si.Rmd

---
title: "The energy and carbon inequality corridor for a 1.5 degree compatible and just Europe: Supplementary Information"
author:
- Ingram S. Jaccard:
    email: jaccard@pik-potsdam.de
    institute: [PIK]
    correspondence: false
- Peter-Paul Pichler:
    email: pichler@pik-potsdam.de
    institute: [PIK]
    correspondence: false
- Johannes Többen:
    email: toebben@pik-potsdam.de
    institute: [PIK, GWS]
    correspondence: false
- Helga Weisz:
    email: weisz@pik-potsdam.de
    institute: [PIK, HU]
    correspondence: false
institute:
- PIK: Social Metabolism and Impacts, Potsdam Institute for Climate Impact Research,
    Member of the Leibniz Association, PO Box 60 12 03, Potsdam, 14412, Germany
- HU: Department of Cultural History & Theory and Department of Social Sciences, Humboldt
    University Berlin, Unter den Linden 6, Berlin, 10117, Germany
- GWS: Gesellschaft für Wirtschaftliche Strukturforschung (GWS) mbH, Heinrichstraße
    30, 49080 Osnabrück, Germany
output:
  word_document:
    fig_caption: yes
    reference_docx: ../templates/template.docx
    pandoc_args:
    - --lua-filter=../templates/scholarly-metadata.lua
    - --lua-filter=../templates/author-info-blocks.lua
    - --lua-filter=../templates/pagebreak.lua
bibliography: references.bib
csl: ../templates/vancouver.csl
content: |
  x pages, x tables, x figures
always_allow_html: yes
---

Content: `r rmarkdown::metadata$content`

```{r setup, echo = FALSE, include = FALSE, message = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  warning = FALSE,
  message = FALSE,
  echo = FALSE,
  comment = "#>",
  fig.path = "../figures/",
  dpi = 300
)

if (!require("pacman")) install.packages("pacman")
pacman::p_load(tidyverse,
               janitor,
               here,
               wbstats,
               ISOcodes,
               viridis,
               hrbrthemes,
               wesanderson,
               glue,
               ggridges,
               patchwork,
               kableExtra,
               flextable)

pal <- wes_palette("Cavalcanti1", 5, type = "discrete")
extrafont::loadfonts()

options(scipen=999)

```

```{r libraries}

library(here)
```

# Supplementary Materials and Methods

In this paper our first aim was to decompose an Environmentally-Extended Multi-Regional Input-Output (EE-MRIO) model's household final demand expenditure by income quantile, and then multiply this income-stratified expenditure by 'direct and indirect supply chain' environmental intensities calculated in the EE-MRIO to estimate income-stratified national household environmental footprints. An EE-MRIO can calculate national environmental footprints from final demand expenditure. Final demand expenditure on different production sectors, in monetary units, is multiplied by 'direct and indirect supply chain' environmental intensities per production sector to calculate the environmental footprint (for one year). The 'direct and indirect supply chain' intensities per production sector estimate the total physical amount of environmental extension, whether emissions, energy use, etc., anywhere along the supply chain per monetary unit of final demand expenditure. In this way, the global amount of environmental pressure in that year is allocated to each country based on their final demand expenditure (this 'footprint' approach is also called consumption-based accounting as opposed to territorial-based accounting). The 'direct and indirect supply chain' intensities per production sector are calculated using standard EE-MRIO calculations. 

The final demand expenditure, and thus the national footprint, is typically disaggregated into several final demand categories, including households, non-profits serving households, government, gross-fixed capital formation, change in inventories and valuables. To the authors' knowledge, current publicly available EE-MRIOs do not decompose their final demand expenditure by income quantile. The underlying distribution of final demand expenditure and footprint across income groups is therefore hidden. In order to decompose the EE-MRIO final demand expenditure and footprint by income quantile, a second data input is needed with information on the income/expenditure distribution. This could be a household budget survey (HBS) decomposed by income quantile or, at a more aggregate level, the national income distribution. In this paper we use:

1) EE-MRIO: EXIOBASE version3 ixi, from: https://zenodo.org/record/3583071#.XjC7kSN4wpY [accessed on 12.03.2020] [@stadler_exiobase_2018 @stadler_exiobase_2019]

2) HBS: European household budget survey from EUROSTAT, macro-data, from : https://ec.europa.eu/eurostat/web/household-budget-surveys/database [accessed on 22.05.2020] [@eurostat_database_nodate]

We discuss each of these in turn, including additional data inputs needed to complement the HBS. We then present our methodology for our results in the main paper, and data gaps and limitations. The final sub-section in 'supplementary materials and methods' presents an alternative methodology, and the final section of this supplementary information document presents supplementary results from the methodology used in the main paper and the alternative methodology. The whole analysis was performed in RStudio [@r_core_team_r:_2020], using a variety of R packages [@wickham_welcome_2019 @firke_janitor:_2021 @muller_here:_2020 @piburn_wbstats:_2020 @buchta_isocodes:_2020 @garnier_viridis:_2018 @rudis_hrbrthemes:_2020 @ram_wesanderson:_2018 @hester_glue:_2020 @wilke_ggridges:_2021 @pedersen_patchwork:_2020 @zhu_kableextra:_2020 @wickham_readxl:_2019 @gohel_flextable:_2021 @south_rworldmap:_2016 @arnold_ggthemes:_2021].

## EXIOBASE

We use standard input-output calculations to calculate 'direct and indirect supply chain' intensity vectors in EXIOBASE [@miller_input-output_1985]. EXIOBASE publishes the A matrix, the final demand matrix, the satellite extensions matrix, and satellite extensions direct from final demand matrix. We use the industry-by-industry (ixi) EXIOBASE data tables from EXIOBASE version3. This means 163 industry production sectors and 6 final demand categories for 49 regions worldwide (44 countries and 5 rest-of-world regions), from 1995 - 2016. All monetary units are in million current Euros. Stadler et al. (2018) @stadler_exiobase_2018 describe the EXIOBASE version3 compilation procedure in detail, including nine supporting information documents with further detailed information on the compilation of the monetary tables (S1), energy (S2), emissions (S3), and others. 

For each year, we first load the A matrix and calculate the Leontief inverse (the inverse of the A matrix). We load the final demand matrix and calculate total output ($x$) by pre-multiplying the Leontief inverse ($L$) by the row sums of the final demand matrix ($Y$): 

$$
x = L ° sum(Y)
$$

We then load the satellite extensions matrix and extract the relevant extensions. To calculate direct intensity vectors ($DIV$) we divide the satellite extension vectors ($f$) by total output ($x$): 

$$
DIV = f/x
$$

The 'direct and indirect supply chain' intensity vectors ($TIV$) are calculated by pre-multiplying the direct intensity vectors ($DIV$) by the Leontief inverse ($L$):

$$
TIV = DIV ° L
$$

The footprint is then calculated by row-wise multiplying the TIV by final demand:

$$
fp = TIV * Y
$$

Before that final step, however, we decompose national household final demand expenditure by income quintile according to the structure of the EUROSTAT household budget survey, explained in the 'EUROSTAT HBS' section below. 

The results in the main paper also present the footprint broken down by its domestic, other European, and non-European parts. To calculate these domestic and foreign parts of the footprint, we row-wise multiply the direct intensity vectors ($DIV$) by the Leontief inverse ($L$):

$$
TIV breakdown = DIV * L
$$

### Environmental extensions

The environmental extensions we use are emissions of CO2-equivalence (in kilograms) and gross total energy use (in terajoules). We create the CO2-equivalence extension by summing together the greenhouse gases CO2, CH4, N2O, SF6, HFCs, and PFCs, from combustion, noncombustion, agriculture and waste. We use Global Warming Potential (GWP) values for a 100-year time horizon taken from the IPCC Fifth Assessment Report [@myhre_g._anthropogenic_2013 (p.73-79)]: 28 for CH4, 265 for N2O and 23500 for SF6 (HFCs and PFCs are in CO2-equivalence already in the EXIOBASE environmental extensions). 

The 'gross total energy use' extension in EXIOBASE converts final energy consumption in the IEA energy balance data from the territorial to residence principle following SEEA energy accounting principles. In their Supporting Information 2, Stadler et al. (2018) @stadler_exiobase_2018 describe the compilation of the energy extensions in EXIOBASE version3. Energy supply and use tables from the International Energy Agency (IEA) are converted from the territory to the residence principle, before being allocated to the EXIOBASE industries and final demand categories. 

The conversion to the residence principle means that the EXIOBASE energy extensions refer to the functional border of a country's economy. In this case, the system border is defined by the 'residence' of the agent. This means that energy supply and use from international transport by ships, airplanes, fishing vessels, cars and trucks are allocated to the resident units of a country, independent from where these activities take place. In EXIOBASE version3, because emissions from these transport activities are estimated from the energy extensions via emission factors, the emissions extensions follow the residence principle as well. 

### Environmental extensions direct from households

For CO2-equivalence emissions and energy use direct from households, the EXIOBASE extensions provide one number of physical emissions and energy use direct from households per country. This number is made up of some mix between, primarily, direct household vehicle fuel use and direct household fuel use for housing heating and cooling, along with some other, smaller miscellaneous uses. To estimate the split between these three activities, we use two further EUROSTAT emissions and energy tables to split 'Total activities by households' between heating/cooling (HH_HEAT), transport activities (HH_TRA), and other (HH_OTH). Full definitions of what is included in these can be found in EUROSTAT's 'manual for air emissions accounts' (2015, p.66) @eurostat_manual_2015. While this disaggregation exists for nearly all EUROSTAT HBS countries, 2015 is the earliest year in our sample with complete coverage (except for Turkey in energy, which we impute using the Bulgarian splits). Therefore, we also use the 2015 splits between these 3 categories for our 2005 and 2010 estimates (the 2005 and 2010 results are shown only in this SI document). The two data tables are:

1) For energy, the EUROSTAT data table 'Energy supply and use by NACE Rev. 2 activity' [env_ac_pefasu] at: http://appsso.eurostat.ec.europa.eu/nui/show.do?dataset=env_ac_pefasu [accessed on 03.06.2020]. [@eurostat_eurostat_2020]

2) For emissions to air, we download the EUROSTAT data table 'Air emissions accounts by NACE Rev. 2 activity' [env_ac_ainah_r2] at: https://appsso.eurostat.ec.europa.eu/nui/show.do?dataset=env_ac_ainah_r2&lang=en [accessed on 03.06.2020]. [@eurostat_eurostat_nodate]

## EUROSTAT HBS

The EUROSTAT HBS compiles national household budget surveys from European countries. Countries provide EUROSTAT with their HBSs in micro-data form, and EUROSTAT has aggregated and published these survey data in macro-data form every five years since 1988. Of the publicly available data tables, we use two:

1) 'Mean consumption expenditure by income quintile (hbs_exp_t133)'

2) 'Structure of consumption expenditure by income quintile and COICOP consumption purpose (hbs_str_t223)'

'Mean consumption expenditure by income quintile' is expressed in purchasing power standards (PPS) per year, country and income quintile, in two possible units; per household and per adult equivalent. Purchasing power standard (PPS) is a common currency measure that eliminates differences in national price-levels. The income quintiles are determined by household, ie. all households in the sample are ranked by income and evenly distributed into five quintiles, thus there are the same number of households in each income quintile. For per adult equivalent, the mean consumption expenditure by income quintile is adjusted for household size between countries, years, and income quintiles, using the modified OECD scale: the first adult in the household is given a weight of 1.0, each adult thereafter 0.5, and each child 0.3 @eurostat_description_2016. 

The 'Structure of consumption expenditure by income quintile and COICOP consumption purpose' table gives the distribution of consumption expenditure across COICOP consumption categories in each income quintile, expressed in 'parts per mille (pm)'. There are three 'levels' of COICOP breakdown. All countries have level 1 (12 consumption categories) and 2, but there are only a few with level 3. For the current analysis, we select our own mix of COICOP level 1 and 2. We use COICOP level 1, except for the categories of food (CP01), housing (CP04) and mobility (CP07), where we use level 2. 

This is primarily because of the diversity of level 2 categories, especially within those three aggregate level 1 categories. This is most clearly seen in the housing category, where, at level 2, housing is broken down into: 'Actual rentals for housing' (CP041), 'Imputed rentals for housing' (CP042), 'Maintenance and repair of the dwelling' (CP043), 'Water supply and miscellaneous services relating to the dwelling' (CP044), and 'Electricity, gas and other fuels' (CP045). Mapping all shelter-related EXIOBASE production sectors only to the HBS level 1 'housing' consumption category (CP04) would obscure the difference between level 2 categories with extremely different effects on the footprint (electricity production vs. rental payments). The COICOP consumption categories we thus use are: CP011 ('Food'), CP012 ('Non-alcoholic beverages'), CP02 ('Alcoholic beverages, tobacco and narcotics'), CP03 ('Clothing and footwear'), 'rent' (we collapse CP041 with CP042), CP043, CP044, CP045, CP05 ('Furnishings, household equipment and routine household maintenance'), CP06 ('Health'), CP071 ('Purchase of vehicles'), CP072 ('Operation of personal transport equipment'), CP073 ('Transport services'), CP08 ('Communications'), CP09 ('Recreation and culture'), CP10 ('Education'), CP11 ('Restaurants and hotels'), CP12 ('Miscellaneous goods and services').

National environmental footprints are often expressed in per capita terms; the national environmental footprint divided by total national population. This masks any underlying inequality in per capita footprints across income groups. As mentioned above, the EUROSTAT HBS 'mean consumption expenditure by income quintile' macro-data table is expressed only per household and per adult equivalent, but not per capita. We use per adult equivalent as our unit of analysis throughout the paper, and in order to express our footprint estimates per adult equivalent, we needed the total number of private households in each country and year, and for this, two additional data tables were needed. We used:

1) The 'lfst_hhnhtych' table from EUROSTAT, selecting all available years and total households [accessed on 04.05.2020]. [@eurostat_eurostat_nodate-1]

2) Norway is missing from the 'lfst_hhnhtych' EUROSTAT table. We download Norwegian data from the Norwegian statistical office: https://www.ssb.no/en/statbank/table/10986/. We select 'Private households', 'the whole country', no household type selection, all years (2005-2019), and continue with 'Table - Layout 1', then save the table as a 'Tab delimited without heading (csv)' file [accessed on 04.05.2020]. [@statistics_norway_10986:_nodate]
  
## Method for main paper results

For our results in the main paper, we first decompose the EXIOBASE national household final demand expenditure (before calculating the footprint) by income quintile, using the EUROSTAT HBS. We do this for 2005, 2010 and 2015, but only present 2015 in the main paper. The initial step is mapping the COICOP consumption categories in the HBS to the production sectors in EXIOBASE. Because the share of each consumption category/production sector in the total amount of expenditure is not identical between the HBS and EXIOBASE, there are two possible methods for decomposing the EXIOBASE household final demand expenditure: one that keeps the EXIOBASE production sector shares of total EXIOBASE expenditure intact (breaking the HBS consumption category shares), and one that keeps the HBS consumption category shares of total HBS expenditure intact (breaking the EXIOBASE production sector shares). 

Our results in the main paper use the first method, keeping the EXIOBASE production sector shares of total EXIOBASE expenditure intact. This means that the total footprint is identical to when it is calculated in EXIOBASE without any decomposition 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 production sector is now multiplied by the same original 'direct and indirect supply chain' intensity for that production sector. We present the alternative method and some results in the last sections of this document. 

In this current section we use a two sector toy model to illustrate the method behind the main paper results. In the two sector model, the term 'sector' represents HBS consumption categories/EXIOBASE production sectors that have already been mapped to each other. 

Step 1) Multiply 'mean consumption expenditure by income quintile' in purchasing power standard per household (pps hh) by the 'structure of consumption expenditure by income quintile and COICOP consumption purpose' (in 'parts per mille' or pm) to calculate the consumption expenditure structure in 'pps hh'. Then calculate the shares of each income quintile within each sector. Table S1 shows the two sector example, where 'pps hh' is multiplied by the shares of each sector ('parts per mille' divided by 1000) to calculate the expenditure on each sector per income quintile in 'pps hh' ('s1 (pps hh)' and 's2 (pps hh)'). 's1 (q share)' and 's2 (q share)' are each income quintile's share of the total amount of expenditure (in 'pps hh') on that sector, according to the HBS.

```{r tableS1, tab.cap = "**Table S1: HBS structure with calculations of quintile shares per sector.**"}

#"HBS structure with calculations of quintile shares per sector."

quintile = c("q1","q2","q3","q4","q5")
pps_hh = c(10,13,20,33,40)

pm_sector1 = c(200,300,400,500,600)
pm_sector2 = c(800,700,600,500,400)

hbs = data.frame(quintile, pps_hh, pm_sector1, pm_sector2) %>%
  mutate(pps_hh_sector1 = pps_hh*(pm_sector1/1000),
         sector_1_shares = pps_hh_sector1/sum(pps_hh_sector1),
         pps_hh_sector2 = pps_hh*(pm_sector2/1000),
         sector_2_shares = pps_hh_sector2/sum(pps_hh_sector2)) %>%
  mutate_if(is.numeric, round, digits = 2)

flextable(hbs) %>%
  autofit() %>%
  set_header_labels(quintile = "quintile", 
                    pps_hh = "pps hh",
                    pm_sector1 = "s1 (pm)",
                    pm_sector2 = "s2 (pm)",
                    pps_hh_sector1 = "s1 (pps hh)",
                    sector_1_shares = "s1 (q share)",