Box 9: Summary of Technical Annex
This Technical Annex sets out new economic modelling quantifying the potential effect of a Brexit driven reduction in migration on both the UK and Scotland economies, and the relative importance of such a reduction in migration to Scotland's economy compared to the rest of the UK. 
Assumptions on extent of reduction in migration: In order to estimate the economic impact, it is necessary first to consider what the level of migration could be if recent migration trends continued and then second to consider what the level of migration could be after Brexit.
Historic trends show variability in net overseas migration but in 2016 the figure was 22,900.
There are a number of alternative projections for net overseas migration in future years. We take the high migration variant migration projection to represent the level of migration if recent migration trends continued. The level of net long-term international migration in Scotland associated with this projection is 15,500 per year. (It should be noted that this is below the levels seen in recent years.)
We then take the principal projection to represent the level of migration in the event of Brexit. Net long-term international migration in Scotland associated with this projection is 7,000 per year.
The difference between these two projections – approximately 8,500 per year – is what we take as the Brexit-driven reduction in migration.
Given the uncertainty over such an outcome, other projections are also possible and this is discussed in the sensitivity analysis. The approach for the rest of the UK adopts the same assumptions, that is, uses the difference between the ONS high migration variant and the principal projection to represent the level of Brexit-driven reduction in migration.
Model: A dynamic computable general equilibrium model ( CGE) of the Scottish economy and the rest of the UK economy was used to examine the net additional economic impact by modelling a decrease in labour supply (a reduction in the working age population).
Findings: Our modelling estimates that real GDP in Scotland will be 4.5% lower by 2040 than it would have been otherwise, as a result of the Brexit-driven reduction in migration. This is equivalent to a fall of almost £5 billion per year in GDP by 2040.
The impact across the rest of the UK is found to be smaller. Real GDP in the rest of the UK could be 3.7% (£47.5 billion) lower by 2040 as a result of the Brexit-driven reduction in migration.
Scotland experiences a proportionally larger negative impact relative to the rest of the UK. This is because Scotland relies more heavily on migration to grow its working age population than the rest of the UK, which enjoys higher levels of natural population growth. The proportionately larger impact on Scotland is equivalent to £1.2 billion per year by 2040.
Implications: The modelling confirms that Scotland will suffer a proportionately larger negative economic impact as a result of the Brexit-driven reduction in migration. This is because of the different demographic profile of Scotland compared to the rest of the UK.
Therefore lower migration represents a specific risk to Scotland and suggests that UK-wide migration policy may not fit Scottish economic needs.
Further modelling set out in this Technical Annex shows that if a different approach to migration policy in Scotland leads to higher levels of migration then a growing labour force could boost the economy.
This Technical Annex also provides an overview of the key literature on the impact of migration on the economy. It then builds on the findings from the literature review to set out new economic modelling showing how lower migration as result of Brexit will impact on the Scottish economy and the rest of the UK respectively.
Overview of literature on the contribution of migration to economic growth: Productivity, skills, and innovation
Most of the economic literature on migration finds that, overall, migrant workers have a positive effect on the host country and can contribute to higher economic growth.
This growth can be achieved through incoming migrants providing a boost to the labour supply, thereby expanding the productive capacity of the economy, resulting in higher levels of economic activity and employment, making the economy as a whole more competitive. As well as adding to the supply side of the economy (expansion in the labour force), migrants also contribute to increased demand for goods and services in the economy (as migrants are also consumers).
Recent Scottish Government modelling undertaken for the response to the MAC looked at the economic contribution of EU citizens to the Scottish economy. This work found that on average, each additional EU citizen working in Scotland contributes a further £34,400 in GDP. As there are approximately 128,400 EU citizens employed in Scotland, this analysis implies that the total contribution of EU citizens working in Scotland is approximately £4.42 billion per year. Migrants also make a contribution to tax revenues – the modelling shows that each additional EU citizen working in Scotland contributes £10,400 in government revenue.
A review of the wider economic literature suggests that migrants who move for economic reasons are likely to pay more in taxes than they receive in benefits.  This means that the host country receives a fiscal contribution from their employment.
There is also evidence that these workers can also have a dynamic effect in helping to improve productivity . Migrant workers bring new skills and expertise into the country, they provide additional resources to help ensure that businesses can manage skills and staffing shortages, and typically have high levels of entrepreneurship which helps lay the foundations for future economic growth. 
There are a number of sources outlining the positive economic benefits of skilled migrants. For example, a summary of the available evidence by the Bank of England suggests that EU workers may have filled skill gaps or specialised in different tasks. Specifically at the firm level, the Bank points to research by Rolfe et al (2013)  that found that employers in the pharmaceuticals, IT, banking and universities sectors recruited from outside the UK in order to fill skills gaps that exist in the resident population, and to complement the skills of non-migrants.
Work by Ortega and Peri (2014) finds evidence that migration boosts long term GDP per capita, through increased diversity of skills and through higher innovation activity.  In-migration is found to have both direct effects on company productivity as well as indirect impacts by raising the productivity of the native human capital through transfer of know-how.
This study also provides evidence that as well as the direct boost to productivity; the resident population may also gain via any indirect effects of skilled immigration on productivity. These positive benefits may arise through enhanced specialisation of procedures, job creation in complementary tasks, and wider dynamic effects on the labour market
More recent work by Ottovanio et al (2016)  finds a productivity and general export promotion effect of immigrants. The study also finds that immigrants promote bilateral exports across service industries to their countries of origin, with an economic magnitude near the upper range of estimates found with respect to goods trade.
Furthermore, available evidence  has suggested that migration does not appear to have had a statistically significant impact on the average wages and employment opportunities of the UK-born population in periods when the economy is strong, although there is some evidence of labour market displacement when the economy is in recession.
The available evidence for the UK indicates that any adverse wage effects of migration are likely to be greatest for resident workers who are themselves migrants. Evidence also suggests that displacement effects dissipate over time, as the labour market adjusts.
Modelling the economic impact of lower working age population on the economies of Scotland and the rest of the UK
The economic modelling uses a macroeconomic model of the Scottish and the rest of the UK economy. The type of model used is known as a dynamic computable general equilibrium ( CGE) model. CGE models take account of the inter-dependencies between different sectors, agents (private sector, government and households) and markets in the economy.
We use the Scottish Government's own CGE model, which has itself previously been used to model a range of economic policies, with variations of the model used in similar studies by academic institutions.  A description of the model can be found on the Scottish Government website. 
Our framework models Scotland and the rest of the UK simultaneously. This is vital as Scotland and the rest of the UK experience different demographic projections and any economic spill-over effect from Scotland into the rest of the UK and vice versa is captured within the model. Additional details of the model and the underlying assumptions are presented in a technical addendum at the end of the Annex.
Lower migration leads to a reduction in the working age population which in turn contracts the supply-side capacity of the economy. As this is a permanent shift, the economy converges to a new equilibrium, characterised by a lower level of economic activity and employment. The reduction in labour capacity allows wages and prices to adjust in such a way that the economy as a whole becomes less competitive, causing exports to fall.
The negative impact on the economy leads to lower household consumption, investment and real GDP. Given that Scotland relies more heavily on migration to grow its working age population than the rest of the UK, Scotland experiences a greater negative impact on all these economic variables than the rest of the UK.
Assumptions on extent of reduction in migration
As set out in the main paper, Scotland has a markedly different demographic profile both in terms of trends and also in terms of projections.
In order to estimate the economic impact, it is necessary first to consider what the level of migration could be if recent migration trends continued; and then to consider the level of migration after the UK leaves the EU. This is done as follows:
- Historic trends show variability in net overseas migration but in 2016 the figure was 22,900.
- There are a number of alternative projections for net overseas migration in future years  and the chart below summarises these.
- We take the NRS overseas migration projection known as the 'high migration projection' to represent the level of migration if recent migration trends continued. The long-term level of migration associated with this projection is 15,500 a year. It should be noted that the level of net overseas migration associated with this projection is below the levels seen in recent years. For example, the 15,500 is a 32% reduction from the levels of overseas net migration to Scotland reached in 2016. Similarly, it is well below the increase of 32,000 a year in working age population which Scotland would need to maintain dependency ratio at its current level.
- We then take the NRS overseas migration projection, known as the 'principal projection' to represent the level of migration in the event of Brexit. The long-term level of migration associated with this projection is 7,000 a year.
- The difference between these two projections – approximately 8,500 a year for Scotland and 72,000 a year for the rest of the UK – is the level of Brexit driven reduction in migration
- Given the uncertainty over such an outcome, other projections are also possible. This is analysed in the sensitivity analysis.
- The approach for the rest of the UK adopts the same assumptions, that is, uses the difference between the ONS 'high projection' and the 'principal projection' to represent the level of Brexit-driven reduction in migration.
Figure 4.1: Scottish net overseas migration, historical data and projections
The Brexit driven reduction in migration is then simulated through the economic model and the size of the shocks are estimated by calculating the percentage change in working age population between the two projections.
In our simulation, we model changes in the number of people of working age from 2018 to 2040. As highlighted in the table below, Scotland experiences a larger decrease in working age population than the rest of the UK.
Table 4.1: Change in working age population for Scotland and the rest of UK
|rest of the UK||-93,000||-344,000||-660,000||-980,000||-1,316,000||-1,533,000|
The key findings of this analysis measuring the impact of a Brexit driven reduction in migration are presented below.
- Our modelling estimates that real GDP in Scotland will be 4.5% lower by 2040 than it would have been otherwise, as a result of Brexit-driven reduction in migration. This is equivalent to a fall of almost £5 billion a year in GDP by 2040.
- The impact across the rest of the UK is found to be smaller. Real GDP in the rest of the UK could be 3.7% (£47.5 billion) lower by 2040 as a result of Brexit-driven reduction in migration.
- The Brexit driven reduction in migration produces negative impacts on Scottish GDP which are proportionately greater than for the rest of the UK. The larger economic cost faced by Scotland is equivalent to £1.2 billion a year by 2040.
- Therefore a Brexit driven reduction in migration represents a specific risk to Scotland and suggests that a UK-wide migration policy may not fit Scottish economic needs.
- Figure 4.2 shows the economic impact of lower working age population in Scotland and the rest of the UK as a result of the Brexit driven reduction in migration.
Figure 4.2: Change in real GDP, Scotland and rest of the UK from lower working age population
This decrease in the working age population would also have a proportionately larger impact on tax revenue raised in Scotland than in the rest of the UK. The analysis shows that the reduction in revenue would be 3.5% (£1.5 billion) in Scotland compared to 2.7% (£12 billion) in the rest of the UK by 2040.
Sensitivity analysis: alternative assumptions on the extent of reduction in migration
As noted above, there are alternative projections for overseas migration. We therefore undertake sensitivity analysis to explore the economic impact of these alternative projections on the Scottish and rUK economies.
The two sensitivity analyses we explore are based on the '50% EU migration projection'  and the 'low migration projection'.  These replace the 'principal projection' in the base case analysis. That is to say, the first sensitivity analysis models the difference between the 'high migration projection' and the '50% EU migration' projection and the second sensitivity analysis models the difference between the 'high migration projection 'and the 'low migration projection'. These differences represent the reduction in migration from Brexit and as such both these sensitivity analyses result in even lower levels of migration than under the base case analysis.
The 50% EU migration projection assumes that EU migration will decrease by half from 2018 onwards reaching a long-term level of 4,300 a year. The difference in net overseas migration between the high migration and the 50% EU migration projection is approximately 11,200 a year. This outcome may occur if migration from the EU to the UK falls substantially as a result of Brexit. The Scottish Fiscal Commission made the judgment to use the demographic variant of 50% reduction in EU migration for the purpose of producing five year economic and fiscal forecast for Scotland.  In the report accompanying its forecast the Scottish Fiscal Commission stated "given the potential impact of changes in the UK's relationship with the EU, the Commission's judgement is that a lower migration assumption is more appropriate. Therefore the Commission uses the ONS 50% EU migration variant projection".
The low migration projection assumes that overseas migration to the UK will fall and reach 85,000 a year by 2022. This is consistent with the UK Government target to reduce net migration to the tens of thousands. Under this scenario, Scotland is projected to experience negative long-term overseas migration equal to 1,500 migrants a year. This means 1,500 more people a year would leave Scotland than arrive from overseas. The difference in net overseas migration between the high and the low migration is close to 17,000 a year.
The economic impact of lower migration is presented in table 4.2.
Table 4.2: Impact on Scottish and rest of the UK ( rUK) real GDP of lower migration relative to the high migration projection
|'50% reduction EU migration' projection||-0.6%||-0.5%||-3.1%||-3.0%||-6.2%||-5.9%|
|'Low migration projection'||-0.9%||-0.8%||-4.7%||-4.0%||-9.3%||-7.6%|
Under the 50% reduction in EU migration scenario, Scottish real GDP is lower by 6.2% (£6.8bn) and ' rUK' real GDP by 5.9% (£75.4bn) than it would have been the case if Scotland and the rest of the UK followed a path of high migration. This outcome presents a more pessimistic outcome on both Scotland and the rest of the UK than our original analysis. In the worst case scenario of low migration, Scottish real GDP is lower by 9.3% (£10.2 billion) and the rest of the UK real GDP by 7.6% (£96.3 billion).
The overall conclusion of this sensitivity analysis is that, the more pessimistic the projections of working age population are, the larger the negative impact on the economy of Scotland and the rest of the UK.
The economic boost to the Scottish economy if higher levels of migration could be achieved
Further modelling is undertaken to demonstrate the economic benefits that would flow if Scotland could achieve higher levels of migration under three scenarios.
We simulate three scenarios based on a long-term annual increase in net overseas migration of 5%  , 10%  and 20%  above the level of overseas migration assumed in the high migration projections for Scotland. Under these three scenarios, overseas net migration would reach 16,000, 17,000 and 19,000 a year respectively. These levels of migration are still lower than the net overseas migration of 22,900 reached in 2016. In addition, the three scenarios are still below the increase of 32,000 a year in working age population which Scotland would need to maintain its dependency ratio at the current level. In our modelling, we assume no change in the level of overseas migration to the rest of the UK.
Increasing Scotland's working age population would have a positive impact on the economy. Higher migration results in a growing working age population which leads to more economic activity and employment. The economic impact of pursuing these demographic trajectories can be seen in the graph below.
Higher levels of overseas migration of 5%, 10% and 20% leads to a long-term increase in real GDP equal to 0.4% (£0.5bn), 0.8% (£0.9bn) and 1.6% (£1.8bn). Moreover the increase in economy activity has a positive impact on real Government revenues which rise by 0.3% (£0.2bn), 0.7% (£0.3bn), and 1.4% (£0.6bn) respectively. If Scotland were to follow the path of net overseas migration set out in the base case of 'principal projection' then the benefits of achieving the level of higher migration of these three scenarios would be even greater.
The conclusion is that if further migration powers could achieve higher levels of migration into Scotland then our economic modelling suggests that a growing labour force would have a positive economic impact.
Figure 4.3: Impact of an increase in working age population due to higher migration on Scottish GDP
The economic literature suggests that migrant workers can fill skill gaps, complement the skills of domestic workers and help drive productivity improvements in the economy.
Migration can also help mitigate the demographic pressures arising as a result of Scotland's aging population. Scotland has a markedly different demographic profile from the rest of the UK and migration has been crucial in turning around Scotland's trend of population decline. Migration will only be more important as our population continues to age, particularly in boosting the working age population.
The vote to leave the European Union therefore adds an additional headwind to Scotland's demographics. The economic impact of Brexit driven reduction in migration is estimated to be equal to a reduction in real GDP of 4.5% in Scotland and 3.7% in the rest of the UK by 2040. Such a reduction would also result in a decline in Government revenue of 3.5% in Scotland and by 2.7% in the rest of the UK.
The sensitivity analysis also highlights that if the projection followed the UK net migrationtarget GDP would have been even lower. By 2040 real GDP would fall by 9.3% in Scotland and 7.6% in the rest of the UK.
The economic modelling shows that lower migration has substantial negative consequences on both the Scottish and the rest of the UK economies. However, given the considerable larger negative impact on Scotland's economy, there is a strong economic case for additional immigration powers in Scotland. This appears to be the best way to mitigate the negative impact that demographic changes are likely to have on Scotland's economy.
If further immigration powers could achieve higher levels of migration into Scotland then our economic modelling suggests that a growing labour force would have a positive economic impact. For example, if overseas migration were to increase by 5%, 10% and 20%, in 2040 real Scottish GDP would rise by 0.4%, 0.8% and 1.6% respectively.
Table 4.3: Summary of the modelling results - Impact on Scottish and rest of the UK real GDP of changes in migration in 2040
|GDP (%)||Government Revenue (%)||GDP (£)||Government Revenue (£)|
|Base case -||-4.5%||-3.5%||-£4.9 5bn||-£1.5bn|
|Rest of the UK|
|GDP (%)||Government Revenue (%)||GDP (£)||Government Revenue (£)|
|Base case -||-3.7%||-2.7%||-£47.5bn||-£12bn|
As with all economic models, a set of assumptions are made about how the economy adjusts to the shock applied. The key assumptions made are:
- all labour is homogenous. This means new entrants in the labour market work the same number of hours and have the same productivity level and skill set as those already in the labour force;
- wage bargaining takes place, where real wages are a decreasing function of unemployment levels; and
- the Government aims to balance its fiscal balance. Any fluctuations in government revenue will be reflected in changes in government expenditure. As the tax base contracts, less can be collected in revenue, reducing public sector expenditure. This is consistent with the idea that any decrease in labour supply will be seen as a permanent reduction of Government services such as health and education. As a result the Government would adjust and reduce its expenditure.
CGE models  are large-scale simultaneous equation models which combine General Equilibrium theory with real economic data to derive computationally the economic impact of policies or shocks. We model the changes in demographics by shocking labour supply for 25 years consecutively. We do not shock the model in any other respect, and as such future policy changes are not modelled.
Figure 4.4: Diagram of CGE Modelling
Computable general equilibrium ( CGE) models take into account the inter-dependencies between different sectors, agents and markets in the economy. This allows analysis to shed light on the wider economic impact of policies, revealing combined direct and indirect effects of shocks.
The model is made up of numerous structural equations which describe the behaviour of different agents in the economy, such as households, firms and government. Households and firms aim to maximize their objective functions subject to some constraints, whilst government aims to maintain the chosen fiscal closure.
In absence of any economic shocks, the model is in steady state equilibrium. In this equilibrium, demand equals supply in every market and markets clear. After an economic shock, the economy falls out of equilibrium and imbalances occur across the economy. As a result of market clearing conditions, all markets adjust across time until a new equilibrium is achieved. Unlike many CGE models, the Scottish Government CGE model accounts for non-market clearing of the labour market, allowing for unemployment in the model.
The dataset which forms the backbone of the CGE model is the Social Accounting Matrix ( SAM). It captures the flows of all economic transactions which take place in the economy in a single year. Its primary data sources are the Input-Output tables and the national accounts, complemented by a range of other data on tax, income and expenditure.
In the Two-Region Scottish Government CGE Model, the rUK economy is treated as endogenous to the Scottish economy. This difference from the Single-Region CGE model allows for economic shocks to reverberate across the entire UK economy, reflecting the interdependencies that exist between the Scottish and rUK economies. This model is calibrated using a SAM for Scotland, and a SAM for rUK. Shocks can be imposed on either the Scottish or rUK economy independently, or combined.