Annex 4 analytical methods

The dynamic spatial general equilibrium model features discrete time, multi-sector, dynamic discrete choice migration decisions, and investment determined as the solution to an intertemporal consumption-investment problem. The economy consists of many locations that differ in productivity, amenities, bilateral trade costs and bilateral migration costs. There are two types of infinitely-lived agents: workers and factor-owners. Workers are endowed with one unit of labour that is supplied inelasticity and are spatially mobile subject to migration costs. Workers do not have access to an investment technology and hence live “hand to mouth”. They make forward-looking migration decisions, taking into account migration costs and the expected continuation value from optimal future location decisions. Factor-owners are spatially immobile and own the capital stock in their location. They make a forward-looking decision over consumption and investment in this local stock of capital to maximise intertemporal utility. Capital is spatially immobile once installed and depreciates gradually at a constant rate. There are two sources of dynamics in the model: forward-looking investment decisions of the immobile factor (capital structures) and forward-looking migration decisions of the mobile factor (labour). To relax the assumption of perfect foresight, the model is linearised, allowing to derive a closed-form solution for the economy’s transition path in terms of impact conditions, which captures the impact of (policy) shocks in the period in which they occur, and transition conditions, which governs the evolution of the state variables from one period to the next in response to these shocks. The policy impact and transition paths depend on observable trade and migration shares. Agglomeration is captured through clustering forces in production (productivity spillovers) and residential decisions (amenity spillovers).

In the endogenous input-sourcing version of the model, production technology is vertically organised. Downstream producers sourcing from upstream suppliers along the supply chain produce a composite good in N production tiers that need to be performed sequentially. For the sake of tractability, in the baseline model we assume two tiers in the production process, though the model is more general and extends to any number of tiers straightforwardly. Firms in the upstream tier only use the local factor. Firms in the second tier combine the local factor with intermediate inputs produced in any location in the first tier. Both inputs – local factor and intermediate components – are required in the tier-two production, no output can be produced with one input only. If either labour or at least one source of intermediate inputs (or both) are not supplied, no production can take place in this location. The optimal input sourcing location at the different production tiers of the supply chain is determined by a cost minimisation of downstream firms. Final goods can be produced using different sets of intermediate inputs that can be sourced from any location. Firm-specific technique - a production function that specifies from which locations and suppliers intermediate inputs to source - can differ in terms of productivity. When choosing a production technique, a firm can adjust the importance of a supplier e.g. by including or dropping that supplier. Production techniques are chosen at the beginning of the period, firms have to produce with the selected input suppliers. These decisions, when aggregated, lead to changes in the supply network along both the intensive and extensive margins, which have implications to the supply chain's robustness. Firms can adjust the input sourcing path at the end of the period. The downstream firm’s problem in the vertically organised supply chain consists of choosing the least-cost path of production to manufacture a final composite good’s variety and deliver to consumers in their location.

EU-EMS requires detailed data across multiple dimensions –. Key data inputs include regional economic variables like GDP, employment, and capital stock by location; trade flows between regions, capturing goods, services, and labour mobility; production and consumption data for different industries; and demographic information such as population, migration patterns, and household preferences. Additionally, infrastructure and transportation costs, regional policies, and environmental factors (e.g., land use, emissions) are crucial. Time series data is needed to capture dynamic elements like investment, technological change, and policy impacts, ensuring the model accurately simulates spatial and temporal interactions.

Model output indicators include metrics assessing policy progress and effectiveness. For clean growth and net zero, indicators include emission reductions, energy efficiency, and renewable energy adoption. Technological sovereignty looks at innovation output and digital infrastructure. Security and democracy is measured by policy enforcement, cybersecurity, and public trust. People, skills, and preparedness gauges workforce training, education, and adaptability. Cohesion and reforms include economic equality, policy integration, and regional growth. Economic security uses productivity, trade balance, and crisis resilience. Environment indicators track resilience, circular economy progress, and sustainable transport. Overall, transparency, implementation, and simplification reflect government efficiency.

1. Factor supply by households (capital, labour) in each region
2. Education by skill level and region
3. Income of households in each region
4. Taxes payed on income by households in each region
5. Savings of households in each region
6. Aggregate consumption of households in each region
7. Price index of consumption goods in each region
8. Household consumption in each region & sector
9. Price of exports from each NUTS2 region to each NUTS2 region
10. Average selling price in each region & sector
11. Average production cost in each region & sector
12. Profits in each region & sector
13. Fixed cost of production
14. Marginal cost of production in each region & sector
15. Aggregate intermediate input in each region & sector
16. Aggregate input of primary factor in each region & sector
17. Price of aggregate intermediate input in each region & sector
18. Intermediate input demand in each region & sector
19. Total factor productivity in each region & sector
20. Aggregate capital-factor demand in each region & sector
21. Aggregate labour-factor demand in each region & sector
22. Price of aggregate capital-factor demand in each region & sector
23. Price of aggregate labour-factor demand in each region & sector
24. Price of firm output in each region & sector
25. Demand for factors (capital, labour) in each region & sector
26. Taxes payed on factors in each region & sector
27. Taxes payed on intermediate inputs in each region & sector
28. Income of investor in each region
29. Aggregate investment in each region
30. Price of investment good in each region
31. Investment demand in each region & sector
32. Supply of factors (capital, labour) by government in each region
33. Taxes rate on household income in each region
34. Income of government in each region
35. Aggregate consumption of government in each region
36. Composite price of government consumption good in each region
37. Government consumption in each region & sector
38. Transfers from government to households in each region
39. Government savings
40. Demand for composite import good in each region & sector
41. Price of composite import good each region & sector
42. Exports from each NUTS2 region to each NUTS2 region
43. Price of factors (capital, labour) in each region
44. Unemployment rate for each region
45. Firm sales in each region & sector
46. Number of firms in each region & sector

EU-EMS can address skills and preparedness, which is essential to ensuring economic prosperity and social cohesion. Model can demonstrates that societies with strong vocational training programs, lifelong learning initiatives, and digital literacy efforts outperform those that neglect human capital development. Economic reforms targeting education, labour mobility, and equity help reduce regional disparities, promoting inclusive growth. Skills preparedness is closely linked to labour market flexibility, facilitating smoother transitions during periods of economic restructuring or technological disruption. The model emphasises clean energy as a pivotal driver of long-term sustainability and economic competitiveness. A just transition to a net-zero economy ensures energy security while fostering innovation in green technologies. Investments in renewable energy, circular economy, and sustainable transport systems help align industrial strategies with climate goals. The model can show how economies that proactively implement net-zero targets experience growth in sectors like clean tech, electric vehicles, and energy storage. However, without preparedness, skills, and cohesion reforms, these transitions could lead to job losses in traditional energy sectors, thus requiring robust upskilling and reskilling programs. EU-EMS can model technological sovereignty and innovation capacity that are critical for maintaining global competitiveness. Model simulations can show that economies investing in AI, 5G, and next-gen manufacturing processes see productivity gains, boosting their international trade position. Countries and regions that prioritize R&D, support start-ups, and streamline innovation processes exhibit stronger industrial strategies. A focus on cybersecurity and data governance within technological sovereignty helps safeguard democratic processes and ensure security, especially in critical infrastructure. EU-EMS can demonstrate that security threats, both digital and physical, are heightened by international instability. The model can illustrate that democracies with robust crisis management frameworks and transparent governance tend to maintain higher levels of public trust and resilience. Reforms aimed at improving transparency, governance, and preparedness enhance economic security and industrial growth. The intersection of security and democratic resilience in EU-EMS show how strong institutions can better respond to crises, be they financial, political, or environmental. The model can analyse the importance of strategic trade policies that align with domestic industrial goals while preserving global economic ties. Countries that strike a balance between protecting key sectors and engaging in international trade see greater economic security and productivity. Simplifying regulatory frameworks and reducing barriers to trade and innovation helps foster business growth, especially for small and medium enterprises (SMEs) and start-ups. The model can be sued for identifying economies adopting streamlined processes for business creation, regulatory compliance, and financial services integration (through initiatives like the Savings and Investments Union) see higher levels of entrepreneurship and investment.

• Climate action 
• Education and training 
• Economy, finance and the euro 
• Employment and social affairs 
• Energy 
• Regional policy 
• International cooperation and development 
• Digital economy and society 
• Research and innovation 
• Single market 
• Trade