*4.3. A descriptive Analysis of the Data*

The energy consumption structure in China by sectors is very skewed (transport 8.2 percent, industry 29.0 percent, building 16.7 percent, electricity 40.1 percent, and others 6.1 percent) [44]. Concerning primary energy consumption, the problems facing China's energy use include a very high proportion of coal use, low thermal efficiency, high unit energy consumption, high growth rate of consumption, and trade disputes with the US which influence energy efficiency with an impact on industry. From a spatial perspective, the level of economic development in different regions of China is very different. While there are differences in climate, geographical environment, and resources, there are also differences in energy structures in different regions.

The model used in this study is parametric and it allows for modeling the relationship between energy use and its determinants conditioned on different control variables. The main control variables are energy policy (investments in environment protection) (*xenv*); the degree of trade openness (*xexp*); and environmental and regulatory variables including education investments (*xedu*), R&D investments (*xR*&*D*), population (*xpop*), and urbanization (*xurb*). The variables which may influence energy use efficiency are *z*<sup>1</sup> (PM2.5), *z*<sup>2</sup> (CO2), and (municipal solid waste treated). PM2.5 refers to atmospheric fine particulate matter (PM) that has a diameter of less than 2.5 micro-meters. We also use the log of GDP per capita (*xgdp*) as a main indicator. To see the variations in energy use, we use the cost function approach and the log of energy use per capita (ENEcost) as the dependent variable. The series used in this analysis is at the province level and contains all provinces in China (except Tibet due to lack of data) observed yearly from 2010 until 2017.

Table 2 shows that all the indicators are logarithmically transformed, except for investments in environment protection, which are defined as a percentage of regional GDP or gross regional product GRP (*xenv*) and urbanization (*xurb*) in the production function variables. Energy use cost per capita ranges between 427.638 and 5665.779 CNY among the sample provinces, with a mean of 1556.498 and dispersion of 1039.165 CNY. The GRP per capita varies in the interval of 1350.430 and 89,705.230 CNY in the provinces. The mean value is 21,652.784 with a dispersion of 16,997.766 CNY.


**Table 2.** Summary statistics of input and output data (2010–2017) (30 × 8 = 240 observations).


**Table 2.** *Cont*.

Note: Monetary variables are in fixed Chinese yuan, CNY. Source: Based on data from the National Bureau of Statistics of China (2018).

## **5. An Analysis of the Results**

The three stochastic frontier models are specified and estimated using the data described earlier, and the estimation results are given in Table 3.


**Table 3.** Stochastic frontier models' estimation results (NT = 240 observations).

Note: significant at less than the 0.05 (\*) and less than the 0.01 (\*\*) percent level of significance.

In Table 3 we present the estimation results of the three energy efficiency models. In Model 1, GDP, R&D investments, and environment protection are all statistically significant predictors of energy use. In Model 2, GDP and R&D investments are predictors of energy use. However, environment protection is a statistically insignificant predictor of energy use. In Model 3, GDP and R&D investments are significant variables that predict variations in energy use. However, environment protection is not found to be a significant predictor of energy use.

Another result that can be attained from Table 3 is attributed to the use of time as a driver of efficiency, which reduces the inefficiency component of the overall residual.

The Wald test is a joint test for multiple regressors. It mainly tests how much the model changes if the variables added are removed. In other words, the distance from the coefficient of each variable to zero is measured. The test results (see Table 4) show that the independent variable contributes significantly to the model and cannot be eliminated. The *p*-values of the fit of the three models are all less than 0.01, indicating that the models fit the data well.



The rest of this section analyzes the results. The analysis is in the form of a comparison of the different model's estimation results and an analysis of time-variance patterns as well as regional differences in energy use efficiency.
