Modelling the long-run economic impacts of a stylised US tariff increase: technical paper

Methodology

Model structure

To capture spillover effects between Scotland and the rest of the UK (rUK), we adopt a two-region CGE model. The model is parametrised to an inter-regional Social Accounting Matrix (SAM) for Scotland and the rest of the UK for 2013. There are three transactor groups in each region – firms, household and government – and twenty productive sectors. The model runs for fifty periods, which is to be interpreted as fifty years. We define the long run as approximately ten to twenty years after the shock occurs, once capital stocks, labour markets, and trade flows have stabilised.

Production structure

The model is built on a sectoral input-output production structure where sectors use each other’s output in their own production. In each sector, local intermediate inputs are combined with imports from the other region and the rest of the world. Value is added in each region by a combination of capital and labour. Intermediate input is combined with value added to determine the sector’s gross output.

Resource allocation

Labour and capital are allocated across sectors. There is imperfect competition in the labour market, so real wages are inversely related to unemployment. Labour is homogenous, with a single unemployment rate and wage for each region and there is no migration so potential labour supply in each region is stable. While capital reallocates to sectors with higher returns to capital, labour reallocates to sectors where labour is demanded based on firm profit maximisation.

Trade

International exports are exogenous, split into EU and non-EU aggregates. Export demand of the other UK region is fully endogenous, depending not only on relative prices, but also on all elements of intermediate and final demand in the other region.

Import demand is endogenous and sourced from a Rest of the World (RoW) aggregate. Imports enter the economy through household consumption, investment, and intermediate inputs, and are allocated based on relative prices using Armington trade functions which assume imperfect substitution between domestic and imported goods.

Households

Households allocate their income between consumption and saving, with consumption decisions made to optimise utility. They choose between goods from different sectors based on relative prices, and further differentiate between domestic and imported varieties using Armington assumptions (Armington, 1969). Total consumption is influenced by disposable income, which accounts for wages, capital income, transfers, and taxes. In the forward-looking closure, households also consider intertemporal trade-offs, smoothing consumption over time based on expected future income.

Government

Government behaviour is defined by closure rules that determine whether expenditure, the budget balance, or tax rates are fixed or endogenous. In our setup, tax rates are exogenous and government spending adjusts to keep the budget balanced.

Investment

Investment demand is determined endogenously and allocated across industries between domestic and imported capital goods. The level of investment in each sector is influenced by the expected return on capital, adjustment costs, and the user cost of capital. In the forward-looking closure, investment decisions are based on intertemporal optimisation, where firms invest to maximise the present value of future returns, subject to capital accumulation dynamics and adjustment costs.

Table: Summary of model closures in our CGE simulations

Model Component: Labour Market

Closure setting: Regional wage bargaining

Effect on Results: Wages respond to regional unemployment

Model Component: Agents

Closure setting: Forward-looking

Effect on Results: Consumption and investment are smoothed over time. Firms maximise profit while households maximise utility

Model Component: Government

Closure setting: Fixed balance

Effect on Results: Government spending adjusts to keep the fiscal balance stable

Tariff policy is applied at the UK level, and any shock affects both Scotland and the rest of the UK. The two-region model includes both Scotland and rUK as endogenous regions feeding in to each other, allowing for interregional feedback effects. To examine the spillover on Scotland from the shock to the rUK economy, we run the simulation twice: first shocking just Scotland, and second shocking Scotland and the rest of the UK. Comparing the results allows us to identify the effect of the rUK shock on Scotland economy.

Shock definition

Exports are split in to EU and non-EU in the database using OECD Trade in Value Added (TiVA) data for 2020 to split service exports for rUK and Export Statistics Scotland data for 2021 to split service exports for Scotland. RTS data for 2024 is used to split goods exports for both rUK and Scotland.

OECD TiVA statistics are directly mappable to the CGE industrial classifications while we used judgement to map RTS goods to CGE industries (see annex C).

For the export shocks a 10% price increase is applied to non-EU exports from Scotland and rUK , scaled by the share of non-EU exports from each region to the US. We model the impact of symmetric retaliation by applying a 10% price shock to Scotland and rUK international imports, scaled by the US’s import share for each region. See Annex D for the shares fed in to the model.

Full passthrough of the cost of the tariff is assumed and an import demand elasticity of 2 is applied which captures the longer term substitution away from more expensive imports to domestic produce (Gibson, 1990). See Annex F for sensitivity analysis.

Limitations and considerations

There are several limitations and considerations to this analysis. First, the model is calibrated to a 2013 Social Accounting Matrix (SAM), and economic linkages may have evolved since then.

Secondly, while we have carefully mapped RTS product categories to CGE industries, it is possible that there is not full alignment.

Furthermore, there is inherent uncertainty around the trade elasticity parameter. This elasticity determines how responsive import volumes are to changes in relative import versus domestic prices. In practice, elasticities vary significantly across products, sectors, and time horizons. Higher elasticities imply greater responsiveness and are typically used in long-run simulations, where economic agents have more time to adjust to new trading conditions.

Recent studies illustrate this variation. The Office for Budget Responsibility (OBR) used a relatively low elasticity of -0.4, based on Bank of England estimates for UK import demand.^[5] Meanwhile, empirical academic studies often find larger values for long-term trade elasticities. For example, Fontagne et al. (2022)^[6] report considerable heterogeneity in trade elasticity across products, with an average elasticity of around -5. Boehm et al. (2022)^[7] estimate short-run elasticities of around −0.76 and long-run values of around −2. Reflecting this, we adopt a central elasticity of -2, consistent with a long-term perspective in which firms and households can substitute away from more expensive imports. This implies that a 10% increase in import prices leads to a 20% reduction in import demand. However, applying a uniform elasticity across all sectors is a simplification, as real-world responsiveness varies by industry. See Annex F for sensitivity analysis.

The shock also ignores global tariff policy announcements. This includes exemptions for the UK in the US-UK deal, and also US tariff policy on all other global partners. Furthermore, splitting exports in to EU and non-EU, the model captures some trade diversion from non-EU to EU, but it doesn’t account capture trade diversion within the non-EU region.

There is also consideration to be given to the presentation of results. Given the homogeneous labour force in the model, a shock to the goods sector affects labour costs across the whole economy. Under flexible wages, this can lead to misleading increases in real output in some industries due to falling input costs across the economy, even though in reality labour cost adjustments tend to vary by sector. To more accurately reflect the economy-wide impact of the demand shock, we report changes in nominal output, which capture both price and quantity effects.