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5.2.2 Dynamic models: A System GMM estimation
5.2.2.1 Testing for endogeneity of the regressors
As mentioned in Chapter 2 and in Subsection 4.3.1, it is well-documented in corporate governance literature that all corporate governance variables used in equation (4.2) are endogenous variables. This subsection empirically checks the endogeneity of the regressors before proceeding with the System GMM specification. Accordingly, the DWH test for endogeneity of all the regressors is executed under the null hypothesis that the endogenous regressors may be actually treated as exogenous variables (Baum et al., 2007). Test statistics follow a Chi- squared (Chi-sq) distribution with the degrees of freedom equal to the number of suspected regressors (laglnq, female, nonexe, dual, lnbsize, block, fsize, and lev).
This study follows Schultz et al. (2010) and conducts the test based on the levels equation of firm performance and corporate governance variables in which one- year lagged differences of the regressors are employed as instrumental variables.
The industry dummies and lnfage are included in the test specification and treated as exogenous variables. It is found that the null hypothesis cannot be accepted at any conventional levels of significance (Chi-sq(8) = 24.621; p = 0.002), thus suggesting that the regressors cannot be treated as exogenous variables, and that the System GMM model will be superior in terms of consistency when compared with the OLS and FE models.
5.2.2.2 The validity of the System GMM estimator
As mentioned in Subsection 4.3.5.2, the consistency of the System GMM estimator is significantly contingent upon the validity of instrumental variables
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employed. This subsection diagnoses empirically whether the instruments are valid, (i.e., they are exogenous) by using the Hansen-J test of over-identification and the difference-in-Hansen tests of the exogeneity of instrument subsets. As reported in the last row of Table 5.11, the Hansen-J test yields a p-value of 0.299, suggesting that the null hypothesis of the test cannot be rejected at any conventional levels of significance. In other words, this suggests that the instruments employed in the System GMM model are valid.
This study also follows the recommendation of Roodman (2009b) about good practices in implementing the System GMM estimation and applies the difference-in-Hansen test to the subsets of System GMM-type instruments, as well as standard instrumental variables for the levels equation. Table 5.10 presents difference-in-Hansen tests of the exogeneity of instrument subsets, under the null hypothesis of joint validity of a given instrument subset. The results reported in Table 5.10 indicate that there is no statistical evidence to reject the null hypothesis, thus suggesting that the subsets of instruments are econometrically exogenous. Thus, the F-test statistic for the overall significance of the regression65 (Table 5.11), and the results from Hansen-J test (Table 5.11), and difference-in- Hansen tests (Table 5.10), all support the view that the System GMM model appears to be well-specified.
5.2.2.3 Empirical results from the System GMM model
Taking into account the concern of the dynamic nature of the board structure–firm performance relationship, this study follows Wintoki et al. (2012) in employing
65 Based on small-sample corrections, Chapters 5 and 6 report t-test instead of z-test statistics for the estimated coefficients. Likewise, F test statistics are reported for the overall fit of the System GMM models instead of Wald Chi-squared test statistics.
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the System GMM estimator. The results reported in column 1 of Table 5.11 show that the percentage of female directors is positively and statistically significantly related to Tobin’s Q at the 5% level (p = 0.066), thus supporting hypothesis HVN1. To avoid duplication and save space, the empirical results reported in Table 5.11 are not interpreted, while the empirical results obtained from the System GMM model will be interpreted in more detail in the next subsection 5.2.3.1.
Table 5.10: Difference-in-Hansen tests of exogeneity of instrument subsets Tested instrument subsets
Test statistics
Degrees of freedom
p- value
Panel A: System GMM-type instruments
Instruments for levels equation as a group 9.27 8 0.320
lnqit-2 and lnqit-3 (for transformed equation) 2.05 2 0.359
Δlnqit-1 (for levels equation) 2.86 1 0.091
Instruments for board structure variables 6.07 12 0.913 Instruments for other corporate governance
and control variables 13.54 9 0.140
Panel B: Standard instruments
2009 and 2010 year dummies, and lnfage 7.63 3 0.054
Note: This table presents difference-in-Hansen tests of exogeneity of instrument subsets, under the null hypothesis of joint validity of a specific instrument subset. The variables are as defined in Table 4.6. The test statistics are asymptotically Chi-squared distribution with the degrees of freedom equal to the number of questionable instruments (Roodman 2009).
GMM instrument subset used for levels equation includes one-year lagged differences of firm performance, board structure, ownership structure, capital structure, and control variables (Δlnqit- 1 ; Δfemaleit-1 ; Δnonexeit-1 ; Δdualit-1 ; Δlnbsizeit-1 ; Δblockit-1 ; Δfsizeit-1 ; and Δlevit-1). GMM instrument subset used for board structure variables includes lag 1 of the first differences; lags 2 and 3 in levels of board structure variables (female; nonexe; dual and lnbsize).
GMM instrument subset used for other corporate governance and control variables includes lag 1 of the first differences; lags 2 and 3 in levels of these variables, including block, fsize, and lev.
The subset of standard instruments for levels equation includes 2009 and 2010 year dummies, and lnfage. 2008 and 2011 year dummies are dropped due to collinearity.
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