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 While the EUROSTAT HBS is compiled for cross-country comparison purposes and aims for harmonization, there remains imperfect harmonization in the frequency of surveys, timing, content and structure between countries and years [@eurostat_eu_2020]. Some types of households may also be excluded from the samples, including super-rich households, for example in Germany, which excludes households with over €18,000 monthly net income [@eurostat_eu_2020]. Sensitive goods and services, such as alcohol, may be under-reported in household budget surveys, while expenditure on infrequent purchases such as a vehicle may create artificially large expenditure differences between households depending on the timing of the survey [@eurostat_eu_2020]. The EUROSTAT HBS macro-data also does not report direct foreign purchases, and we assumed that the expenditure shares between income quintiles of direct final demand for foreign goods and services was the same as direct final demand for domestic goods and services.
 
-We used EXIOBASE as the EE-MRIO for this study because of its European focus, with nearly all countries in the EUROSTAT HBS also found as stand-alone countries in EXIOBASE, its detailed satellite extension data, and its year coverage (specifically version3.7, industry-by-industry), but there are well known limitations when using and selecting an EE-MRIO [@moran_convergence_2014]. The production sectors in EXIOBASE are harmonized across countries and years, but needing to map the EUROSTAT HBS to EXIOBASE meant that the most recent year of 2015 could only use the industry-by-industry version of EXIOBASE version3.7. This version assumes fixed product sales. Furthermore, because EXIOBASE version3.7 is extrapolated beyond 2011, caution should be used when comparing results over time. This, and the fact that harmonization guidelines in the EUROSTAT HBS have changed over time, were the justification for presenting only the 2015 results in the main paper, and presenting 2005 and 2010 results only here in the SI. We also show 2010 results using the product-by-product version of EXIOBASE version3.7 in the final section of this SI document. 
+We used EXIOBASE as the EE-MRIO for this study because of its European focus, with nearly all countries in the EUROSTAT HBS also found as stand-alone countries in EXIOBASE, its detailed satellite extension data, and its year coverage (specifically version3.7, industry-by-industry), but there are well known limitations when using and selecting an EE-MRIO [@moran_convergence_2014]. The production sectors in EXIOBASE are harmonized across countries and years, but needing to map the EUROSTAT HBS to EXIOBASE meant that the most recent year of 2015 could only use the industry-by-industry version of EXIOBASE version3.7. This version assumes fixed product sales. Furthermore, because EXIOBASE version3.7 is extrapolated beyond 2011, caution should be used when comparing results over time. This, and the fact that harmonization guidelines in the EUROSTAT HBS have changed over time, were the justification for presenting only the 2015 results in the main paper, and presenting 2005 and 2010 results only here in the SI. We also show 2010 results using the product-by-product version of EXIOBASE version3.4 in the final section of this SI document. 
 
 The correspondence between the EUROSTAT HBS COICOP consumption categories and the industry production sectors in EXIOBASE is not one-to-one. Both the EUROSTAT HBS and EXIOBASE are limited in their consumption category/production sector level of detail. The share of each consumption category/production sector in the total amount of expenditure is also not identical between the HBS and EXIOBASE. As discussed in the 'methods for main paper results' section of this SI document, there are alternative methods for stratifying the EXIOBASE household final demand expenditure: one that keeps the EXIOBASE production sector shares of total expenditure intact, and one that keeps the HBS consumption category shares of total expenditure intact. Our results in the main paper use the first method, keeping the EXIOBASE sectoral shares of total expenditure intact, which means that the total footprint is identical to when it is calculated in EXIOBASE without any stratification by income quantile. The alternative method, on the other hand, results in a different total footprint because a different amount of final demand expenditure in each sector is multiplied by the same original 'direct and indirect supply chain' intensities, but stays faithful to the original HBS consumption category shares of total HBS expenditure. We show the alternative method below, and some results in the last sections of this SI document. We also stay at a relatively aggregated level for our energy and carbon footprints, as our primary goal was to connect aspects of the aggregate European household environmental footprint distribution with the decarbonisation and minimum energy use scenarios. Work specifically investigating distributional aspects of the European carbon footprint, sometimes at a finer sectoral level than we do here, can be found in the refs. [@ivanova_unequal_2020; @gore_t._confronting_2020; @sommer_carbon_2017] and [@bianco_understanding_2019].