Instrumental-variable diagnostics
| ESG component | Test type | Statistic | Value | P-value | Critical values (Stock-Yogo) | Conclusion |
|---|---|---|---|---|---|---|
| Environmental (E score) | Under identification | Kleibergen–Paap rk LM statistic | 26.765 | p < 0.01 | – | IV is relevant; model is correctly identified |
| Weak identification | Cragg-Donald Wald F statistic | 37.993 | – | 10%: 16.38, 15%: 8.96, 20%: 6.66, 25%: 5.53 | IV is not weak; exceeds critical values | |
| Kleibergen-Paap rk Wald F statistic | 26.974 | – | – | Confirms IV strength | ||
| Social (S score) | Under identification | Kleibergen-Paap rk LM statistic | 26.765 | p < 0.01 | – | IV is relevant; model is correctly identified |
| Weak identification | Cragg-Donald Wald F statistic | 37.993 | – | 10%: 16.38, 15%: 8.96, 20%: 6.66, 25%: 5.53 | IV is not weak; exceeds critical values | |
| Kleibergen-Paap rk Wald F statistic | 26.974 | – | – | Confirms IV strength | ||
| Governance (G score) | Under identification | Kleibergen-Paap rk LM statistic | 26.765 | p < 0.01 | – | IV is relevant; model is correctly identified |
| Weak identification | Cragg-Donald Wald F statistic | 37.993 | – | 10%: 16.38, 15%: 8.96, 20%: 6.66, 25%: 5.53 | IV is not weak; exceeds critical values | |
| Kleibergen–Paap rk Wald F statistic | 26.974 | – | – | Confirms IV strength |
| Test type | Statistic | Value | P-value | Critical values (Stock-Yogo) | Conclusion | |
|---|---|---|---|---|---|---|
| Environmental (E score) | Under identification | Kleibergen–Paap rk | 26.765 | – | ||
| Weak identification | Cragg-Donald Wald F statistic | 37.993 | – | 10%: 16.38, 15%: 8.96, 20%: 6.66, 25%: 5.53 | ||
| Kleibergen-Paap rk Wald F statistic | 26.974 | – | – | Confirms | ||
| Social (S score) | Under identification | Kleibergen-Paap rk | 26.765 | – | ||
| Weak identification | Cragg-Donald Wald F statistic | 37.993 | – | 10%: 16.38, 15%: 8.96, 20%: 6.66, 25%: 5.53 | ||
| Kleibergen-Paap rk Wald | 26.974 | – | – | Confirms | ||
| Governance (G score) | Under identification | Kleibergen-Paap rk | 26.765 | – | ||
| Weak identification | Cragg-Donald Wald | 37.993 | – | 10%: 16.38, 15%: 8.96, 20%: 6.66, 25%: 5.53 | ||
| Kleibergen–Paap rk Wald | 26.974 | – | – | Confirms |
Because the same endogenous regressor and first-stage specification are used across the environmental, social and governance models, the IV diagnostic statistics are identical across the Three ESG dimensions
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