Endogeneity and the Dynamics of Corporate Governance * M. Babajide Wintoki a, † March 19, 2007 a Terry College of Business, University of Georgia Abstract There is growing evidence that corporate governance and firm performance are not strictly exoge- nous; both are jointly determined by (partially) unobservable variables and in addition, corporate governance adjusts to past firm performance. Ordinary least squares and fixed effects cross-sectional regression analyses of the relationship between corporate governance and firm performance do not adequately control for these sources of endogeneity and may be biased. I estimate the relationship between governance and performance using a generalized method of moments estimator that con- trols for unobserved heterogeneity, allows governance and performance to be jointly determined and also allows governance to adjust to changes in past firm performance. In a panel of over 6,000 firms between 1991 and 2003, I find no relationship between any aspect of board structure or inside own- ership, and firm performance. The results stand in contrast with some of those from prior studies that suggest an inefficient exogenous relationship between certain aspects of corporate governance and firm performance. The results support the alternative hypothesis that corporate governance structures are, in general, efficiently determined by firms in response to their specific contracting and competitive environments. * I would like to specially thank Jim Linck, Jeff Netter and Tina Yang for their help in obtaining the boards of directors data and for useful comments. I would also like to thank Audra Boone, Harold Mulherin, Paul Irvine, Chris Stivers, seminar participants at the University of Georgia and the University of Kansas for helpful comments on earlier drafts. † Email:[email protected]
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Endogeneity and the Dynamics of Corporate
Governance∗
M. Babajide Wintokia,†
March 19, 2007
aTerry College of Business, University of Georgia
AbstractThere is growing evidence that corporate governance and firm performance are not strictly exoge-nous; both are jointly determined by (partially) unobservable variables and in addition, corporategovernance adjusts to past firm performance. Ordinary least squares and fixed effects cross-sectionalregression analyses of the relationship between corporate governance and firm performance do notadequately control for these sources of endogeneity and may be biased. I estimate the relationshipbetween governance and performance using a generalized method of moments estimator that con-trols for unobserved heterogeneity, allows governance and performance to be jointly determined andalso allows governance to adjust to changes in past firm performance. In a panel of over 6,000 firmsbetween 1991 and 2003, I find no relationship between any aspect of board structure or inside own-ership, and firm performance. The results stand in contrast with some of those from prior studiesthat suggest an inefficient exogenous relationship between certain aspects of corporate governanceand firm performance. The results support the alternative hypothesis that corporate governancestructures are, in general, efficiently determined by firms in response to their specific contractingand competitive environments.
∗I would like to specially thank Jim Linck, Jeff Netter and Tina Yang for their help in obtaining the boards ofdirectors data and for useful comments. I would also like to thank Audra Boone, Harold Mulherin, Paul Irvine,Chris Stivers, seminar participants at the University of Georgia and the University of Kansas for helpful commentson earlier drafts.
and firm performance. This is the largest panel that has been used to date, to study the perfor-
mance/governance relationship. In particular, the results cast some doubt on the robustness of the
previously documented negative relationship between board size and firm performance. The results
obtained are important not just to academic researchers, but could have implications for regulators,
shareholder activists and groups that promote mandatory, “one size fits all” board structures.
The rest of this paper is structured as follows. In section 2, I present a brief overview of the
sources and implications of endogeneity in empirical corporate governance research and discuss the
advantage of dynamic GMM estimation over other kinds of estimators. In section 3, I present a
Monte Carlo simulation that illustrates the biases of OLS and fixed-effects estimation in the face
of both unobserved heterogeneity and dynamic endogeneity, and also illustrates the power of the
dynamic GMM estimator. In section 4 and 5, I present empirical results from my estimation of
the relationship between firm performance and board structure and between firm value and insider
6
ownership respectively. In section 6, I discuss the implications of my results, and conclude.
2 Review of endogeneity and panel data estimation techniques in
corporate governance
In estimating the empirical relationship between performance and corporate governance, most em-
pirical studies have estimated a variant of the following model:
yit = xitβ + zitγ + ηi + εit, i = 1 . . . N, t = 1 . . . T (2.1)
where yit is some measure of firm performance (e.g. return on assets, stock returns), xit contains
the governance variables of interest, zit contains a set of observable control variables and ηi is a
firm-specific effect (usually assumed to be fixed) that captures unobservable heterogeneity across
firms. Examples of such studies abound in the literature and include Yermack (1996), where the
key governance variable is board size; Agrawal and Knoeber (1996), where the governance variables
include management shareholding and board structure; Himmelberg, Hubbard, and Palia (1999),
where the governance variable of interest is management ownership; Bhagat and Black (2002),
where the governance variables are board size and composition; and Gompers, Ishii, and Metrick
(2003), where the key variable of interest is an index of shareholder protection.
In setting up the empirical specification, most researchers include control variables which are
associated with firm performance that may also be correlated with corporate governance. Thus zit
usually includes observable firm characteristics like firm size, firm risk, industry, growth opportu-
nities etc. In contrast, η (which may or may not explicitly stated by the researcher) is assumed to
represent the unobservable that firm characteristics that may affect firm performance, e.g., man-
agerial productivity, corporate culture, director ability etc.
2.1 OLS and simple instrumental variable (IV) estimation
Both simple OLS (when T = 1) and pooled OLS (when T > 1), ignore unobserved heterogeneity
by assuming that neither the governance variables nor the control variables are correlated with
unobserved firm characteristics, i.e., E(x′itηi) = 0 and E(z′itηi) = 0. It is quite easy to see that
7
this assumption is unlikely to hold when estimating the relationship between performance and
governance. If, for example, η includes such unobservable factors as the ability of the directors,
it not only has a direct impact on performance, but is also likely to be correlated with board
composition. For example, a firm with one very able outside director will not need as many
outsiders as one with only mediocre directors. All these suggest that OLS estimates are likely to
be severely biased.
In corporate governance it is very difficult to use simple instrument variable (2SLS) regressions
to eliminate the bias introduced by unobserved heterogeneity. Valid identification would require us
to find purely exogenous instruments which are not only correlated with the governance variables
(xit) but are independent of the unobserved firm characteristics (ηi) and are not already in the
control variable set (zit). It is easy to see how this could be difficult, in practice, when attempting
to estimate (2.1). The choice of observable instruments (e.g. firm size, growth opportunities,
firm risk etc.) are likely to be correlated with the unobserved firm characteristics. One might
be tempted to use lagged performance (yit−1) as an instrument for xit in (2.1); but this would
be invalid instrument since yit−1 is obviously correlated with the unobserved firm characteristics,
ηi. To further complicate matters, the number of exogenous instruments required for identification
increases with the number of endogenous variables in the empirical specification.
Aside from unobserved heterogeneity, OLS estimation of (2.1) relies on the assumption that
neither the governance variables (xit) nor the control variables (zit) are correlated with the error
term, εit, i.e., E(x′itεit) = 0 and E(z′itεit) = 0. If performance and corporate governance are
simultaneously determined, then this assumption is clearly violated, and OLS will be biased. A
number of researchers (e.g. Bhagat and Black (2002)) have focused on this simultaneity bias and
have suggested the use of simultaneous equations estimation methods as a way to eliminate this
bias. So for example, a typical simultaneous equation system will include the following:
y = f(x, z1, z2, . . . , zk−1, zk) (2.2)
x = g(y, z1, z2, . . . , zk−1) (2.3)
where one of the control variables (zk) has been left out of the governance (x) equation, in order
8
to permit identification of the performance (y) equation. The assumption is that zk is purely
exogenous in the sense that, while it determines performance, it is completely independent of the
governance variable. Again, the practical difficulty of identifying such an instrument is obvious,
and in the absence of strong, underlying structural models, the choice of which element (zk) to
leave of out of (2.3) seems somewhat arbitrary. In addition to all these, simultaneous equations
models do not necessarily address the bias introduced by unobserved heterogeneity (η) from (2.1).
2.2 Fixed-effects (within) estimation and strict exogeneity
In order to solve the serious problems raised by unobserved heterogeneity, researchers (e.g. Yer-
mack (1996) and Himmelberg, Hubbard, and Palia (1999)) have increasinly turned to panel data
estimation methods, especially fixed-effects estimation. Thus a fixed-effects transformation of (2.1),
eliminates the unobserved firm effect (η) and leaves:
∆yit = ∆xitβ + ∆zitγ + ∆εit, i = 1 . . . N, t = 1 . . . T (2.4)
where ∆yit = yit − yi, ∆xit = xit − xi, ∆zit = zit − zi and ∆εit = εit − εi.
However, while the fixed-effects estimation eliminates the unobserved heterogeneity, it could
potentially introduce another source of endogeneity − dynamic endogeneity. Consistent estimation
of (2.4) relies on the assumption that E(∆x′it∆εit) = 0 and E(∆z′it∆εit) = 0. This particular
assumption is much stronger than it at first looks. ∆εit contains information about the error term
across all time periods, since
∆εit = εit − εi = εit −1T
t=T∑t=1
εit (2.5)
Thus, (2.5) implies that for the fixed effects estimation of (4) to be consistent, we have to assume
thatE(x′
isεit) = 0 ∀ t, s (2.6)
This is a strict exogeneity assumption. The implication of this assumption is that the corporate
governance variable (e.g. board structure) that we observe today is completely independent of any
past, present and future shocks or innovations to firm performance. This means that in carrying
out a fixed-effects estimation of (2.1), the researcher is in effect assuming that previous realizations
9
of firm performance have no effect whatsoever on current governance structures. In any estimation
of the relationship between governance and performance, (2.6) is not only a restrictive from an
econometric perspective, but is also likely to be violated from an economic perspective.
There is plenty of empirical to suggest that current governance and ownership structures are
strongly and directly influenced by past performance. Hermalin and Weisbach (1988) finds that,
in U.S. firms, board composition is likely to change following poor performance, a result that is
confirmed in studies by Denis and Sarin (1999), Bhagat and Black (2002) and Easterwood and
Raheja (2007). Kaplan and Minton (1994) also finds that this is also true with Japanese firms.
In a similar vein, Kole (1996), finds that current managerial ownership is strongly influenced by
previous firm performance.
Governance structures can also be indirectly influenced by past performance. At least as far
back as Demsetz and Lehn (1985), researchers have suggested, and empirically demonstrated that
governance structures are determined by the nature and scope of agency costs specific to each firm.
The studies have used observable firm characteristics such as size, growth opportunities, number
of business segments, age and the uncertainty of the firm’s business environment to proxy for
these agency costs. Recent studies including those by Mulherin (2005), Boone, Field, Karpoff, and
Raheja (2006), Coles, Daniel, and Naveen (2006) and Linck, Netter, and Yang (2006a) find that
board structures are closely related to these firm characteristics. Similarly, Himmelberg, Hubbard,
and Palia (1999) and Demsetz and Villalonga (2001) also confirm the original Demsetz and Lehn
(1985) results which suggested that management ownership is related to those firm characteristics
that proxy for agency costs. So if firm characteristics like size and growth opportunities help
determine board structure and these characteristics are in turn determined by prior performance,
then these determinants themselves constitute an additional indirect link between past performance
and current governance.
Thus, fixed-effects estimation of the relationship between firm performance and corporate gov-
ernance as specified in (2.1) is likely to be inconsistent because the strict exogeneity assumption
of (2.6) is likely to be violated if there is a dynamic relationship between firm performance and
10
corporate governance.1
2.3 A consistent estimator for the relationship between corporate governance
and firm performance
Consistent estimation of (2.1) will require the use of an estimation technique which controls for
unobserved heterogeneity and simultaneity while exploiting (or at least controlling for) the dynamic
association between corporate governance and performance.
A promising estimation technique is the GMM dynamic panel data estimation procedure. This
estimator was introduced by Holtz-Eakin, Newey, and Rosen (1988) and Arellano and Bond (1991),
and further developed in a series of papers including Arellano and Bover (1995) and Blundell and
Bond (1998). The dynamic modeling approach has been used in other areas of economics where
the structure of the problem suggests a dynamic relationship between dependent and independent
variables. Examples of these include the empirical measurement of economic growth convergence
(Caselli, Esquivel, and Lefort (1996)), estimation of a labor demand model (Blundell and Bond
(1998)) and the empirical estimation of the relationship between the level of financial intermediary
development and economic growth (Beck, Levine, and Loayza (2000)).
The dynamic GMM estimator dispenses with the strict exogeneity assumption in (2.6), and
instead relies for consistency on a weaker form of exogeneity, sequential exogeneity, which for the
estimation equation in (2.1) can be written as:
E(x′isεit) = 0 ∀ s < t (2.7)
The sequential exogeneity assumption seems to be a more reasonable one to make in the cor-
porate governance and firm performance context. The assumption allows the governance variables
to be determined by past (and present realizations) of performance, but not future values. This
is a fairly reasonable assumption. As Keane and Runkle (1992) point out, if we assume rational
expectations, we expect the governance variables to be affected by past and current innovations
in the performance, but not future innovations in the board structure. This does not mean that1Strict exogeneity as specified in (2.6) also excludes the possibility of simultaneity between performance and
corporate governance. Thus fixed-effects estimation does not control for simultaneity.
11
the economic actors connected with the firm do not adjust their actions in relation to the expected
performance, it simply means that they cannot adjust their actions for future shocks, or unexpected
innovations to performance.
This suggests that the governance/performance relation should be treated as a dynamic unob-
yit = ρyit−1 + xitβ + zitγ + ηi + εit, i = 1 . . . N, t = 1 . . . T (2.9)
Arellano and Bond (1991) develop a first difference GMM estimator for the system represented
by (2.8) and (2.9) that exploits the sequential exogeneity assumption of (2.7). Transforming (2.9)
into a system of T − 1 equations in first differences:
∆yi = ∆Xiβ + ∆εi, i = 1 . . . N (2.10)
where Xi includes the governance variables (xit), control variables (zit) and lagged performance,
yit−1. This step eliminates the unobserved heterogeneity and allows us to have a model where our
governance variables can be arbitrarily correlated with any unobserved firm-specific effects.
Next, we can exploit the sequential exogeneity assumption of (2.7) to define a matrix of instru-
ments containing lagged values of performance and the explanatory variables:
Zi =
x0i1 0 0 · · · 0
0 x0i2 0 · · · 0
.... . .
...
0 0 0 · · · x0iT−1
(2.11)
where the rows correspond to the first-differenced equations for periods t = 3, 4, . . . , T and x0i1 ≡
Xi1, x0i2 ≡ Xi1,Xi2, . . ., x0
iT ≡ Xi1,Xi2, . . .XiT−1. We use lagged values of our variables
as GMM instruments for our transformed system which has been first differenced in (2.10). For
example, for the first equation in the system, (y3 − y2) = (X3 −X2)β+ (ε3 − ε2), we can use X1 as
12
an instrument, since the sequential exogeneity assumption means that E(ε3, ε2|X1) = 0. Similarly,
for the second equation in the system, (y4 − y3) = (X4 −X3)β + (ε4 − ε3), we can use X1 and X2
as instruments since E(ε3, ε4|X1,X2) = 0, and we continue in this manner through the system as
defined by (2.10) and (2.11).
We can then carry out GMM estimation based on the moment conditions
E(Z′i∆εi) = 0 (2.12)
In general, the asymptotically efficient GMM estimator based on the moment conditions in (2.12)
minimizes the criterion: [Z′
i(∆yi −∆Xi)]′
W[Z′
i(∆yi −∆Xi)]
(2.13)
The GMM estimator that minimizes this criterion is obtained as:
βGMM =[(∑
i
∆X′iZi
)W
(∑i
∆Z′iXi
)]−1(∑i
∆X′iZi
)W
(∑i
∆Z′iyi
)(2.14)
where the optimal weighting matrix, W = Λ−1, and
Λ = E(Z′i∆εi∆ε
′iZi) (2.15)
The choice of instruments in (2.11) means that we have explicitly modeled the governance
variables to be completely determined by their history, as well as the firm’s past and present
performance. Eliminating the unobserved heterogeneity by first differencing means that we do not
have to worry about the possible correlation between the governance variables and unobserved
firm effects like managerial productivity, director ability etc. We also do not have to impose any
structure on the lag-length of the relationship suggested by (2.9) in order to obtain consistent
estimates of the model in (2.10).
While the particular ‘difference’ GMM estimator obtained by using (2.14) is economically ap-
pealing it does have at least three econometric shortcomings. First, Beck, Levine, and Loayza (2000)
note that if the original model is conceptually one that is in levels, differencing may attenuate the
signal to noise ratio and reduce the power of our tests. Secondly, Arellano and Bover (1995) point
out that variables in levels may be weak instruments for first-differenced equations. Thirdly, first-
13
differencing may exacerbate the impact of measurement errors in the dependent variables (Griliches
and Hausman (1986)).
Arellano and Bover (1995) and Blundell and Bond (1998) suggest that we can mitigate these
shortcomings and improve the GMM estimator by including the equations in levels in the estimation
procedure. We can then use the first-differenced variables as instruments for the equations in levels,
in a ‘stacked’ system of equations that includes the equations in both levels and differences. This
will produce a ‘system’ GMM estimator. The problem that arises here is that the equations in
levels still includes the unobserved heterogeneity. If, however, we are willing to make the additional
assumption that while the governance (and control) variables may be arbitrarily correlated with
the fixed effects, this correlation is constant over time. This is a reasonable assumption, if the
unobserved effects proxies for factors like unobserved director ability, managerial productivity etc.
The assumption leads to an additional orthogonality condition:
E(∆X′itηi) = 0 (2.16)
The ‘system’ GMM estimator enables us to obtain efficient estimates while maintaining all the es-
sential elements of controlling for unobserved heterogeneity, simultaneity and dynamic endogeneity.
2.4 Testing for strict exogeneity
When faced with empirical data, the researcher has to decide whether or not to assume a dynamic
model or to rely on fixed-effects estimation. If the system is not dynamic, GMM estimation might
be less efficient than fixed-effects estimation since dynamic GMM estimation would then involve
using weak instruments for our endogenous variables. So even if we suspect that our system is
dynamically endogenous, an econometric test of endogeneity can certainly better inform our choice
of which panel data estimation technique to employ.
Wooldridge (2002) present a regression-based test for strict exogeneity that is relatively easy
to implement. If Xit contains the explanatory variables, a test of strict exogeneity is obtained by
carrying out fixed-effects estimation on the equation:
yit = Xitβ + Wit+1δ + ηi + εit, t = 1 . . . T − 1 (2.17)
14
where Wit+1 is a subset of Xit+1. Under the null hypothesis of strict exogeneity, δ = 0. Intuitively,
if δ 6= 0, then current governance depends on past performance (or conversely, present performance
affects future corporate governance and ownership).
Thus, if we can reject the hypothesis that δ = 0, fixed-effects estimation is likely to be biased
by the presence of dynamic endogeneity and we are likely to obtain less biased and more consistent
estimates using a dynamic estimation procedure.
3 Estimating the bias from ignoring dynamic endogeneity: Monte
Carlo evidence
Consider the dynamic unobserved effects model:
yit = ρyit−1 + xitβ + ηi + εit, i = 1 . . . N, t = 1 . . . T (3.1)
As discussed in the previous section, OLS estimation will be biased if ρ 6= 0 (since yit−1 is obviously
correlated with ηi) or if any of the variables in xit are correlated with ηi. Similarly, fixed-effects
estimation will be biased if xit = f(yit−1, yit−2, . . . , yit−k), since this would be a violation of the
strict exogeneity assumption required for consistency of fixed effects estimation.
Awareness of the biases introduced from assuming strict exogeneity when explanatory variables
are not strictly exogenous goes at least as far back as Nerlove (1967). Nickel (1981) and Sevestre and
Trognon (1985) show that as N → ∞, the inconsistency of the fixed-effects estimator is O(1/T ),
which means that the inconsistency of fixed effects estimation should decrease as T increases.
However, Judson and Owen (1999) show that even when T is as large as 30, the bias of the fixed
effects estimator can still be quite large and significant. This is of special concern to empirical
researchers in corporate governance because in practice we are often confronted with short panels;
typically, T < 10.2 Thus, it is very unlikely that the typical corporate governance panel will be
long enough (in the time dimension) to eliminate any potential biases of fixed effects estimation.
Since this paper is the first to explore the role of dynamic enogeneity in empirical corporate2For example, any study carried out today that used the the Investor Responsibility Research Center (IRRC) data
that starts from 1996, is limited to a panel of T = 10. If the researcher is concerned about the independence ofyear-to-year data and is forced to sample at large time intervals, the T is even smaller
15
governance research, it is instructive to look at the nature and magnitude of this bias when it is
ignored. Unfortunately, there is no closed form solution for the bias due to dynamic endogeneity if
the dependent variable is endogenous (the best approximation is probably that by Kiviet (1995) but
even this only holds in the case where the dependent variable consists of one autorgressive variable
and one strictly exogenous variable). The exact magnitude (and sign) of the bias will depend on
the exact form of the endogeneity and the relationship between the dependent and independent
variables. Thus, I use Monte Carlo simulations to illustrate the bias from ignoring dynamic endo-
geneity. The simulations also show the ability the dynamic GMM estimator to eliminate the biases
that may arise from dynamic endogeneity. The use of Monte Carlo simulations is very much in the
spirit of other studies in this areas including, for eaxmple, Arellano and Bond (1991), Arellano and
Bover (1995), Kiviet (1995) and Bruno (2005).
Consider the case where the true model (data generating process) for firm performance (yit) is:
Thus, x is endogenous in two senses. First it exhibits dynamic endogeneity from its relationship to
past performance, y, through the parameter, λ. λ represents the factor by which the governance
variable adjusts to performance and captures the key aspect of dynamic endogeneity. Second, x is
also correlated to the unobserved firm specific factor, η. Any estimation of this system would have
to account for both dynamic endogeneity and unobserved heterogeneity. Of course, the researcher
is unaware of the true model. Most likely the researcher will be estimating (2.1) with the intention
of making some inference from the magnitude and significance level of the estimated coefficient, β.
I simulate the system given by (3.2) and (3.3) and generate panel data sets of time and cross-
16
sectional dimensions that are typical in corporate governance (T = 5, 10) and (N = 500). I then
carry out an estimation (2.1) using OLS, fixed effects and the dynamic GMM estimator of Arellano
and Bond (1991). Details of the data generation procedure are given in an appendix.
Table 1 shows the results of the simulation. Data generation for the reported results was carried
out using the following parameters: γ = 0.6, κ = 0.9, α = 0.7, π = 0.2, δ = 0.53, and a range
of values of the dynamic adjustment factor, λ. The reported coefficients and standard errors are
based on 1,000 replications. I have reported results for different values of λ, since this essentially
captures the dynamic nature of the panel.
The results show that in every case where λ 6= 0, the various estimates of β (except those
obtained by GMM) are biased. OLS estimates are obviously biased largely because of the presence of
unobserved heterogeneity. Fixed-effects estimates are less biased than the OLS estimates since fixed-
effects eliminate the unobserved heterogeneity, but are still biased because of dynamic endogeneity.
Only in the singular case when λ = 0 (in which case there is no dynamic ‘feedback’) are the
fixed-effects estimates unbiased. Of course, as T increases, the bias of the fixed-effects estimates
decreases, but we will need a long time series to eliminate the bias completely. However, as I
have noted earlier, in practice, most corporate governance studies have limited time-series; usually,
T < 10.
Panel A of Table 1 is particularly interesting; it shows the results of the simulation when
the true β = 0. In this case, there is no relationship between performance and the governance
variable. However, OLS and fixed-effects estimate are significantly biased and produce a spurious
correlation between governance and firm performance. For example when the true β is zero and
there is a modest amount of dynamic endogeneity (λ = −0.1), fixed-effects estimation produces
a statistically significant estimate of 0.3787 (standard error of (0.0740) in a sample where T = 5.
Ignoring dynamic endogeneity (and unobserved heterogeneity) would lead us to wrongly infer that
governance was correlated with performance if we carried out estimation using either OLS or fixed
effects.
Table 1 also shows that GMM estimation carried out using the Arellano and Bond (1991) es-3The choice of which set of parameters’ results to report is somewhat arbitrary. The simulation was repeated with
different values of the parameters (ranging from 0 to 1) and the results are similar.
17
timation procedure produces unbiased results regardless of the magnitude of λ. The estimation
procedure uses lagged variables of all the dependent and independent variables as GMM instru-
ments. This procedure not only controls for the dynamic endogeneity, it actually exploits it to
obtain unbiased results. In addition, the GMM procedure does not even require knowledge of the
dynamic process that generates the endogenous variable in order to produce consistent and unbiased
estimation results.
Figure 1 presents a graphical illustration of the bias that results from dynamic endogeneity (and
unobserved heterogeneity). In this particular simulation, the true β is zero. The figure shows the
severity of the bias (β− β) from ignoring either unobserved heterogeneity or dynamic endogeneity.
Fixed effects estimation is negatively biased when the dynamic endogeneity factor (λ) is negative
and positively biased when λ is positive. Even modest of dynamic endogeneity (small values of
|λ|) can lead to significant biases in fixed-effects estimation. Again, we see that only the GMM
estimation produces consistent estimates for β.
Overall, this limited numerical example illustrates the pitfalls inherent in ignoring both dynamic
endogeneity and unobserved heterogeneity in carrying out estimation with panel data samples. The
example also illustrates the relative power of GMM dynamic estimation techniques in cases where
your variable of interest adjusts to past realizations of the dependent variable, which is likely to be
the case with corporate governance variables.
4 Estimating the relationship between board structure and firm
performance
In this section, I estimate the empirical relationship between firm performance, board size, board
composition and board leadership.
4.1 Measuring firm performance
The key measure of firm performance used in this study is return on assets (ROA), where ROA is
defined as operating income before depreciation (COMPUSTAT item #13) divided by fiscal year
18
end total assets (COMPUSTAT item #6). For every firm in the sample, I compute an industry
adjusted ROA which is obtained by subtracting the median industry ROA from the individual
firm’s ROA. Industry is defined by the 2-digit SIC code.
Many studies of the governance/performance relationship have focused on the use of Tobin’s Q
as a measure of firm performance. This can be a problem for a number of reasons. Tobin’s Q (which
is usually defined as some market-to-book ratio) is a strong proxy for growth opportunities and
there is strong theoretical motivation to expect that growth opportunities are a cause, rather than a
consequence, of governance structures. There is also some empirical evidence to support this; both
Boone, Field, Karpoff, and Raheja (2006) and Linck, Netter, and Yang (2006a) find that market-
to-book values determine both board size and board composition. So in my empirical estimation, I
use market-to-book as a control variable, making it inappropriate for use as a performance measure.
One concern that has been raised about using return on assets (ROA) as a measure of per-
formance is that it is sensitive to accounting artifact problems, but as Demsetz and Villalonga
(2001) point out, Tobin’s Q also suffers from accounting artifact problems, and may in fact, be
more severely affected. For one thing, the numerator of both ROA and Tobin’s Q are essentially
the same (book value of assets). In addition, the market-to-book measure assumes that the firm’s
future revenues will be generated purely from tangible assets, which could introduce severe biases
if used to measure the performance of firms whose values lie mostly in intangible assets. These
problems suggest that Tobin’s Q offers few advantages over ROA as a performance measure and it
is probably more appropriate to consider Tobin’s Q as a determinant of governance and used as a
control variable.
4.2 Governance variables
I consider the effect of past performance on three board structure variables - board size, board
composition and board leadership. More precisely, these variables are defined as follows:
• LogBSIZE, the logarithm of the number of directors on the board
• INDEP , the proportion of outside (non-executive) directors on the board
• CEO CHAIR, a dummy variable equal to 1 if the CEO is also the chairman of the board
19
4.3 Control variables
Recent studies (Raheja (2005), Coles, Daniel, and Naveen (2006), Boone, Field, Karpoff, and Raheja
(2006) and Linck, Netter, and Yang (2006a)) suggest that firms will chose their board structures
based on the relative costs and benefits of each governance mechanism. The cost/benefit ratio of any
particular board structure will depend on the unique agency costs that each firm faces and board
structure will reflect the monitoring costs, the private benefits of control and scope and complexity
of each firm’s operations. Thus, in line with prior literature on the determinants of board structure,
I propose using size, age, the number of business segments, growth opportunities, and leverage as
determinants of board structure. These variable might also be related to firm performance itself
and as such they also serve as control variables in our empirical specification.
In summary, my control variables are defined as follows:
• LogMV E, logarithm of the market value of equity.
• MTB, ratio of market-to-book value. This is obtained as market value of equity plus book
value of assets (COMPUSTAT item #6) minus book value of equity (COMPUSTAT item
#60) minus deferred taxes (COMPUSTAT item #74), all divided by book value of assets.
• RETSTD, standard deviation of (the past twelve months) of the firm’s stock returns.
• LogAGE, the logarithm of the firm’s age, where age is computed from the time the firm first
appears on CRSP.
• LogSEGMENTS, the logarithm of the number of business segments.
• DEBT , the ratio of the firm’s long-term debt (COMPUSTAT item #9) to total assets (COM-
PUSTAT item #6).
4.4 Data and Sample Selection
Board structure tends to change very slowly, and is highly persistent. This can lead to attenuation of
the signal-to-noise ratio and reduce the power of empirical tests. Dynamic estimation also requires
us to assume that transient errors are uncorrelated. To overcome these issues, I sample at two-year
20
intervals, and use governance data from 1991, 1993, 1995, 1997, 1999, 2001 and 2003. Longer
sampling intervals might improve the tests, but I am forced to make a trade-off between sampling
interval and the length of the time series (T ), based on data availability.
The board data from this study is taken from the DISCLOSURE database. This is a fairly
large database of governance data for over 7,000 firms starting from 1991. Since my empirical tests
include a number of control variables, I match the data obtained from DISCLOUSRE with data
from CRSP and COMPUSTAT for each of sample years. This leaves me with a sample consisting
of over 6,000 unique firms and over 16,000 firm-years. To the best of my knowledge, this is the
largest panel, to date, that has been used to study the performance/governance relationship.
Table 2 shows the sample characteristics of the data that I use in my estimation. In order to
avoid sample selection issues, I do not require a balanced panel, so that the number of firms differs
from year to year and my estimation strategy uses as many observations as available. The data
also includes a wide selection of both large and small firms, unlike most previous studies that tend
to focus on exclusively either large or small firms.
The distribution of board characteristics appears to be fairly stable over the sample period.
While mean board size declines slightly from 7.71 in 1991 to 7.37 in 2000 (and then increasing to
7.93 in 2003), the median firm has 7 board members throughout most the sample period, with a
small up-tick in 2003. In 1991, in 59% of the firms, the CEO was also the chairman of the board,
this number is 56% in 2003; the median firm has the CEO holding both positions. The average
number of outside directors appears to have increased slightly from two-thirds at the beginning
of the sample period to just over 70% at the end of the sample period. The major variables that
change substantially over the sample period is firm size. Mean and median firm size increased
threefold between 1991 and 2003.
4.5 Econometric tests of strict exogeneity
As I have discussed in previous sections, the strict exogeneity assumption in corporate governance
is likely to be violated and the estimates obtained under this assumption are likely to be biased
and inconsistent. While, there is substantial economic justification to suspect that the governance
21
and control variables are not strictly exogenous, I confirm this with an econometric test of strict
exogeneity.
In the previous section of the paper, I discuss a regression based test of strict exogeneity sug-
gested by Wooldridge (2002). If Xi,t contains the explanatory variables, a test of strict exogeneity
can be obtained by carrying out fixed-effects estimation of the equation:
Since I do not generate the lagged dependent variable, I set ρ = 0 and generate the panel data
variables, y, x and z using (6.4), (6.8) and (6.9) respectively.
30
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Table 1Measuring the bias when explanatory variables is endogenous: Simulation results
In this table, I report the simulation results from estimating a model with OLS, fixed effects (FE) and GMM when theexplanatory variable is dynamically endogenous and correlated with unobservable effects. The model estimated is: yit =xitβ + zitγ + ηi + νit. The true data generating process (DGP) for zit is zit = κzit−1 + ξit; and that for xit is xit =αxit−1 + πzit + λyit−1 + δηi + εit. Thus, xit is endogenously related to yit−1 through the parameter λ and is endogenouslyrelated to the unobserved heterogeneity, η. The parameters used for generating the data are : β = 0; γ = 0.6, κ = 0.9, α = 0.7,π = 0.2, δ = 0.5.
yit is return on assets (ROA); xit includes board size (LogBSIZE), board independence (INDEP ) and a dummyvariable which is 1 if the CEO is the board chair (CEO CHAIR); zit includes firm size (LogMV E), market-to-bookratio (MTB), standard deviation of stock returns (RETSTD), number of business segments (LogSEGMENTS),firm age (LogAGE) and leverage (DEBT ). t-statistics are reported in parentheses. All t-statistics are based onrobust standard errors. a, b, c represent significance at the one percent, five percent and ten percent level respectively.Year dummies are included in all specifications.
Dependent Variable (ROA) Pooled Fixed SystemOLS Effects GMM
1. m1 and m2 are tests for first-order and second-order serial correlation in the first-differenced residuals asymp-totically distributed as N(0, 1) under the null of no serial correlation. p-values are in parentheses
2. J-statistic is from the Hansen test of over-identifying restrictions,asymptotically distributed χ2, under the nullof instrument validity p-values are in parentheses.
3. The instruments used in the GMM estimation are:differenced equations: yit−6,yit−8,. . . ,yi,1991, xit−6,xit−8,. . . ,xi,1991,zit−6,zit−8,. . . ,zi,1991; level equations: ∆yit−6,∆xit−6, ∆zit−6
37
Table 5Does board structure affect current firm performance? Alternative performance measure
In this table, I report results from the estimation of the model:
yit is return on sales (ROS); xit includes board size (LogBSIZE), board independence (INDEP ) and a dummyvariable which is 1 if the CEO is the board chair (CEO CHAIR); zit includes firm size (LogMV E), market-to-bookratio (MTB), standard deviation of stock returns (RETSTD), number of business segments (LogSEGMENTS),firm age (LogAGE) and leverage (DEBT ). t-statistics are reported in parentheses. All t-statistics are based onrobust standard errors. a, b, c represent significance at the one percent, five percent and ten percent level respectively.Year dummies are included in all specifications.
Dependent Variable (ROS) Pooled Fixed SystemOLS Effects GMM
1. m1 and m2 are tests for first-order and second-order serial correlation in the first-differenced residuals asymp-totically distributed as N(0, 1) under the null of no serial correlation. p-values are in parentheses
2. J-statistic is from the Hansen test of over-identifying restrictions,asymptotically distributed χ2, under the nullof instrument validity p-values are in parentheses.
3. The instruments used in the GMM estimation are:differenced equations: yit−6,yit−8,. . . ,yi,1991, xit−6,xit−8,. . . ,xi,1991,zit−6,zit−8,. . . ,zi,1991;level equations: ∆yit−6,∆xit−6, ∆zit−6
38
Table 6Does board structure affect current firm performance? Inclusion of director ownership
In this table, I report results from the estimation of the model:
yit is return on assets (ROA); xit includes board size (LogBSIZE), board independence (INDEP ), a dummy variablewhich is 1 if the CEO is the board chair (CEO CHAIR) and director ownership (DIR OWN); zit includes firmsize (LogMV E), market-to-book ratio (MTB), standard deviation of stock returns (RETSTD), number of businesssegments (LogSEGMENTS), firm age (LogAGE) and leverage (DEBT ). t-statistics are reported in parentheses.All t-statistics are based on robust standard errors. a, b, c represent significance at the one percent, five percent andten percent level respectively. Year dummies are included in all specifications.
Dependent Variable (ROA) Pooled Fixed SystemOLS Effects GMM
1. m1 and m2 are tests for first-order and second-order serial correlation in the first-differenced residuals asymp-totically distributed as N(0, 1) under the null of no serial correlation. p-values are in parentheses
2. J-statistic is from the Hansen test of over-identifying restrictions,asymptotically distributed χ2, under the nullof instrument validity p-values are in parentheses.
3. The instruments used in the GMM estimation are:differenced equations: yit−6,yit−8,. . . ,yi,1991, xit−6,xit−8,. . . ,xi,1991,zit−6,zit−8,. . . ,zi,1991;level equations: ∆yit−6,∆xit−6, ∆zit−6
39
Table 7Summary statistics of ownership and control variables
The table contains the summary statistics of ownership and control variables of the firms used in the study. Theownership variables data comes from the DISCLOSURE database. The control variables data comes from CRSPand COMPUSTAT. IOWN is the percentage of the firm’s shares owned by the firm’s chief officers, LogSALESis the logarithm of the firm’s total revenue, ASSETS/SALES is tangible assets (property, plant and equipment)divided by sales, CAPEX/ASSETS is capital expenditure divided by tangible assets, OP.INCOME/SALES isoperating income divided by sales, R&D/ASSETS is R&D expenditure divided by tangible assets, ADV/ASSETSis advertising expenditure divided by tangible assets.
Panel A: Mean (Median) Values of Ownership Variable
y is industry-adjusted firm value (Q), x is insider ownership (IOWN), log of sales (LogSALES), tangible assetsdivided by sales (ASSETS/SALES), capital expenditure divided by assets (CAPEX/ASSETS), operating incomedivided by sales (OP.INCOME/SALES), R&D expenditure divided by assets (R&D/ASSETS), advertising ex-penditure divided by assets (ADV/ASSETS), dummy variables equal to 1 if R&D or advertising expenditure isreported (RDUM and ADUM). All t-statistics (in parentheses) are based on robust standard errors. a, b, c representsignificance at the one percent, five percent and ten percent level respectively. Year dummies are included in allspecifications.
Dependent Variable:Q Pooled Fixed SystemOLS Effects GMM
1. m1 and m2 are tests for first-order and second-order serial correlation in the first-differenced residuals asymp-totically distributed as N(0, 1) under the null of no serial correlation. p-values are in parentheses
2. J-statistic is from the Hansen test of over-identifying restrictions,asymptotically distributed χ2, under the nullof instrument validity p-values are in parentheses.
3. The instruments used in the GMM estimation are:differenced equations: yit−6,yit−8,. . . ,yi,1991, xit−6,xit−8,. . . ,xi,1991,zit−6,zit−8,. . . ,zi,1991;level equations: ∆yit−6,∆yit−8,. . . ,∆yi,1991,∆xit−6,∆xit−8,. . . ,∆xi,1991, ∆zit−6,∆zit−8,. . . ,∆zi,1991
42
Figure 1The relationship between estimation bias and dynamic endogeneity
This figure graphically illustrates the bias introduced by dynamic endogeneity when carrying out OLS andfixed-effect estimation. The model estimated is: yit = xitβ + zitγ + ηi + νit. The true data generatingprocess (DGP) for zit is zit = κzit−1 + ξit; and that for xit is xit = αxit−1 + πzit + λyit−1 + δηi + εit. Thus,xit is endogenously related to yit−1 through the parameter λ and is endogenously related to the unobservedheterogeneity, η. The parameters used for generating the data are : β = 0; γ = 0.6, κ = 0.9, α = 0.7, π = 0.2,δ = 0.5. I use a range of λ from −0.9 to 0.9. Details of the simulation are included in an appendix. Thevertical axis gives the bias in the estimate of β. The horizontal axis represents the magnitude of dynamicendogeneity, λ. The dimensions of the panel data set are T = 5 and N = 500.
-0.2
0
0.2
0.4
0.6
0.8
1
-0.9 -0.7 -0.5 -0.3 -0.1 0.1 0.3 0.5 0.7 0.9
λ (Dynamic endogeneity)
Bia
s
OLS
FE
GMM
Notes1. All estimated biases and standard errors are based on 1,000 replications. Standard errors of biases are in
parentheses.
2. GMM estimation is carried out using the Arellano and Bond (1991) estimation procedure. Instruments usedare: yt−2, yt−3, . . . , y1, xt−1, xt−2, . . . , x1, zt−1, zt−2, . . . , z1