Frontier-based approaches to eco-efficiency measures have long been controversial because no normative definition is provided. Previous studies have used technical efficiency, environmental efficiency, and other variables as a proxy. To standardize its definition, we propose a formal eco-efficiency indicator, the ratio of actual gross domestic product (GDP) to environmental impact to potential GDP to environmental impact. To quantify it, we develop the biennial meta-frontier non-radial directional distance function (BMNDDF), which addresses the potential threats of technology heterogeneity, the slack variable, and linear programming infeasibility. Using this new indicator, we assess the city-level eco-efficiency in the Yellow River Basin from 2008 to 2017 to identify the harmonious relationship between ecological protection and economic development. The empirical results show a 5.73% increase in eco-efficiency per year, with the technology leadership effect as the main contributor. Because the central region is defined by heavy emissions and many underdeveloped cities, it suffers from more severe conflicts between outputs and emissions than other regions.

Quantifying the shadow price (SP) of CO₂ emissions is the key to achieving China’s “double carbon” targets. Considering technology heterogeneity, this study applies stochastic frontier analysis combined with meta-frontier technology to estimate the environmental technical efficiency (ETE) and SP of CO₂ emissions for China’s fossil fuel power plants from 2005 to 2015. This approach overcomes the lack of statistical inference and consistency of traditional methods and improves the reliability of results. The main results are as follows: (a) the average ETE of China’s power plants is 0.9444, indicating that inefficient production accounts for 5.66%. The difference in efficiency between the central and local groups is significant. (b) The national average SP of CO₂ is 266.8 US dollars per ton, which is much higher than the carbon price in the emission trading system. This result implies the need to design a carbon trading price mechanism. (c) The distribution of SP shows obvious corporation and geographical characteristics that are closely related to the level of regional economic development. Finally, the findings provide policy implications for the improvement of the efficiency and abatement of costs of power plants and the determination of carbon prices.