Nonlinear relationship and heterogeneity effects of energy and new quality productivity: Insights from technological innovation threshold.

New Quality Productivity (NQP) represents an advanced productivity paradigm aligned with China's new development philosophy. As a fundamental factor of production, the role of energy in fostering and developing NQP is a crucial question. To this end, this study constructs an evaluation framework for NQP and measures its level across 30 Chinese provinces during 2015-2022 using the Entropy Weight-TOPSIS method. Subsequently, employing the threshold model and Quantile-on-Quantile Regression method, this study investigates the role of technological innovation in the energy-NQP nexus. The robustness was confirmed using the Difference Generalized Method of Moments, sliding time windows, and additional control variables. Key findings reveal that: (1) China's NQP development exhibits a dependence on fossil energy. Crucially, technological innovation serves as a significant threshold: above the threshold, the positive contribution of both fossil and renewable energy consumption to NQP is enhanced. (2) Above the threshold, the impact of renewable energy on NQP follows a U-shaped curve as NQP levels increase, whereas the influence of fossil energy demonstrates an inverted U-shaped trajectory. (3) Below the threshold, renewable energy generally shows a pattern of decrease-increase-decrease across NQP quantiles, while fossil energy exhibits an initial increase, subsequent decrease, and a final rise. These results imply that promoting targeted technological upgrading is paramount for activating beneficial energy-NQP interactions. Regions above the threshold of technological innovation need to explore a wider range of scenarios for the application of renewable energy, while those below the threshold should rationally assess the supporting role of fossil energy at the current stage.