Multivariate analysis using instrumental variables regression

Multivariate analysis refers to the analysis of three or more variables simultaneously using regression analysis. Multivariate analysis helps in assessing the strength of the relationship between a dependent variable and one or more independent variables (Saunders, Lewis, & Thornhill, 2009).

Studies exploring the relationship between corporate governance and bidder returns face some methodological challenges. One such problem is endogeneity. Endogeneity problem exists when an independent or explanatory variable in an equation is correlated with the error term leading to biased and inconsistent parameter estimates (Roberts & Whited, 2013). “One form of endogeneity problem [affecting corporate governance-abnormal relationship] is an omitted variable bias” (Masulis et al., 2007, p. 1876). The problem is mainly as a result of independent variables being choice variables and some of their determinants affecting the dependent variables as well, and are omitted from the structural equation (Larcker & Rusticus, 2010). The omission of these determinants means the ordinary least squares (OLS) parameter estimates will be inconsistent and biased. The results will, therefore, be interpreted based on unreliable estimates of economic significance.

This study uses instrumental variables (IV) estimation procedures to mitigate the endogeneity problem. An instrumental variable is a variable which is uncorrelated with the error term but correlated with an independent or explanatory variable (Larcker & Rusticus, 2010). However, due to lack of well-developed theory or model of the economic

116 determinants of corporate governance, it is difficult to find suitable instrumental variables to deal with endogeneity issues in our setting (Ashbaugh-Skaife, Collins, & LaFond, 2006, p. 235). This study, therefore, relies on empirical studies that have attempted to address potential endogeneity of the corporate governance choice following Larcker and Rusticus (2010).

Informed by literature, we identify three instrumental variables used in the 1st stage fitted regressions. Masulis et al. (2007) point out that there may be some unobservable bidder traits that could affect both the level of corporate governance in a firm and abnormal returns. They reiterate that management quality could be one such a factor. For example, firms with good management have greater skills to separate good and bad corporate governance practices (Ariff, Ibrahim, & Othman, 2007). Some studies report that poor past performance (bad management) leads to increases in board independence (Bhagat & Bolton, 2013; Hermalin & Weisbach, 2003). Thus, management quality, proxied by industry-adjusted sales growth and Tobin’s q, are used as instrumental variables for state ownership and independent directors. Industry-adjusted sales growth (Tobin’s q) is measured by industry median sales growth (Tobin's q) a year prior to the M&A announcement. Another factor could be the effect of the share-split reforms launched in 2006 that allowed non-tradable state shares in listed firms to be traded on the stock exchanges. Empirical evidence shows that the reforms strengthen managerial accountability (Hou, Lee, Tong, & Stathopoulos, 2011) and improves corporate governance (Yu, 2013). To examine this possibility, we include post-reform variable as an instrumental variable for state ownership and independent directors, measured by a dummy variable equal to 1 if the M&A deal was announced after 2005 and 0 otherwise.

For the purposes of this study, state shares and independent directors are used as endogenous regressors and, industry-adjusted Tobin’s q, industry-adjusted sales growth and post-reform were used as instrumental variables. Separate endogeneity tests were carried out for all six corporate governance variables and could not reject the null hypothesis that four variables legal-person ownership, executive ownership, board size and CEO role duality are exogenous.

To use the IV, the instruments must be strongly correlated with the instrumented variables and not correlated with the error term. To verify the first assumption, we compare the Cragg-Donald Wald F-statistic to Stock and Yogo (2005) critical values to test for weak

117 instruments. To verify the second assumption, we use the Hansen J test. We also use the Durbin-Wu-Hausman (DWH) test to test for differences between OLS and 2SLS instrumented results and to determine which estimation method is appropriate for statistical inference (Bhagat and Bolton, 2013). As a robustness test, we perform sensitivity analyses of the instruments by running several types of instrumental variables regressions, that is, two-stage least squares with instruments (IV-2SLS), limited information maximum likelihood with instruments (IV-LIML) and generalised methods of moments with instruments (IV-GMM), and compare the results across the regressions. The results reported in Table 6.4 and Table 7.4 show the instruments have a strong relationship with instrumented regressors and the model is valid and is correctly specified. The Sargan test statistics (𝜒2 _{= 0.272, 𝑝 = 0.6021 for the short-term and 𝜒}2 _{= 0.035, 𝑝 = 0.8519 for the}

long-term) show that the instruments are uncorrelated with the error term. This may suggest that the instruments are valid and the model is correctly specified. The F-statistics (132.32 for state shares and 155.80 for independent directors) are both greater than the Cragg- Donald Wald F-statistic of 35.06. Also, the Cragg-Donald Wald F-statistic is larger compared to the Stock-Yogo weak instruments identification test critical value of 13.43 at 10% maximal IV size. This suggest that the instruments are strong. The DWH test statistics (𝜒2 _{= 5.648, 𝑝 = 0.059 for the short-term and 𝜒}2 _{= 56.615, 𝑝 = 0.000 for the long-term)}

show that endogeneity may be a concern in this study suggesting IV estimation technique is the best.

Of the several types of IV regressions, IV-GMM estimation is used for statistical inference. GMM estimates are preferable because they have been widely used in accounting and finance literature. They have large sample properties that are easy to characterise in ways that facilitate comparison and can be constructed without specifying the full data generating process (Hansen, Hausman, & Newey, 2008). In addition, they are more efficient especially when the error term is heteroscedastic, while even in absence of heteroscedasticity, GMM is asymptotically better (Baum, Schaffer, & Stillman, 2003).

The estimation framework adopted for this study, informed by previous empirical studies, is ran using Stata 14.2 and is specified as:

𝑌_𝑖 = 𝛽₀+ 𝛽₁𝑋_1𝑖 + 𝛽₂𝑋_2𝑖+ 𝛽₃𝑋_3𝑖+ 𝛽₄𝑋_4𝑖+ 𝜀_𝑖

Y is the dependent variable which is either CAR [-5, +5] or SMTBVBHAR [+1, +24]. CAR [-5, +5] is defined as cumulated abnormal returns around announcement period over an

118 eleven-day event window using market model parameters estimated over 200-day estimation period. SMTBVBHAR [+1, +24] is defined as the mean size and market-to-book value adjusted buy-and-hold abnormal returns over the twenty-four-month period calculated using the market index as the benchmark. X1 is the vector of the ownership

structure variables (state shares, legal-person shares and executive shares), X2 is the vector

of the board structure variables (board size, board independence and CEO role duality), X3

is the vector of the firm-specific characteristics variables (log total sales, financial leverage, Tobin’s q, return on assets, stock price run-up and sales growth), and X4 is the vector of the

deal-specific characteristics variables (high-tech deals, deal value, target listing status and payment method). Mean industry sales growth, mean industry Tobin’s q and post-reform are used as instruments for state shares and independent directors.