*3.1. Variables Selection*

Electricity consumption (*y*). The electricity consumption is an endogenous variable, which is measured by the electricity consumption of urban residents.

Power price (*P*). The power price is the core explanatory variable, which is measured by the average selling price of electricity used by residents. The power price has both rising and falling periods, and the impact of rising and falling price on the demand for electricity is not completely reversible. However, the direct rebound effect is mainly related to the falling price. So the power price is decomposed into three parts [4]:

$$P\_{\rm it} = P\_{\rm max,it} \times P\_{\rm rev,it} \times P\_{\rm cut,it} \tag{7}$$

where *Pit*, *Pmax*,*it*, *Prec*,*it* and *Pcut*,*it* represent the actual price, maximum price, cumulative rising price and cumulative falling price in province *i* in year *t*, respectively. The decomposed price is calculated as follows:

$$P\_{\max, \it t} = \max \{ P\_{i1}, P\_{i2}, \dots, P\_{\prime \prime} \} \tag{8}$$

$$P\_{\text{rec},it} = \prod t\_{j=0} \max \left\{ 1, \frac{P\_{\text{max},ij-1} / P\_{ij-1}}{P\_{\text{max},ij} / P\_{ij}} \right\} \tag{9}$$

$$P\_{cnt,it} = \prod t\_{j=0} \min \left\{ 1, \frac{P\_{max,ij-1}/P\_{ij-1}}{P\_{max,ij}/P\_{ij}} \right\} \tag{10}$$

The power price is also decomposed into two parts [28]:

$$P\_{\rm inc,it} = P\_{\rm max,it} \times P\_{\rm rec,it} \tag{11}$$

$$P\_{\text{dec,it}} = P\_{\text{max,it}} \times P\_{\text{cut,it}} \tag{12}$$

The two decomposition methods are both used for a robust test.

Degree day (*DD*). The degree day, referring to the deviation between the daily average temperature and the base temperature, is an environmental factor that should be controlled. It reflects the climate characteristics. Urban residents will use household appliances such as air conditioners more frequently with high degree days, so the electricity consumption is larger. Degree days are divided into heating degree days (HDD) and cooling degree days (CDD), and their calculation is as follows [28]:

$$HDD = \sum\_{m=1}^{12} \left( 1 - rd \right) \left( T\_{b1} - T\_m \right) \times M \tag{13}$$

$$CDD = \sum\_{m=1}^{12} rd(T\_m - T\_{b2}) \times M \tag{14}$$

where *HDD* and *CDD* are the heating degree day value and the cooling degree day value. *Tm* is the monthly average temperature. *Tb*<sup>1</sup> and *Tb*<sup>2</sup> represent the base temperature of the heating degree day and the cooling degree day, respectively. *rd* is a dummy variable, and if the monthly average temperature is higher than the base temperature, it is 1. Then, *DD* = *HDD* + *CDD*.

Income (*I*). Income is an economic factor that should be controlled, which is measured by the per capita disposable income of urban residents. Income is an important factor affecting consumer spending. Since 2006, urban residents' income has been increasing with a high rate.

Population (*POP*). Population is measured by the number of permanent residents of urban residents. Obviously, the more people, the greater electricity consumption. In order to accurately measure the increase in electricity consumption induced by efficiency, it is necessary to control the population factor.
