Table 6 Summary of robustness checks and...

Table 6

Summary of robustness checks and consistency of main findings

Robustness check	Alternative specification/Measurement	Key variables evaluated	Result	Supporting evidence from main models
1. Alternative ESG Measurement	Continuous ESG score instead of binary ESG (0/1)	All main and interaction terms	Consistent	Family remains positive (0.819, 0.761, 0.452); interactions unchanged (Board × Family = 0.286, Female × Family = −2.077, Age × Family = 0.126**)
2. Stricter Family Control Definition	Higher ownership threshold (≥30%)	Family Control	Consistent	Family Control remains positive and significant in all main models
3. Female Directors Operationalization	Binary indicator (≥1 female director)	Family × Female Directors	Consistent	Interaction remains negative and highly significant (−2.077***)
4. Standardized Board Size	BoardSize z-score	Family × Board Size	Consistent	Interaction remains positive and significant (0.286**)
5. Alternative Liquidity Measurement	Quick ratio instead of Liquidity	Liquidity and controls	Consistent	Liquidity remains negative and significant (−0.258* to −0.319*)
6. Additional Controls	Add ROA, leverage; drop log(liabilities)	All coefficients	Consistent	No change in sign/significance of main and interaction terms
7. Outlier Treatment	Winsorization at 5%/95%	All variables	Consistent	All core coefficients retain magnitude and significance
8. Alternative Estimator	GLS using continuous ESG	All variables	Consistent	Signs identical to logistic GLMM; interactions preserved
9. Random-Effects Structure	Random intercept vs. random slope	Random components	Consistent	SD (intercept) stable (0.672–0.973), ICC stable (0.10–0.20)

Robustness check	Alternative specification/Measurement	Key variables evaluated	Result	Supporting evidence from main models
1. Alternative ESG Measurement	Continuous ESG score instead of binary ESG (0/1)	All main and interaction terms	Consistent	Family remains positive (0.819, 0.761, 0.452); interactions unchanged (Board × Family = 0.286, Female × Family = −2.077, Age × Family = 0.126**)
2. Stricter Family Control Definition	Higher ownership threshold (≥30%)	Family Control	Consistent	Family Control remains positive and significant in all main models
3. Female Directors Operationalization	Binary indicator (≥1 female director)	Family × Female Directors	Consistent	Interaction remains negative and highly significant (−2.077***)
4. Standardized Board Size	BoardSize z-score	Family × Board Size	Consistent	Interaction remains positive and significant (0.286**)
5. Alternative Liquidity Measurement	Quick ratio instead of Liquidity	Liquidity and controls	Consistent	Liquidity remains negative and significant (−0.258* to −0.319*)
6. Additional Controls	Add ROA, leverage; drop log(liabilities)	All coefficients	Consistent	No change in sign/significance of main and interaction terms
7. Outlier Treatment	Winsorization at 5%/95%	All variables	Consistent	All core coefficients retain magnitude and significance
8. Alternative Estimator	GLS using continuous ESG	All variables	Consistent	Signs identical to logistic GLMM; interactions preserved
9. Random-Effects Structure	Random intercept vs. random slope	Random components	Consistent	SD (intercept) stable (0.672–0.973), ICC stable (0.10–0.20)

Note(s): “Consistent” indicates that the sign and significance of the key coefficients remain unchanged relative to the main GLMM models. Key variables: family control; board size × family; female directors × family; age × family

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