Table 3

Model diagnostic results and estimator implementation

Panel A: LM, Hausman, and Mundlak tests
EqModelLM χ2LM p-valueρHausman χ2 (df)Hausman p-valueMundlak χ2 (df)Mundlak p-value
(1)Composite ESG30,281.95<0.00010.739515.88 (9)<0.0001642.95 (9)<0.0001
(2)Moderation (SOE × Board)442.01 (16)<0.0001671.64 (9)<0.0001
(3)System-GMM (Dynamic ESG)N/AN/AN/AN/AN/AN/AN/A
(4-E)Environmental Score24,649.23<0.00010.679716.83 (9)<0.0001845.14 (9)<0.0001
(4-S)Social Score26,005.81<0.00010.705864.20 (9)<0.00011 212.01 (9)<0.0001
(4-G)Governance Score23,508.36<0.00010.63180.63 (9)<0.0001165.03 (9)<0.0001
Panel B: Estimator Decisions and justifications
EqModelEstimatorDecision BasisExplanation
(1)Composite ESGFELM, Hausman, MundlakSignificant firm effects and regressor correlation justify FE
(2)Moderation (SOE × Board)FEHausman, MundlakInteractions endogenous; RE invalid
(3)System-GMM (Dynamic ESG)System-GMMNot applicableGMM controls endogeneity and unobserved heterogeneity
(4-E)Environmental ScoreFELM, Hausman, MundlakPanel structure and regressor correlation support FE
(4-S)Social ScoreFELM, Hausman, MundlakStrong regressor–effect correlation
(4-G)Governance ScoreFELM, Hausman, MundlakSignificant 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/(σu2e2) 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

Source(s): Calculated by authors

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