Model diagnostic results and estimator implementation
| Panel A: LM, Hausman, and Mundlak tests | ||||||||
|---|---|---|---|---|---|---|---|---|
| Eq | Model | LM χ2 | LM p-value | ρ | Hausman χ2 (df) | Hausman p-value | Mundlak χ2 (df) | Mundlak p-value |
| (1) | Composite ESG | 30,281.95 | <0.0001 | 0.739 | 515.88 (9) | <0.0001 | 642.95 (9) | <0.0001 |
| (2) | Moderation (SOE × Board) | – | – | – | 442.01 (16) | <0.0001 | 671.64 (9) | <0.0001 |
| (3) | System-GMM (Dynamic ESG) | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
| (4-E) | Environmental Score | 24,649.23 | <0.0001 | 0.679 | 716.83 (9) | <0.0001 | 845.14 (9) | <0.0001 |
| (4-S) | Social Score | 26,005.81 | <0.0001 | 0.705 | 864.20 (9) | <0.0001 | 1 212.01 (9) | <0.0001 |
| (4-G) | Governance Score | 23,508.36 | <0.0001 | 0.63 | 180.63 (9) | <0.0001 | 165.03 (9) | <0.0001 |
| Panel A: LM, Hausman, and Mundlak tests | ||||||||
|---|---|---|---|---|---|---|---|---|
| (1) | Composite ESG | 30,281.95 | <0.0001 | 0.739 | 515.88 (9) | <0.0001 | 642.95 (9) | <0.0001 |
| (2) | Moderation (SOE × Board) | – | – | – | 442.01 (16) | <0.0001 | 671.64 (9) | <0.0001 |
| (3) | System-GMM (Dynamic ESG) | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
| (4-E) | Environmental Score | 24,649.23 | <0.0001 | 0.679 | 716.83 (9) | <0.0001 | 845.14 (9) | <0.0001 |
| (4-S) | Social Score | 26,005.81 | <0.0001 | 0.705 | 864.20 (9) | <0.0001 | 1 212.01 (9) | <0.0001 |
| (4-G) | Governance Score | 23,508.36 | <0.0001 | 0.63 | 180.63 (9) | <0.0001 | 165.03 (9) | <0.0001 |
| Panel B: Estimator Decisions and justifications | ||||
|---|---|---|---|---|
| Eq | Model | Estimator | Decision Basis | Explanation |
| (1) | Composite ESG | FE | LM, Hausman, Mundlak | Significant firm effects and regressor correlation justify FE |
| (2) | Moderation (SOE × Board) | FE | Hausman, Mundlak | Interactions endogenous; RE invalid |
| (3) | System-GMM (Dynamic ESG) | System-GMM | Not applicable | GMM controls endogeneity and unobserved heterogeneity |
| (4-E) | Environmental Score | FE | LM, Hausman, Mundlak | Panel structure and regressor correlation support FE |
| (4-S) | Social Score | FE | LM, Hausman, Mundlak | Strong regressor–effect correlation |
| (4-G) | Governance Score | FE | LM, Hausman, Mundlak | Significant firm effects invalidate RE |
| Panel B: Estimator Decisions and justifications | ||||
|---|---|---|---|---|
| (1) | Composite ESG | FE | LM, Hausman, Mundlak | Significant firm effects and regressor correlation justify FE |
| (2) | Moderation (SOE × Board) | FE | Hausman, Mundlak | Interactions endogenous; RE invalid |
| (3) | System-GMM (Dynamic ESG) | System-GMM | Not applicable | GMM controls endogeneity and unobserved heterogeneity |
| (4-E) | Environmental Score | FE | LM, Hausman, Mundlak | Panel structure and regressor correlation support FE |
| (4-S) | Social Score | FE | LM, Hausman, Mundlak | Strong regressor–effect correlation |
| (4-G) | Governance Score | FE | LM, Hausman, Mundlak | Significant firm effects invalidate RE |
Note(s): The LM χ2 and associated p-values are from the Breusch–Pagan Lagrange Multiplier test of panel effects (H0: Var(μi) = 0); the intra-class correlation ρ = σu2/(σu2+σe2) is taken from the random-effects specification; the Hausman χ2 and p-values test the null that the random-effects estimator is consistent (no correlation between μi and X), with rejection indicating fixed effects; the Mundlak χ2 and p-values are Wald tests on time-averaged regressors to detect correlation with μi (H0: no correlation); “—” indicates the test was not conducted, “N/A” indicates it is not applicable to the dynamic GMM model; all χ2 statistics are significant at p < 0.001 unless stated otherwise; firm-clustered robust standard errors are used throughout
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