** 8 Empirical methodology**

**8.2 Model specification and hypothesis testing .1 CSP and idiosyncratic volatility**

**8.2 ** **Model specification and hypothesis testing **

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Secondly, the Lagrange multiplier test on the disaggregated CSP component and idiosyncratic volatility. The results for time effects, firm effects, and two way effects returned χ test statistics of 21,022, 2,011, 23,033, respectively. All three test statistics are highly statistical significant and suggest both

individual and firm effects. The pooled linear regression approach is therefore not optimal.

The Hausman test statistic was highly statistically significant. The fixed effects approach is

therefore more appropriate. There was a highly statistically significant DW test statistic of 1.882. There was a significant χ test statistic of 39.198. Both tests indicate autocorrelation. The Breusch-Pagan test for heteroscedasticity was conducted. The test returned a highly statistically significant test statistic of 5,952.7, which indicates the presence of heteroscedasticity. None of the explanatory variables exhibited a VIF greater than 10, which supports the assertion that the risk of highly multicollinearity in the explanatory variables is low.

In conclusion, the relationship between the disaggregated components of CSP and idiosyncratic volatility was estimated using the following multiple linear regression model with firm-fixed and time-fixed effects:

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‘HAC’ standard errors were used (Brooks, 2014).

Research question 1a is also addressed using the following hypothesis tests:

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**8.2.2 ** **CSP and downside idiosyncratic volatility **

Firstly, the Lagrange multiplier test was applied on aggregate CSP and downside idiosyncratic volatility. The results for time effects, firm effects, and two way effects returned χ test statistics of 19,670, 1,759.8, and 21,430, respectively. All three test statistics are highly statistical significant and suggest both individual and firm effects. The pooled linear regression approach is therefore not optimal.

The Hausman test statistic was highly statistically significant. The fixed effects approach is therefore more appropriate. There was a highly statistically significant DW test statistic of 1.9053. There was a highly statistically significant χ test statistic of 25.166. Both tests indicate autocorrelation. The Breusch-Pagan test for heteroscedasticity was conducted. The test returned a highly statistically significant test statistic of 5,787.8, which indicates the presence of heteroscedasticity. None of the explanatory variables exhibited a VIF greater than 10, which supports the assertion that the risk of highly multicollinearity in the explanatory variables is low.

The relationship between the aggregate CSP and downside idiosyncratic volatility was estimated using the following multiple linear regression model with firm-fixed and time-fixed effects:

.

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‘HAC’ standard errors were used (Brooks, 2014).

Research question 1b (i.e., is there a relationship between ESG measures and downside idiosyncratic risk?) is addressed using the following hypothesis test:

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The Lagrange multiplier test was applied on disaggregated CSP component and downside idiosyncratic volatility. The results for time effects, firm effects, and two way effects returned χ test

statistics of 19,618, 1,759.2, and 21,377, respectively. All three test statistics are highly statistical significant and suggest both individual and firm effects. The pooled linear regression approach is therefore not optimal.

The Hausman test statistic was highly statistically significant. The fixed effects approach is therefore more appropriate. There was a highly statistically significant DW test statistic of 1.9066. There was a highly statistically significant χ test statistic of 24.475. Both tests indicate autocorrelation. The Breusch-Pagan test for heteroscedasticity was conducted. The test returned a highly statistically significant test statistic of 5,823.7, which indicates the presence of heteroscedasticity. None of the explanatory variables exhibited a VIF greater than 10, which supports the assertion that the risk of highly multicollinearity in the explanatory variables is low.

The relationship between the disaggregated components of CSP and downside idiosyncratic

volatility was estimated using the following multiple linear regression model with firm-fixed and time-fixed effects:

.

. _{,}

‘HAC’ standard errors were used (Brooks, 2014).

Research question 1b is also addressed using the following hypothesis tests:

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**8.2.3 ** **CSP and upside idiosyncratic volatility **

The Lagrange multiplier test was applied on aggregate CSP and upside idiosyncratic volatility. The results for time effects, firm effects, and two way effects returned χ test statistics of 20,092, 1,996.8, and 22,089, respectively. All three test statistics are highly statistical significant and suggest both individual and firm effects. The pooled linear regression approach is therefore not optimal.

The Hausman test statistic was highly statistically significant. The fixed effects approach is therefore more appropriate. There was a highly statistically significant DW test statistic of 1.8808. There was a highly statistically significant χ test statistic of 39.861. Both tests indicate autocorrelation. The Breusch-Pagan test for heteroscedasticity was conducted. The test returned a highly statistically significant test statistic of 5,738.9, which indicates the presence of heteroscedasticity. None of the explanatory variables exhibited a VIF greater than 10, which supports the assertion that the risk of highly multicollinearity in the explanatory variables is low.

The relationship between the aggregate CSP and upside idiosyncratic volatility was estimated using the following multiple linear regression model with firm-fixed and time-fixed effects:

.

. _{,}

‘HAC’ standard errors were used (Brooks, 2014).

Research question 1c (i.e., is there a relationship between ESG measures and upside idiosyncratic risk?) is addressed using the following hypothesis test:

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The Lagrange multiplier test was on disaggregated CSP component and upside idiosyncratic volatility. The results for time effects, firm effects, and two way effects returned χ test statistics of 19,959, 1,995.7, and 21,954, respectively. All three test statistics are highly statistical significant and suggest both individual and firm effects. The pooled linear regression approach is therefore not optimal.

The Hausman test statistic was highly statistically significant. The fixed effects approach is therefore more appropriate. There was a highly statistically significant DW test statistic of 1.8819. There was a highly statistically significant χ test statistic of 39.159. Both tests indicate autocorrelation. The Breusch-Pagan test for heteroscedasticity was conducted. The test returned a highly statistically significant test statistic of 5,759.6, which indicates the presence of heteroscedasticity. None of the explanatory variables exhibited a VIF greater than 10, which supports the assertion that the risk of highly multicollinearity in the explanatory variables is low.

The relationship between the disaggregated components of CSP and upside idiosyncratic volatility was estimated using the following multiple linear regression model with firm-fixed and time-fixed effects:

.

. _{,}

‘HAC’ standard errors were used (Brooks, 2014).

Research question 1c is also addressed using the following hypothesis tests:

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Finally, research question 1d (i.e., How do these relationships, or lack thereof, compare with each other?) is addressed by examining the results of the preceding hypothesis tests and the strengths and directions of the associations suggested by the regression coefficients.

**8.2.4 ** **CSP and idiosyncratic skewness **

The Lagrange multiplier test was applied on aggregate CSP and idiosyncratic skewness. The results for time effects, firm effects, and two way effects returned χ test statistics of 340.8, 0.91554, and 341.71, respectively. The test statistics for time and two ways effects are highly statistical significant. The test

statistic for firm effects is not statistically significant. This suggests time and twoway effects. To confirm, an F test for time effects was conducted which returned a highly statistically significant F statistic of 8.2724.

An F test for twoway effects returned a statistically insignificant F statistic of 1.0481. This suggests time effects. The pooled linear regression approach is therefore not optimal.

The Hausman test statistic not statistically significant. The fixed effects approach is therefore more appropriate. There was a highly statistically significant DW test statistic of 1.9445. There was a highly statistically significant χ test statistic of 8.3195. Both tests indicate autocorrelation. The Breusch-Pagan test for heteroscedasticity was conducted. The test returned a statistically insignificant test statistic of 0.485, which suggests the lack of presence of heteroscedasticity.

The relationship between the aggregate CSP and idiosyncratic skewness was estimated using the following linear regression model with time-fixed effects:

‘HAC’ standard errors were used (Brooks, 2014).

Utilizing the connection between idiosyncratic skewness and the proportion of each component of idiosyncratic risk to total idiosyncratic risk, research question 1d will also be partially addressed using the following hypothesis test:

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The Lagrange multiplier test was on disaggregated CSP component and idiosyncratic skewness. The results for time effects, firm effects, and two way effects returned χ test statistics of 332.2, 0.8414, and 333.05, respectively. The test statistics for time and two ways effects are highly statistical significant. The test statistic for firm effects is not statistically significant. This suggests time and twoway effects. To confirm, an F test for time effects was conducted which returned a highly statistically significant F statistic of 8.1922. An F test for twoway effects returned a statistically insignificant F statistic of 1.0507. This suggests time effects. The pooled linear regression approach is therefore not optimal.

The Hausman test statistic was not statistically significant. The random effects approach is therefore more appropriate. There was a highly statistically significant DW test statistic of 1.9435. There was a highly statistically significant χ test statistic of 8.6428. Both tests indicate autocorrelation. The Breusch-Pagan test for heteroscedasticity was conducted. The test returned a statistically insignificant test statistic of 3.874, which suggests the lack of presence of heteroscedasticity. None of the explanatory variables exhibited a VIF

greater than 10, which supports the assertion that the risk of highly multicollinearity in the explanatory variables is low.

The relationship between the disaggregated components of CSP and idiosyncratic skewness was estimated using the following multiple linear regression model with random time effects:

,

‘HAC’ standard errors were used (Brooks, 2014).

Research question 1c is also addressed using the following hypothesis tests:

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**8.2.5 ** **CSP and abnormal returns **

The Lagrange multiplier test was on aggregate CSP and abnormal returns. The results for time effects, firm effects, and two way effects returned χ test statistics of 2,838, 3.8752, and 2,841.8,

respectively. All three test statistics are highly statistical significant and suggest both individual and firm effects. The pooled linear regression approach is therefore not optimal.

The Hausman test statistic was highly statistically significant. The fixed effects approach is therefore more appropriate. There was a statistically insignificant DW test statistic of 2.0897. In contrast, the Breusch-Godfrey/Wooldridge test for higher order autocorrelation returned a highly statistically significant χ test statistic of 21.8. This suggests autocorrelation. The Breusch-Pagan test for

heteroscedasticity was conducted. The test returned a highly statistically significant test statistic of 196.2, which indicates the presence of heteroscedasticity.

The relationship between the aggregate CSP and abnormal returns was estimated using the following linear regression model with firm-fixed and time-fixed effects:

‘HAC’ standard errors were used (Brooks, 2014).

Research question 2a (i.e., there a relationship between ESG measures and market return?) is addressed using the following hypothesis test:

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The Lagrange multiplier test was applied on disaggregated CSP component and abnormal returns.

The results for time effects, firm effects, and two way effects returned χ test statistics of 2,852.3, 3.9329, and 2,856.2, respectively. The test statistics for time and two ways effects are highly statistical significant.

All three test statistics are highly statistical significant and suggest both individual and firm effects. The pooled linear regression approach is therefore not optimal.

The Hausman test statistic was highly statistically significant. The fixed effects approach is therefore more appropriate. There was a statistically insignificant DW test statistic of 2.0897. There was a highly statistically significant χ test statistic of 21.808. This suggests autocorrelation. The Breusch-Pagan test for heteroscedasticity was conducted. The test returned a highly statistically significant test statistic of 254.6, which indicates the presence of heteroscedasticity. None of the explanatory variables exhibited a VIF greater than 10, which supports the assertion that the risk of highly multicollinearity in the explanatory variables is low.

The relationship between the disaggregated components of CSP and abnormal returns was estimated using the following multiple linear regression model with firm-fixed and time-fixed effects:

Research question 2a is also addressed using the following hypothesis tests:

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‘HAC’ standard errors were used (Brooks, 2014).

**8.2.6 ** **CSP and excess log returns **

The Lagrange multiplier test was applied on aggregate CSP component and excess log returns. The results for time effects, firm effects, and two way effects returned χ test statistics of 390,610, 0.17923, 390,610, respectively. The test statistics for time and two ways effects are highly statistical significant. The test statistic for firm effects is not statistically significant. This suggests time and twoways effects. To confirm, an F test for time effects was conducted which returned a highly statistically significant F statistic of 415.33. An F test for twoway effects was conducted which returned a highly statistically significant F

statistic of 6.74. This suggests twoway effects. The pooled linear regression approach is therefore not optimal.

The Hausman test statistic was highly statistically significant. The fixed effects approach is

therefore more appropriate. There was statistically insignificant DW test statistic of 2.0774. In contrast, the Breusch-Godfrey/Wooldridge test for higher order autocorrelation returned a highly statistically significant χ test statistic of 16.235. This suggests autocorrelation. The Breusch-Pagan test for heteroscedasticity was conducted. The test returned a highly statistically significant test statistic of 159.4, which indicates the presence of heteroscedasticity.

The relationship between the aggregate CSP and excess log returns was estimated using the following linear regression model with firm-fixed and time-fixed effects:

‘HAC’ standard errors were used (Brooks, 2014).

Research question 2a is also addressed using the following hypothesis test:

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The Lagrange multiplier test was applied on disaggregated CSP components and excess log returns.

The results for time effects, firm effects, and two way effects returned χ test statistics of 389,600, 0.13591, and 389,600, respectively. The test statistics for time and two ways effects are highly statistical significant.

The test statistic for firm effects is not statistically significant. This suggests time and twoway effects. To confirm, an F test for time effects was conducted which returned a highly statistically significant F statistic of 359.9. An F test for twoway effects was conducted which returned a highly statistically significant F statistic of 6.734. This suggests twoway effects. The pooled linear regression approach is therefore not optimal.

The Hausman test statistic was highly statistically significant. The fixed effects approach is therefore more appropriate. There was a statistically insignificant DW test statistic of 2.0777. In contrast, the Breusch-Godfrey/Wooldridge test for higher order autocorrelation returned a highly statistically significant χ test statistic of 16.377. This suggests autocorrelation. The Breusch-Pagan test for

heteroscedasticity was conducted. The test returned a highly statistically significant test statistic of 213.3, which indicates the presence of heteroscedasticity. None of the explanatory variables exhibited a VIF

greater than 10, which supports the assertion that the risk of highly multicollinearity in the explanatory variables is low.

The relationship between the disaggregated components of CSP and excess log returns was estimated using the following multiple linear regression model with firm-fixed and time-fixed effects:

‘HAC’ standard errors were used (Brooks, 2014).

Research question 2a is also addressed using the following hypothesis tests:

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