Multivariate Analysis: Research Question 1

In this section results from the ordinary least square regressions (OLS) that relate to research question 1 will be presented and discussed. The first research question of this study is: which theoretical framework is the best predictor of board diversity and financial performance? Carter et al. (2010) posit that no one theory can directly predict the nature of the relationship between board diversity and financial performance;

therefore, it is important to adopt several theories across different disciplines to provide insight into this relationship. This study addresses research question 1 in three ways. First, in Chapter 2, a review of the literature showed that the majority of previous corporate governance studies are dominated by a single theoretical framework and they do not adopt an integration of different theories. Second, the chosen theoretical framework of the study that comprises agency, resource dependence and upper echelons theories is discussed in Chapter 3. Chapter 3 also discusses the need to adopt a theoretical framework that encompasses these three theories in order to predict the relationship between board diversity and performance including the variables that arise from this study’s theoretical framework.

Lastly, the first research question is addressed in this section by evaluating four OLS models comprised of different variables in order to find the model that best explains any variations in the dependent variable. The first model displays the OLS results for all the variables derived from the theoretical framework. Model two displays the OLS results for the variables derived from agency theory, these are, highest experience band, experience diversity and the board index. Model three displays the OLS results for the variables derived from resource dependence theory;

these are highest education band, education diversity, highest experience band, experience diversity and directorships. Model four displays the OLS results for the variables derived from upper echelons theory; these are age diversity, gender diversity, highest education band, education diversity, highest experience band, experience diversity and directorships.²⁴ Examining the four models is useful in identifying the

24 Table 3.2 in the theoretical framework chapter presented a summary of the research questions and theories alongside a summary of the variables that arise from each theory.

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explanatory variables of the individual theories and assessing whether there was a need to combine the three theories together to gain greater explanatory power.

5.5.1 OLS Regression and Akaike Information Criteria Findings

The OLS regression results are presented in Tables 5.5 and 5.6. Table 5.5 presents the OLS results using Tobin’s Q as the dependent variable whereas Table 5.6 presents the OLS results using ROE and ROA as alternative measures of financial performance. The sign of coefficients and significance together with the R-squared and F statistics are reported in the tables. The diagnostics presented in Chapter 4 displayed that OLS was not the best linear unbiased estimator for this study’s data set.

However, when addressing the first research question, OLS is the most appropriate technique in comparing the regression models and evaluating the model fit. Three statistics in the OLS regression can be used to evaluate the model fit, R-squared, F-test and the Root Mean Square Error (RMSE). The R-squared measures the overall fit of the model and looks at the proportion of the variation on the dependent variable that is explained by the independent variables (Flora, 2018). Table 5.5 shows that the applicable R-squared values range from 0.2394 to 0.1976 for the models, with model one explaining the greatest proportion of the variation on Tobin’s Q by the independent variables. Notably, model four has an R-squared of 0.2368, which is slightly lower than that of model one.

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Table 5.5 Full Sample OLS results of Tobin’s Q

The sample consists of 949 firm-year observations from 2004 to 2014. Model 1 presents the OLS results for all the variables derived from the theoretical framework.

Model 2 presents the OLS results for the variables derived from agency theory, whilst model 3 presents the OLS results for the variables derived from resource dependence theory. Model 4 presents the OLS results for the variables derived from upper echelons theory. The dependent variable used is Tobin’s Q. The independent and control variables are defined in Table 4.5 of Chapter 4. Robust standard errors are used in the OLS regression to account for heteroskedasticity. The coefficients are reported in the unstandardized form. Superscripts ***, ** and * stand for statistical significance based on two-tailed tests at the 1%, 5% and 10% significance levels respectively.

Model 1 Model 2 Model 3 Model 4

Tobin’s Q Tobin’s Q Tobin’s Q Tobin’s Q

Coef. (Std. err.) Coef. (Std. err.) Coef. (Std. err.) Coef. (Std. err.) Explanatory variables

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Table 5.6 Full Sample OLS results of ROE and ROA

The sample consists of 949 firm-year observations from 2004 to 2014. Model 1 presents the OLS results for all the variables derived from the theoretical framework.

Model 2 presents the OLS results for the variables derived from agency theory, whilst model 3 presents the OLS results for the variables derived from resource dependence theory. Model 4 presents the OLS results for the variables derived from upper echelons theory. The dependent variable used is Tobin’s Q. The independent and control variables are defined in Table 4.5 of Chapter 4. Robust standard errors are used in the OLS regression to account for heteroskedasticity. The coefficients are reported in the unstandardized form. Superscripts ***, ** and * stand for statistical significance based on two-tailed tests at the 1%, 5% and 10% significance levels respectively.

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The results in Table 5.5 suggest that the variables derived from upper echelons theory alone explain a large proportion of the variance in the dependent variable and are highly comparable with those derived from the three integrated theories. Table 5.6 shows a similar trend with R-squared values ranging from 0.1473 to 0.1721 when using ROE as a dependent variable and R-squareds ranging from 0.1723 to 0.1994. In both instances, model one had the highest squared and model two had the lowest R-squared. Further to this, the F-test indicates whether the predicted relationship between the dependent variable and the set of predictors is statistically reliable. The F statistics for all the models show that all of the regression models are significant, with p-values that are zero to four decimal points. In regards to the RMSE, it is an absolute measure of fit that indicates how accurately the model predicts response. As lower values of RMSE indicate a better fit, it is evident in Tables 5.5 and 5.6 that model one has the lowest RMSE in most cases, indicating that this model is a better fit. However, Table 5.6 shows that when using ROE as the dependent variable, model four has the lowest RMSE. These results suggest that model one with the variables derived from this study’s theoretical framework is overall a better fitting model than the models with variables from the individual theories.

In order to further assess and compare the four models, the Akaike Information Criteria (AIC) was used. AIC was developed by Akaike (1974) and is one of the most popular techniques used to compare different models based on maximum likelihood.

Model selection is important as an over-fitted model may lose generality whist an under-fitted model may not show the true nature of the variability in the dependent variable (Snipes & Taylor, 2014). Akaike (1974) proposed that selection of the best model can be determined by an AIC score, which STATA calculates as follows:

AIC = -2*ln (likelihood) + 2*k (5.1)

Where k is the number of parameters estimated and ln is the log. AIC is a measure that combines both fit and complexity, whereby fit is calculated negatively by -2*ln (likelihood) and complexity is calculated positively by 2*k (Akaike, 1974).

The model with the lowest AIC score is considered the most parsimonious model, that

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is, the simplest model with the least assumptions and greatest explanatory power for the given data (Snipes & Taylor, 2014). The results from this measure are presented in Table 5.7. Model one received the lowest AIC scores when using Tobin’s Q and ROA as dependent variables (AIC = 2174.474, AIC =6351.608), whereas model four had the lowest AIC score (AIC =7516.514) when using ROE as the dependent variable. However, there is a significant difference in the AIC scores using the different dependent variables and the models that use Tobin’s Q have much lower AIC scores. Overall the regression statistics and AIC scores indicate that model one with the variables derived from the study’s theoretical framework is the best model for the given data. These findings have several implications on the literature and theoretical perspectives of board diversity and financial performance.

Table 5.7 AIC Results