Appendix A Input-output modelling of the Scottish economy
Through the estimation of heat demand and the simulation of competition between boiler types, we can estimate how the boiler composition can change over time under the influence of policy portfolios aimed at heat decarbonization in Scotland. From the boiler composition, estimates for consumer investment in boilers and final energy demand, and therefore consumer expenditure, can be calculated. Based upon these model results, the wider economic impacts of heat decarbonization in Scotland can be estimated via Input-Output analysis and will yield impacts on employment and GVA (Scottish Government 2015).
The key input into this analysis was the Scottish Supply, Use and Input-Output table for 2017, which shows interlinkages between sectors, and how these combine to meet final demand for industrial output. Type I multipliers were taken from the published tables; as such, the economic impacts calculated include direct and indirect impacts only – the jobs and economic activity that is created/lost in the changed production of the goods/services for final demand, and those created/lost through supply chains (i.e. the production of intermediate goods/services which contribute in one way or another to production of the final output). Induced effects are excluded in our analysis – these are the multiplicative impacts which result from changes in employment via direct and indirect effects. For example, if net employment and aggregate wages in an economy are higher via direct and indirect impacts, those wages would ultimately be re-spent back into the economy, generating further demand for output and therefore employment. However, these induced effects are subject to some uncertainty (and substantial debate amongst economists), and for the sake of clarity are excluded from this analysis.
An input-output led approach like this is well-suited to short- and medium-term analysis such as that carried out in this report, which seeks to assess outcomes to 2030. The approach relies upon static input-output tables; the economic structure of the economy (i.e. the inter-sectoral supply chain linkages) do not change in this type of analysis, and this is a more important restriction the further into the future the analysis goes.
Other key characteristics of the analysis are described in more detail below.
A.1 Quantifying impacts
Direct impacts can broadly be defined as the effects of the changes in final demand for heating technology and fuels, excluding knock-on impacts in the wider economy. These further effects, indirect impacts, are felt through supply chains to the industries directly affected.
The method draws upon outputs from the heat technology modelling:
- Demand for different heating technologies;
- Costs of each heating technology, with content broken down by economic sector;
- Projections for fuel/electricity prices, sourced from BEIS.
Inputs are supplied for all three scenarios
The model inputs are populated for three scenarios (Subsidy, Regulation and Extended). The structure and nature of the inputs are the same across scenarios.
Characterisation of the supply chain
Initial mapping of each heating technology to economic sectors is based upon expert judgement, and reflects inputs used in previous similar modelling exercises. The further characterisation of the supply chain draws on the linkages implied in the Scottish Input-Output table for 2017.
Once the scenario inputs are characterised, the analysis of direct impacts then seeks to:
- apply evidence from Scottish Input-Output tables to identify impacts on value added;
- apply data on labour intensity to estimate the impact on Scottish employment.
The analysis was divided into four impacts; changes from reduced demand for high-carbon heating technologies, increased demand for low-carbon heating technologies, reduced demand for fossil fuels and increased demand for low-carbon fuels. Value added and employment effects are calculated for each, across each of the scenarios.
The direct impacts relate to the direct impacts of the shifts in consumer expenditure modelled over 2020-30. Indirect impacts are those that occur through supply chains to meet the changes in final demand over the same period.
Gross output effects are calculated by applying sector-by-sector Type I multipliers from the IO tables to the change in final demand in each economic sector, to understand how intermediate demand for other goods and services beyond final demand is affected. Employment impacts are calculated based upon the gross output effects and estimates of labour productivity in 2017 based upon gross output from the IO tables and employee data from NOMIS, the UK Office for National Statistics portal for labour market statistics.
Input-output coefficients tell us the proportion of intermediate inputs used in production. These vary across sectors because different sectors will have different input requirements for production. IO coefficients are calculated by dividing expenditure on intermediate purchases by the value of Total output.
The matrix of IO coefficients used in the analysis contains more sectoral detail. The Type I Leontief inverse table is 98 x 98 where rows correspond to the input sectors and the columns correspond to the output sectors.
The Leontief inverse
As defined by the OECD, the Leontief inverse shows "the input requirements, both direct and indirect, on all other producers, generated by one unit of output". It is therefore central to the analysis as it defines the sensitivity of the model economy to scenario changes. It is derived by matrix inversion using IO coefficients. Specifically, it is derived using the expression . Where L is a 98 x 98 matrix of coefficients, I is an identity matrix and A is a matrix of input-output coefficients.
A.2 Modelling assumptions
All modelling approaches require certain assumptions. The assumptions which are made shape the strength of the modelling approach to different tasks and the robustness to uncertainties about the future.
The approach is suited to impact estimation but not forecasting
The modelling carried out in this report adopts a constant 2017 version of the Scottish economy out to 2030. This is because the objective of the report is to identify accurate and robust impacts (i.e. difference from the baseline) rather than forecasts (e.g. the level of GDP in 2030).
The approach needs to make assumptions about accounting relationships in the economy
The modelling approach also needs to make a series of assumptions about accounting relationships within the economy. For instance, if the electrical equipment sector experiences a boost to output (and revenue), we need to build a picture of how that additional revenue is spent. The approach needs to know how much revenue gets taken as surplus by firms and how much gets spent on employees, inputs to production and taxes. Building this picture across all sectors of the economy, the approach characterises how sectors of the economy trade with one another.
The modelling does not capture changes to accounting relationships over time
These details are created in the modelling approach by using the existing Scottish Input-Output relationships. Crucially, the information is only available in historic data (the latest year at the time of analysis was 2017). This means that the modelling does not capture changes to accounting relationships over time.
For instance, suppose that because of technological change, the electrical equipment sector relies less on mining sectors and more on service sectors in future years. This would mean that, if the electronics sector is shocked in 2025, the approach would over-estimate the knock-on impacts on the mining sector and under-estimate the knock-on impacts on services sectors.
This being said, changes to accounting relationships in the wider economy over time are typically very gradual and the forecast period (2020-2030) does not extend extremely far into the future.
Ex-ante impact assessments require assumptions about the future
More generally, the results presented in this report are an ex-ante assessment (i.e. predicting future impacts) and should be interpreted as such. Ex-post impact assessments (i.e. evaluating past impacts) have the advantage of adopting observational data on economic context over time, which affects the sensitivity of the economy to certain shocks. Given that these observations are not available for ex-ante assessments, they are less robust to radical changes in the nature of the wider economy in the future.
The future labour intensity of the opportunities is uncertain
As described earlier in this appendix, direct employment impacts draw on estimates of the labour intensity of the opportunities. This data is based on historical data. However, there are a number of challenges associated with this estimation. Firstly, it is not certain that the labour intensities will scale proportionately. For instance, economies of scale may mean that at higher projected levels of output, labour intensities will differ.
Secondly, the analysis assumes that labour intensity (and hence labour productivity) are constant over time. This is a simplifying assumption. In practice, labour productivity is likely to increase over time and therefore the employment impacts could be lower (all other things being equal) in the future.
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