*4.6. Analysis of the Temporal Change of Direct Rebound E*ff*ect*

In order to investigate the change of direct rebound effect for urban residents' electricity consumption, the coefficient of ln *Pdec*,*it* is allowed to change with time. The estimated results are shown in Table 5.


**Table 5.** Estimation results of SARAR fixed-effect model with partial variable coefficients.

Note: The number in parentheses is the level of significance. \*\*\*, \*\*, and \* indicate significance levels at 1%, 5%, and 10%, respectively.

According to Table 5, the calculating results of direct rebound effect for urban residents' electricity consumption in some years are shown in Table 6.

**Table 6.** Calculation results of direct rebound effect for urban residents' electricity consumption.


Note: The number in parentheses is the level of significance. \* indicates significance levels at 10%.

Table 6 shows that direct rebound effect for urban residents' electricity consumption declined from 2006 to 2009, but the decline is very small. The calculation results of direct rebound effect after 2009 are not significant, indicating that there is no obvious downward trend in direct rebound effect in the short term. The changes of RE, SRE and the total effect (abbreviated as TE) are displayed in Figure 3.

**Figure 3.** The changes of RE, SRE and TE from 2006 to 2015.

Figure 3 shows that the change characteristics of the three effects are similar, and the decrease range is small. In order to verify this conclusion, the significance of the power price and time interaction term are tested. The test results still cannot reject the null hypothesis at 10% significance level, meaning that the direct rebound effect is fixed over these years, so the direct rebound effect for urban residents' electricity consumption will not decrease currently.

According to Zhang et al. [33], consumers' energy demand tends to be saturated with income growth, and direct rebound effect will decline. However, the empirical test in this paper shows that direct rebound effect for urban residents' electricity consumption in China has not shown a significant downward trend although the urban residents' income has been increasing. The main reason is that China's urbanization rate increased by 1.31% annually from 2006 to 2016, indicating that China's urbanization is large and the process is relatively fast. It has caused the rigidity of electricity demand. In particular, the transfer of rural residents to urban areas will bring a large-scale marginal consumer group. Therefore, the rigidity of electricity demand and the large marginal consumer group will eventually offset the inhibition effect of income growth on the direct rebound effect.

## **5. Conclusions and Policy Implications**

Based on price decomposition methods and spatial econometric models, the calculation method of the direct rebound effect is improved. The panel data of China's urban residents' electricity consumption are used for our empirical analysis. The conclusions are as follows:

First, spatial analysis indicates that there are four types of spatial aggregation in China's urban residents' electricity consumption, and the global spatial correlation has a significant positive value. Studies of the direct rebound effect for urban residents' electricity consumption should not ignore the spatial feedback effect and spatial spillover effect. The improved model can subdivide the calculation results into direct rebound effect and its spatial spillover effect, improving the accuracy and explanatory power of the results. In addition, due to the asymmetric influence of price on demand, the introduction of the price decomposition methods can avoid the upward bias of the calculation results to some extent.

Second, the direct rebound effect for urban residents' electricity consumption in China and its spatial spillover effect are 37.00% and 13.30%, respectively. This shows that although improving the electricity efficiency has induced a direct rebound effect, the direct rebound effect is not serious, and improving efficiency is still an important measure to curb the urban residents' electricity consumption. Moreover, compared with the spatial spillover effect of direct rebound effect, direct rebound effect induced by energy efficiency improvement in the local region is still the main factor affecting the implementation effect of energy efficiency policy in the same region.

Third, direct rebound effect for urban residents' electricity consumption without spatial spillover effects does not show a significant downward trend. The reason is that the rapid urbanization process at the current stage has caused rigid residents' electricity demand and large-scale marginal consumer groups, which offsets the inhibition effect of income growth on the direct rebound effect.

According to the analysis above, the main policy implications are as follows: first, the government must attach importance to the direct rebound effect, and establish a comprehensive, multi-sectoral monitoring system for direct rebound effect, so as to avoid failure of energy efficiency policy caused by serious direct rebound effect. Second, the direct rebound effect is mainly caused by the price effect. The government should promote the marketization of power prices through environmental regulations (such as resource taxes), and reduce the excessive consumption of electricity due to low cost. At the same time, in order to achieve the expected energy-saving goals of energy efficiency policies more effectively, local governments should focus on the synergy of policy formulation and implementation between the local region and adjacent areas.

**Author Contributions:** Data curation, Y.H.; Formal analysis, J.S.; Funding acquisition, Y.H. and J.S.; Investigation, Y.W.; Methodology, J.S.; Software, J.S. and Y.Y.; Writing—original draft, J.S.; Writing—Review & Editing, J.S.

**Funding:** This work was funded by the General Planning Project of the Social Science Fund of the Ministry of Education (18YJA790031), the Major projects of the National Social Science Fund (15ZDC034) and the Liaoning Natural Science Foundation (201602267).

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Appendix A**

There are some equivalent definitions of direct rebound effect, which allows identification of the rebound effect

Firstly, we define the energy efficiency. Energy efficiency at the household level can be expressed as the ratio of energy services to energy inputs:

$$
\varepsilon = \mathcal{S}/E \tag{A1}
$$

where ε, *S*, and *E* denote the energy efficiency, energy services and energy inputs, respectively.
