Persistent and transient inefficiency in China’s provincial energy demand: A four-component stochastic frontier model

Improving energy efficiency is essential for advancing the clean energy transition and achieving decarbonization targets under the Paris Agreement, which makes accurate measurement of energy efficiency vitally important. Standard measures, such as energy intensity and two-step frontier procedures, can confound noise with inefficiency and induce omitted-variable bias. We develop a single-step four-component stochastic demand frontier that separates unobserved heterogeneity from inefficiency, decomposes inefficiency into persistent and transient components, and embeds observed drivers in the log-mean of the transient term. A Bayesian estimator delivers joint inference for the frontier, the decomposition, and driver effects. Applying the method to a panel of 30 provinces in China over 2003–2021, we find that omitting drivers tends to overstate energy efficiency, while including them reduces the share attributed to persistence to below one-half in several provinces and highlights the importance of short-run factors. Average transient efficiency is about 0.89, compared with roughly 0.69 for persistent efficiency. Overall, the unified design provides internally consistent, noise-robust efficiency measures and policy-relevant benchmarks that distinguish near-term operational levers from longer-horizon structural reforms.