Endogeneity and the dynamics of internal corporate governance☆
Introduction
Empirical corporate finance research, which attempts to explain the causes and effects of financial decisions, often has serious issues with endogeneity. This is because it is generally difficult to find exogenous factors or natural experiments with which to identify the relations being examined. However, the implications for the empirical work's usefulness if it does not properly deal with endogeneity can be substantial. In a review article that provides guidance on addressing endogeneity issues in corporate finance, Roberts and Whited (forthcoming) note that “endogeneity leads to biased and inconsistent parameter estimates that make reliable inference virtually impossible.” A large body of empirical research suggests that certain governance structures drive improved performance, but this research is plagued with endogeneity issues. We often cannot ascertain if the causation is actually reversed (e.g., performance drives governance) or if governance is merely a symptom of an underlying unobservable factor, which also affects performance. Thus, it is difficult to determine what the parameter estimates actually suggest.
We respond to these endogeneity concerns in a specific setting, the relationship between boards and performance. This paper applies a well-developed panel GMM estimator to a data set of 6,000 firms over a 13-year period from 1991 to 2003. We find no relation between current board structure and current firm performance. This result is inconsistent with much earlier work and policy recommendations of many commentators. To strengthen our empirical argument, we also illustrate why estimators that find a relation may be biased. We demonstrate how the panel GMM estimator can be used to control for the dynamic nature of the performance–governance relationship suggested by theorists, while accounting for other sources of endogeneity in corporate finance research.
Most empirical corporate finance researchers acknowledge at least two potential sources of endogeneity: unobservable heterogeneity and simultaneity. However, one source of endogeneity that is often ignored (explicitly or implicitly) arises from the possibility that current values of governance variables are a function of past firm performance. Neglecting this source of endogeneity can have serious consequences for inference. This is especially true since the difficulty in identifying natural experiments or exogenous instruments in many settings means that corporate governance researchers often rely on panel data and fixed-effects estimates for inference. Traditional fixed-effects estimation can potentially ameliorate the bias arising from unobservable heterogeneity. However, it does this at the expense of a strong exogeneity assumption, one that is often not explicitly recognized by researchers. That is, it assumes that current observations of the explanatory variable (e.g., board structure) are completely independent of past values of the dependent variable (typically firm performance, value, or some other governance attribute), an assumption that we argue is not realistic.
We recognize that ignoring the dynamic nature of the structure performance relationship in empirical work presents significant concerns. To deal with this issue, we have two broad goals in this paper: (1) understand the dynamic relation between boards and performance, and (2) understand how to use dynamic panel estimators in this context (and similar situations). There are four basic steps in our analysis. First, we present intuitive and theoretical arguments, and empirical results, that suggest that corporate governance is dynamically related to past firm performance. Second, we show how a well-developed dynamic estimator is well suited to deal with the dynamic nature of the relation between corporate governance and performance. Third, we apply the dynamic GMM estimator to our panel to estimate the relationship between board structure and performance and the determinants of board structure. Fourth, we discuss the implications of our results with the dynamic GMM estimator for dealing with endogeneity in the governance–performance relationship and other governance estimations, as well as caveats to its use.
We start with theoretical arguments building on Hermalin and Weisbach's (1998) model, which shows that board structure is partly a function of the bargaining process between the chief executive officer (CEO) and the board, and that since the CEO's bargaining position is a function of her ability (measured by past firm performance), board structure depends on past firm performance. Consistent with this argument, we find empirical evidence that board independence is negatively related to past firm performance.
Another argument we advance, which combines insights from theoretical work by Raheja (2005) and Harris and Raviv (2008), is that past performance has a direct influence on the firm's information environment, profit potential, and the opportunity cost of outside directors, all of which are factors that may affect the optimal board structure. Indeed, we find empirical evidence that firm characteristics that proxy for these factors (e.g., firm size, market-to-book ratio, etc.) are themselves related to past firm performance. While the theoretical models we invoke are not explicitly dynamic, the implications we draw from them, and our empirical evidence, suggest that any empirical estimation of the effect of board structure on past firm performance that ignores the dynamic relation between current board structure and past performance (as do traditional fixed-effects estimators) will yield inconsistent estimates.
Next, we show that, subject to caveats, the dynamic nature of the relation between corporate governance and performance actually sets up a powerful methodology for identifying the causal effect of governance on performance. This dynamic panel GMM estimator, developed in a series of papers by Holtz-Eakin, Newey, and Rosen (1988), Arellano and Bond (1991), Arellano and Bover (1995), and Blundell and Bond (1998), improves on ordinary least squares (OLS) or traditional fixed-effects estimates in at least one of three important ways. First, unlike OLS estimation, we can to include firm-fixed effects to account for (fixed) unobservable heterogeneity. Second, unlike traditional fixed-effects estimates, it allows current governance to be influenced by previous realizations of, or shocks to, past performance. Third, unlike either OLS or traditional fixed-effects estimates, a key insight of the dynamic panel GMM estimator is that if the underlying economic process itself is dynamic – in our case, if current governance is related to past performance – then it may be possible to use some combination of variables from the firm's history as valid instruments to account for simultaneity. Thus, an important aspect of the methodology is that it relies on a set of “internal” instruments contained within the panel itself: past values of governance and performance can be used as instruments for current realizations of governance. This eliminates the need for external instruments.
We apply the dynamic panel GMM estimator to two often-studied aspects of corporate governance: (1) the effect of board structure on firm performance and (2) the determinants of board structure, and compare the results to those obtained from OLS or traditional fixed-effects estimates. Most prior studies of the effect of board structure on performance have estimated “static” models of the form: performance=f(board structure, firm characteristics, fixed effects), where board structure reflects board size, independence, or whether or not the CEO is also the chair of the board. We posit that the appropriate empirical model should be a “dynamic” model of the form: performance=f(past performance, board structure, firm characteristics, fixed effects). Our empirical analysis here reveals four key findings.
First, when we apply OLS or traditional fixed-effects to the “static” model as previous studies have done, we find, as these previous studies have, statistically significant relations between board structure and firm performance: there is a negative relation between board size and performance, and the relation between board independence and performance varies from negative to positive as we move from OLS to traditional fixed-effects estimation.
Second, when we apply simple OLS to the “dynamic” model (including past performance but temporarily ignoring unobservable heterogeneity), we get the first clear indication of the importance of dynamics in the governance/performance relation. The R2 rises from 27% in the “static” model to 41% in the “dynamic” model, while the magnitude of the estimated coefficients on both board size and independence fall dramatically (by over 90% in both cases) and become statistically indistinguishable from zero.
Third, when we apply the dynamic GMM panel estimator to the “dynamic” model – when we fully account for unobservable heterogeneity, simultaneity, and the relation between current board structure and past firm performance – we find no statistically significant relation between firm performance and any aspect of board structure. This is one of the key results of our paper and is in contrast with results from prior studies (where some find a positive and some find a negative relationship). Changes in board size or independence are not systematically related to higher (or lower) performance.
Finally, we apply the dynamic GMM methodology to examine how firm characteristics affect board structure. That is, we estimate an empirical model of the form: board structure=f(past board structure, firm characteristics, fixed effects). We find that after accounting for unobserved heterogeneity, simultaneity, and the effect of past board structure on firm characteristics, board structure is closely associated with firm size, growth opportunities, firm risk, age, leverage, and past performance. These results are similar to those obtained in recent studies by Boone, Field, Karpoff, and Raheja (2007) and Linck, Netter, and Yang (2008), and suggest that the effect of past board structure on current firm characteristics may not be as important as the effect of past board structure on current performance. This is as expected since the explanatory variables (size, business segments, etc.) are not strongly determined by past values of the dependent variable (board size or independence); thus, any link from past governance to current firm characteristics will be indirect through the effect, if any, of governance on performance. As a result, any bias arising from the underlying dynamic nature of governance appears to be more important in regressions of governance on performance than in regressions of firm characteristics on governance.
Our results also help reconcile some of the conflicting results in the prior literature, and explain how some reported correlations could arise from ignoring one or more aspects of the endogeneity inherent in the board structure–performance relation. One of the key points we raise in the paper, building on work by Wooldridge (2002) and Roodman (2008), is that if there is a dynamic relation between current values of an explanatory variable and past realizations of the dependent variable, a fixed-effects regression may be biased, and the direction of the bias will be opposite that of the dynamic relation. As we noted earlier, in our empirical analysis we find, similar to Hermalin and Weisbach (1988) and Bhagat and Black (2002), a negative relation between current board independence and past firm performance. Under these conditions, an OLS regression of board independence on performance may be negatively biased, while a traditional fixed-effects regression that ignores the dynamic relationship may be positively biased. We suggest that this may explain, at least in part, the mixed results from previous studies on the effect of board independence on firm performance.
However, the dynamic panel estimation methodology has its limitations. It relies on using the firm's history (lags of dependent and independent variables) for identification. Thus, there is a potential problem with weak instruments, which becomes greater as the number of lags of the instrumental variables increases. This represents an empirical trade-off. Increasing the instruments' lag length makes them more exogenous, but may also make them weaker. While weak instruments do not appear to drive the specific results in our paper, this may be an important issue in other settings. Further, we assume that errors are serially uncorrelated, but this may not hold with persistence for all variables. Additionally, Griliches and Hausman (1986) note that the bias resulting from errors in variables may be magnified when using panel data estimators. Since the dynamic panel GMM estimator relies, at least in part, on first-differencing, dynamic panel estimators may not eliminate measurement error bias unless we make strong and difficult-to-verify assumptions about serial correlation in the measurement error.
The use of lags as instruments also relies on a key assumption, the implications of which should be carefully considered by any researcher that wishes to apply dynamic panel data estimation. The methodology assumes, as a minimum, weak rational expectations (Muth, 1961, Lovell, 1986) on the part of actors in the firm's nexus of contracts. This means that future unexpected changes in performance are purely an expectational error, and implies that our empirical model includes every variable that could conceivably jointly affect both the dependent and explanatory variables (Hansen and Singleton, 1982). Given the imperfect nature of proxies in empirical research, this is unlikely to be the case. It is possible (perhaps even likely) that any cross-sectional regression of governance on performance is misspecified and that there are “omitted” time-varying unobserved variables that affect both governance and performance. Thus, researchers should be careful in relying too much on the statistical tests that examine the validity of the lagged instrument set in justifying their use of dynamic panel data estimation. Simulation results in our paper (and in Roberts and Whited, forthcoming) suggest that these statistical tests may not detect potential misspecification if the coefficient bias introduced by the misspecification falls below a certain threshold (about 25% in our own simulations). However, misspecification is likely to be as big a problem with OLS and traditional fixed-effects estimation as well, and these methods are generally not accompanied by any specification tests. Thus, even given the occasional weakness of the specification tests accompanying the dynamic GMM estimator, it likely still dominates inference from OLS or fixed-effects estimation if the underlying economic process is dynamic.
Finally, we are quick to note that the dynamic panel GMM estimator does not solve all endogeneity problems. When available, natural experiments or carefully chosen strictly exogenous instruments remain the “gold standard” for consistently identifying the effect of an explanatory variable on a dependent variable. However, given the infrequent occurrence of natural experiments, such as unexpected regulatory changes, and the relative paucity of exogenous instruments, inference in corporate finance research is likely to continue to rely on cross-sectional regressions using panel data. Our paper contributes to the literature by providing economic justification for the use of dynamic panel data estimation in corporate governance research, discussing the conditions under which it improves inference beyond OLS and traditional fixed-effects estimates, while highlighting its limitations.
The rest of the paper is organized as follows. In Section 2, we discuss related literature and develop our hypotheses. In Section 3, we lay out the theoretical basis for the biases that may arise in commonly used techniques for estimating the relation between governance and performance. We also describe the dynamic panel GMM estimator and perform numerical simulations to evaluate the power of specification tests associated with this estimator. We describe the data for our empirical applications in Section 4, and provide an empirical analysis of the relation between board structure and firm performance in Section 5. In Section 6, we re-examine the determinants of board structure in a dynamic framework. We conclude in Section 7.
Section snippets
An empirical model for board structure and performance
While endogeneity is pervasive across many aspects of corporate finance, to illustrate the specific effect of endogeneity arising from the dynamic relation between current governance and a firm's history, we focus on the relation between board structure and performance.1
Estimating the relation between governance and firm performance
In 2.1 Related theoretical work on board structure and firm performance, 3.2 Dynamic panel GMM estimation we lay out the theoretical basis for the biases that arise when we use OLS or fixed-effects regressions to estimate the relation between governance and firm performance. We then discuss the dynamic panel general method of moments (GMM) estimator, which mitigates these biases, as well as specification tests of the validity of our dynamic panel assumptions. In Section 3.3, we use a numerical
Data, sample selection and variables
In this section we describe the data for the empirical settings that we use to illustrate the impact of endogeneity in corporate finance: (1) the relation between board structure and firm performance and (2) the determinants of board structure.
The relation between board structure and firm performance
In this section, we examine the empirical relation between board structure and firm performance using the dynamic model developed above. In Section 5.1, we determine how many lags of performance we need to ensure dynamic completeness. Section 5.2 presents direct empirical evidence of the dynamic relation between board structure and the firm's historical performance and characteristics. In Section 5.3, we estimate the relation between board structure and firm performance using the dynamic panel
The determinants of board structure in a dynamic framework
Our analysis thus far has focused on identifying the effect of board structure on firm performance. The analysis itself assumes that the firm characteristics that we have identified as proxies for the firm's operating and contracting environment (size, growth opportunities, risk, age, and leverage) are actual determinants of board structure. In other words, we have assumed that the exogenous components of these characteristics have a causal effect on board structure. While there is strong
Conclusion
It is well known that theoretical and empirical research in corporate finance is complicated by the endogenous relation that exists between the control forces operating on a firm and its decisions. Jensen (1993) broadly classifies these control forces (i.e., governance in a broad sense) as capital markets, the regulatory system, product and factor markets, and internal governance. In much of the extant corporate finance research, researchers attempt to either explain the causes or examine the
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We would like to specially thank Tina Yang for her help in obtaining the boards of directors data and for numerous useful comments. We would also like to thank Bernard Black, Audra Boone, Jeff Coles, Chris Cornwell, Henrik Cronqvist, Campbell Harvey, Matthew Spiegel, Paul Irvine, Dirk Jenter, Harold Mulherin, Annette Poulsen, Chris Stivers, Martin Wells, Jessica Wochner, Yudan Zheng, two anonymous referees, seminar participants at Clemson University, James Madison University, Northeastern University, University of Georgia, University of Kansas, University of Kentucky, the 2007 meetings of the Eastern Finance Association and the Financial Management Association, the 2008 meeting of the Western Finance Association, the 2009 meeting of the American Economic Association, the 2009 Conference of Empirical Legal Studies and the 2009 CEPR European Summer Symposium in Financial Markets, for helpful comments on earlier drafts. Any errors of analysis and interpretation are our own.