Analysis Method: System Generalized Methods of Moments

Why System GMM? While developing a causal relationship between antecedents and performance, the noble approach is the instrumental variable approach.

However, finding a suitable instrumental variable that fits the research design is not always feasible. Therefore, to tackle the unobserved heterogeneity and endogeneity problem inherent in panel regression, System GMM as a method is suggested where time and industry dummies are used as instruments, lagged dependent variable is used as a control variable.

I test the hypothesis by following the latest specification and argumentation to use system GMM (Keil et al. 2015). There are five key reasons, as shown in Table 12, for the system GMM estimator to be the robust estimator for this dissertation.

First, the type of data demands this method as current data is panel data with few time periods and many companies. Second, the dependent variable is driven by the previous levels of performance. This requires the use of a lagged dependent variable as a control. Third, the panel data is inherent with heteroscedasticity and autocorrelation that needs to be controlled. Fourth, my explanatory variables can be correlated with past and current realizations of the error term. And fifth, the method is prudent for the most prevalent control for unobserved heterogeneity.

The major methods in panel data design are fixed effect and random effect modeling in the presence of the Hausman test to choose between fixed or random effects. However, due to the nature of the panel data, as reported in Table 12, I follow system GMM. Roodman (2015) outlines the history and use of the system GMM. Following Roodman's (2015) recommendations, I use the system GMM for this research with Stata command xtabond2. This command can fit two closely related dynamic panel data models—Arellano-Bond (1991) and Arellano and Bover (1995) but fully developed in Blundell and Bond (1998) estimator. The first treats the model as a system of equations for each time period. Differing in instruments, the specification is divided into predetermined and endogeneous variables.

The inherent problem with the original Arellano-Bond estimator is that lagged levels are deemed to be poor instruments for first differences and was improved by Arellano and Bover (1995) by choosing predetermined and endogenous variables in levels and instrumenting with suitable lags of their own first differences. This version was improved by Blundell and Bond (1998). The original estimator is named “difference GMM”, and the latter ones as “system GMM”. The latter can have one- and two-step options and standard error corrections implemented by Windmeijer (2005). Therefore, I use the two-step option in the modeling.

There are inherent benefits of using a lagged dependent variable as a control.

Lagged dependent variables (Wooldridge, 2009: p. 310-312) can be used with time series and panel data where many observations in multiple times are used.

Lags refer to time-related to other variables. In current data, when I lag data by one year, say for all variables measured in 2014, I use the value from 2013 in the analysis. In arguing for causality, the second condition, called temporal precedence, can be handled through a lagged variable. Lagging a variable means using a value from an earlier time point, and in this way, we can include an earlier value of the dependent variables as an explanatory variable in the regression analysis. Wooldridge explains that lagged dependent variables can be used to account for unobserved effects that persist over time. Lagged dependent

variables are very useful and very commonly used when longitudinal data are available and the purpose is to control for stable omitted causes or historical effects (Wooldridge, 2009:311–313). The system GMM uses lagged variables on the specification itself.

Table 12. Differentiating Advantages of System GMM (Developed from Keil et al. 2015)

Key issues in panel data analysis Does System

GMM Handle it?

Panel data with few time periods and many companies Yes The dependent variable is driven by the previous levels of performance and the need for

lagged dependent variable as a control Yes

The panel data is inherent with heteroscedasticity and autocorrelation that needs to be

controlled. Yes

Perhaps the explanatory variables are correlated with past and current realizations of the

error term Yes

Need to control for unobserved heterogeneity Yes

Girod and Whittington (2016) argue the use of system GMM to avoid the endogeneity issue while using lagged dependent variables. Apart from the possibility of introducing individual effects, system GMM deals with endogenous regressors. As argued by Girod and Whittington (2016), the method makes possible the use of predetermined but not strictly exogenous regressors, such as past performance. Following the guidelines by Roodman (2009), Girod and Whittington (2016) suggested using collapse option in controlling the proliferation of instruments in system GMM. I follow these guidelines in my analysis. Another issue discussed in the context of panel data is serial correlation or autocorrelation (Wooldridg 2009:350), which occurs when a variable correlate with itself over time. The system GMM not only handles first-order serial correlation but goes one step further to handle second-order serial correlation.

Following prior research (Uotila et al. 2009), industry and year controls were treated as exogenous variables, and all the other variables were treated as predetermined. Due to many variables and years in current data, I limited the number of instruments to the first available lagged levels to avoid overfitting bias.

Semadeni, Withers and Trevis Certo (2014) highlighted the dire state of endogeneity in strategic management research. Endogeneity makes the ordinary least squares (OLS) regression estimator biased, and not many papers in the field tackle this genuine problem. Some papers that have used the instrumental variable approach to solving this problem have not been able to find good instrumental variables either, making the estimates even biased. One of the statistical methods in the absence of good instruments is called GMM and its variant is called system GMM as used by Wintoki, Linck and Netter (2012). The authors have successfully benefitted from the dynamic nature of internal

governance choices as they are very valuable instruments to address the main causes of endogeneity, unobserved heterogeneity, and simultaneity. With a panel data of 6,000 firms from 1991 to 2003, the findings suggested that there is no causality between board structure and current firm performance. The claim is noteworthy because it rules out the major cause of endogeneity using system GMM as a method.

Following the recommendations by Wintoki et al. (2012), another very interesting paper on a longitudinal study of S&P 500 firms for the period from 1999 to 2007 is by Keil et al. (2015), which also used the system GMM. In both papers, the key assumptions to use system GMM is justified, as suggested by Arellano and Bond (1991). This thesis also has similar assumptions to those reported by Keil et al. (2015). The thesis has more companies (269) compared to few time-period (i.e. 10 years), the dependent variable is driven by the past performance, and this should be controlled for by inserting a lagged value in the estimation. This must control for the generally inherent problem of heteroscedasticity and autocorrelation of independent variables most probably linked with past and current realizations of the error terms.

Above all, system GMM is good in handling unobserved heterogeneity (Keil et al.

2015). Since these conditions are similar in current work, I follow the analysis procedure suggested by Keil et al. (2015). Due to the nature of the research setting outlined above, using the fixed-effects estimator is not justified in handling all the challenges at hand, and I opted for dynamic GMM (Arellano &

Bond, 1991; Roodman 2015) and argued by Keil et al. (2015) as well. I used the two-step estimator option, as suggested by Windmeijer (2005), to handle for panel-specific autocorrelation and heteroscedasticity (Keil et al. 2015).

The difference GMM estimator is not a suitable option in this case but the system GMM estimator is, to get the benefit of time-invariant regressors, such as industry dummies. The major issue in using GMM is to select variables as predetermined and exogenous ones. Following Keil et al. (2015), predetermined variables are all independent and control variables while year and industry dummies are treated as exogenous. The first lag of the predetermined variables and the current values of the exogenous variables are used as instruments.

Following Roodman's recommendations, I checked whether instruments are lower than several groups used in the analysis.