Table 1 Tests for selecting... | Emerald Publishing

Table 1

Tests for selecting Discroll–Kraay fixed effect as estimator

Test	Purpose	Result	Decision
Breusch–Pagan LM	RE vs. pooled OLS	p = 1.000 (all models)	Fail to reject H₀; no firm-specific random effects detected. RE offers no advantage over pooled OLS, though this alone doesn't confirm OLS is optimal
Hausman	FE vs. RE	p < 0.001 (all models)	Reject H₀; FE preferred, as unobserved firm characteristics correlate with ESG disclosure and controls
Modified Wald	Groupwise heteroskedasticity	p < 0.001 (all models)	Reject H₀; residual variance differs across firms, making conventional FE standard errors potentially inefficient
Wooldridge	Serial correlation	p < 0.001–0.0006 (all models)	Reject H₀; first-order autocorrelation present, indicating shocks persist over time within firms
Pesaran CD	Cross-sectional dependence	Significant in 2 of 4 models	Mixed evidence; some models show firms are affected by common shocks (e.g. regulatory or economic changes), others do not
Final approach/estimator used	Robust inference under FE	Driscoll–Kraay FE (xtscc, fe) applied	Corrects standard errors for heteroskedasticity, serial correlation and cross-sectional dependence, ensuring reliable inference across all final specifications

Test	Purpose	Result	Decision
Breusch–Pagan LM	RE vs. pooled OLS	p = 1.000 (all models)	Fail to reject H₀; no firm-specific random effects detected. RE offers no advantage over pooled OLS, though this alone doesn't confirm OLS is optimal
Hausman	FE vs. RE	p < 0.001 (all models)	Reject H₀; FE preferred, as unobserved firm characteristics correlate with ESG disclosure and controls
Modified Wald	Groupwise heteroskedasticity	p < 0.001 (all models)	Reject H₀; residual variance differs across firms, making conventional FE standard errors potentially inefficient
Wooldridge	Serial correlation	p < 0.001–0.0006 (all models)	Reject H₀; first-order autocorrelation present, indicating shocks persist over time within firms
Pesaran CD	Cross-sectional dependence	Significant in 2 of 4 models	Mixed evidence; some models show firms are affected by common shocks (e.g. regulatory or economic changes), others do not
Final approach/estimator used	Robust inference under FE	Driscoll–Kraay FE (xtscc, fe) applied	Corrects standard errors for heteroskedasticity, serial correlation and cross-sectional dependence, ensuring reliable inference across all final specifications