**1. Introduction**

After the 2008 economic crisis, the situation in the world stabilized in 2010. According to the yearly China Economic Report [1], China's annual GDP increased from 6.066 trillion US dollars in 2010 to 8.271 trillion US dollars in 2017, with a total growth rate of 36.35 percent showing the highest growth among the top 15 large global economies. But the China Energy Statistics Yearbook 2018 [2] shows that the GDP growth rate gradually decreased from 10.7 percent in 2010 to 6.9 percent in 2017. In 2017, the global primary energy consumption was 13.5 billion tons of oil equivalent. The annual consumption growth rate in 2010–2017 was 1.4 percent. The economic growth rate slowed down in China.

According to the BP World Energy Statistics Yearbook [3] during 2010–2017, the gap between China's energy demand and energy supply increased over time. As China continues to promote urbanization and industrialization and gradually upgrades its consumer energy consumption structure, inequalities between China's energy supply and energy demand will remain severe until 2020. This gap will play an increasingly important role in energy security. In the face of rigid growth in energy demand, China's energy supply is expected to face severe challenges with increased supply pressures.

The BP Energy Outlook [4] predicts a radical energy transition. The ongoing transition to a lower-carbon fuel mix is led by renewables and natural gas which account for 85 percent of the growth in energy and are gaining in importance relative to traditional primary sources of oil and coal. It is forecast that the consumption of liquid fuels will grow over the next decade, but it will plateau as efficiency improvements in the transport sector are realized. A reduced use of the abundant global oil resources is likely to lead to a more competitive market and lower oil prices that will boost oil demand. The use of natural gas has grown dramatically and this growth is driven by its use in industry and power generation. Europe and China are two of the largest importers of gas. The growth in renewable energy is faster than that in oil and dominated by the developing world with China, India, and other Asian countries accounting for almost half the growth in global renewables. China and India drive global economic growth and together with other developing countries account for over 80 percent of the expansion in world output. Improvements in living standards in developing countries lead to an increase in energy demand.

The BP Energy Outlook [4] further suggests that the pattern of energy used within industry is expected to shift as a result of China's changing economic role. The process leading to the growth in energy used in industry will shift from China to other developing countries. By 2040, renewables are expected to overtake coal as the largest source of power generation. Global coal demand flatlines, with the fall in China and the OECD, but will be offset by gains in India and other emerging Asian countries; however, the growth in coal consumption will still slow down. By the mid-2020s, India will be the world's largest economic growth market. China and India both started with relatively coal-intensive fuel mixes. In a scenario of energy transition, China's coal share will fall from 60 percent in 2017 to around 35 percent in 2040 and will be offset by increasing shares of renewables, natural gas, and nuclear energy to match the growth in Chinese energy demand over the Energy Outlook's period, which is 2017–2040.

Two transition scenarios are predicted—evolving and rapid transition. According to the evolving transition scenario, the energy consumption for 1995, 2017, and 2040 is estimated at 891, 3132 and 4017 Mtoe (million tons of oil equivalent). The transition (from 1995 to 2017 and from 2017 to 2040) will lead to changes in consumption estimated at 2241 and 885 Mtoe. This corresponds to a 252 and 28 percent change which, on an annual basis, is 5.9 and 1.1 percent, respectively. In a rapid transition scenario, the estimated energy consumption is 891, 3132, and 3700 Mtoe. The changes are estimated to reach 2241 and 568 Mtoe with 252 and 18 percent total changes or 5.9 and 0.7 percent changes annually (BP Energy Outlook [4] pp. 135–137).

China's energy consumption per unit of GDP is twice that of the world average and four times that of developed countries. In recent decades, industrialized countries have invested in and developed energy saving and alternative energy technologies. It is difficult to meet the fast-growing energy demand simply by increasing energy supply. Saving energy and improving energy efficiency are extremely important and effective ways for China to meet its energy related challenges and the challenges of climate change. In such a situation one can ask, what is the status of energy efficiency in China specifically at the province level?

The Chinese government's interventions in energy use and energy efficiency mainly include government investments in the energy industry and the enforcement of energy policies targeting the energy industry. However, from the perspective of energy utilization and environmental protection, government interventions should also consider such incentives as encouraging and punishing different energy consumption industries. These include various programs such as tax incentives and subsidies for the introduction of environmentally friendly energy-saving products.

In 2013, the State Council of China issued the 'Action Plan for Air Pollution Prevention and Control' called 'Atmosphere Ten' which clearly states that the overall improvement in air quality in the country in five years led to a reduction in heavy air pollution in Beijing-Tianjin-Hebei, Yangtze River Delta, and Pearl River Delta of 15–25 percent. In 2017, the government's work report proposed to win the 'blue sky defense war' and speed up the resolution on coal-fired air pollution. As a relatively efficient and clean energy source, natural gas is favored by the government and the market. The policy of 'coal to gas' is an important substitution measure for improving air quality and it has been widely promoted in the past. This requires Beijing, Tianjin, Hebei, Shanxi, Shandong, and Henan provinces

and other cities to complete 3.55 million units of 'coal to gas' and 'coal to electricity' transformations in energy technology.

However, due to China's large regional heterogeneity as compared to other countries, the feedback on energy efficiency policies in its regions is different. Therefore, energy market reforms conductive with environmental policy must be actively promoted, and, in parallel, reduce government interventions in the energy market. Regional heterogeneity in energy consumption is evident in the demand for energy and its impact on economic growth. Giving full flexibility to the endowment of energy factors improving energy efficiency can effectively promote economic development. Given these conditions it will be interesting to know whether China's energy efficiency has improved with technological innovations, and what kind of typical regional heterogeneity exists in China's energy efficiency.

Based on existing research, the methods for measuring efficiency mainly include the data envelopment analysis (DEA) and the stochastic frontier analysis (SFA). The former does not need to estimate the specific production function form, thus avoiding the problems caused by the choice of a wrong functional form. DEA uses information on inputs and outputs, but it does not describe the production process fully. Conversely, SFA describes individual producers' production processes by estimating the production function, thus controlling efficiency estimates. In addition to inputs and outputs, SFA also uses production and market environmental factors. Thus, this approach assumes a functional form.

At present, most scholars adopt the DEA method for efficiency analyses, while the SFA method is less frequently used. Only a few scholars have used it for empirical research related to energy use efficiency. The simple Cobb-Douglas production function is also a commonly used functional form for describing a regional economy. Considering the heterogeneity of China's economic regions, it is appropriate to use the SFA approach for measuring regional energy efficiency. Unlike DEA, SFA is a parametric method which allows for modeling the relation between energy use and its determinants and in addition to the inputs and outputs that one can control for firm, industry, province, and other environmental and policy characteristics. Further, the importance of extra information can be tested statistically.

Literature and evidence on inefficiencies and differences in regional level energy use in China is vast. By analyzing panel data for 30 provinces in 2005–2014 using the DEA efficiency model to measure total factor energy efficiency in China, [5] showed that total factor energy efficiency was high in the East and low in the West of the country. The eastern region had higher total factor energy efficiency and characteristics of lack of energy resources. However, the western region had the characteristics of lower total factor energy efficiency while it was rich in energy resources. The allocation of production elements of 'more input and less output' also existed in the central region, leading to an enormous waste of energy resources in these areas.

Ref [6] points out that the government should and can solve the problems and inefficiencies of energy allocation in the market and enforce these using mandatory energy policies. By studying the relationship between government interventions, natural resources, and economic growth, [7] found that appropriate government interventions can reduce the negative impact of pollution of natural resources on economic growth. One can ask, what are the energy policies that China has adopted for improving energy efficiency during the development process?

It is evident that production in China is very energy intensive. Energy sources are mainly fossil fuel based with extremely negative health, environmental, and climate effects. This paper evaluates energy use efficiency as a tool for reducing energy consumption and air emissions. This research does a panel data analysis of energy use efficiency in China at the province level. The method is at the forefront of research and allows for accounting province heterogeneity and temporal changes in energy use efficiency, making the results informative and useful.

In analyzing energy use efficiency, this paper uses three different models—[8], the true fixed-effects model [9,10], and four components of the stochastic frontier model. The stochastic frontier panel model approach is parametric and allows for modeling the relationship between energy use and its determinants conditioned on different control variables. The main control variables are energy policy, and environmental and regulatory variables. The data is from the province level and covers all provinces in China (except Tibet due to lack of data availability) observed over the period 2010–2017. Three different models are estimated accounting for the panel nature of the data; province-specific heterogeneity and province-specific energy use inefficiency effects are separated. The models differ because of their underlying assumptions but also complement each other considering the directions that literature has developed in, namely assumptions about the distribution of inefficiency effects, estimation methods, and time-variance of inefficiency and its separation from province heterogeneity. The degree of inefficiency in the use of energy is also explained by its possible determinants including those related to public energy policy and environmental regulations. This research supplements existing research from the perspective of energy policy and regional heterogeneity. It shows that there is enormous potential for improving energy efficiency in the western and northeastern regions of China. These findings provide new empirical evidence for estimating and evaluating China's energy use efficiency and transition to cleaner energy sources.

The rest of the paper is organized as follows. After this brief introduction, Section 2 presents a literature review on energy efficiency. The evolution of methods for estimating energy efficiency and the approaches used are also discussed in this section. Section 3 outlines the methodologies of the three different models used. Section 4 describes the data and the specifications of the empirical model. Section 5 discusses the results both by comparing the models and by distinguishing between regional heterogeneity in China. Section 6 gives the conclusion and implications of the findings of the study.
