*3.4. Household Size and Population Density Interaction*

In this section, we discuss the magnitude and significance of interaction effects depicted in Figure 8 (*HHSIZE*×*DENSE)* across EU countries (the model in blue in Figure 5, controlling for income, household size, population density and region). The majority of EU countries show insignificant interaction coefficients, suggesting no significant differences in the *HHSIZE* effect between densely and sparsely populated areas in the EU.

**Figure 8.** Interaction effect between household size and population density (*HHSIZE*×*DENSE*) across countries. Dependent variables—the log of per capita carbon (**a**) and energy (**b**) footprints. We excluded the *HHSIZE*×*INTERMEDIATE* interaction term as no significant differences of the household size effects between intermediately and sparsely populated areas were noted. See Data and Methods for the model specification. Household weights provided by the HBS have been applied.

However, several countries such as Czech Republic and Germany demonstrate negative *HHSIZE* effects and positive interaction effects (*HHSIZE*×*DENSE*), both of which are significant at the 5% level. This result suggests that adding another household member in a sparsely populated (rural) environment is associated with larger household economies of scale compared to doing so in a densely populated (urban) environment. While adding a household member to a rural household reduces per capita energy footprints by 7–11%, adding a household member to a dense urban household reduces them by 4–7% (Figure 5, Figure 8). The lower household economies of scales in densely populated environments are noted particularly for electricity, housing fuels, appliances, equipment and furniture, and food. This is plausible because these types of environmental impacts tend to be higher in rural areas in these countries, compared to urban areas, so that greater household sizes can reduce these impacts more in rural areas.

We find negative interaction effects for other countries, particularly for Greece, Estonia, Cyprus and Croatia, suggesting that households in densely populated regions encounter higher household economies of scale in these countries, compared to sparsely populated areas. The analysis of consumption categories suggests that these negative interaction effects are primarily associated with consumption of household services (e.g. water and waste), other services and manufactured products.

These negative interaction effects may contradict our previous hypothesis that the interaction between household and urban economies of scale leads to higher household economies of scale in rural and sparsely populated areas [24,25]. However, these are all countries where per capita environmental footprints tend to be higher in urban compared to rural areas (SM2), so it is plausible that adding a household member in urban areas leads to greater reductions of per capita environmental footprints there compared to rural areas.

#### **4. Discussion and Conclusions**

#### *4.1. Household Dynamics within the EU*

One-person households are the most carbon and energy intensive in per capita terms, contributing to 17-18% of the EU total carbon and energy footprint. The per capita carbon and energy footprint of a one-member household is about twice that of a five- or more person household in the EU. The share of those living in one-person households varies from 40% in Finland and Denmark to 19% in Spain, Malta and Romania, with an EU average of 31% from the total number of households.

We note substantial differences in household sizes across various EU countries as well as the role of household size for per capita carbon and energy impacts. Adding an additional household member results in a carbon and energy reduction of above 10% on average in some EU countries. This result confirms that shrinking household sizes across the EU and globally are of key concern for climate change mitigation. They should thus be adequately considered in modelling work, e.g., prospective scenarios of socio-demographic trends and their influence on carbon and energy footprints and pathways to meet carbon targets. Household dynamics should also be regarded in the context of mitigation solutions and experimentation with alternative household formations.

Substantial differences in the household economies of scale are noted for various consumption domains, with a higher potential in housing-related items such as electricity use (up to 21% reduction with an additional household member), real estate services (up to 37%) and household services such as waste collection and water supply (up to 24%). Food and fuel consumption show moderate household economies of scale with up to 18% reduction of the carbon footprint with an additional household member in some EU countries. We note lower or no household economies of scale in other domains of consumption (e.g., transport, manufactured products and services), where an increase in the household size likely corresponds to an increase in consumption needs (e.g., second household vehicle, more clothing, educational or health services with an additional household member).

Furthermore, the majority of EU countries have comparable household economies of scale between urban and rural areas (insignificant interaction term). Other countries such as Czech Republic and Germany report higher household economies of scale in sparsely populated areas, in line with prior evidence [24] (positive interaction term). We also found a negative interaction effect between household size and population density for a third group of countries, which counters our original hypothesis; yet, these are countries in which per capita emissions and energy use tend to be higher in urban compared to rural areas, unlike most other EU countries.
