The inversely U-shaped relation between board size and company performance

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UNIVERSITY OF AMSTERDAM

FACULTY OF ECONOMICS AND BUSINESS

BSc Economics & Business

Bachelor Specification Finance and Organization

The inversely U-shaped relation between board size and company

performance

Author:

D. Oostendorp

Student number: 10650903

Thesis supervisor: Dr. J.J.G. Lemmen

Finish date:

31 January 2018

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Statement of Originality

This document is written by Dirk Oostendorp who declares to take full responsibility for the contents of this document.

I declare that the text and the work presented in this document are original and that no sources other than those mentioned in the text and its references have been used in creating it.

The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.

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ABSTRACT

Using a recent sample of 153 companies from the S&P500 from the information technology, consumer staples, and health care industry, I examine the relation between firm performance and board structure in 2015. I find that board structure is partially determined by past performance, and control for this by using a dynamic generalized method of moments (GMM) estimator. My key conclusion is that I find a positive relation between board size and firm performance, and a negative relation between board size squared and firm performance. These results suggest the relation between board size and firm performance is inversely U-shaped. These results support the theory of Lipton and Lorsch (1992), and Jensen (1993), about the existence of an optimal board size. I use Tobin’s Q as approximation for company performance, and numerous controls for board characteristics and firm-specific characteristics. The results are not robust to the use of return on assets as dependent variable. In most of the previous research, the relation between board structure and firm performance is

estimated without systematically controlling for unobserved heterogeneity, simultaneity, and dynamic endogeneity. This might be an explanation for the conflicting evidence on the relation between board size and firm performance.

Keywords: Corporate governance; Board size; Firm performance; Endogeneity; Dynamic GMM estimator

JEL Classification: G30

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LIST OF TABLES

Table 1 The effect of board size on performance: summary of previous studies

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Table 2 Descriptive statistics on board characteristics variables 15

Table 3 Descriptive statistics on company performance and firm-specific variables 16

Table 4 Relationship between board structure and firm-specific variables, and past

performance 18

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1. Introduction

In this paper I examine the relation between board size and firm performance for publicly traded large cap U.S. firms in the information technology, consumer staples and health care industry. At least in theory, the board of directors is one of the most important corporate governance systems to let corporate managers pursue the interest of shareholders. The board has to carefully advise and monitor top management. Several aspects of the board might influence its performance, such as: board

independence, board composition, CEO power, and board size.

Lipton and Lorsch (1992) and Jensen (1993) were among the first to argue that an optimal board size exists, setting it at 8 or 9 directors. They suggest that smaller boards lack the necessary resources to advise top management properly. On the other hand, larger boards can be less effective because of increased agency problems like free riding, causing the board to neglect its monitoring duties. The first empirical research on board size finds a significant negative relation between board size and company valuation for large firms in the US (Yermack, 1996) and small privately held firms in Finland

(Eisenberg et al., 1998). These early findings are inconsistent with a unique optimal board size. Some recent papers debated the way previous research handled the issue of endogeneity in corporate governance (Boone et al., 2007; Coles et al., 2008; Linck et al., 2008). They argue that board size is determined by firm-specific characteristics such as: firm age, firm size, profitability and

Tobin’s Q. Because profitability is negatively related to board size, previous studies are criticized for not properly controlling for the endogeneity issue (Wintoki et al., 2012).

Wintoki et al. (2012) argue that endogeneity in corporate governance research can be caused in three ways. Which is through unobservable heterogeneity, simultaneity, and dynamic endogeneity. First, Wintoki et al. (2012) argue that unobservable heterogeneity is a source of endogeneity if there are factors unobservable by the researcher that affect both firm performance and the explanatory variables. Theory suggests that this is the case. Second, Wintoki et al. (2012) argue simultaneity arises in the board structure/firm performance relation if, as theory suggests, firms choose their board structure in a period, with view of a particular level of performance in that period. Then while performance may influence board structure, the reverse is also true. Third, Wintoki et al. (2012) suggest that dynamic endogeneity exist in corporate governance research because past performance has a direct influence on the firm’s information environment and profit potential, all of which are factors that determine a firm’s board structure (Boone et al., 2007; Coles et al., 2008; Linck et al., 2008).

Wintoki et al. (2012) argue that traditional OLS and fixed-effect estimates are biased that the best way to control for the endogeneity is to use a generalized method of moments (GMM) estimator, which allows for a dynamic relationship between board size and firm performance. Wintoki et al. (2012) find no significant relationship between board size and firm performance.

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In this paper I will, using a dynamic GMM estimator, examine whether the predictions of Lipton and Lorsch (1992) and Jensen (1993) about optimal board sizes are true for U.S. publicly traded companies in 2015 from the information technology, consumer staples, and the health care industries. Following the theory of Lipton and Lorsch (1992), the relationship between board size and Tobin’s Q is expected to be inversely U-shaped, (from a certain point the agency costs will outweigh the resource benefits of adding another director).

This paper contributes to the existing literature by examining recent data, and by testing whether the theory of Lipton and Lorsch (1992) and Jensen (1993) about optimal board sizes hold, by

estimating a non-linear relation using the GMM estimator. In most of the previous research, the relation between board size and firm performance is estimated without systematically controlling for endogeneity issues. This might be an explanation for the conflicting evidence on the relation between board size and firm performance. This paper also contributes to existing literature by using more control variables and provides a new measure for CEO power. Jensen (1993) suggests that greater control by the CEO leads to less candid discussion of managerial performance. Besides the commonly known influence of the fraction of independent board members on CEO power, a new measure for CEO power, the wage dispersion between the CEO and the CFO will be added. Differences in total compensation between the CEO and other board members are often quite substantial. In a recent paper on team performance, Breunig et al. (2014) found a negative relation between wage dispersion and team performance using game-level data from Major League Baseball. Their findings are

generalizable to many labor economic situations and group performance.

In a sample of 153 large public information technology, consumer staples, and health care companies from the S&P500 in 2015, I find, using the dynamic GMM estimator, an inversely U-shaped relation between firm performance, as represented by Tobin’s Q, and the size of the board of directors. This result supports the theory that initially, increasing board size will lead to higher performance (resource dependency theory). But, when boards become too large, they become less effective because of increased agency problems like free riding. This result is not robust when using ROA as performance measure. When I estimate the relation using static and dynamic OLS estimators, I find no significant relation between Tobin’s Q and board size.

I also find evidence that supports the theory of Hermalin and Weisbach (1998) that firms with high performance have less independent boards. I find no evidence for a relation between board ownership and firm performance in any of the estimated equations. Similarly, I find no evidence for a relation between CEO power and firm performance.

The remainder of this paper is as follows. Section 2 gives an overview of prior literature on board size. Section 3 explains the methodology. Section 4 describes the data used. Section 5 presents the empirical results, and section 6 concludes.

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2. Prior literature on board size

Two of the main functions of the board of directors are advising and monitoring (Adams and Fereirra, 2007). The advisory role involves providing expert advice to the CEO and access to resources and information (Jensen, 1993). According to Fama and Jensen (1983), this expert advice is provided by both inside and outside directors. Fama and Jensen (1983) state that the outside directors act as arbiters in arguments between inside directors and perform tasks that would otherwise involve serious agency problems, like replacing a top management position or setting executive compensation. An advantage of a larger board size is that there is a greater source of information and resources; hence increasing the board size will lead to higher performance (resource dependency theory) (Dalton et al., 1999). In its role as monitor, the board has to discipline malfunctioning management teams and ensure that management maximizes shareholder value. Raheja (2005) argues that inside directors offer a lot of firm-specific information, but may have a conflict of interest for private benefits and a lack of independence from the CEO. Guest (2009) states that outside directors are more independent and provide better monitoring, but are less informed about firm-specific business compared to inside directors. Similar as for advising, a larger board size and an increasing fraction of outside directors increases the total information possessed by the board, which leads to better monitoring (Lehn et al., 2009). Therefore, both the advising and the monitoring function initially advocate that larger boards’ sizes will increase firm performance.

However, larger boards are not always better; eventually a large board size will have a negative effect on performance. Hackman and Gersick (1990) argue that in large groups individuals are less likely to take initiative to move the group out of its dysfunctional behavior. This also holds for corporate boards due to coordination costs and free rider problems in large boards (Lipton and Lorsch, 1992; Jensen, 1993). Jensen (1993) also suggests that another effect of a large board size is less candid discussion of managerial performance and large boards may lead to greater control by the CEO. Since an individual director’s incentive to acquire information and monitor managers is low in large boards, CEO’s may find larger boards easier to control (Jensen, 1993). Lipton and Lorsch (1992) and Jensen (1993) both suggest that an optimal board consists of respectively eight or nine and seven or eight directors because they think that the inefficiency costs of having more directors outweigh the benefits from a certain point.

The key findings of existing empirical studies are reported in Table 1 below. The majority of empirical research from the U.S. suggests a negative relation between board size and company performance. Yermack (1996) finds a negative relation between board size and Tobin’s Q for 452 large U.S. corporations between 1984 and 1991. Yermack (1996) argues one other thing that influences Tobin’s Q are future investment opportunities. Yermack (1996) controls for this by using the ratio of capital expenditures over sales as a proxy for future investment opportunities. His findings

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Table 1. The effect of board size on performance: summary of previous studies

This table reports the findings of previous studies that examine the relation between board size and firm performance. OLS stands for ordinary least squares regression models. FE stands for fixed-effects models. IV stands for instrumental variable models. GMM stands for generalized method of moment models. Relationship with board size is: None if significance is lower than 10% level.

Author(s) Region _periodTime

Depende nt variable

Method Relationship Board size Control variable(s) Yermack, D. (1996) U.S. 1984-1991 TobinsQ, ROA

OLS, FE OLS: Negative FE: Negative Company performance, Size, Growth opportunities, Diversification, Board structure Eisenberg et al. (1998) Finland 1992-1994 ROA OLS IV OLS: Negative IV: Negative Size, Diversification, Age, Investment opportunities, Board structure Conyon & Peck (1998) U.K., NL, Denmark, France, Italy 1992-1995

TobinsQ GMM Negative Size, Previous performance Dalton et al. (1999). U.S. Not specifie d ROA Meta-analysis

Positive Firm size, Board structure Beiner et

al. (2004)

Switserland 2001 TobinsQ OLS, IV None Leverage, Size, Growth, Previous performance, Board structure Adams & Mehran (2005) U.S. 1986-1999

TobinsQ FE, IV FE: Positive IV: Positve Haniffa & Hudaib (2006) Malaysia 1996-2000 TobinsQ, ROA

OLS TobinsQ: Negative ROA: Positive Board structure, Previous performance, Size, Capital expenditures Coles et al. (2008) U.S. 1992-2001

TobinsQ OLS Negative for total regression

Significant Positive for large diversified firms

Risk, Previous performance, Intangible assets, Firm size, Business segments, Leverage, Board structure Guest, P.M. (2009) U.K. 1981-2002 ROA, TobinsQ, TSR OLS, FE, GMM OLS: Negative FE: Negative GMM: Negative

Size, Age, Debt, T&D, STDDEV, Segments, Board structure Davidson et al. (2010) U.S. 1988-1999

TobinsQ FE Negative Board structure, Size, ROA Wintoki et al. (2012) U.S. 1991-2003 ROA, TobinsQ, ROS GMM, OLS, FE GMM: None OLS: Negative FE: Negative Size, Age, Leverage, Segments, Risk, Previous performance

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are supported by other U.S research (Coles et al., 2008, Davidson et al., 2010), although Coles et al. (2008) find a positive relation between Tobin’s Q and board size for large diversified firms. Only one U.S study finds a positive relation between board size and company performance (Dalton et al., 1999). Adams and Mehran (2005) also find a positive, but less robust effect of board size on company performance.

Findings in studies from other countries show very similar results. In a study in Finland a significant negative correlation between board size and profitability is found for small and midsized firms from Finland (Eisenberg et al., 1998), which extends previous findings to small firms with small boards. In another study in Europe, Conyon and Peck (1998) find a significant relation between return on assets and board size for firms from five different countries. In a study in the UK of 2746 listed firms over 1981-2002, Guest (2009) finds that board size has a strong negative impact on profitability, Tobin’s Q and share returns. For Switzerland Beiner et al. (2004) find no significant relation between board size and Tobin’s Q, although they do find that board size is an independent governance

mechanism. In their research Beiner et al. (2004) argue that their findings are consistent with

expectations of Lipton and Lorsch (1992) and Jensen (1993) that there is an optimal size of the board. Beiner et al. (2004) argue that when studying firms with board sizes that are at an “optimal” level, no statistically significant relation is expected to be found between board size and firm valuation. For 25 state owned enterprises in Canada from 1976-2000, Bozec (2005) finds a statistically negative relation between return on sales and board size, but no statistically significant relation for other performance measures. In a study of 347 Malaysian companies listed on the Kuala Lumpur Stock Exchange (KLSE) between 1996-2000, Haniffa and Hudaib (2006) find a significant negative relationship between board size and Tobin’s Q.

Theoretical and empirical research on corporate governance is complicated by the endogenous relation between the control forces operation on a firm and its decisions (Wintoki et al., 2012). Wintoki et al. (2012) argue that three types of endogeneity bias estimates of how board size affects company performance or valuation: unobservable heterogeneity (which arises if there are

unobservable factors that affect both board size and company performance), simultaneity (which arises if board size is simultaneously determined with firm performance), and finally dynamic endogeneity (which occurs if board size is determined by past performance). Previous studies tried to overcome this problem by using fixed effect models (Yermack, 1996) and instrumental variable techniques (Eisenberg et al., 1998; Adams and Mehran, 2005; Beiner et al., 2004; Guest, 2009). Although these techniques could possibly eliminate the endogeneity problems, Wintoki et al. (2012) argue that these methods require the identification of strictly exogenous instrumental variables, which is almost impossible in corporate finance research. Wintoki et al. (2012) therefore argue that the most appropriate model for investigating the relation between board size and performance is the GMM estimator. Using this model, Wintoki et al. (2012) find no significant negative relation between board

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Some recent studies looked at the determinants of board size (Boone et al., 2007; Coles et al., 2008; Linck et al., 2008). They all argue that board size is positively related to firm scale, complexity and a firm’s greater need of information. All studies find a significant positive relation between board size and firm size, and some proxies for firm complexity, including leverage, R&D expense, number of business segments disclosed in financial statements and firm age (Boone et al., 2007; Coles et al., 2008; Linck et al., 2008). These findings suggest that board size is endogenously influenced by firm-specific variables and that the effect of board size on performance and valuation may differ among different types of firms. Coles et al. (2008) indeed find that complex firms, which require more advice than simple firms, need a larger board of directors with more outsiders.

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3. Method

3.1. Models and hypothesis

Following the econometric approach of Wintoki et al. (2007), I will illustrate that other commonly used estimators that ignore the dynamic relation between current board structure and past performance may be biased. First, I test whether the relation between board size and Tobin’s Q is inversely U-shaped, using a static and a dynamic OLS regression.

LogTobin’s Q = α+ k1yit-1+ k2yit-2+ β1Board Size +β2Board Size Squared + Controls +ε (1)

For the static model, it is assumed that k1 = k2 = 0. Second, following the work of Wintoki et al. (2012), I will estimate this relation using a dynamic Generalized Mixed Methods (GMM) estimator.

LogTobin’s Q = α1 + k1yit-1+ k2yit-2+ β1Board Size +β2Board Size Squared + Controls +ε (2)

For all three models I test whether the coefficients β1>0 and β2<0 since then the inverse U-shaped relation between firm performance and board size holds. Following previous research (Wintoki et al., 2007), I use 2 lagged values of all endogenous independent variables as instruments for this

estimation. That is, I use historical values of firm performance, board structure, and other firm-specific variables as instruments for current changes in these variables. Wintoki et al. (2012) find that when they add more than two lags as instruments the older lags become insignificant. Hence, Wintoki et al. (2012) use two recent lags because these lags also include information from the older lags. I assume all independent variables except age to be endogenous.

3.2. Measuring company performance

The key performance measure I use as dependent variable is Tobin’s Q. This allows for easily

comparing results with previous research. Tobin’s Q is book value of total assets plus market value of equity minus book value of equity divided by book value of total assets. The proxy for Tobin’s Q is defined as

Approximate Tobin’s Q=(MVE+PS+DEBT)/TA. (3)

Where MVE is the product of a firm’s share price and the number of common stock

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firm’s total assets (Chung and Pruitt, 1994). These inputs for Tobin’s Q are obtained from Compustat. A high Tobin’s Q (greater than one) implies that the value of a firm’s stock is greater than the

replacement costs of its assets. This suggests that the market value reflects some unmeasured or unrecorded assets of the company. High Tobin's Q values encourage companies to invest more in capital because they are "worth" more than the price they paid for them. On the other hand, if Tobin's Q is low (between 0 and 1), the market value is less than the recorded value of the assets of the company. This suggests that the market may be undervaluing the company. Some studies found empirical evidence for the theory that Tobin’s Q is a proxy for growth opportunities, and that growth opportunities are a cause rather than a consequence of governance structures (Boone et al., 2007; Link et al., 2008). Thus, for robustness I will also estimate the models using the firm’s return on assets (ROA) as performance measure, where ROA is defined as net income divided by fiscal year-end total assets.

3.3. Governance variables

Our key explanatory variable is board size, which is measured as the total number of directors. In the analysis we consider the effect of five board structure variables on firm performance: board size, board size squared, board composition, board ownership and CEO power. I define the board characteristics as follows:

• Bsize, the number of directors on the board. • Bsize2, Board size*Board size.

• Indep, the proportion of independent directors on the board.

• Ownership, the proportion of shares held by all directors divided by total common shares outstanding.

• CEOcontrol, a dummy equal to one if the CEO earns more than four times as much as the CFO, and zero if otherwise. Total compensation data as reported in SEC filing obtained from ExecuComp.

3.4. Control variables

Recent studies, including those by Boone et al. (2007), Coles et al. (2008) and Linck et al. (2008), suggest that board size is determined by firm-specific variables and that firms choose their board structure depending on their firm-specific benefits and costs of monitoring, the scope and the complexity of its operations. They all argue that board size is positively related to firm scale, complexity and a greater need of information. As suggested by previous research, I use size, the

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number of business segments, leverage, research and development (R&D), age and future investment opportunities as determinants of board structure. I define these firm-specific control variables as follows:

• LogSize, logarithm of total sales.

• SEG, the number of business segments for which the firm reports.

• LEV, the proportion of book value of total liabilities divided by total assets. • R&D, the proportion of research and development expenses divided by sales. • AGE, the number of years since IPO.

• FIO, Future Investment Opportunities, calculates as the proportion of capital expenditures divided by sales.

3.5. Specification tests

The validity of the GMM estimator depends, at least partly , on two critical specification tests (Wintoki et al. 2012). First, the test of over-identification (Hansen J) of the validity of the instruments is a test under the assumption that I have the correct specification under the null hypothesis that the over-identifying restrictions are valid. Wintoki et al. (2012) point out that the power of the Hansen J specification test to detect misspecification increases with sample size.

Second, the test of exogeneity of the instruments. The GMM estimator makes an assumption about the exogeneity of the instruments. The assumption that any correlation between the endogenous variables and the unobserved fixed effect is constant over time. This assumption enables the use of lagged values as instruments. According to Wintoki et al. (2012) this assumption can be tested using the difference-in-Hansen test of exogeneity. This test also yields a J-statistic and is under the null-hypothesis that the subset of instruments I use are endogenous.

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4. Data

In this section I describe the data I use to illustrate the relation between board size and performance, the determinants of board size and the impact of endogeneity on empirical research in corporate finance.

4.1. Data

My analysis uses annual data on firms listed in the S&P500 at year-end in 2015. I use a sample selection rule that requires each company to be in one of the following industries; information technology, consumer staples and health care industry. For the dynamic GMM estimator I use two annual lagged values of all independent variables, except age as instruments. The sources for my board characteristic data are ISS, ExecuComp and annual proxy statements. Data on company financials is obtained from Compustat. The final sample in this paper consists of 153 large U.S. companies, divided over three different industries. Table 2 presents the descriptive statistics on board characteristics. Below, Table 3 presents the descriptive statistics on firm performance and all firm-specific control variables

Table 2.Descriptive statistics on board characteristics variables

In this table I report the descriptive statistics on board characteristic variables. The results are based on a sample of 153 firms (t=2015). Board characteristic data come from ExecuComp and ISS.

Variable Number Mean Median Standard deviation Minimum Maximum Board Sizet 153 10.699 11 1.960 5 15 Indepenencet 150 0.823 0.857 0.104 0.333 1 Ownershipt 151 0.036 0.01 0.102 0 1 CEOcontrolt 153 0.131 0 0.338 0 1

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Table 3. Descriptive statistics on company performance and firm-specific variables

In this table I report the descriptive statistics on company performance and firm-specific variables. The results are based on a sample of 153 firms (t=2015). Firm characteristic data come from Compustat. Tobin’s Q is book value of total assets plus market value of equity minus book value of equity divided by book value of total assets. Size is the total sales. Segments is the number of business segments the firm operates in. Lev the proportion of book value of total liabilities divided by total assets. R&D is the proportion of research and development expenses divided by sales. FIO is Future Investment Opportunities, calculates as the proportion of capital expenditures divided by sales. AGE is the number of years since IPO.

Variable Number Mean Median Standard deviation

Minimum Maximum

Tobin’s Qt 151 2.207 1.716 1.580 0.312 12.338

Sizet (millions U.S. $) 153 27582 9256 53002 1032 483521

Segmentst 152 2.664 2 1.852 1 8

Levt 152 0.591 0.565 0.224 0.100 1.450

R&Dt 152 0.087 0.060 0.114 0.000 0.960

FIOt 153 0.044 0.036 0.036 0.002 0.248

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5. Regression analysis

In this section I examine the empirical relation between board size and company performance using a static OLS model, a dynamic OLS model and a dynamic GMM estimator. My econometric approach closely follows that of Wintoki et al. (2007). Section 5.1 presents empirical evidence for the dynamic relation between board structure and the firm’s historical performance and firm-specific

characteristics. In section 5.2, I estimate the relation between board size and firm performance using a static and a dynamic OLS estimator and a dynamic GMM estimator. In section 5.3, I check the robustness of my results.

5.1.The dynamic relation between current board structure and the past

Wintoki et al. (2007) argue it is empirically important to have sufficient lagged values of all variables to capture all information from the past. They argue it is important for two reasons. First, if not all of the influence of the past on the present is captured, then there could be omitted variable bias. Second, Wintoki et al. (2007) argue that all the older lags are exogenous with respect to the residuals of the present, thus they can be used as instruments in the dynamic GMM estimator. Glen, Lee, and Singh (2001) and Gschwandtner (2005) suggest that two lagged values are sufficient to capture the influence of the past on the performance/governance relation.

One of the greater issues of empirical research on corporate governance is the endogeneity between the dependent variable and the control variables. In Table 4, I show some empirical evidence of the relation between board structure and firm-specific variables, and past performance. Following the approach of Wintoki et al. (2007), I present results from OLS regressions of performance and firm-specific characteristics from two years before on current board structure and firm characteristics. I find that board size is significantly positively related to past performance and significantly negatively related to past board independence. This result suggests that firms that performed well in the past will have larger boards. Current board size is significantly negatively related to past board independence, indicating that when a board becomes more independent in the past, the board size will decrease. In contrast to results of Wintoki et al. (2007), I do not find evidence to support the theory of Fama and Jensen (1983). In my analysis, I do not find a significant relation between firm size and firm

performance. Hence, I cannot argue that firms that have done well in the past will be larger today, and have a larger board as result.

Table 4 does show that the potential control variables are dynamically endogenous. Current levels of research and development expense (R&D) and the number of business

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Table 4 Relationship between board structure and firm-specific variables, and past performance

In this table I report the results of OLS regressions of current board size (Bsize), independence (Indep), and current firm-specific variables, on past performance and historic values of board structure and firm-specific variables. Performance is measured by the logarithm of Tobin’s Q (LogTob). The firm-specific variables include firm size (LogSize), research and development expense (R&D), number of business segments (SEG), leverage (LEV), future investment opportunities (FIO) and firm age (AGE). Other board characteristics include board size squared (Bsize2), board stock ownership (Ownership) and CEO control (CEOcontrol). The results are based on a sample of 153 firms selected every year (2013, 2014 and 2015). All board characteristics data are obtained from ISS and ExecuComp. All firm characteristic data is obtained from Compustat. Table 2 reports the results of the regressions in which the dependent variables are current levels. All t-statistics (in parenthesis) are based on robust standard errors.

Bsize Indep LogSize R&D SEG LEV FIO Dependent variable is level at time t

LogTob (t-2) 0.521** (2.222) -0.006 (-0.604) -0.265 (-1.618) 0.036** (2.288) -0.754*** (-2.974) 0.019 (0.615) 0.008 1.517 LogSize (t-2) 0.219* (1.717) -0.003 (-0.535) -0.016** (-2.107) 0.184 (1.435) 0.035** (2.186) -0.003 -1.029 R&D (t-2) -1.382 (-1.010) -0.004 (-0.071) -2.676*** (2.686) -0.793 (-0.491) -0.411** (-2.191) 0.023 0.730 SEG (t-2) 0.097 (1.269) -0.006* (-1.908) 0.114** (2.120) -0.002 (0.398) -0.018* (-1.704) 0.000 0.235 LEV (t-2) -0.805 (-1.146) 0.044 (1.458) 0.569 (1.189) -0.131*** (-2.965) -0.868 (-1.143) -0.049*** (-3.412) FIO (t-2) -1.709 (-0.399) 0.007 (0.036) -0.247 (-0.081) 0.200 (0.688) -0.120 (-0.025) -1.530*** (-2.710) AGE (t-2) 0.002 (0.254) 0.000 (0.545) 0.013*** (2.989) 0.000 (1.042) 0.013* (1.796) 0.001 (0.808) 0.000 (0.669) Bsize (t-2) 1.576*** (4.297) 0.026 (1.654) Bsize2 (t-2) -0.470*** (-2.757) -0.001 (-1.486) Indep (t-2) -3.137** (-2.143) 0.788*** (12.675) Ownership (t-2) 2.038 (0.903) -0.162* (-1.699) CEOcontrol (t-2) 0.192 (0.519) 0.007 (0.455) R2 _0.723 _0.829 _0.495 _0.450 _0.382 _0.408 _0.399 Adjusted R2 0.477 0.656 0.213 0.169 0.110 0.131 0.124 No. observations 137 135 149 149 150 150 149

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segments (SEG) are both significantly related to past performance. While the t-statistics firm size (LogSize) and future investment opportunities (FIO) are nearly significant as well (-1.618 and 1.517 respectively). These results imply that it is not only the corporate governance variables that are endogenous, but also the firm-specific control variables used to proxy a firm’s environment.

5.2. The relation between board size and board size squared, and firm performance

In this section, I will examine the results from estimating the relation between board size and board size squared, and firm performance. To be able to compare results with previous research, and to show the problems of ignoring the dynamic relationship, I will estimate the following models:

• A static OLS model. • A dynamic OLS model.

• A dynamic fixed-effects model (GMM)

Table 5 reports the results for these estimations when the natural logarithm of Tobin’s Q is used as dependent variable (LogTobinsQ). Following the empirical approach of Wintoki et al. (2007) I include two lags of performance in the dynamic models. For all endogenous variables I include two lags, sampling annually, as instruments in the GMM estimate. My assumption, following that of Wintoki et al. (2007), is that all regressors except firm age are endogenous.

In the simple static OLS model, board size and board size squared are not significantly related to firm performance. These findings are similar to those obtained by recent studies including Beiner et al. (2004), Bozec (2005) and Wintoki et al. (2007). These coefficients remain statistically insignificant when I estimate the dynamic OLS model that includes two lags of performance. The magnitude of the estimates coefficients on board size and board size squared drop even further. For example, the coefficient on board size is insignificant in the static model (0.065, t=0.352), and insignificant (0.061, t=0.153) in the dynamic model. The adjusted R2 does improve from 27.1% in the static model to 76.0% in the dynamic model, and the coefficient for the one-year lagged performance is significantly positive (0.712, t=4.493). This indicates that previous performance explains a significant proportion of the variation in current performance. The drop in magnitude of the estimated coefficients on board size when I include the lagged performance variables in the dynamic OLS model suggest that current board size is correlated with past firm performance, which is an indicator of the endogeneity problem arising when estimating the relation between board size and firm performance. However, according to

Wintoki et al. (2007) it is possible that the lagged performance variables do not capture all of the unobserved heterogeneity. Following Wintoki et al. (2012) I estimate the relation between board size and firm performance using the GMM model, which enables me to estimate the relation, while including both fixed effects and past performance to account for the dynamic endogeneity problems

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Table 5 Relationship between board size and firm performance In this table I report the results from estimation of the model:

Yit= α1+ k1yit-1+ k2yit-2+ βXit+ γZit+ θDit+ εit, t=2015.

Yit is the natural logarithm of Tobin’s Q (LogTobinsQ). Xit includes board size (Bsize), and board size squared (Bsize2). Zit includes board

independence (Indep), board stock ownership (Ownership), a dummy variable to proxy CEO control which is one if the CEO earns four times as much as the CFO as reported to the SEC (CEOcontrol), firm size (LogSize), number of business segments (Segments), leverage (LEV), research and development expense (R&D), and future investment opportunities (FIO). Dit is the age of the firm (AGE). The results

are based on a sample of 153 firms selected every year (2011, 2012, 2013, 2014 and 2015). All board characteristics data are obtained from ISS and ExecuComp. All firm characteristic data is obtained from Compustat.For the static models, it is assumed that k1 =k2= 0. All

t-statistics (in parenthesis) are based on robust standard errors. The Hansen test of over-identification is under the null that all instruments are valid. The Diff-in-Hansen test of exogeneity is under the null that instruments used for the equations in levels are exogenous.The instruments used in the GMM estimation are: differenced equations: yit-3, yit-4_{, X}it-1, Xit-2, Zit-1, Zit-2.

Static model Dynamic models

Dependent variable (LogTobinsQ) OLS OLS GMM

Bsize 0.065 (0.352) 0.016 (0.153) 0.510*** (2.643) Bsize2 -0.002 (-0.233) -0.000 (-0.081) -0.025** (-2.567) Indep -0.485 (-1.035) 0.036 (0.132) -1.275* (-1.926) Ownership 0.340 (0.740) 0.294 (1.113) -0.422 (-0.839) CEOcontrol 0.030 (0.230) 0.001 (0.012) 0.141 (1.294) LogSize -0.136*** (-3.438) -0.062*** (-2.706) -0.071*** (-3.185) Segments -0.099*** (-3.935) -0.029* (-1.905) -0.058*** (-2.934) LEV 0.376* (1.775) 0.169 (1.387) 0.301*** (2.890) R&D 1.500*** (3.735) 0.380 (1.556) 0.133 (0.581) FIO 0.559 (0.439) -1.570** (-2.117) -1.101 (-1.521) AGE 0.003 (1.304) 0.002 (1.561) 0.010** (2.149) LogTobinsQ (t-1) 0.712*** (4.493) 0.786* (1.752) LogTobinsQ (t-2) 0.103 (0.691) 0.051 (0.123) R2 0.571 0.884 Adjusted R2 0.271 0.760

Hansen test of over-identification (p-value) 0.594

Diff-in-Hansen test of exogeneity (p-value) 0.6464

No. observations 146 146 131

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arising when estimating the governance/performance relation.

When I estimate using GMM, the results show that the coefficient of board size becomes positively significant (0.510, t=2.643) and the coefficient of board size squared becomes negatively significant (-0.025, t=-2.567). This is in contrast with estimates obtained from the static and dynamic OLS estimates, where both the coefficients of board size and board size squared are insignificant. These results support the theory of Lipton and Lorsch (1992), and Jensen (1993), about the existence of an optimal board size. Hence, these results support the hypothesis that the relation between board size and firm performance is inversely U-shaped.

The static and dynamic model, OLS estimates suggest no significant relation exist between board independence and firm performance. However, when I estimate the relation using the dynamic GMM model, board independence is negatively significantly related to firm performance (-1.275, t=-1.926). This result supports the theory of Hermalin and Weisbach (1998) that managers who have the highest level of skill, will be monitored less intensively by shareholders, so firms with managers with a high skill level will have less independent boards. Logically, these firms are firms with high levels of performance.

I find no evidence for a relation between board ownership and firm performance in any of the estimated equations. Similarly, I find no evidence for a relation between CEO power and firm

performance.

Table 5 also reports the results of the Hansen J test of over-identifying restrictions, and a test of the exogeneity of a subset of the instruments. The reported p-value of the J-statistic is 0.594, indicating I cannot reject the null hypothesis that the used instruments are valid. Table 5 shows a p-value of 0.6464 for the J-statistic produced by the difference-in-Hansen test. This implies I cannot reject the hypothesis that the additional set of instruments used in the GMM model is exogenous. If the p-value of the J-statistic produced by this test is significant, the assumption that enables the GMM estimator to use levels of lagged values would no longer be valid.

5.3. Robustness tests for GMM estimator

To make sure my results are accurate, I conduct two robustness tests. First, I use the market value of equity (calculated as price per share at year end * the number of common shares outstanding) as an alternative measure of firm size. The results are very similar, the only noteworthy change is that the relation between board independence and firm performance becomes insignificant (-0.985, t=-1.337), and the variable CEO control becomes positively significantly related to firm performance (0.192, t=1.759).

Second, I regress the model using the GMM estimator, while I use return on assets (ROA) as dependent variable and market value of equity as a measure for firm size. All the estimated

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coefficients in this model have the same direction, except the coefficient on firm size is now positive. However, all coefficients on board size and other board structure variables become insignificant. Thus, in contrast to the estimation using Tobin’s Q, when I use ROA as performance measure I find no significant relation between board size and performance. These findings are similar to those obtained by Wintoki et al. (2007). Consequently, I find no evidence that supports the theory of Lipton and Lorsch (1992), and Jensen (1993), about the existence of an optimal board size. One possible

explanation for this difference in results is that ROA is a backward-looking measure of performance. While Tobin’s Q as a measure of performance is a mix between backward looking (denominator) and forward looking (numerator).

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6. Conclusion

Using a recent sample of 153 companies from the S&P500 from the information technology, consumer staples, and health care industry, I examine the relation between firm performance and board structure. I find that board structure is partially determined by past performance, and control for this by using a dynamic GMM estimator. My key conclusion is that I find a positive relation between board size and firm performance, and a negative relation between board size squared and firm

performance. Table 5 shows both coefficients are significant, so the hypothesis of a non-linear relation between Tobin’s Q and board size is accepted. The results suggest the relation between board size and firm performance is inversely U-shaped. These results support the theory of Lipton and Lorsch (1992), and Jensen (1993), about the existence of an optimal board size. I find the optimal board size in my research by setting the first derivative of the GMM equation equal to zero, and calculate the maximum. The following formula is used, where X1 is the point where the relation changes sign:

X1 = - β1 / (2 * β2) (4)

The outcome is approximately - (0.510 / 2 * 0.025) = 10.2, so Tobin’s Q is at a maximum at a board size of approximately 10.2 board members.

The inversely U-shaped relation between board size and firm performance is consistent with arguments made by Dalton et al. (1999) that, initially, increasing board size will lead to higher performance (resource dependency theory). The results also support the theory of Lipton and Lorsch (1992), and Jensen (1993), that when boards become too large, they become less effective because of increased agency problems like free riding. Causing the board to neglect its monitoring duties, resulting in a decrease in performance. The result of an optimal board size of approximately ten is a little higher than predictions by Lipton and Lorsch (1992), and Jensen (1993), of an optimal board size of respectively eight or nine and seven or eight. It is also worth noting that firms might want to choose an odd board size to prevent equality of votes. The results are robust to a different control variable for firm size. However, when I use ROA as performance measure the significance of the coefficients drops, resulting in no significant relation between board size and firm performance. This result is consistent with findings of Wintoki et al. (2007).

This paper has some limitations. First, my study is unlike many other studies not longitudinal. However, I include two lagged values of all regressors as instruments to account for the dynamic relations inherent to corporate governance. Second, I only included three industries in my research. Hence, my results are not generalizable to all industries. Third, the results of research on management and corporate governance are not generalizable to all countries due to major cultural and corporate differences (Hofstede, 1993). I recommend follow-up studies, using a larger longitudinal dataset, on

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more sectors, as well as on individual sectors. As well as research on data from countries with a different corporate culture than the U.S.

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