Thesis Outline

3.6.1 Panel Data Ordinary Least Square

The Ordinary Least Square (OLS) technique built in panel data analysis was used to estimate the models.Regression analysis is basically concerned with the study of the dependence of one variable (dependent variable) on one or more other explanatory or independent variables (regressors) with the view to finding out or estimating/predicting the mean or average value of the former in terms of known or repeated values of the latter(Gujarati and Porter, 2009).Before estimating the models, diagnostic tests of heteroscedasticity, serial correlation, Ramsey RESET Test, Multi-collinearity and normality test were conducted. This is to ensure that the models are in line with basic econometric assumptions. The panel regression model took the form of the fixed effects model, random effects model and the pooled ordinary least square model in order to establish the most appropriate regression with the highest explanatory power that is better suited to the data set employed in the study, that is, a balanced panel but the pooled ordinary least square in the first instance.

However, in view of the weaknesses associated with it, the fixed effects model and random effect model were conducted to capture the performance of the firms considered in the study.

In order to choose the most appropriate model of interpretation, the Hausman specification

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test was conducted. The Hausman specification test is the conventional test of whether the fixed or random effects model should be used. The question is whether there is significant correlation between the unobserved unit of observation specific random effects and the independent variables. If no such correlation exists, then the random effects model may be more appropriate. But when such a correlation exists, the fixed effects model would be more suitable because the model would be inconsistently estimated.

3.6.1.1 Test of Autocorrelation

When pooled form of data is used, the serial test of correlation is performed to detect the presence of autocorrelation. Autocorrelation in any estimated model may cast dent to the reliability of the regression output.

3.6.1.2 White Test of Heteroskedasticity

This is Language Multiplier (LM) test for autoregressive conditional heteroskedasticity in the residuals. The rationale behind choosing this heteroskedasticity specification was based on the fact that in many financial time series, the magnitude of residuals appears to be related to the magnitude of recent residuals.

3.6.1.3 Ramsey RESET Test

The Ramsey RESET test determine the how well the model was fitted. This is because if non-linear combinations of the independent variables have any power in explaining the dependent variable, the model is not well specified.

3.6.1.4 Test of Multicollinearity

The correlation matrix estimation is a way of detecting multi-collinearity in any model. The presence of multi-collinearity between the independent variable results in a biased regression output.

3.6.2Panel Unit Root Test

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In an attempt to estimate the relationship between environmental cost and performance of quoted firms in Sub-Saharan Africa, the first task is to test for the presence of unit root. This is necessary in order to ensure that the parameters are estimated using stationary time series data. Thus, this study seeks to avert the occurrence of spurious results. To do this, both the Levin, Lin and Chu (LLC) Testand Breitung panel unit root tests were employed. The null hypothesis of the LLC test is that the variable is stationary. The null hypothesis of stationarity is accepted only when the p-value is less than 0.05. On the other hand, the Breitung panel unit root test method differs from LLC in two distinct ways. First, only the autoregressive portion (and not the exogenous components) is removed when constructing the standardized proxies. Second, the proxies are transformed and detrended.

3.6.3Granger Causality Test

The Granger Causality test was used to examine the effect of environmental cost on performance of quoted firms in Sub-Saharan Africa. Granger Causality approach ascertains the extent to which current performance of quoted firms can be explained by past values of environmental cost. Whenenvironmental cost helps in the prediction of performance of quoted firms, then performance of quoted firms is said to be Granger caused by environmental cost. Alternatively, environmental cost is said to be Granger caused by performance of quoted firms when the coefficients on the lagged of financial reporting quality of performance of quoted firms are statistically significant.

3.6.4Kao Residual Co-integration Test

Kao panel Co-integration test is an Engle-Granger based co-integration for panel data. Kao (1999) noted that the null hypothesis of no co-integration for panel data exists in two test.

The first is a Dickey-Fuller types test while the other is an Argumented Dickey-Fuller type test.

3.6.5Vector Error Correction Mechanism

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The essence of the VECM is to ascertain if or not all the variations in dependent variable were as a result of the co-integrating vectors trying to return to equilibrium and the error correction term that captures this variation.

3.6.6 Pedroni Residual Co-integration

The Pedroni Residual co-integration is a panel co-integration test for heterogeneous panels with multiple regressors. The null hypothesis of Pedroni‟s test is no co-integration, and the test allows for unbalanced panels, including heterogeneity in both the long-term co-integration vectors. There are seven panel co-co-integration statistics, first part is based on the within dimension approach, including the panel v statistic, the panel rho Statistic, the panel PP statistic and the panel ADF statistic; the second part is based on the between-dimension approach, including the group rho statistic, the group PP statistic and the group ADF statistic