**2. Methodology**

### *2.1. Primary Fossil Energy Consumed in China*

The structure of the MRIO model can be expressed as **x** = **Ax** + **f**, where **x** = (*x<sup>r</sup> i*) (*r* = 1, . . . , *R*; *i* = 1, . . . , *N*) is the vector of outputs of *N* sectors of *R* provinces, and **f** =(*f r i* ) is the vector of the total final demand for sector *i* of province *r*, including rural household consumption, urban household consumption, governmen<sup>t</sup> consumption, fixed capital formation, and exports. Furthermore, **A** = (*zrsij* /*x<sup>s</sup> j*)=(*arsij* ) (*r*, *s* = 1, . . . , *R*; *i*, *j* = 1, . . . , *N*) is the input coefficient matrix, where *zrsij* denotes the intermediate deliveries from sector *i* of province *r* to sector *j* of province *s*.

In the mixed-units approach (i.e., hybrid approach), if *i* is an energy sector, *x<sup>r</sup> i* , *zrsij* , and *f r i* are measured in energy units (tonnes of coal equivalent in this study). As in the previous studies [12,16,17], the solution of the hybrid MRIO model is **x** = **Lf**, where **L** = (**I** − **A**) −1 is the Leontief inverse matrix. It should be noted that the hybrid MRIO database of China describes both domestically produced energy and imported energy. The domestically produced primary fossil energy consumption in China triggered by the final demand can be estimated as follows:

$$\mathbf{d} = \hat{\mathbf{e}} \mathbf{L} \mathbf{f} \tag{1}$$

where **d** = (*dr i*) represents the fossil energy consumptions provided by energy sector *k* of province *r*, triggered by the domestic final demand of China and its exports (when *i* = *k*). It should be noted that **^ e** is a diagonal matrix with diagonal elements of 0 and 1. When *i* is a fossil energy sector (coal mining, crude oil, and natural gas) of province *r*, *er i*= 1, and otherwise, *er i*= 0.

The physical energy import triggered by the domestic final demand of China and its exports can also be estimated as follows:

$$\mathbf{h} = \mathbf{M} \mathbf{L} \mathbf{f} \tag{2}$$

where **h** = (*hk*) represents the imported energy (*k*) consumed in China, and **M** = ( *mskj*) is the energy import coefficient matrix expressing the physical amount of energy (*k*) imported to produce one unit of output of sector *j* of province *s* (see the Supporting Information).

The fossil energy (*k*) consumed in China triggered by total final demand can be expressed as follows:

$$P\_k = \sum\_{r=1}^{R} d\_k^r + h\_k \tag{3}$$
