I-O basic equation

The basic I-O relationship can be expressed as (UN 1999): 𝐱 = (𝐈 − 𝐀)−1_{𝐘 = 𝐋𝐘}

where 𝐱 is the gross output, 𝐀 is the domestic input coefficients of matrix, 𝐘 is the final demand, and 𝐋 is the Leontief inverse matrix representing structural interdependencies.

The satellite accounts of GHG emissions14 _{is then linked to the I-O model to form a so-}

called environmentally extended I-O analysis (Leontief 1966; Leontief and Ford 1970; UNSD 2017). By applying an emission intensity matrix 𝐪 (kg/SEK) to the equation above, the carbon footprint 𝑄 can be formulated as:

𝑄 = 𝐪𝐋𝐘.

Emissions embodied in imported commodities 𝑄_𝑀 resulting from domestic consumption are handled separately. In this study, we use an imported emission intensity matrix 𝐪_𝑀 from the PRINCE project (Palm 2018) which utilised the EXIOBASE model (Tukker 2013). 4.2.2 Virtual laboratory

Constructing MRIO tables can be time-consuming and labour intensive, but in recent years, the use of virtual laboratory technology for compiling sub-national I-O tables has become an alternative solution, reducing costs related to MRIO table development (Faturay et al. 2017). Virtual laboratories started in Australia (Lenzen et al. 2014), and since then have spread to other countries, such as Indonesia (Faturay et al. 2017), China (Wang 2017), Japan (Wakiyama et al. 2018), Taiwan (Faturay et al. 2018) and the USA (Faturay et al. 2019). The applications from these labs have resulted in various analyses, including of regional employment multipliers in Indonesia, carbon emissions in China, food loss in Japan, disaster impact assessments in Taiwan, and renewable energy in the USA. Since work in a virtual laboratory significantly accelerates outcomes in MRIO- related research, we, therefore, chose to build a time-series of sub-national MRIO tables for Sweden in a virtual laboratory, called the SwedenLab.

The SwedenLab offers flexibility in customising regional and sectoral classifications, incorporating data constraints, and selecting particular years of MRIO tables. As with other labs, constructing a sub-national MRIO database in the SwedenLab requires

14 _{The satellite accounts refer to data from the System of Environmental-Economic Accounts (SEEA) that}

was established in the revision of the System of National Accounts in 1993 at global level to link the environment to the economy in the same framework. Sweden started producing data from the SEEA in

national I-O tables. These national I-O tables are then disaggregated into sub-national MRIO tables using non-survey regionalisation methods (Sargento et al. 2012), which is a widely used technique for generating sub-regional MRIO tables. A total of 10 different non-survey methods, such as the location quotients (LQ) and cross-hauling variants, are available in the SwedenLab. The user’s choice of non-survey method may have an impact on the results. In this study, we chose Flegg’s Location Quotient15 _{(FLQ, Flegg and Webber}

2000) to regionalise the Sweden national I-O table due to the superior performance of the FLQ over basic regionalisation methods (such as Simple LQ and Cross Industry LQ) for estimating inter-regional input coefficients (Bonfiglio and Chelli 2008). The regionalisation of the national I-O tables into sub-national MRIO tables is accomplished using regional weights, describing the relative size of industries of a region in comparison to the nation.

At this stage, the MRIO table can be tailored using specific classifications. The available sectoral classifications for SwedenLab are 21 sectors, 59 sectors, and 821 sectors, and the regional classifications are available for 8 regions, 21 regions, and 291 regions. However, the current data is not quality assured at the maximum level of detail. It is also possible to construct MRIO tables beyond these classifications by creating a concordance matrix connecting their own classifications with the root classification. The use of a root classification is the key to the lab’s flexibility since it captures the maximum regional and sectoral classifications. From this root, more aggregated sectors and regions can be selected to represent the final table. The root classifications are extracted from labour data that is available at a satisfactory level of disaggregation for all regions and sectors. Labour data also becomes the proxy quantity for the regionalisation process. The outcome of this regionalisation process is used as an initial estimate for the MRIO table. The initial estimate is a preliminary user-specific MRIO table that serves as an input into a reconciliation process, where a set of constraints and balanced conditions are enforced. Reconciliation is carried out using a code system known as AISHA (Geschke et al. 2014). The MRIO tables need constraints to control elements in the final demand, value-added, and trade blocks. For example, the detailed GDP for Stockholm are used for constraining

elements in the Stockholm’s final demand block. Users must also consider the availability of data constraints. If the data are available at the county level, users should not attempt to create MRIO tables capturing municipalities. In this study, the MRIO tables consist of 59 sectors (at the county level) of 21 regions for the years from 2008 to 2016, due to data only being available up to that point.

It should be noted that the SwedenLab allows users to integrate new datasets and update existing constraints. Incorporating new data into a virtual laboratory, however, requires an in-depth understanding of programming workflow (Geschke and Hadjikakou 2017). For example, users have to be familiar with Matlab software, and ALANG files. Given the complexity of the virtual laboratory framework, working collaboratively with researchers who are already familiar with the lab’s environments is preferable. The collaborative work undertaken within the virtual laboratory community has resulted in at least 30 published articles (see Wiedmann 2017 for complete list).

4.2.3 Data sources

All data for this study come from Statistics Sweden (Statistics Sweden 2019). National I- O tables for Sweden are available for 2008–2016, consisting of 59 sectors. The currency unit is 1 million Swedish Krona (SEK), the final demand has eight fixed components16_{, and}

the primary inputs have twelve fixed categories17_{. Statistics Sweden publishes national}

input-tables on a regular basis, once a year. In addition, we utilise labour survey data to regionalise national I-O tables. Table 4.1 shows the primary data for the SwedenLab. Two regional datasets are available to use: disposable income (for constraining the consumption expenditure by households in the final demand matrix), and aggregated value-added (for constraining the value-added matrix). Moreover, regional GHG

16 _{Final consumption expenditure by households; Final consumption expenditure by non-profit}

organisations serving households (NPISH); Final consumption expenditure by government; Gross fixed capital formation by industry; Gross fixed capital formation by government; Changes in inventories; Acquisitions less disposals of valuables; and Export.

17 _{Wages and salaries; Employers' social security contributions; Consumption of fixed capital; Operating}

surplus and mixed income, net; Other taxes on production; Other subsidies on production; Customs; Taxes; Subsidies; Value-added tax (VAT); Direct purchases abroad by residents; and Purchases on the domestic

emissions presented in CO2 equivalents are used as satellite accounts. Since all regional

data consist of 21 counties, we generated Sweden MRIO tables at this level of detail. To measure the effects of international trade on Sweden’s regional emissions, we utilise carbon intensity information from PRINCE project (Palm 2018).

Table 4.1. Primary data for the SwedenLab.

Data Years Regions Sectors _constrained MRIO part

1. National I-O tables 2008-2016 1 59 ID, FD, VA, Imp, Exp, _GO

2. Disposable income 2008-2016 291 1 FD

3. Value-added 2008-2016 291 2 VA

4. Labour survey 2008-2016 291 821 _{regionalisation} Proxy for

5. GHG emissions 2008-2016 21 17 Satellite accounts

Note: All data comes from Statistics Sweden. ID = Intermediate Demand, FD = Final Demand, VA = Value- Added, Imp = Import, Exp = Export, and GO = Gross Output. The text under column header “MRIO part constrained” describes the specific MRIO elements that are constrained by the respective data source. The text “Proxy for regionalisation” means that the respective data source was used in the non-survey approach for disaggregating the national I-O tables into sub-national MRIO tables.

4.3 Results