Table 4 Summary of mediation effects...

Table 4

Summary of mediation effects using different methods

	Estimate	Statistical inference
	Estimate	Std. Error	Test stat	p-value	95% CI
System GMM (Sobel test)
Path a: OE_(t−1) → ESG_(t)	2.618*	1.17	2.236	0.025	[0.323, 4.912]
Path b: ESG_(t−1) → ROA_(t)	0.046**	0.016	2.847	0.004	[0.014, 0.077]
Path c: OE_(t−2) → ROA_(t)	1.098**	0.421	2.611	0.009	[0.274, 1.923]
Path c′: OE_(t−2) → ROA_(t) \| ESG_(t−1)	0.808*	0.4	2.018	0.044	[0.023, 1.593]
Indirect Effect: a × b	0.119	0.068	1.759	0.079	[–0.014, 0.252]
Monte Carlo Simulation (10,000 draws)
Path a: OE_(t−1) → ESG_(t)	2.6176*	1.1705		0.025	[0.323, 4.911]
Path b: ESG_(t−1) → ROA_(t)	0.0455**	0.0160		0.004	[0.014, 0.076]
Indirect Effect	0.119*	0.071		0.033	[0.007, 0.281]
Firm Cluster Bootstrap (500 replications)
Indirect Effect	0.124**	0.06		0.008	[0.026, 0.253]
SEM: OE_(t−1) → ESG_(t → ROA_(t+1)
Indirect Effect (clustered by firm)	0.047***	0.012	3.807	<0.001	[0.023, 0.072]
Indirect Effect (clustered by year)	0.047***	0.009	5.237	<0.001	[0.030, 0.065]
OLS: OE_(t-2) → ESG_(t-1) → ROA_(t)
ACME (Indirect)	0.080***	0.008	9.931	<0.001	[0.064, 0.096]
ADE (Direct)	0.100***	0.019	5.413	<0.001	[0.064, 0.136]
Total Effect	0.180***	0.017	10.358	<0.001	[0.146, 0.214]

	Estimate	Statistical inference
	Estimate	Std. Error	Test stat	p-value	95% CI
System GMM (Sobel test)
Path a: OE_(t−1) → ESG_(t)	2.618*	1.17	2.236	0.025	[0.323, 4.912]
Path b: ESG_(t−1) → ROA_(t)	0.046**	0.016	2.847	0.004	[0.014, 0.077]
Path c: OE_(t−2) → ROA_(t)	1.098**	0.421	2.611	0.009	[0.274, 1.923]
Path c′: OE_(t−2) → ROA_(t) \| ESG_(t−1)	0.808*	0.4	2.018	0.044	[0.023, 1.593]
Indirect Effect: a × b	0.119	0.068	1.759	0.079	[–0.014, 0.252]
Monte Carlo Simulation (10,000 draws)
Path a: OE_(t−1) → ESG_(t)	2.6176*	1.1705		0.025	[0.323, 4.911]
Path b: ESG_(t−1) → ROA_(t)	0.0455**	0.0160		0.004	[0.014, 0.076]
Indirect Effect	0.119*	0.071		0.033	[0.007, 0.281]
Firm Cluster Bootstrap (500 replications)
Indirect Effect	0.124**	0.06		0.008	[0.026, 0.253]
SEM: OE_(t−1) → ESG_(t → ROA_(t+1)
Indirect Effect (clustered by firm)	0.047***	0.012	3.807	<0.001	[0.023, 0.072]
Indirect Effect (clustered by year)	0.047***	0.009	5.237	<0.001	[0.030, 0.065]
OLS: OE_(t-2) → ESG_(t-1) → ROA_(t)
ACME (Indirect)	0.080***	0.008	9.931	<0.001	[0.064, 0.096]
ADE (Direct)	0.100***	0.019	5.413	<0.001	[0.064, 0.136]
Total Effect	0.180***	0.017	10.358	<0.001	[0.146, 0.214]

Note(s): *, **, *** denote p < 0.1, 0.05, 0.01, 0.001 respectively

GMM includes firm and time fixed effects

Test Stat. Column contains z-values from GMM robust estimates and the Sobel z-value for the indirect effect

SEM uses bootstrap CIs

SEM Model Fit: RMSEA = 0.066, CFI = 0.928, SRMR = 0.015

OLS uses OE_(t-2) → ESG_(t-1) → ROA_(t) with year controls

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