*3.2. Household Economies of Scale for Total Carbon and Energy Footprints*

Figure 5 portrays results from a multi-variate OLS regression on the role of *HHSIZE* for per capita carbon and energy footprints in logarithmic form (dependent variables). There are additional variables in the models such as income, urban-rural typology and geographical region (see the Data and Methods section for the model specification). The figure shows two model specifications, including (in blue) and excluding (in red) the *HHSIZE*×*DENSE* interaction terms.

**Figure 5.** Household size effect across countries with dependent variables—the log of carbon footprints per capita (**a**) and energy footprint per capita (**b**). The blue coefficients depict the *HHSIZE* coefficient acquired from the model including interaction effect (*HHSIZE*×*DENSE*) and the red coefficient—the *HHSIZE* coefficient from the model without any interaction term. All models control for income, rural-urban typology and region. See Data and Methods for the model specification. Household weights provided by the HBS have been applied.

Figure 5 shows considerable variation across countries: while most countries display strong and moderate household economies of scale, there are also countries with no household economies of scale, or even with positive *HHSIZE* effects. Most countries (15 out of 25) in the EU sample show a negative and significant *HHSIZE* effect, which is in line with our initial hypothesis.

An increase in the EU household size by one member brings about a 5%-reduction in the carbon footprint and 7%-reduction in the energy footprint (Figure 5, in blue). The countries with the strongest household economies of scale include Luxembourg, Slovenia and Czech Republic, described by negative and significant *HHSIZE* at the 5% level coefficients, ranging from −0.11 to −0.13. The coefficients suggest that an increase in household size by one member decreases the per capita carbon and energy footprint by up to 12% (taking the exponent of the coefficient). Other countries—such as Belgium, Germany, Finland, France and the United Kingdom—are characterized by moderate household economies of scale. Their *HHSIZE* effects vary between −0.03 and −0.10, suggesting that an increase in the household size by one member reduces per capita carbon and energy footprints by 3–10%.

However, Figure 5 also points to countries—such as Cyprus and Lithuania—with no visible household economies of scale for the total carbon and energy footprint per capita. Against our initial hypothesis, several countries even stand out with positive and significant *HHSIZE* coefficients such as Spain, Italy, Greece, Portugal and Croatia. There are no significant differences between the *HHSIZE* coefficients for carbon and energy footprints in most countries (see SM Figure S9), suggesting similar economies of scale for energy and emissions.

The 95% confidence intervals of the *HHSIZE* coefficients in blue and red are also largely overlapping across EU countries, meaning that there is no significant difference of the *HHSIZE* effect magnitude regardless of whether or not the interaction term is included.

The following two sections explore these inter-country differences (1) for different consumption domains; and (2) in their interaction with population density. We consider contextual differences between countries to discuss these results in the Discussion section.

#### *3.3. Household Economies of Scale by Consumption Categories*

Figure 6 provides an overview of the *HHSIZE* regression coefficients across the various consumption categories with the logarithm of the carbon footprint by consumption category as a dependent variable. We note substantial differences between EU countries within each consumption category, both in terms of household economies of scale and carbon contribution. Figure 7 shows the *HHSIZE* regression coefficients and their 95% confidence intervals across the EU countries. A detailed overview of the sectors included in each consumption category can be found in the supplementary material.

The coefficient ranges highlight the differences of the magnitude of household economies of scale and point to some of the products and services associated with higher sharing rates compared to others. For example, the strongest household economies of scale are noted for housing categories such as rents and mortgages, electricity and household services. These housing categories have median carbon shares of 5%, 8% and 4%, respectively (Figure 6). At the same time, some of the weakest household economies of scale are noted in the transport domain, which is also characterized with the highest median carbon share of 25%.

(**b**)

**Figure 6.** A summary of the *HHSIZE* regression coefficients of EU countries (displayed on Figure 7) with the logarithm of the per capita carbon footprint by consumption category as dependent variables (**a**) and the proportion of the individual consumption categories of the overall carbon footprint of EU countries (**b**). The categories are ordered by the median *HHSIZE* effect depicting the importance of the household economies of scale from the strongest to the weakest.

**Figure 7.** *Cont.*

**Figure 7.** *Cont.*

**Figure 7.** Regression coefficients for household size effects on the logarithm of the per capita annual carbon footprint by consumption category. Categories: (**a**) Actual and imputed rent; (**b**) Electricity; (**c**) Household services, e.g., waste treatment, water supply, insurance; (**d**) Food; (**e**) Gas, liquid and solid fuels; (**f**) Other services and manufactured products; (**g**) Appliances, equipment and furniture; and (**h**) Transport. The categories are ordered by the median *HHSIZE* effect depicting the importance of the household economies of scale from the strongest to the weakest. Household weights provided by the HBS have been applied.

#### 3.3.1. Housing

Substantial household economies of scale are noted for home- and housing-related categories, particularly housing rent or real estate services (Figure 7(a)), electricity (Figure 7(b)) and household services such as waste treatment, water supply and insurance (Figure 7(c)). The *HHSIZE* effect associated with rents and mortgages vary between −0.08 (for Estonia) and −0.47 (for the United Kingdom) (the category includes development of building projects, management and support services). This means that an increase in the household size by one member is associated with an 8–37% reduction (taking the exponent of the coefficient) in the carbon footprint associated with real estate services. With regards to electricity, negative and significant *HHSIZE* coefficients between −0.05 for Estonia and −0.23 for the United Kingdom and Slovenia are noted; this suggests a 3-21% reduction in the related per capita carbon footprint with an additional household member. Cyprus and Sweden stand out with insignificant *HHSIZE* effects (the Swedish HBSs offered a lower level of consumption detail aggregating all home-related energy consumption). Similarly, strong household economies of scale are noted in terms of household services with the largest (negative) coefficients noted for Slovakia (−0.28), Lithuania and Estonia (−0.25). That is, the increase of household size by one member results in a reduction of the household services emissions by as much as 24%.

While similar ranges of the household economies of scale are noted for electricity and housing fuels (Figure 6), the strong positive outliers in terms of *HHSIZE* effects lower the median household economies of scale for housing fuels. We found negative and significant *HHSIZE* coefficients varying between −0.17 (for Czech Republic) and −0.04 (for Germany and Slovenia) across most EU countries (Figure 7(e)). The positive and significant effects—especially for Malta and Cyprus—could potentially be explained by product allocation inconsistencies of fuel use from marine bunkers [45] (where we do not expect household economies of scale) being inaccurately allocated to household fuels in the national accounts.

The strong household economies of scale in the household domain are in line with prior claims that household size is one of the largest determinants of domestic energy consumption [48] and shelter carbon footprints [4]. They result from the sharing of space and embodied energy in buildings, energy for heating, cooling, lighting and shared appliances and activities [9].

#### 3.3.2. Food

Food-related economies of scale in larger households may occur when household members prepare (e.g., when sharing food ingredients) and manage food together (e.g., when they better manage food waste [49], which we were not able to test in this study). Furthermore, larger households may be more likely to buy food in larger quantities, which may cost less per unit [50]. While this may allow for a reduction in embodied emissions, e.g., through reduced packaging, in our model we were unable to capture any differences in carbon intensities within food products. As we applied monetary-based carbon intensities, any reduction in food spending due to lower price is reflected in our model in lower carbon footprints, which may be misleading in cases of large price variation within products. Finally, there may be other carbon reduction potential associated with the use of common utensils, appliances for cooking and storing food and shared shopping for larger households. These effects are included in the estimates for housing and transport in our analysis.

Figure 7(d) denotes significant negative coefficients between −0.20 (for Slovenia) and −0.05 (for Denmark, Spain and Greece), suggesting that an increase in the household size with one member leads to a decrease in the food-related carbon footprint by 5–18%.

#### 3.3.3. Equipment, Transport and Other Consumption

While we expected substantial household economies of scale for shared appliances, equipment and furniture, we find that most EU countries report positive *HHSIZE* regression coefficients (Figure 7(g)). A potential explanation of this result is that while some appliances, machinery and furniture are shared within households, the sectoral detail of EXIOBASE does not allow us to distinguish between typically shared and individually-used items. Furthermore, this category only includes the purchase of items (and hence their embodied carbon footprint), while the direct emissions associated with the use phase is included in the analysis of electricity and housing fuels. Notable exceptions with moderate household economies of scale for home appliances and equipment include Luxembourg and Slovenia with regression coefficients of −0.09 and −0.05, respectively.

We did not find consistent household economies of scale for transport—with positive or insignificant coefficients for all EU countries (Figure 7(h)). Larger households have potential to stabilize car ownership [51,52], where additional household members do not require additional number of cars. Prior longitudinal analysis of French car sharing practices shows that while household car sharing is a regular practice concerning almost half of the French car fleet, this trend is decreasing [53]. Their analysis further highlighted gender differences in terms of car sharing within households, with a higher proportion of main users being male and a higher proportion of secondary users being female [53].

However, our analysis suggests that the benefits of shared travel within the household are not realized in many countries in Europe (Figure 7(h)). The lack of household economies of scale with regards to personal vehicles and equipment (SM4) suggests that additional household members may also activate a need for another household car, e.g., following a partnership formation [54]. There may also be offsetting effects such as using the car more intensively or having a larger car in single-car households [55]. Furthermore, no household economies of scale were noted for other transport modes such as air travel, for which there is a growing demand with rising incomes in Europe [31].

Finally, we did not observe substantial household economies of scale with regards to other services and manufactured products (Figure 7(f)). There may also be additional factors that strongly correlate with household size (e.g., demographic, social, cultural and economic characteristics) that we could not include in our model due to lacking data, which may explain the variation in coefficients.
