 we present the outcome of OLS regressions in which the dependent variable isthe logarithm of board size We use the log because board size is bounded below by zero.11

The focus explanatory variable is the probability of information-based trading (PIN) Table

3 presents the results from several specifications of the board size regression both with arestricted and a full set of explanatory variables We include industry and year dummies inthe set of explanatory variables.12 In our setting, cross-correlation and autocorrelation inour dependent variable are likely to occur In such a case, conventional standard errors may

be biased downwards Therefore, all reported t-statistics are adjusted for heteroskedasticityand within-firm correlation using clustered standard errors In addition, the inclusion of yeardummies accounts for some forms of cross-sectional dependence We do not use firm fixedeffects because the time-series dimension of the data is too short, which is a problem if theexplanatory variables vary little over time In such a case, fixed-effects regressions may fail

to detect relationships in the data even when they exist.13

Column (1) presents the results of an OLS univariate regression of board size on PIN.There is strong evidence of a negative and significant relation between board size and PIN.The estimated PIN coefficient is -1.8769, with a very high t-statistic of -14.01 This effect isalso economically significant: a one-standard deviation increase in PIN predicts a decrease inboard size of roughly one director (for a board with average size) This finding corroboratesour model’s first prediction (see Proposition 1)

Controlling for firm characteristics that are related to board size does not change thequalitative results, although the coefficients and the robust t-statistics are attenuated Col-

11 We obtain similar results using board size as the dependent variable.

12 We obtain similar results when we do not include industry or year dummies in the regression specification.

13 See, for example, Hamermesh (2000) and Zhou (2001) If individual firm effects are uncorrelated with the other right-hand side variables, a model using random effects would also correct for within-firm correlation However, Hausman tests indicate that the assumptions of the random effects model are not satisfied and that the random effects estimator is not valid Therefore, we use OLS regressions with clustered robust standard errors to account for within firm correlation of the error terms, i.e observations within a firm are not treated as independent, but observations across firms are For a review of error correction methods in panel data studies, see Petersen (2005).

umn (2) of Table 3 reports the estimates for such a case The estimated coefficient on PIN

in column (2) is -0.5127 with a t-statistic of -2.93 We conclude that the probability of formed trading displays a statistically significant negative relationship with board size Aftercontrolling for firm characteristics and potential heterogeneity across industries and years,

in-we find that a one-standard deviation increase in PIN is associated with a decrease in boardsize of roughly a quarter of a director (for a board with average size)

Most of the other firm-level characteristics that are included as controls enter with theexpected signs and are usually statistically significant Firm size, leverage, firm age, and thenumber of business segments are positive and significant in the board size regressions Thesefindings are consistent with the scope of the operations hypothesis in that more complexfirms require larger boards We also find that growth firms (high book-to-market and R&Dexpenditures), firms with high stock price volatility, and firms with high CEO ownershiphave smaller boards Return on assets enters negatively and significantly in all specifications.These findings are consistent with the literature on board structure determinants (e.g Boone,Field, Karpoff, and Raheja (2006) and Linck, Netter, and Yang (2007))

Columns (3) - (5) further control for other firm characteristics, such as the governance dex (GIM) and variables measuring total institutional ownership and institutional ownershipconcentration The negative relation between board size and PIN is robust to these addi-tional control variables The GIM coefficient is positive and statistically significant, which

in-is consin-istent with the idea that board size in-is increasing in the degree of insulation from themarket for corporate control and of managerial entrenchment This finding is consistent withthe empirical evidence in Gillan, Hartzell, and Starks (2006) The institutional ownershipconcentration variables (as well as total institutional ownership) are not significantly related

to board size

4.2 Board Independence and Price Informativeness

In Table 4 we present the outcome of OLS regressions in which the dependent variable is alogistic transformation of the fraction of independent directors (i.e y = ln(z/1 −z)) We usethe logistic transformation because the fraction of independent directors is bounded betweenzero and one.14 The specifications in each column of Table 4 replicate exactly the ones fromTable 3 All regressions include industry and year effects, and t-statistics are adjusted forheteroskedasticity and autocorrelation using clustered standard errors

Column (1) presents the estimated coefficient of a univariate regression of the fraction

of independent directors on PIN There is strong evidence of a negative and significantrelationship between board independence and PIN The estimated PIN coefficient is -1.9477with a high t-statistic of -6.14 This effect is also economically significant: a one-standarddeviation increase in PIN predicts a decrease in board independence of roughly 1.7 percentagepoints (for a board with average independence) This finding corroborates our model’s secondprediction (see Proposition 2)

Controlling for firm characteristics that are related to board independence does notchange the qualitative results In column (2), the PIN coefficient is -1.1266 with a t-statistic

of -2.86 Overall, we find that the probability of informed trading displays a statisticallyand economically significant relationship with board independence After controlling forfirm characteristics and potential heterogeneity across industries and years, we find that aone-standard deviation increase in PIN is associated with a decrease in board independence

of roughly 1 percentage point (for a board with average independence)

With respect to the other explanatory variables, we find that leverage, firm age, and thenumber of business segments are positively and significantly related to board independence,while firm size enters with a positive but insignificant coefficient at the 5% level in themajority of the specifications These findings are consistent with the scope of the operations

14 We obtain similar results using the fraction of independent directors or the logarithm of the fraction of independent directors as dependent variables.