Shrinking household size and CO₂ emissions in China evidence from machine learning and input output models

Summary

Owing to variations in expenditure structure among residents of different household sizes, their impacts on production and consumption activities within the economic system lead to significant variations in carbon footprint characteristics. Based on machine learning and input-output models, we quantify the carbon footprints of residents across different household sizes from 2010 to 2020 and analyze the underlying mechanisms. Per capita expenditure and population scale in one-person households are the main drivers for the increase in direct and indirect CO₂ emissions, respectively. From 2010 to 2020, housing expenditure accounts for 71.9% (115.22 Mt) of the increase in indirect CO₂ emissions associated with one-person households, followed by transportation (14.7%, 23.54 Mt) and household equipment (10.4%, 16.59 Mt). Notably, the per capita expenditure level effect in the transportation sector significantly contributes to rising emissions, and this increase may not be fully offset by the mitigation effects from improving emission intensity and optimizing production structure.

Highlights

• •The impact of household downsizing on sectoral carbon emissions is explored
• •Consumption structure of residents grouped by household size is described in detail
• •Household downsizing has promoted the growth of consumption-based carbon emissions
• •Targeted sectoral emission reduction policies may be taken when household downsizing occurs

Environmental analysis; Environmental science; Global change

Introduction

Global climate change may pose a disastrous hazard for human beings, which is intrinsically linked to greenhouse gas (GHG) in the atmosphere. It has emerged as a significant global concern.^1,2 China is the biggest emitter of CO₂ after more than three decades of fast economic expansion in all countries since 2007.^3,4 China’s total carbon emissions reached 12.6 Gt CO₂ in 2024, surpassing those of the United States (4.5 Gt), the EU-27 (2.4 Gt), and India (3.0 Gt).⁵ In the 2015 Paris Agreement on climate change, the government of China committed to achieving CO₂ emissions peak in the year of 2030 and decreasing its GDP’s carbon intensity by 60–65% compared to 2005.⁶ To achieve this objective, the government has introduced a wide range of policies aimed at sectors with high energy expenditure, including chemical sector,⁷ metallurgical sector,⁸ and transportation.⁹ Furthermore, escalating urbanization and economic globalization in China have heightened the consumption for products and services among the residents in China, resulting in annual growth of fossil energy use and CO₂ emissions within industrial sector.¹⁰ However, most of these studies overlook that household expenditure is the fundamental motivating factor for CO₂ emissions from industrial sector. Household CO₂ emissions have emerged as a primary source for China’s CO₂ emissions.¹¹ For instance, Tian et al. (2014) determined that household expenditure constitutes 35% of China’s overall carbon footprint.¹² Consequently, understanding household CO₂ emissions can assist policymakers in enhancing carbon reduction strategies.¹³

Household CO₂ emissions typically have direct and indirect components.⁴ Direct emissions are determined by multiplying the household’s fossil fuel usage by the corresponding carbon emission factor.¹⁴ In contrast, indirect emissions are more complex to quantify, as they involve estimating the CO₂ emissions generated throughout the entire production and supply chain of the products consumed by the household.¹⁵ The primary approaches of investigating home CO₂ emissions are the consumer lifestyle approach (CLA) and input-output analysis (IOA). CLA provides a comprehensive assessment approach linking lifestyle characteristics to their environmental impacts.¹⁶ Nowadays, scholars are increasingly adopting this method to estimate household CO₂ emissions.¹⁷ For instance, Feng et al. (2011) utilized a CLA methodology to analyze household energy use and CO₂ emissions from 2005 to 2007, revealing that food expenditure significantly contributed to CO₂ emissions.¹⁸ The CLA methodology offers valuable insights into the impact of specific expenditure activities on CO₂ emissions and enables the identification of carbon-intensive behaviors.¹⁹ However, these studies often treat household expenditure in isolation, without accounting for the influence of supply chains in producing products.²⁰ IOA is extensively employed to assess indirect CO₂ emissions resulting from household expenditure.²¹ This methodology was initially employed by the American economist Leontief to analyze the interdependence across different sectors of social production²² and was subsequently utilized in several domains, including environmental and energy studies.²³ Numerous investigations underscore the benefits of IOA for precisely measuring the indirect CO₂ emissions related to household expenditure.^24,25 Druckman and Jackson (2009) employed IOA to indicate that recreation and leisure constituted over 25% of total household emissions.²⁶ Similarly, Ding et al. (2017) utilized IOA to investigate household expenditure activities’ direct and indirect effects on energy utilization in China, including clothing, food, housing, and transportation.¹⁶

Household carbon footprints are presumably affected by several expenditure factors of the household.²⁷ Scholars have displayed that factors such as household income,^28,29 dwelling size,^30,31 and geographic location³² can significantly impact CO₂ emissions at varying levels. In addition, the individual traits of household members may also influence household CO₂ emissions.^33,34 For instance, plenty of studies have investigated the impact of education on household CO₂ emissions, although the nature of this influence remains ambiguous.³⁵ Among household characteristics, household size significantly influences the factors driving household CO₂ emissions. Within households, there are many shared resources, or household public goods. Energy services such as indoor heating, lighting, and hot water, as well as services provided by durable goods such as washing machines, refrigerators, and televisions, are typically consumed jointly by multiple household members rather than used independently by each individual.³⁶ Once these resources are provided, the marginal cost of use declines significantly as the number of household members increases. Feng et al. (2021) pointed out that, as a unit of resource allocation, household consumption behavior cannot be simply regarded as the linear sum of individual consumption, but is instead shaped by the degree of sharing and the intensity of use. This sharing mechanism constitutes the microeconomic foundation for economies of scale associated with household size.³⁷ Larger households benefit from economies of scale, as the expenditure of shared household goods is relatively non-rivalrous, allowing resources to be efficiently distributed among family members.³⁸ Consequently, per capita energy use and CO₂ emissions are reduced in large-size households.³⁹ Multi-member households can collectively utilize products and services, including housing and appliances, contributing to CO₂ emissions.⁴⁰ Empirical evidence suggests that carbon inequality is strongly shaped by wealth and capital disparities,⁴¹ implying that differences in carbon footprints reflect not only income gaps but also deeper structural inequalities.^42,43 Meanwhile, cross-country analyses indicate that rising energy costs disproportionately burden elderly households, particularly those in low-income groups,⁴⁴ suggesting that decarbonization pathways may generate uneven welfare impacts.⁴⁵ Moreover, recent research on China shows that population aging and rising affluence jointly contribute to increasing household carbon emissions,⁴⁶ implying that demographic transition and lifestyle upgrading may reinforce each other.⁴⁷ In contrast, one-person households cannot capitalize on the efficiencies of scale, leading to typically higher carbon footprints.⁴⁸ For instance, in the United States, the carbon footprint of multi-member families is roughly 23% lower than that of one-person households.⁴⁹ Additionally, smaller home sizes frequently lead to a rise in the overall number of households, requiring the acquisition of additional durable items to satisfy individual requirements.⁵⁰ This indirectly drives additional energy expenditure and CO₂ emissions.

In recent years, China has experienced a trend toward smaller household sizes, which may have significant implications for household carbon footprints.⁵¹ The average household size in China has decreased from 5.3 persons per household in 1950 to 2.5 persons per household in 2024. Moreover, the number of households living alone in China exceeds 107 million, accounting for more than 19% of the total households in 2020.⁵² Additionally, the reduction in household size elevates the overall number of households, amplifying demand for housing, durable goods, and energy, which contributes to heightened CO₂ emissions.⁵⁰ As the total national population remains fixed, household size fluctuations will significantly impact household CO₂ emissions.⁵³ The enactment of China’s two/three-child policy and increasing divorce rates will likely result in significant alterations to household size in the forthcoming years.⁵⁴ Consequently, the CO₂ emissions associated with household size will play a pivotal role in China’s efforts to achieve its carbon peak and carbon neutrality targets.⁵⁵

Current research on CO₂ emissions from household expenditure has several limitations. Regarding how the reduction in household size affects CO₂ emissions, most related studies have merely compiled the expenditure structures of residents from households of different sizes in a simplistic manner, without controlling for heterogeneous factors influencing household size effects. Furthermore, they have failed to delve into the macro-level transmission mechanism through which transformations in household structure (such as miniaturization) reshape carbon emissions within the industrial system via changes in consumption demand, as well as the comparison of household size effects between urban and rural areas. Therefore, this study employs a hybrid machine learning approach to estimate the consumption structures of households of varying sizes across different years, while controlling for three key confounding factors—age, education level, and gender. Subsequently, based on input-output structural decomposition analysis, it constructs an accounting model to characterize the carbon emission distribution of residents across different household sizes. The study then evaluates the temporal evolution and explores the influencing mechanisms of household size reduction on CO₂ emissions in China from 2010 to 2020, integrating perspectives from both resident expenditure patterns and sectoral production linkages. It systematically evaluates and discusses the temporal evolution characteristics, urban-rural disparities, and transmission mechanisms within the industrial system of the impact of household size miniaturization on CO₂ emissions in China from 2010 to 2020, from the perspectives of both residents’ expenditure patterns and sectoral production activities. This research not only addresses the lack of detailed delineation of residents’ expenditure structures in existing studies but also elucidates how transformations in household structure reshape carbon emissions within the industrial system, providing a heterogeneous analysis of household size effects from the perspective of urban-rural disparities. These findings offer valuable insights for researchers to advance scientific understanding and for policymakers to develop differentiated and systematic emission reduction strategies tailored to urban and rural households.

Results

Carbon emission distribution

Total carbon footprint related to household expenditure

To investigate the differential impacts of household size on CO₂ emissions, households were classified by the number of members, ranging from one-person to 2-person, 3-person, 4-person, 5-person, and households with five or more individuals. Figures 1A–1C presents the total CO₂ emissions linked to residents’ energy and product expenditures in China for 2010, 2015, and 2020. The direct CO₂ emissions from 3-person households were relatively high, reaching 127.43 Mt in 2010, 187.34 Mt in 2015, and 176.46 Mt in 2020. In contrast, direct emissions from households with five or more members were the lowest. For example, in 2015, direct emissions from these larger households amounted to 74.78 Mt, only 0.42 times those of 3-person households. As shown in Figures 1D–1F, per capita direct CO₂ emissions for one-person households were substantially higher than for other household types in all three years. This indicates that household downsizing leads to greater per capita energy expenditure and, consequently, higher direct emissions. For instance, per capita direct emissions for one-person households were 0.42 tonnes (2010), 0.86 tonnes (2015), and 0.85 tonnes (2020), markedly exceeding those of other household sizes in the same years.

Figure 1.

Distribution of direct and indirect CO₂ emissions caused by household expenditure in China from 2010 to 2020

The panels A–C describe the total direct （orange bars） and indirect（green bars）carbon emissions of the residents grouped by household size.

The panels D–F describe the per capita direct （light blue bars） and indirect（light orange bars）carbon emissions of the households grouped by household size.

The panel G describe the total carbon emissions structure of the residents grouped by household size.

Regarding indirect CO₂ emissions (Figures 1A–1C), those from 3-person households were generally high, reaching 572.23 Mt in 2010, 702.21 Mt in 2015, and 709.95 Mt in 2020. However, indirect emissions from households with more than five members were the lowest across all household types. In 2015, for example, indirect emissions from these households were 202.26 Mt, merely 0.29 times those from 3-person households. From a per capita perspective (Figures 1D–1F), the disparity in indirect CO₂ emissions from product expenditure becomes more pronounced with varying household size. The per capita indirect emissions of one-person households were significantly greater than those of other multi-person households in all three years—2.75 tonnes (2010), 3.47 tonnes (2015), and 3.56 tonnes (2020)—exceeding the levels for households with over five members by 67.4%, 64.1%, and 59.7%, respectively. This further confirms that household miniaturization drives increased product expenditure and higher indirect emissions per capita. From the perspective of emission structure (Figure 1G), the share of total CO₂ emissions (from both energy and product expenditure) attributable to one-person and two-person households has increased annually, rising from 6.4% to 20.4% in 2010 to 10.9% and 26.1% in 2020, respectively. This trend aligns with the ongoing miniaturization of household size in China.^56,57

Carbon footprint from different energy types and sectors

Regarding CO₂ emissions from different energy types (Figure 2), emissions from one-person households increased annually between 2010 and 2020, primarily driven by expenditure on coal and electricity. For example, coal-related emissions from residents living alone rose from 4.93 Mt in 2010 to 14.39 Mt in 2020, while emissions from electricity consumption increased from 9.94 Mt to 47.34 Mt over the same period. This rapid growth is largely because, in multi-person households, energy costs are shared, whereas individuals living alone bear the full expense alone. Moreover, with rising living standards, solo dwellers may prioritize comfort and convenience, leading to increased use of coal and electrical appliances for heating and entertainment.⁴⁶

Figure 2.

Distribution of emissions linked with the residents’ energy expenditure

From a production-sector perspective (Figure 3), per capita indirect CO₂ emissions resulting from one-person households are higher, mainly due to their greater emissions in agriculture, chemicals, entertainment products, electricity and heat, and transportation. For instance, in 2010, 2015, and 2020, emissions from these product categories for one-person households were 3.1, 2.9, and 2.47 times those of households with more than five members, respectively. Ellsworth-Krebs (2020) also concluded that smaller households lead to higher emissions from housing, household equipment, and services92. Notably, the per capita emission gap between one-person and other household types is significantly larger than gaps among multi-person households, particularly in electricity/heat and transportation sectors. For the electricity and heat sector, high emissions are driven not only by direct consumption but also by the energy required to produce, transport, and dispose of other goods consumed by solo residents.⁵⁸ In the transportation sector, individuals living alone typically bear all mobility costs themselves. Their travel patterns may be more flexible and less shared, often resulting in higher per capita transportation expenditure and associated emissions compared to those in shared households. This finding is generally consistent with Xu et al. (2015)⁵⁹ and Ding et al. (2017).¹⁶ Compared to these studies, the present research not only reaffirms the positive correlation between household miniaturization and the increase in per capita carbon emissions but also further distinguishes between direct and indirect emissions. Additionally, it identifies the persistent upward trend in the proportion of total emissions contributed by one-person and two-person households, thereby more clearly revealing the long-term impact of household structure transformation on carbon emissions from residential consumption.

Figure 3.

Per capita indirect emissions by sector caused by the residents’ products expenditure

The panels A–C describe the sectoral per capita carbon emissions of the urban and rural households grouped by household size in the years of 2010, 2015 and 2020.

The reshaping of carbon emissions by household structure

From 2010 to 2020, the average household size in China showed a continuous downward trend, decreasing from approximately 3.44 persons in 2010 to 3.10 persons in 2015, and further dropping to 2.62 persons in 2020. This represents a cumulative decline of about 0.82 persons, or a decrease of approximately 23.8%. Concurrently, the distribution of household sizes underwent significant adjustments: The proportion of one-person households increased from 14.5% in 2010 to 17.0% in 2020, while the proportion of two-person households rose from 24.4% to 31.3%, reflecting increases of 2.5 and 6.9 percentage points, respectively. Meanwhile, the proportion of households with four or more persons declined from 34.2% to 28.5%, a decrease of nearly 5.7 percentage points, while the proportion of three-person households remained relatively stable overall.

Changes in household size not only reflect adjustments in household structure itself but also lead to a systematic restructuring of household consumption patterns (as shown in Figure 4). As household size decreases, the share of household expenditures on housing, energy, transportation, and service purchases generally tends to rise, while the proportion spent on food and clothing declines relatively. For example, in 2020, the per capita consumption expenditure of one-person households was approximately 28,500 yuan, with housing-related expenses accounting for 19% and transportation expenses accounting for 15%. In contrast, the per capita consumption expenditure of households with five or more persons was about 19,200 yuan, with housing-related expenses and transportation expenses accounting for 12% and 9%, respectively. This disparity indicates that although larger households typically have higher total household consumption, smaller households bear a higher per capita expenditure burden in consumption areas with stronger sharing effects, such as housing and transportation.

Figure 4.

Per capita consumption structure by household size in different years

The restructuring of consumption patterns triggered by changes in household size ultimately manifests in significant differences in per capita carbon emissions among households of varying sizes. Measurement results indicate that, within the same period, smaller household sizes are generally associated with higher levels of per capita direct and indirect carbon emissions. Taking 2020 as an example, the per capita carbon emissions of one-person households were approximately 4.4 tons of CO₂, of which direct emissions accounted for about 0.8 tons and indirect emissions for about 3.6 tons (as shown in Figures 1D–1F). In comparison, two-person households emitted around 3.1 tons, three-person households about 2.4 tons, four-person households about 2.0 tons, five-person households about 1.9 tons, and households with five or more persons approximately 1.6 tons. Compared to households with five or more persons, one-person households exhibited per capita carbon emissions that were about 2.7 tons higher, representing an increase of over 50%. The gap in per capita carbon emissions between one-person households and households with five or more persons widened from approximately 1.9 tons in 2010 to 2.3 tons in 2015 and further increased to 2.7 tons in 2020. This suggests that, against the backdrop of simultaneous consumption upgrading and household miniaturization, the high-carbon consumption characteristics of smaller households are gradually intensifying. The reduction in household size not only alters the household structure itself but also significantly elevates per capita carbon emissions related to consumption through the restructuring of consumption patterns and the weakening of sharing effects. Imran et al. (2022)⁶⁰ point out that as household size declines, per capita living space, ownership of durable consumer goods, and individualized travel demand tend to increase, thereby driving up consumption-related carbon emissions. Our findings are consistent with these conclusions, but also provide further extensions. On the one hand, based on three time points—2010, 2015, and 2020—this study reveals a continuous widening of the per capita carbon emission gap between one-person households and households with more than five members, indicating that the high-carbon consumption characteristics of smaller households have been further intensified under the combined effects of household miniaturization and consumption upgrading.

Using semi-elasticity analysis, we found that, assuming the total population remains constant, a 1 percentage point increase in the proportion of one-person households leads to an approximate 0.08% rise in total carbon emissions (as shown in Figure 5). In terms of sectoral distribution, most of the incremental emissions originate from the residential sector, household equipment sector, and transportation sector. Among these, the residential sector shows the largest increase in emissions (0.09%), which is slightly higher than the overall average growth rate. The household equipment sector and transportation sector also exhibit notable increases, at 0.07% and 0.06%, respectively. In contrast, the clothing sector, while also showing growth, experiences relatively smaller increases (0.04%). This indicates that the rise in emissions driven by the reduction in household size is primarily achieved through expanded energy use and housing-related demands that occur on a per-household basis.

Figure 5.

Rate of change in carbon emissions from various types of consumption when the proportion of one-person households increases by 1%

Discussion on urban-rural heterogeneity

From the perspective of total household carbon emissions across urban and rural households of different sizes during 2010–2020, urban households consistently emitted significantly more carbon than rural households in both direct and indirect forms, with indirect emissions remaining the dominant component throughout the period (as shown in Figure 6). Carbon emissions of all household types showed an overall upward trend over time, revealing pronounced urban-rural and household-size heterogeneity. In terms of the distribution across household sizes, indirect household emissions did not increase linearly with household size in either urban or rural areas; rather, they generally followed an inverted-U pattern, with medium-sized households tending to record the highest levels. Taking urban households as an example, indirect emissions rose from 95.39 MT for one-person households in 2010 to 453.65 MT for three-person households, and then declined to 303.63 MT, 186.21 MT, and 106.45 MT for four-person, five-person, and households with more than five members, respectively. In 2015, three-person households still had the highest indirect emissions, reaching 532.05 MT. By 2020, however, two-person households became the highest-emitting group, at 627.18 MT, exceeding the 559.94 MT recorded for three-person households. Rural households exhibited a similar pattern: Three-person households had the highest indirect emissions in both 2010 and 2015, at 118.58 MT and 170.16 MT, respectively, and remained the highest in 2020, at 150.01 MT. In other words, in both urban and rural areas, the highest levels of indirect emissions were mainly concentrated in two-person and three-person households, whereas one-person households and households with more than five members generally recorded lower levels. This suggests that, under the total-emissions measure, medium-sized households tend to generate higher overall consumption-related emissions, largely because such household sizes are more prevalent in the sample. As for direct carbon emissions, both urban and rural households displayed a similar pattern, with medium-sized households recording relatively higher levels and both smaller and larger households showing comparatively lower levels, although the variation was less pronounced than that observed for indirect emissions.

Figure 6.

Household carbon emissions across urban and rural households of different sizes during 2010–2020

The panels A and B describe the total carbon emissions of the urban and rural households grouped by household size.

The panels C and D describe the per capita carbon emissions of the urban and rural households grouped by household size.

Turning to per capita carbon emissions across urban and rural households of different sizes from 2010 to 2020, both per capita indirect and per capita direct emissions also exhibited clear temporal trends and urban-rural disparities. Regarding per capita indirect emissions, both urban and rural residents showed an overall upward trend over the period, but the increase was faster in urban areas, where levels remained consistently higher than in rural areas. In 2010, per capita indirect emissions for urban one-person, two-person, and three-person households were 1.64 tons, 1.58 tons, and 2.15 tons, respectively, compared with 0.68 tons, 0.75 tons, and 1.00 ton for their rural counterparts, meaning that urban levels were approximately 2.41, 2.11, and 2.15 times those in rural areas. By 2020, per capita indirect emissions for urban one-person households had risen to 11.95 tons, compared with 3.20 tons for rural one-person households, with the former being about 3.73 times the latter. For urban two-person and three-person households, the corresponding figures were 5.89 tons and 2.98 tons, compared with 1.34 tons and 0.80 tons in rural areas, widening the urban-rural gap to 4.40 times and 3.73 times, respectively. These results indicate that the disparity in per capita indirect emissions between urban and rural residents not only persisted over time but also tended to widen further among smaller household types.

With respect to per capita direct carbon emissions, the urban-rural gap was smaller than that observed for per capita indirect emissions. Overall, urban households still recorded slightly higher levels than rural households, and both showed a common pattern in which smaller households had higher per capita emissions while larger households had lower levels. In 2010, per capita direct emissions for urban one-person, two-person, and three-person households were 0.11 tons, 0.14 tons, and 0.25 tons, respectively, compared with 0.09 tons, 0.11 tons, and 0.17 tons for rural households, indicating a modest urban advantage. By 2015, the urban-rural difference had narrowed substantially; for example, per capita direct emissions of one-person households were 0.32 tons in urban areas and 0.31 tons in rural areas, while those of three-person households in both areas were close to 0.20 tons. In 2020, per capita direct emissions for urban one-person households rose to 0.73 tons, compared with 0.55 tons for rural one-person households, with the urban level being about 1.33 times the rural one. At the level of three-person and four-person households, urban values were 0.18 tons and 0.15 tons, respectively, while the corresponding rural values were 0.15 tons and 0.13 tons, indicating only limited differences. This suggests that, compared with indirect emissions, the per capita urban-rural gap in direct energy consumption, such as cooking, heating, household energy use, and transport fuels, is relatively small. Moreover, the relatively rapid increase in recent years among rural households has contributed to a tendency toward convergence in direct-emission disparities between urban and rural areas. Yang et al.(2025)³⁶ and Lv et al.(2024)⁶¹ suggested that urban residents tend to generate higher direct and indirect carbon emissions than rural residents, mainly because they have higher income levels, consumption structures that are more oriented toward services and durable goods, and greater access to modern energy use. This study further finds that such urban-rural differences are more pronounced among smaller households, especially for one-person and two-person households, where the gap in per capita indirect emissions is larger. This indicates that household miniaturization and urban-rural consumption disparities do not operate independently, but rather jointly shape the heterogeneous pattern of household carbon emissions.

The impact of various influencing factors

The influence of various factors on total CO₂ emissions

Figure 7A illustrates the effects of three factors on the growth of direct CO₂ emissions from Chinese household expenditure. From 2010 to 2015, increases in per capita energy expenditure and population scale contributed to rising direct CO₂ emissions. The per capita energy expenditure effect played the dominant role, accounting for 94.6% of the total emission increase. In contrast, changes in energy expenditure structure alone resulted in a decline in direct emissions, offsetting 4.6% of the total rise during this period. Between 2015 and 2020, changes in per capita energy expenditure, energy expenditure structure, and population scale all promoted the growth of direct CO₂ emissions. However, compared to the 2010–2015 period, the contribution of the per capita energy expenditure level effect decreased by 84.9%, leading to a relatively weaker increase in direct emissions from 2015 to 2020.

Figure 7.

The influence of each effect on the rising CO₂ emissions in China

The panel A describe the impact of each effect on direct carbon emissions.

The panel B describe the impact of each effect on indirect carbon emissions.

Figure 7B shows the effect of each factor on total CO₂ emissions from residents’ product expenditure in China. From 2010 to 2015, the per capita expenditure level effect and the population scale effect contributed to the growth of indirect CO₂ emissions. The per capita expenditure effect was the primary driver, accounting for 95.4% of the total increase. Meanwhile, the emission coefficient effect, industrial structure effect, and expenditure structure effect all led to a reduction in indirect emissions, jointly offsetting 71.3% of the emission growth during this period. From 2015 to 2020, changes in emission intensity and production structure significantly promoted CO₂ emission reduction. Concurrently, compared with the 2010–2015 period, the contribution of the per capita expenditure level effect to emission growth weakened substantially, decreasing by 43.6%. The combined influence of these effects resulted in a relatively modest increase in total indirect CO₂ emissions from 2015 to 2020.

Effects on direct emissions of different household size groups

Table 1 presents the effect of each factor on the rise in CO₂ emissions from residents’ energy expenditure in China. According to the “Total Effect” column, from 2010 to 2015, direct CO₂ emissions from small household groups such as one- and two-person households ranked third and second, respectively, among all groups. They contributed 32.42 Mt and 54.80 Mt, accounting for 41.2% and 24.1% of the net increase in total direct CO₂ emissions from Chinese residents. From 2015 to 2020, while contributions from other household groups slowed or diminished, emissions from one-person and two-person households increased by 26.79 Mt and 39.00 Mt, respectively. Consequently, these two groups became the primary contributors to direct CO₂ emissions during 2015–2020, representing 37.3% and 54.3% of the net rise in total direct emissions from residents’ energy expenditure.

Table 1.

Effect of factors on CO₂ emissions from residents’ energy expenditure (unit: MT)

Year	Household size	Per capita energy expenditure level	Energy expenditure structure	Population scale	Total
2010–2015
	one-person	23.36	−0.87	9.93	32.42
	two-person	51.84	−1.86	4.82	54.80
	three-person	73.30	−2.83	−10.56	59.91
	four-person	38.08	−2.79	−5.69	29.60
	five-person	21.58	−1.71	1.16	21.03
	more than five	18.58	−0.99	12.23	29.83
	in total	226.75	−11.06	11.89	227.59
2015–2020
	one-person	−1.69	0.58	27.91	26.79
	two-person	0.60	1.23	37.16	39.00
	three-person	−0.12	0.80	−11.56	−10.88
	four-person	7.80	0.09	−1.41	6.47
	five-person	7.63	0.48	−14.92	−6.80
	more than five	19.99	0.27	−3.03	17.23
	in total	34.21	3.45	34.15	71.81

Since household miniaturization may affect direct CO₂ emissions through changes in residents’ energy expenditure, we also explore the effects of three factors—per capita energy expenditure, energy expenditure structure, and population scale—on CO₂ emissions resulting from residents’ energy expenditure. Regarding per capita energy expenditure, from 2010 to 2015, changes in this factor for all household sizes contributed to rising direct CO₂ emissions. The increase attributable to one-person households ranked fourth among all groups, representing 10.3% of the total rise from this effect. From 2015 to 2020, per capita energy expenditure for one-person households slowed emission growth, while that for households with four or more members significantly promoted it, adding 35.24 Mt. In terms of energy expenditure structure, from 2010 to 2015, changes in this factor for all household types slowed direct emission growth. The reduction achieved by one-person households ranked last, accounting for 7.9% of the total decrease from this effect. Between 2015 and 2020, changes in energy expenditure structure for all household types caused a slight increase in direct emissions. The contribution from one-person households ranked third, making up 16.8% of the total increase from this effect. As for population scale, in both 2010–2015 and 2015–2020, population growth in the one-person and two-person household groups caused increases in direct CO₂ emissions, accounting for 42.9% and 57.1% of the total increase from this effect, respectively. Their contribution in the latter period was significantly stronger—2.8 and 7.7 times that in the earlier period, respectively. Specifically, the direct emissions of three-person households decreased during the period 2015–2020. The primary driver behind the decrease in direct carbon emissions from three-person households during this period is the significant reduction in their population size. Between 2015 and 2020, the number (or proportion) of three-person households in China declined noticeably. This demographic shift directly led to a decrease in the total energy consumption demand of this group in areas such as housing, heating, and private transportation, thereby resulting in a downward trend in their total direct carbon emissions. The population scale effect contributed negatively to changes in direct carbon emissions during 2015–2020 (−11.56 MT) and was the most influential factor among all effects.

Overall, the contribution of one-person households to the increase in direct CO₂ emissions during 2010–2015 was primarily driven by changes in their per capita energy spending. Correspondingly, the rise in direct emissions from one-person residents during that period was mainly due to the growth of the one-person household population.

Effects on indirectly emissions of different household size groups

Table 2 shows the impact of each factor on CO₂ emissions resulting from product expenditure across different household size groups in China. Overall, in terms of the total effect, all household types contributed to rising indirect CO₂ emissions during 2010–2015. The increase attributable to four-person households was the highest, amounting to 107.16 Mt and accounting for 22.7% of the total rise during this period. In contrast, the increase from three-person households was the lowest (18.31 Mt), representing 3.8% of the total. From 2015 to 2020, the rise in indirect CO₂ emissions was primarily driven by expenditure from two-person households, which increased by 161.96 Mt and accounted for 51.1% of the total growth during this period—a level 64.5% higher than in the previous stage. Notably, the incremental emissions from one-person households’ product expenditure also rose significantly, showing a 41.3% increase compared to the 2010–2015 level. Conversely, three-person, four-person, and five-person and more households slowed the growth of indirect emissions, accounting for 28.5%, 29.3%, and 42.2% of the total emission reduction from 2015 to 2020, respectively. This shift occurred mainly because the per capita product expenditure of these larger household groups, which had been a key driver of emission increases in 2010–2015, grew only weakly in 2015–2020. At the same time, changes in their expenditure structure and population scale significantly dampened the rise in indirect emissions linked to their consumption. As a result, the overall emission growth contributed by these three household types decreased substantially.

Table 2.

Effect of factors on the CO₂ emissions from residents’ products expenditure (unit: MT)

Year	Household size	Emission intensity	Production structure	Per capita expenditure level	Expenditure structure	Population scale	Total
2010–2015
	one-person	−38.07	−37.01	97.90	−12.13	55.70	66.39
	two-person	−108.12	−102.46	360.28	−77.76	26.49	98.43
	three-person	−151.55	−143.89	376.60	−13.74	−49.11	18.31
	four-person	−114.23	−106.89	386.78	−31.76	−26.74	107.16
	five-person	−73.37	−69.79	240.68	−3.72	5.43	99.23
	more than five	−43.87	−40.03	107.35	−2.74	62.24	82.95
	in total	−529.21	−500.07	1,569.59	−141.85	74.02	472.47
2015–2020
	one-person	−28.84	−56.53	73.65	−10.17	115.72	93.83
	two-person	−72.69	−143.66	224.07	−16.35	170.59	161.96
	three-person	−77.13	−145.89	226.54	−27.91	−45.12	−69.52
	four-person	−59.33	−116.43	123.54	−13.32	−5.94	−71.48
	five-person	−36.68	−71.71	98.52	−30.41	−62.68	−102.96
	more than five	−23.79	−49.25	139.13	5.60	−10.65	61.04
	in total	−298.47	−583.47	885.45	−92.56	161.93	72.88

Since household downsizing may influence indirect CO₂ emissions through changes in residents’ product expenditure, this study also analyzes the contributions of five factors to the rise in indirect CO₂ emissions across different household sizes in China: the emission intensity effect (i.e., changes in sectoral carbon emission coefficients), the production structure effect (i.e., changes in inter-sectoral linkages), product expenditure structure, per capita product expenditure level, and population scale. The results are also presented in Table 2.

Changes in both emission intensity and production structure promoted the decrease in CO₂ emissions during the study periods. Regarding emission intensity, the reduction achieved by the single-living population ranked last and second to last among all household size groups in 2010–2015 and 2015–2020, accounting for 7.2% and 9.7% of the total emission reductions from this effect, respectively. Similarly, for the production structure effect, the CO₂ emission decrease attributable to this factor for one-person households also ranked last and second to last across all groups during the two periods, accounting for 7.4% and 9.7% of the total reduction from this effect, respectively. In both periods, the emission decline driven by changes in production structure was smaller for residents living alone compared to other household types.

In terms of expenditure structure effects, those for one-person households only slightly weakened the increase in CO₂ emissions in both 2010–2015 and 2015–2020, accounting for 8.5% and 11.0% of the net emission decrease from this effect in each period, respectively. This was mainly because the proportion of energy-intensive goods (e.g., household appliances) in the expenditure of residents living alone changed only slightly. As for the per capita expenditure level effect, changes in this factor for all household groups drove an increase in CO₂ emissions. In both 2010–2015 and 2015–2020, the contribution from one-person households ranked last among all groups, accounting for 6.2% and 8.3% of the total emission increase from this effect, respectively. This lower contribution was because one-person households typically consist of young entrants to the workforce or elderly individuals living alone, groups that generally have more limited and slower-growing incomes, leading to smaller rises in their per capita expenditure. Regarding the population scale effect, in both 2010–2015 and 2015–2020, population growth in one- and two-person households significantly contributed to rising CO₂ emissions, accounting for 39.3% and 45.2% of the total increase from this effect over the entire observation period, respectively. Notably, these shares were smaller than the corresponding proportions of national population growth contributed by these household types (67.8% and 110.5%, respectively).

Overall, during both periods, the impacts of emission intensity and expenditure structure changes on indirect CO₂ emissions for one-person households and two-person households were far smaller than the impacts of population scale and per capita expenditure level, which were the primary drivers of emission growth for these groups. Particularly from 2015 to 2020, the population scale effect for one-person households and two-person households was pronounced, ranking first and second among all residential groups, respectively. This led to a greater total emission increase for these two groups compared to others during this period.

Figure 8 illustrates the effect of each factor on changes in CO₂ emissions related to product expenditure by residents living alone from 2010 to 2020. From a consumer perspective, considering sectors such as household equipment and transportation, the emission increases driven by population growth in the single-living group were similar (16.59 Mt and 23.54 Mt, respectively). However, the influences of other factors differed substantially between the two sectors. For the household equipment sector, the reduction in its carbon intensity and the optimization of its production structure offset 22.5% of the total CO₂ emission growth. In contrast, changes in per capita expenditure level contributed 20.6% to the emission increase. For the transportation sector, the corresponding values were 10.3% and 11.5%. This indicates that although expenditure on household equipment by the single-living group grew rapidly (per capita expenditure level effect), this growth did not directly translate into a proportional rise in emissions from the household equipment sector. This was because most of the emission increase driven by rising per capita expenditure was offset by concurrent improvements in the sector’s emission intensity and production structure. In the transportation sector, however, the emission reductions achieved through lower carbon intensity and structural optimization were insufficient to offset the emission increase driven by rising per capita expenditure levels.

Figure 8.

Effect of every factor on the indirect CO₂ emissions change linked to the one-person households in 2010–2020

Note: The X axis shows final expenditure sectors. The Y axis shows the cumulative amount of change in CO₂ emissions from the production sector to satisfy final expenditure.

Discussion

On the basis of a detailed description of expenditure structure for residents of different household sizes using a hybrid machine learning approach, this study examines the carbon footprint across household sizes from the perspectives of expenditure patterns and production activities. It discusses the influencing mechanisms and sectoral focus of household downsizing on the carbon footprint from residents’ energy and product expenditure, and analyzes the contribution of each influencing factor to rising CO₂ emissions for one-person and other household size groups in China. This can help clarify the effect of changes in residents’ expenditure structure on household expenditure CO₂ emissions, thereby providing a basis and inspiration for policymakers to design emission reduction policies aligned with China’s actual situation. The key conclusions are as follows:

Across the three study years, the per capita direct and indirect CO₂ emissions of one-person households were significantly higher than those of other multi-person households. For direct emissions, per capita figures for one-person households were 0.42 tonnes, 0.86 tonnes, and 0.85 tonnes in 2010, 2015, and 2020, respectively, primarily driven by expenditure on coal and electricity. During 2010–2015, the mitigation of direct CO₂ emissions from one-person residents was mainly due to changes in their per capita energy expenditure. From 2015 to 2020, the population scale effect became the dominant driver of rising direct emissions for this group. Regarding indirect CO₂ emissions, per capita figures for one-person households were 2.75 tonnes, 3.47 tonnes, and 3.56 tonnes in 2010, 2015, and 2020, respectively. These higher emissions were largely attributable to expenditure in agriculture, chemicals, entertainment products, electricity and heat, and transportation. The per capita product expenditure level effect and the population scale effect were the key factors promoting rising indirect emissions for this group in 2010–2015 and 2015–2020, respectively. From 2010 to 2020, 71.9% (115.22 Mt) of the increase in indirect CO₂ emissions linked to one-person households was associated with residential expenditure, 14.7% (23.54 Mt) came from transportation, and 10.4% (16.59 Mt) from household equipment. Notably, compared to the household equipment sector, although the transportation sector achieved some success in reducing emission intensity and optimizing its production structure, these reductions did not offset the CO₂ emission increases resulting from elevated expenditure levels driven by population growth.

In view of the fact that direct emissions from one-person households are mainly concentrated in coal and electricity consumption, priority should be given to promoting clean heating, cooking electrification, and the substitution of distributed low-carbon electricity in urban communities with high concentrations of single residents, old residential neighborhoods, and rental housing, so as to reduce the use of scattered coal and inefficient end-use energy. However, targeted subsidies may be provided for energy-saving equipment in small-sized dwellings. The precise distribution of targeted subsidies requires a well-established resident information database, and the current data coverage and update mechanisms remain insufficient. To address these barriers, the existing community-based grid management system can be leveraged to establish a dynamic database of residents’ energy consumption and income levels, thereby providing data support for the precise allocation of subsidies. Given the relatively high transportation expenditure and associated emissions of one-person households, their flexible, dispersed, and individualized travel patterns tend to result in higher per capita emissions. Subsidies could therefore be offered for the use of car-sharing services. However, the promotion of car-sharing services is constrained by the immature profit models of operating enterprises and the long cycle required to cultivate user habits. In response, local governments may collaborate with car-sharing platforms to explore a combined “carbon credit and consumption voucher” subsidy model. Community-based publicity campaigns and trial ride experiences can be used to gradually cultivate residents’ shared mobility habits, while big data can be leveraged to optimize vehicle dispatch and improve operational efficiency. In response to the tendency for household equipment and durable goods to be more frequently duplicated in small households, policy should shift from “encouraging purchases” to “improving utilization efficiency and sharing levels.” It is advisable to encourage composite living arrangements featuring shared kitchens, shared laundry facilities, and shared public activity spaces, thereby partially restoring the economies of scale and sharing effects that are lost under household downsizing. However, the promotion of composite living models faces obstacles such as existing housing structure constraints and difficulties in property management coordination, making large-scale implementation in the short term less feasible. To overcome these barriers, pilot projects for standardized “shared functional area” design can be introduced in newly built affordable housing and long-term rental apartment projects, incorporating shared kitchens and shared laundry rooms into building codes to reduce implementation costs at the source. Furthermore, relevant laws and regulations should be improved to clarify the rights, responsibilities, and fee standards for property management under shared living models, thereby providing institutional guarantees for scaled-up promotion.

Limitations of the study

The limitations of this study are as follows: Due to limitations in data availability, the IO tables and household expenditure-related data used in this study exhibit a certain degree of lag. As data availability improves in the future, this study will further update the relevant data, which will help to more closely fit with the current reality and grasp the connection between the shrinking of family sizes and CO₂ emissions. In addition, considering the regional differences in China’s economy, emission levels, and population structure, future research can also explore the impact of shrinking family sizes on CO₂ emissions across various provinces of China. This will provide decision-makers with new insights for the coordinated governance of issues related to regional emission reduction and changes in family structure.

Resource availability

Lead contact

Requests for further information and resources should be directed to and will be fulfilled by the lead contact, Weiwei Huang (weiweihuang@zjnu.edu.cn).

Materials availability

This study did not generate new unique reagents.

Data and code availability

• •All data reported in this paper will be shared by the lead contact upon request.
• •This paper does not report original code.
• •Any additional information required to reanalyze the data reported in this paper is available from the lead contact upon request.

Acknowledgments

This work is supported by the Zhejiang Philosophy and Social Science Foundation (grant no. 26NDJC021YBMS), A Project Supported by Scientific Research Fund of Zhejiang Provincial Education Department (grant no. Y202457096), the project of the Beijing Summit of the Forum on China-Africa Cooperation and building a model for local cooperation between China and Africa in the new era (grant no. JHZF202516YB), the Project on Jinhua City’s Support for Zhejiang Normal University’s African Regional Country Studies, the General Program of the China Postdoctoral Science Foundation (grant no. 2025M784257), and the Zhejiang Soft Science Research Program (grant no. 2026C25027).

Author contributions

Conceptualization, Y.Y.; methodology, Y.Y. and H.W.; investigation, Y.Y.; writing – original draft, Y.Y.; writing – review and editing, W.H.; funding acquisition, H.W.; resources, H.W. and T.Q.; supervision, W.H.

Declaration of interests

The authors declare no competing interests.

STAR★Methods

Key resources table

REAGENT or RESOURCE	SOURCE	IDENTIFIER
Deposited data
China Family Panel Studies(CFPS)	The Institute of Social Science Survey (ISSS), Peking University	https://cfpsdata.pku.edu.cn
Input-output tables in 2010–2020	National Bureau of Statistics	https://data.stats.gov.cn
Carbon Emission Accounts and Datasets (CEADs)	Tsinghua University	https://www.ceads.net/
Software and algorithms
MATLAB R2021b	Commercially Available Software	N/A
Origin 2022	Commercially Available Software	N/A

Method details

Hybrid machine learning approach

This study employs a hybrid machine learning approach to analyze the consumption structures of residents with different household sizes across various years, primarily based on the following reasons: ① Consumption structure analysis is essentially a problem of share estimation, which requires satisfying two fundamental mathematical constraints: the proportion of each consumption category should be non-negative, and the sum of the proportions of all categories should equal 1. ② Traditional regression methods may yield negative coefficients, which are inconsistent with economic reality, while simple arithmetic averaging fails to effectively control the influence of other variables. ③ Consumption data often exhibit multicollinearity issues, which can lead to biased estimates in traditional regression models. ④ Consumption data frequently display skewed distributions and extreme values, necessitating robust handling methods.

To address these challenges, this study has designed a hybrid approach that combines Non-negative Matrix Factorization (NMF) and ElasticNet regression. Our research objective is to identify consumption structure patterns from a large number of samples rather than to predict numerical values. Random forest is primarily designed for supervised prediction, for example, accurately predicting how much a given household spends based on household characteristics.⁶² In contrast, our goal is to estimate a representative benchmark consumption structure from tens of thousands of households. Random forest cannot directly produce such a structured distribution of weights, whereas NMF, as a dimensionality reduction method, is better suited to extracting common group level features from a complex matrix.⁶³

Non-negative Matrix Factorization (NMF) method

Non-negative Matrix Factorization (NMF) is an unsupervised learning algorithm aimed at extracting useful features. Its mathematical model can be expressed as follows: X ˜ WH, Given a data matrix $\mathbf{X}\in {\mathbb{R}}^{n\times m}$ containing n samples and m consumption categories, where $\mathbf{W}\in {\mathbb{R}}^{n\times k}$ is the basis matrix and $\mathbf{H}\in {\mathbb{R}}^{k\times m}$ is the coefficient matrix. In this study, we set k = 1 (i.e., seeking a single consumption structure pattern ${\min }_{\mathbf{W},\mathbf{H}}{\Vert \mathbf{X}-\mathbf{\text{WH}}\Vert }_F^2,\mathrm{s}.\mathrm{t}.\mathbf{W}\ge 0,\mathbf{H}\ge 0$). Through this decomposition, we extract the consumption structure weight vector h from matrix H, and after standardization, obtain estimated proportions for each consumption category: $w_i^{\text{NMF}}=\frac{\max \left(h_i,ϵ\right)}{\sum _{j=1}^m\max \left(h_j,ϵ\right)}$, where ϵ is a minimum threshold set to avoid zero values. The NMF model was independently implemented within each subsample defined by household size, urban–rural status, and year. Setting k equal to 1 within each specific subgroup was intended to filter out random noise in micro household data, such as occasional extreme expenditures from individual samples, so as to extract the most prevalent benchmark consumption structure for that group.^64,65 In this study, heterogeneity is captured through horizontal comparisons of the independently generated k equals 1 vectors across different subgroups, which enables us to exclude the influence of within group variation and identify differences in consumption structure associated with household size.

ElasticNet regression method

ElasticNet regression is a supervised learning algorithm that combines the regularization techniques of Lasso regression and Ridge regression. Its primary advantage lies in its ability to handle multicollinearity among features, a challenge that ordinary least squares (OLS) struggles to address effectively. We employ ElasticNet to estimate the relative impact of various consumption categories on income while controlling for other variables. The formula is as follows:

$${\mathit{min}}_{\beta }\left\{{\parallel y-{\mathit{X}}_c{\beta }_c-{\mathit{X}}_z{\beta }_z\parallel }_2^2+\lambda \left(\alpha {\parallel \beta \parallel }_1+\frac{1}{2}\left(1-\alpha \right){\parallel \beta \parallel }_2^2\right)\right\}$$ (Equation 1)

In Formula 1, y is the vector of log-transformed income values, X_c is the matrix of consumption variables, X_z is the matrix of control variables (including age, education level, and gender), β are the coefficient vectors, λ is the regularization strength parameter, and α is the proportion of L1 regularization. We impose non-negative constraints (β ≥ 0) to ensure the economic plausibility of the coefficients. From the estimated coefficients, we extract those corresponding to consumption variables and standardize them to obtain consumption structure estimates: $w_i^{\text{EN}}=\frac{\max \left({\beta }_{c,i},ϵ\right)}{{\sum }_{j-1}^m\max \left({\beta }_{c,j},ϵ\right)}$.

We have further clarified the theoretical rationale for including age, education, and gender as control variables in the machine learning model. The reasons are as follows: First, the age variable is used to isolate the influence of life cycle differences on consumption structure. The family life cycle theory posits that different age stages correspond to distinct demand structures and resource allocation patterns.^66,67 Since household size itself is closely related to the life cycle stage, controlling for age helps to better identify the effect of household size. Second, education level serves as a key proxy for long-term income expectations, human capital, and consumption preferences. The distribution of education levels may systematically differ across household sizes.⁶⁸ Therefore, controlling for education in the machine learning model helps avoid misattributing education-driven differences in consumption structure to household size itself. Third, gender reflects differences in intra-household decision-making mechanisms and preferences. Moreover, the gender composition of household heads varies significantly across household sizes.⁶⁹ Including gender in the model thus helps control for variations in consumption structure arising from differences in household decision-making structures. The primary focus of this study is to elucidate the transmission mechanism through which “household size” itself influences carbon emissions via “consumption structure”. Income, as a strong confounding variable, simultaneously affects household size (e.g., economic capacity influences fertility and residential choices) and consumption structure. If income were directly incorporated into the model, it might partially “mask” the impact of household size through lifestyle and consumption choices (i.e., the structural effect), which is precisely the core we aim to isolate and identify.

Hybrid weighted ensemble

To ensure the robustness of the results, we integrate the estimation outcomes from the two methods through a weighted average.

$$w_i=\gamma ·w_i^{NMF}+\left(1-\gamma \right)·w_i^{EN}$$ (Equation 2)

In Formula 2, γ = 0.5 is the weight parameter that balances the contributions of the two methods. The final results undergo non-negative processing and standardization again to ensure they satisfy the constraints of non-negativity and summing to one.

Input-output method

This section presents an IO model to quantify direct and indirect household CO₂ emissions. This research employs an econometric model to thoroughly assess the influence of household size on CO2 emissions in China. According to the analysis of home CO₂ emissions and the assessment of household size’s impact on per capita emissions, we recommend specific carbon reduction plans designed for various regions and population groups.

Input-output analysis, as a quantitative economic tool, efficiently illustrates the interdependence between inputs and outputs within different components of a financial system.^70,71 Based on this method, structural decomposition analysis allows for identifying factors influencing a particular indicator within the system.⁷² The indicator can then be disaggregated into changes driven by different influencing factors, enabling the calculation of each factor’s contribution to these changes.⁷³ The method has been applied more frequently in the economic, demographic, and energy-environmental fields.⁷⁴ The method quantifies the influence of various factors on total energy or emission indicators and illustrates the impact on production structure and final demand.⁷⁵ As a result, this method is suitable for studying the contribution of various factors to CO₂ emissions for household sizes. In the specific analysis, the following two main steps are included.

Household direct CO₂ emissions

This study uses Equation 3 to account for the household direct CO₂ emissions:

$$C_{\text{dr}}=\sum C_{kj}=\sum f_k·E_{kj}=\sum f_k·W_{kj}·T_j·Q_j$$ (Equation 3)

Here, k represents the types of energy sources consumed by residents, and j denotes a specific household size group. C_dr refers to the direct CO₂ emissions resulting from household energy expenditure, while C_k,j represents the CO₂ emissions from the expenditure of the k energy source by residents in the j household size group. f_k is the carbon emission coefficient for the k energy source, W_k,j represents the proportion of the k energy consumed by j household size group, E_k,j denotes the quantity of the k energy source consumed by residents in the j household size group, Q_j represents the population size of this j household size group, and T_j indicates per capita energy expenditure for household size group j.

The change in CO₂ emissions from household energy expenditure between two points in time (base year 0 and target year t) can be expressed in terms of ΔC_dr, where the total emission change results from the combined effect of various influencing factors. ΔC_dr can be further decomposed into three key components: the energy expenditure structure effect f(ΔW), the population scale effect f(ΔQ), and the per capita energy expenditure effect f(ΔT), as shown in Equation 4:

$${△C}_{dr}=f\left(△W\right)+f\left(△T\right)+f\left(△Q\right)$$ (Equation 4)

This research utilizes the decomposition method established by Miller and Blair (2009)⁷⁶ to ascertain the determinants of direct CO₂ emissions resulting from household expenditure of energy. Based on Equation 3 and 4, the components f(ΔW), f(ΔT), and f(ΔQ) can be derived as shown in Equation 5, 6, and 7, respectively:

$$f\left(△W\right)=\frac{1}{2}f·△W·T_0·Q_0+\frac{1}{2}f·△W{·T}_t{·Q}_t$$ (Equation 5)

$$f\left(△T\right)=\frac{1}{2}f·W_t·△T·Q_0+\frac{1}{2}f·W_0·△T{·Q}_t$$ (Equation 6)

$$f\left(△Q\right)=\frac{1}{2}f{·W}_t{·T}_t·△Q+\frac{1}{2}f·W_0{·T}_0·△Q$$ (Equation 7)

Household indirect CO₂ emissions

This study decomposes the expenditure of the population as shown in Equation 8:

$$Y=\sum Y_{ij}=\sum R_{ij}·K_j·Q_j$$ (Equation 8)

Here, Ydenotes the total expenditure by residents, R_ij indicates the proportion of products from sector i consumed by this household size j, Y_ij represents the products from sector i consumed by residents in household size j, and K_jrefers to the per capita expenditure of residents in household size j. Q_j represents population size effect in household size j.

Subsequently, Equation 9 is employed to calculate the household indirect CO₂ emissions:

$$C_{dr}=e.{\left(I-A\right)}^{-1}.Y=e.{\left(I-A\right)}^{-1}.R.K.Q=e.L.R.K.Q$$ (Equation 9)

Here, C_dr denotes the indirect CO₂ emissions from residential expenditure and e is the row matrix of carbon intensity factors for each sector. The carbon intensity factor is obtained by dividing the CO₂ emissions consumed by each sector’s production of products by its total output. I denotes the identity matrix, while A is the direct expenditure coefficient matrix, where the matrix element a_ij represents the product or service from the i sector that is directly consumed by one unit of output from the j sector. The term (I-A)⁻¹represents the Leontief inverse matrix, denoted as L.

The change in CO₂ emissions from household expenditure products at two different points in time can be expressed in terms of △C_indr, representing the total CO₂ emissions change resulting from the combined effects of various influencing factors. △C_indr can be further decomposed into several components: the expenditure structure effect f(ΔR), the per capita expenditure level effect f(ΔK), the emission intensity effect f(Δe), and the population scale effect f(ΔQ), the production structure effect f(ΔL), as shown in Equation 10:

$${△C}_{dr}=f\left(△e\right)+f\left(△L\right)+f\left(△R\right)+f\left(△K\right)+f\left(△Q\right)$$ (Equation 10)

Therefore, based on Equation 9 and 10, this study can derive the components f(Δe), f(ΔL), f(ΔR), f(ΔK), and f(ΔQ).

f(Δe), f(ΔL) are shown in Equation 11 and 12, respectively:

$$f\left(△e\right)=\frac{1}{2}△e·L_0{{·R}_0{·K}_0·Q}_0+\frac{1}{2}△e·L_t·R_t{·K}_t{·Q}_t$$ (Equation 11)

$$f\left(△L\right)=\frac{1}{2}{e}_t·△L{{·R}_0·K}_0·Q_0+\frac{1}{2}{e}_0·△L·{R_t·K}_t{·Q}_t$$ (Equation 12)

In particular, Miller and Blair (2009)⁷⁶ point out that ΔL can be further decomposed as shown in Equation 13:

$$\Delta L=L_t-L_0=L_t·A_t·L_0-L_t·A_0·L_0=L_t·\Delta A·L_0$$ (Equation 13)

Consequently, f(ΔL)can be expressed as Equation 14:

$$f\left(\Delta L\right)=\frac{1}{2}{e}_t·L_t·\Delta A·L_0·R_0·K_0·Q_0+\frac{1}{2}{e}_0·L_t·\Delta A·L_0·R_t·K_t·Q_t$$ (Equation 14)

f(ΔR), f(ΔK), and f(ΔQ) are shown in Equation 15, 16, and 17, respectively:

$$f\left(△S\right)=\frac{1}{2}{e}_t{·L}_t·△R·{K_0·Q}_0+\frac{1}{2}{e}_0·L_0·△R{{·K}_t·Q}_t$$ (Equation 15)

$$f\left(△V\right)=\frac{1}{2}{e}_t{L}_t{·R}_t·△K{·Q}_0+\frac{1}{2}{e}_0·L_0{·R}_0·△K{·Q}_t$$ (Equation 16)

$$f\left(△P\right)=\frac{1}{2}{e}_t·L_t·R_t·K_t·△Q+\frac{1}{2}{e}_0·L_0·R_0{·K}_0·△Q$$ (Equation 17)

Data sources

The data about household expenditure of coal, gasoline, kerosene, diesel, natural gas, and electricity for 2010, 2015, and 2020 was obtained from the China Statistical Yearbook.^77,78 The CO₂ emission factor for each energy type is derived from the 2006 IPCC Guidelines for the Preparation of Greenhouse Gas Inventories Revised Edition 2019.¹ The direct emission factor for energy was sourced from the Baseline Emission Factors for Regional Power Grids in China, released by the China’s Ministry of Environmental Protection.⁷⁹ Data on expenditure structures across households of varying sizes were compiled from the China Family Panel Studies (CFPS). Population data by household size were compiled based on proportions from sample surveys representing the total population. The output data for each production sector and the expenditure data of the population were sourced from the China IO Tables. National and provincial sub-sectoral carbon emission data are from the CEADs database. Some data required further processing, as detailed below.

Comparable-price IO tables

The preparation of comparable-price IO tables is necessary to eliminate the impact of price fluctuations across several accounting periods.^80,81 For this study, 2020 was selected as the base year for constructing the comparable-price series. Subsequently, the IO tables for 2010 and 2015 were deflated using the single deflator method.⁸² This study employs the industrial ex-factory price index to adjust the total output and intermediate inputs at current prices for each industrial sector, which are calculated separately for each industrial sector at comparable prices.^83,84 Agriculture, construction, transportation, wholesale and retail sectors, and other services were deflated using sector-specific indices: the agricultural production price index, construction and installation price index, transportation and communication price index, retail merchandise price index, and consumer price index, respectively.⁸⁵ Finally, the IO tables were consolidated into 19 sectors, aligning with the energy use data characteristics for each production or service sector. In this study, the original 42 input-output sectors were aggregated into 19 sectors, primarily based on the following considerations: First, the sector aggregation was conducted according to the key consumption categories in the household consumption structure, ensuring the representativeness and interpretability of the focal sectors in the analysis of consumption-related emissions. Second, this sector classification follows and maintains a framework consistent with major literature in the relevant field,^86,87 which helps enhance the comparability of the research findings.

Expenditure data processing for different household sizes

The domestic expenditure structure of energy and products for households of all sizes across three years was based on data from the CFPS. Descriptive statistics of the sample data can be found in Document S1. The robustness check for the estimation of consumption structure and decomposition results can be seen in the Document S2 and Document S3. To enhance detail, we refined the IO table’s expenditure data to represent households of varying sizes. Following the methodology used in compiling the 2012 IO table, we matched the eight categories of expenditure data to the corresponding production or service sectors in the IO table. Subsequently, we organized the data to reflect the expenditure proportions of products and services within each sector by household size. Finally, the data corresponding to each sector in the IO tables were disaggregated based on the percentage of products or services consumed by residents of various household sizes within those sectors. In addition, to further clarify the decomposition procedure, we add a brief outline of the derivation process in Document S4. And we also perform a sensitivity analysis with k = 2 or k = 3 for the NMF analysis in Document S5.

Quantification and statistical analysis

Quantitative analysis was conducted using Excel, MATLAB, and Origin and the results were reflected in Figure 1, Figure 2, Figure 3, Figure 4, Figure 5, Figure 6, Figure 7, Figure 8.