fig6

Figure 6. Hansen single-threshold regression results (income and environmental regulation). LR: Likelihood-ratio-type improvement statistic LR(γ) = N[RSS_linear − RSS_threshold(γ)] / RSS_threshold(γ), which attains its maximum at the estimated threshold $$ \hat{\gamma} \\ $$ (marked by red dashed lines). Income thresholds are shown in z-score units. In the lower panels, the horizontal coordinates are standardized using the mean and sample standard deviation of the candidate environmental-regulation grid, whereas the annotated threshold values in the callout boxes are on the original 0–1 index scale. N = 390 province-year observations from 30 provinces, 2012–2024; bootstrap B = 300. Regime-specific observation counts (n) are shown in the panels. ***P < 0.01, **P < 0.05, *P < 0.10.