**2. Materials and Methods**

Here, the materials and methodology are defined, including the quantification and decomposition approaches, data utilized, and the methodological and data limitations.

### *2.1. Quantification of Carbon Footprint by Household Consumption*

Household CF is defined as the sum of direct carbon emissions induced by driving a passenger motor car, cooking and household heating ( *D*), and indirect (embodied) carbon emissions generated through the supply chain due to household consumption (*S*). *D* is calculated using Equation (1). 

$$D = \sum\_{k} \sum\_{b} e\_k^{\text{dir}} f\_{k b \nu} \tag{1}$$

where *edir k* represents the direct CO2 emissions per consumption expenditure for energy item *k*. *fkb* denotes the household's final consumption by attribute *b* for energy item *k*. Next, *S* is quantified by Equations (2) and (3). 

$$S = \sum\_{i} \sum\_{b} e\_i^{ind} f\_{ib\nu} \tag{2}$$

$$
\sigma\_i^{ind} = \sum\_j q\_i L\_{ij\prime} \tag{3}
$$

where *eind i* represents the upstream CO2 emissions per consumption expenditure (embodied CO2 emission intensity) for commodity *i k*. *j* denotes the commodity sector. It is estimated by using *qi* and *Lij* = -*I* − *Aij*−<sup>1</sup> which denote the vector containing the direct CO2 emissions per unit production output for commodity *i* and upstream requirements per unit production, respectively. *Lij* is an element of the Leontief inverse matrix [36] obtained from the input–output table.

### *2.2. Index Decomposition Analysis and Structural Decomposition Analysis*

To comprehend the contribution of various indicators to the changes in household CF by using IDA and SDA, we decomposed both the direct CO2 emissions derived from home energy and the indirect CO2 emissions generated through the supply chain of goods and services (commodities) purchased by households, as shown in Equations (4) and (5).

$$\begin{array}{rcl} D &=& \sum\_{k} \sum\_{b} \epsilon\_{k}^{dir} \frac{f\_{kb}}{f\_{b}} \frac{f\_{b}}{p\_{b}} \frac{p\_{b}}{H\_{b}} \frac{H\_{b}}{H} H \\ &=& \sum\_{k} \sum\_{b} \epsilon\_{k}^{dir} \mathcal{Y}\_{kb} w\_{b} s\_{b} d\_{b} H \end{array} \tag{4}$$

$$\begin{array}{rcl} S & = \sum\_{i} \sum\_{b} q\_{i} L\_{ij} \frac{f\_{ib}}{f\_{b}^{\prime}} \frac{f\_{b}^{\prime}}{p\_{b}} \frac{p\_{b}}{H\_{b}} \frac{H\_{b}}{H} H \\ & = \sum\_{i} \sum\_{b} q\_{i} L\_{ij} y\_{ib} w\_{b}^{\prime} s\_{b} d\_{b} H \end{array} \tag{5}$$

where *H* and *p* represent the total number of households and population, respectively. Both *ykb* and *yib* refer to consumption patterns (e.g., medical services are more heavily consumed by elderly households than younger households). *wb* and *wb'* represent the average per-capita consumption volume for energy items and that for all commodities, respectively. *sb* represents the average number of members in each household (i.e., family size). *db* describes the distribution of households (i.e., the proportion of younger households to total households). Thus, Equations (4) and (5) are based on Equations (1) and (2), with household final consumption decomposed into the five factors in line with consumption pattern, consumption volume, family size, household distribution, and number of households. Overall, six drivers are considered for direct CO2 emissions, and seven drivers for indirect CO2 emissions.

When *D* and *S* shift from year *t* to year *t* + 1, there are no unique solutions for how the decomposition should be solved. To quantify the contributions of each factor, this study used the Shapley–Sun decomposition approach (S-S method) [37] for *D*, and the Dietzenbacher and Los decomposition approach (D-L method) [38] for *S*, cognizant of identical decomposition without any residues and the commonality of results [24]. For example, the total difference of Equation (4) can be represented by Equation (6).

$$\begin{aligned} \Delta D &= \sum\_{\substack{k \\ k \end{k}} \sum\_{b} \Delta e\_{k}^{\mathrm{dir}} y\_{kb} w\_{b} s\_{b} d\_{b} H + e\_{k}^{\mathrm{dir}} \Delta y\_{kb} w\_{b} s\_{b} d\_{b} H + e\_{k}^{\mathrm{dir}} y\_{kb} \Delta w\_{b} s\_{b} d\_{b} H \\ &+ e\_{k}^{\mathrm{dir}} y\_{kb} w\_{b} \Delta s\_{b} d\_{b} H + e\_{k}^{\mathrm{dir}} y\_{kb} w\_{b} s\_{b} \Delta d\_{b} H + e\_{k}^{\mathrm{dir}} y\_{kb} w\_{b} s\_{b} d\_{b} \Delta H \end{aligned} \tag{6}$$

where Δ indicates the difference operator. Equation (6) converts six multiplicative terms in the first term of Equation (4) into six additive terms. Each additive term in Equation (6) denotes the contribution to changes in *D* induced by a targeted factor while all other factors are constant. For instance, the first term in Equation (6) refers to the effect on direct CO2 emissions of changes in direct emission

intensity, while consumption patterns, consumption volume, family size, household distribution, and total number of households are constant between *t* and *t* + 1. Each of the contributions were estimated by taking the average of the 6! = 720 decomposition equations possible [37]. Here, the e ffects on direct CO2 emissions that are related to the first, second, third, fourth, fifth, and sixth terms in Equation (6) are referred to as the intensity e ffect (direct), consumption pattern e ffect, consumption volume e ffect, family size e ffect, household distribution e ffect, and household number e ffect, respectively.

In a similar manner, the total di fference of Equation (5) can be demonstrated by Equation (7).

$$\begin{array}{ll} \Delta S = & \sum\_{i} \sum\_{b} \Delta q\_{i} L\_{ij} y\_{ib} w\_{b} s\_{b} d\_{b} H + q\_{i} \Delta L\_{ij} y\_{ib} w\_{b} s\_{b} d\_{b} H + q\_{l} L\_{ij} \Delta y\_{ib} w\_{b} s\_{b} d\_{b} H \\ & + q\_{l} L\_{ij} y\_{ib} \Delta w\_{b} s\_{b} d\_{b} H + q\_{l} L\_{ij} y\_{ib} w\_{b} \Delta s\_{b} d\_{b} H + q\_{l} L\_{ij} y\_{ib} w\_{b} s\_{b} \Delta d\_{b} H \\ & + q\_{l} L\_{ij} y\_{ib} w\_{b} s\_{b} d\_{b} \Delta H \end{array} \tag{7}$$

Finally, each of the contributions were estimated by taking the average of the 7! = 5040 decomposition equations possible [38]. Here, the e ffects on indirect CO2 emissions that are related to the first, second, third, fourth, fifth, sixth, and seventh terms are referred to as the intensity e ffect (indirect), supply chain e ffect, consumption pattern e ffect, consumption volume e ffect, family size effect, household distribution e ffect, and household number e ffect, respectively.
