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### 2.1 GTAP — model structure and tariff mechanics
- GTAP is a comparative static, multi-region, multi-sector, computable general equilibrium model.
- Agents and markets:
  - Representative household per region; representative firm per commodity sector.
  - Sectors produce tradable and nontradable commodities/services, interconnected through input-output structure.
  - Representative firm optimizes over cost of commodity inputs and primary factors; households maximize a utility function subject to a budget of factor incomes and tax revenues.
  - Armington assumption: preferences over a composite of domestic and imported goods differentiated by country of provenance; utility functions usually CES so solutions represented by spending shares.
  - Investment does not cumulate into capital stock; treated as household expenditure determined by relative rates of return across regions.
- Solution and closures:
  - Model solved by linearizing non-linear behavioral and accounting equations; solutions deliver percentage deviations from initial values.
  - Under closure for an import tariff shock, production factors are in fixed supply and fully employed.
  - Deviations of behavioral equations become functions of reduced-form elasticity parameters.
- Tariff shock propagation:
  - A tariff is a price distortion that generates a chain effect on prices; quantities and prices adjust to satisfy firms’ and households’ linearized demands.
  - In the imposing country:
    - Higher prices of imported inputs raise sale prices in trade-exposed sectors.
    - Firms substitute toward domestic inputs, introducing an inefficiency (wedge) allowing less competitive domestic goods to become viable.
    - Imperfect substitutability and higher domestic input prices raise general prices, reduce final demand for trade-exposed sectors, and lower demand for production factors.
  - In the exporting partner:
    - Higher export market prices lead to lower external demand, reducing output and production factors.
  - With fixed factor supplies and full employment, factor prices decline to clear markets; misallocations measured by real factor prices in new steady state.
  - Result: factor returns and output decline relative to no-tariff state; greater trade exposure implies larger productivity/efficiency losses.

### 2.1 GTAP — parameterization and data
- Version used: six regions with thirteen sectors in each region (j= 13).
- Regions: U.S.A., China, Euro Area (Euro), Japan, Emerging Asia (Asia) and Rest of the World (RestWorld). Emerging Asia includes Hong Kong SAR, Indonesia, India, Korea, Malaysia, Philippines, Singapore, Thailand, and Taiwan province of China.
- Database: GTAP database v10 (2014).
- Elasticities:
  - Elasticity of substitution between domestic and foreign goods, ε_j, averages just above 3.
  - Elasticities among imported varieties θ_j set to roughly double ε_j (rule of two).
- Distribution shares and calibration:
  - Shares of domestic vs imported inputs and partner-country import shares are taken from data and calibrated to replicate import shares of output and by partner region, and domestic input-output shares.
- GTAP features 121 economies and 65 sectors (aggregable).

### 3.1 GIMF — channels and dynamics (trade war shock: 10-percentage-point bilateral tariffs)
- Shock: 10-percentage-point increase in bilateral import tariffs between the U.S. and China.
- Short run (SR, year 1) — key dynamics and numbers:
  - Exports of both the U.S. and China fall because bilateral import demand contracts.
  - Under GIMF specification (local currency pricing (LCP) with high pass-through in the short run), exchange-rate dynamics are central to consistency between trade flows, balance of payments and UIP.
  - Despite symmetric tariff increases, asymmetric trade flows lead to asymmetric shocks: U.S. dollar appreciates against the renminbi because China’s exports to the U.S. are significantly larger.
  - Short-run total exports: -2.1 percent (U.S.), -2.2 (China).
  - Short-run GDP changes: -0.19 percent (U.S.), -0.66 percent (China).
  - Renminbi depreciation helps China reorient exports to other destinations in the short run; dollar appreciation reduces U.S. exports to other partners.
- Medium and long run:
  - Long-run dynamics driven by firms’ investment responses to tariff-induced distortions: lower capital stock, lower marginal product of labor, lower labor demand, and lower labor supply.
  - Tariff wedge lowers firms’ profitability in both markets; Armington preferences limit substitution, creating wedges in production costs and contraction pressures on capital and labor utilization.
  - Long-run exchange-rate pass-through to trade prices:
    - China: renminbi depreciation partly offsets investment impulse but raises import costs.
    - U.S.: dollar appreciation reduces import costs but hurts exports to other destinations.
  - On net, long-run investment declines are quite comparable for China and the U.S., despite larger short-run divergence.
- Investment and labor:
  - Investment and labor responses are steep in the short run and milder in the long run.
  - Tariffs have the strongest short-run impact on firms’ investment in China.
  - Investment and labor supply closely track real GDP paths in both countries.

### 3.1 GIMF — spillovers to third countries
- Mechanism and timing:
  - Trade diversion is the main source of short-run spillovers to third countries; nominal and real rigidities and bilateral exchange-rate changes govern magnitude.
- Short run:
  - Sluggish response of China and U.S. total imports (due to import adjustment costs and gradual pass-through) generates diversion toward non-disputing countries.
  - U.S. and China intensify imports from other partners while total demand for foreign goods adjusts slowly, boosting exports and GDP of third countries in the short run.
  - Trade diversion is pronounced in the short run but fades toward the medium run.
- Long run:
  - No significant increase in total exports for third countries in the long run because rigidities dissipate and full exchange-rate pass-through acts as rebalancing or additional negative force.
  - Trade diversion toward third countries is typically weaker in the long run (example: euro area).
- Bilateral patterns (long run):
  - Model predicts a fall in U.S. exports toward all destinations due to dollar appreciation and full pass-through.
  - U.S. bilateral trade balance with China improves somewhat, but aggregate U.S. trade balance remains broadly unchanged because of offsetting losses in other markets.
  - China’s exports to partners other than the U.S. increase due to renminbi depreciation; China’s total export contraction is driven by the large fall to the U.S.
- Numerical highlights preserved:
  - 10-percentage-point increase in bilateral import tariffs.
  - Short-run total export changes: -2.1 percent (U.S.), -2.2 (China).
  - Short-run GDP changes: -0.19 percent (U.S.), -0.66 percent (China).

### 3.2 GTAP — channels, sectoral effects, and aggregates (10-percentage-point bilateral tariffs)
- Mechanism differences vs GIMF:
  - GTAP does not model nominal exchange rates explicitly; focuses on relative prices of goods and production factors.
  - Production factors are fixed net supply at regional level; changes in factor prices reflect reallocation across sectors.
  - Input-output linkages transmit relative price changes along production chains, inducing substitution toward domestic goods or imports from third countries.
- Sectoral outcomes (largest moves):
  - Electronics: China’s production and exports fall; U.S. electronics production increases.
  - Agriculture: U.S. agricultural production and exports decline; Chinese agricultural production increases.
  - Automotive (cars and car parts): Production declines in the U.S. and increases (more modestly) in China.
  - These sectors also show largest production reductions in non-dispute countries, likely due to global trade disruption.
- Factor prices and efficiency:
  - Demand for production factors in trade-exposed sectors falls, putting downward pressure on factor prices under fixed regional endowments/employment.
  - Reallocation toward less trade-exposed sectors generates aggregate efficiency loss measured as decline in factor real returns (deviation from model numeraire).
- GDP impacts (GTAP):
  - China: GDP falls 0.23 percent.
  - U.S.: GDP falls 0.09 percent.
  - Interpretation: larger Chinese loss driven by importance of electronics in Chinese exports and GDP and reallocation away from electronics.
- Terms of trade:
  - Changes larger in GTAP than in GIMF.
  - China: export prices decline relative to import prices, worsening terms of trade in both models.
  - U.S.: GTAP yields a mild decline in U.S. terms of trade (ex-tariff export prices fall); GIMF produces an increase in U.S. relative export prices (owing to exchange-rate appreciation).
- Spillovers to third countries in GTAP:
  - Net spillovers dominated by tariff impacts on external positions of China and the U.S., given absent bilateral nominal exchange-rate movements.
  - Increase in Asia-to-third-country flows present in GIMF disappears in GTAP; total flows dominated by increased exports to the U.S.
  - Trade diversion in GTAP arises from:
    - (i) complex sectoral input-output structure, and
    - (ii) larger expansion of domestic production (than in GIMF) due to fixed net employment.
  - Example: diversion of U.S. imports from China toward Asia in electronics and increased U.S. domestic production can generate higher U.S. imports from Asia and higher Chinese exports to Asian markets through supply chains.
- Excerpted bilateral export changes (percent deviation from steady state) reported in GTAP:
  - To Asia: -1.2, 6.7, -0.8, -1.7, -0.7, 7.5
  - To China: -1.0, -0.7, -1.6, -0.6, -43.8
  - To Euro: -0.7, 7.6, -0.4, -1.0, -0.6, 1.4
  - To Japan: -1.2, 6.1, -1.1, -0.7, 0.8
  - To RestWorld: -0.8, 7.2, -0.7, -1.0, -0.8, 1.1
  - To USA: 7.5, -39.2, 4.4, 4.6, 3.0
  - (Source: IMF calculation. In percentage deviation from steady state.)

### GTAP sensitivity analysis and elasticity calibration
- Benchmark elasticities:
  - Sector-specific domestic-foreign elasticity εγj averages just above 3 (simple average).
  - Elasticity between imported goods from different source countries θj set to double εγj.
- Experiments:
  - Multiply both εγj and θj by 0.5 and by 2 to obtain low and high elasticity scenarios (low roughly equivalent to GIMF’s domestic-foreign elasticity).
- Key results:
  - Under full employment and absent investment dynamics, real GDP response driven mainly by allocative efficiency changes.
  - Higher substitution elasticities amplify shock impacts on exports and GDP via stronger expenditure switching and reallocation.
  - Terms of trade are very sensitive to elasticity choices.
  - China: a decrease in terms of trade can generate a positive impulse to exports that is higher (lower) when elasticity is lower (higher).
- Quantitative ranges:
  - Range of GDP results lies in a very small neighborhood: 0.1 for the U.S. and 0.2-0.3 for China.
  - Full employment in GTAP explains limited GDP variance: domestic production more stable since resources invariant and relative prices/terms of trade adjust.

### Combining GTAP and GIMF — mapping and quantitative implications
- Complementarity:
  - GTAP captures sectoral reallocation and aggregate efficiency losses from misallocation.
  - GIMF captures investment dynamics, labor and capital utilization, and exchange-rate rebalancing absent in standard GTAP.
- Mapping approach:
  - Treat percentage changes in sectoral GDP from GTAP as percentage changes in productivity (residual of an aggregate production function) to apply as shocks in GIMF.
  - Apply GTAP GDP percentage changes as shocks to labor-augmenting productivity and to TFP in GIMF, in addition to the bilateral tariff increase.
  - Calibration: shocks to long-run productivity set to match GTAP GDP changes of -0.09 percent (U.S.) and -0.23 percent (China); productivity shock unfolds gradually, reaching long-run level after 5 years.
- Combined-model quantitative results (percent deviation from baseline of real GDP in GIMF):
  - Mapping GTAP GDP changes into a TFP shock:
    - China: accounting for productivity loss from resource reallocation leads to about 0.5 percentage point worse GDP contraction in the long run.
    - Larger relative impact in China reflects higher baseline investment share of GDP in China versus the U.S.
  - Mapping GTAP GDP changes into a labor-specific productivity shock:
    - China: leads to about just over 0.1 percentage point worse GDP loss in the long run, given a more muted investment reaction.
- Caveats:
  - Using GTAP-derived productivity shocks in GIMF may overestimate overall effect because frameworks allowing factor contraction would produce lower estimates of lost productivity from reallocation.
  - TFP shocks generate much larger GDP responses in DSGE models (especially where investment/GDP shares are high) than labor-specific productivity shocks.

### Concluding synthesis and policy-relevant findings
- Two complementary perspectives on tariffs:
  - GIMF: tariff increases generate exchange-rate appreciation for the imposing country, falls in investment, labor utilization, and exports in short and long run.
  - GTAP: tariff increases produce resource reallocation across sectors and associated aggregate productivity losses when less efficient domestic production replaces previously cheaper imports.
- Policy-relevant synthesis:
  - Combining GTAP’s sectoral estimates of productivity loss with GIMF’s macro-dynamics can more than double GIMF’s long-run GDP effects in some cases, showing that accounting for resource reallocation materially affects macro estimates of tariff impacts.
- Overall finding:
  - Unilateral or bilateral increases in import tariffs produce sectoral resource reallocation and an aggregate loss in productivity in disputing countries; macroeconomic magnitude depends crucially on model features (full employment vs. factor utilization, elasticities of substitution, investment shares).

### Appendix highlights — key equations, parameters, and trade flows
- GTAP solution and equations (linearized system; percentage-change notation):
  - Market clearing for nontradables and primary factors: ∑_j Q^S,i,j = ∑_j Q^D,i,j + Q^H,i (linearized form (A.4)).
  - Fully employed fixed factor supply: 0 = ∑_j V^D,i,j q^D,i,j (A.5).
  - Price transmission (A.8): p^m_i,r = t_i,r + p^w_i; p^D,i,j,r = t^D,i,j,r + p^m_i,r; p^S,i,j,r = t^S,i,j,r + p^m_i,r.
  - Firm demand linearized: q^D,i,j,r = −σ_j S^D,i,j,r p^D,i,j,r + z_j,r (A.21).
  - Household consumption linearized: q^H,i,r = ∑_k η^H,i,k,r p_H,i,r + η^H,i,r y_r (A.27).
  - Tariff simulation solved via Gragg’s method (Harrison and Pearson, 1994): shocks broken into smaller steps to integrate differential system.
- Appendix B (GIMF): key tariff transmission and balance of payments equations:
  - Relative demand for imported vs domestic goods: Y^M_t / Y^H_t = f(Θ; τ_m, φ_t, P^*_t / P_t).
  - Balance of payments (nominal): B^F_t = B^F_{t−1} R^*_t + P^X_t (1 + τ^*_m) Y^X_t − P^M_t (1 + τ_m) φ_t Y^M_t.
  - Intertemporal condition and uncovered interest parity implications (Euler equations).
- Appendix C — GTAP elasticity table (selected exact values):
  - Crops: ϵ_i = 2.5, θ_i = 4.9
  - Meat and livestock: ϵ_i = 3.2, θ_i = 7.4
  - Extraction: ϵ_i = 4.9, θ_i = 11.9
  - Processed food: ϵ_i = 2.1, θ_i = 4.4
  - Textile and apparel: ϵ_i = 3.7, θ_i = 7.4
  - Light manufacturing: ϵ_i = 3.6, θ_i = 7.6
  - Iron and steel: ϵ_i = 3.0, θ_i = 5.9
  - Aluminum and other metals: ϵ_i = 4.2, θ_i = 8.4
  - Auto and parts: ϵ_i = 2.8, θ_i = 5.6
  - Heavy manufacturing: ϵ_i = 3.2, θ_i = 6.7
  - Electronics: ϵ_i = 4.4, θ_i = 8.8
  - Transportation services: ϵ_i = 2.1, θ_i = 4.6
  - Other services: ϵ_i = 1.9, θ_i = 3.8
- GTAP trade flows between partner regions (percent of total exports; exact values preserved):
  - To Asia: Asia 22.8, China 22.4, Euro 5.5, Japan 27.8, RestWorld 12.2, USA 12.1
  - To China: Asia 20.9, China 4.5, Euro 25.9, Japan 9.0, RestWorld 8.7
  - To Euro: Asia 10.2, China 13.2, Euro 41.5, Japan 9.0, RestWorld 25.3, USA 17.4
  - To Japan: Asia 7.1, China 8.2, Euro 1.5, Japan 4.4, RestWorld 5.2
  - To RestWorld: Asia 26.4, China 37.5, Euro 39.4, Japan 21.5, RestWorld 31.6, USA 56.7
  - To USA: Asia 12.5, China 18.7, Euro 7.5, Japan 15.8, RestWorld 17.4
- GIMF key parameter values (one model period = one year; exact region pairs shown):
  - USA / China
    - Real adjustment costs of imports: 1.0 / 1.0
    - Capital as share of GDP: 39.5 / 45.1
    - Investment as share of GDP: 16.9 / 26.1
    - Discount factor (β): 0.982 / 0.973
    - Share of liquidity-constrained households (ψ): 0.25 / 0.25
    - Frisch elasticity of labor supply: 0.5 / 0.5
    - Elasticity of substitution btw domestic and foreign goods: 1.5 / 1.5
    - Elasticity of substitution among foreign goods: 1.5 / 1.5
    - Coeff. on deviation from inflation target (monetary rule): 1.0 / 1.0
    - Coeff. on deviation from output target (monetary rule): 0.0 / 0.0
- GIMF trade flows between partner regions (percent of total exports; exact values preserved):
  - To Asia: Asia 25.4, China 7.8, Euro 26.6, Japan 19.6, RestWorld 12.4
  - To China: Asia 19.5, China 8.2, Euro 22.8, Japan 20.4, RestWorld 10.3
  - To Euro: Asia 8.5, China 17.1, Euro 8.9, Japan 32.6, RestWorld 14.0
  - To Japan: Asia 5.9, China 8.8, Euro 2.6, Japan 5.1, RestWorld 4.9
  - To RestWorld: Asia 54.9, China 24.2, Euro 68.0, Japan 23.3, RestWorld 58.4
  - To USA: Asia 11.3, China 24.4, Euro 13.4, Japan 18.3, RestWorld 22.3

*Source: IMF working paper content (wpiea2020279-print-pdf).*

### 2.1    GTAP

### 2.1 GTAP

### Model structure and agents
- GTAP is a comparative static, multi-region, multi-sector, computable general equilibrium model.
- In each region, there is a representative household and different firms, one for each commodity sector.
- Sectors produce tradable and nontradable commodities/services and are interconnected through an input-output structure.
- In each sector, a representative firm optimizes over the cost of all commodity inputs and primary factors to produce output.
- Market clearing conditions ensure primary factors, which are in fixed net supply at the regional level, are fully employed.
- Households maximize a utility function subject to a budget composed of incomes from production factors and tax revenues.
- An Armington assumption defines preferences over a composite of domestic and imported goods differentiated by country of provenance; utility functions are usually CES so solutions are represented by spending shares.
- Investment does not cumulate into capital stock and is treated as a form of households expenditure, determined by relative rates of return across regions.

### Solution method and closures
- The model is solved by approximating the system of non-linear behavioral and accounting equations with its linearized equivalent so that the solution set delivers the percentage deviation from each variable initial value.
- Under the closure used when a region is hit by an import tariff shock, production factors are in fixed supply and fully employed.
- Deviations of behavioral equations (e.g., demand for a commodity) from initial values become a function of reduced-form elasticity parameters.

### Tariff shock mechanics and propagation
- A trade tariff shock represents a distortion to prices and introduces an inefficiency; a tariff generates a chain effect on prices.
- After a tariff shock, quantities and prices adjust to satisfy the firms’ and households’ (linearized) changes in demand of domestic and imported goods.
- The input-output structure governs propagation of the shock by sector and country.
- In the country imposing the tariff:
  - Higher prices of imported inputs put upward pressure on sale prices in sectors exposed to trade.
  - Firms lower their demand for imported inputs and substitute to some extent with domestic equivalents, introducing an inefficiency (a wedge) that allows less competitive domestic goods to become viable.
  - Imperfect substitutability and higher prices of domestic inputs generate a general increase in prices, a fall in final (domestic and external) demand for sectors exposed to trade, and a lower demand for production factors.
- In the country whose exports are hit by the tariff:
  - The increase in prices in a particular export market leads to downward pressure on output and production factors via lower external demand.
- With fixed supply of production factors and full employment, factor prices decline to clear markets; misallocations from higher import tariffs are measured in terms of the real factor prices prevailing in the new steady state.
- Factor returns and output decline relative to a no-tariff state, indicating less optimal allocation.
- The more exposed a country and its sectors are to trade, the larger the loss in productivity/efficiency arising from the sub-optimal allocation.
- The fall in factor returns determines a decline in the terms of trade that is also greater the more open a country is to trade (see the case of China in the following sections).

### Parameterization and data (GTAP specific)
- The version used in this paper comprises six regions with thirteen sectors in each region (j= 13).
- The regions are: the U.S.A., China, Euro Area (Euro), Japan, Emerging Asia (Asia) and the Rest of the World (RestWorld). Emerging Asia includes Hong Kong SAR, Indonesia, India, Korea, Malaysia, Philippines, Singapore, Thailand, and Taiwan province of China.
- Elasticities of substitution for different commodities are estimated by the GTAP consortium using a complex variety of data. This version uses the GTAP database v10 (2014).
- The elasticity of substitution between domestic and foreign goods, ε_j, averages just above 3 and the elasticities of substitution among imported varieties θ_j for different sectors are set to roughly double this value, following the rule of two.
- Parameters quantifying distribution shares of domestic versus imported input commodities and for imported commodities between partner countries are taken from the data for each sector j, region r and import country s and are calibrated to replicate import shares of output and by partner region in the data (as well as domestic input-output shares).
- GTAP features a total of 121 economies and 65 sectors; these can be aggregated into broader regions and sectors as needed.

*Source: IMF working paper content (2.1 GTAP, section and related parameterization text).*

### 3.1    The channels in GIMF

### 3.1    The channels in GIMF

### 3.1.1    Effects on the countries involved in the trade war
- Shock described: a 10-percentage-point increase in bilateral import tariffs between the U.S. and China.
- Short-run (SR, year 1) dynamics:
  - Exports of both the U.S. and China fall because of the contraction of bilateral import demand.
  - Exchange rate movements exacerbate the impact of the import tariff on total resources (investment and labor supply) by further affecting export flows.
  - Under the GIMF specification used (local currency pricing (LCP) with a high pass-through of the exchange rate in the short run), exchange-rate dynamics play a central role in maintaining consistency between trade flows, the balance of payments and intertemporal (UIP) conditions.
  - Despite symmetric tariff increases, asymmetric trade flows imply differing shocks: U.S. dollar appreciates against the renminbi because China’s exports to the U.S. are significantly larger in volumes and values; the U.S. import tariff increase therefore imposes a larger shock on China than the retaliation imposes on the U.S.
  - Short-run export changes: total exports contract by similar magnitudes: -2.1 percent for the U.S. and -2.2 for China.
  - Short-run GDP impact differs because of export shares in GDP: China GDP contracts by -0.66 percent while U.S. GDP contracts by -0.19 percent.
  - Real depreciation of the renminbi helps China increase exports to other destinations in the short run, partially offsetting loss in U.S. markets; dollar appreciation reduces U.S. exports to other partners, adding to loss from China.
- Medium- and long-run dynamics:
  - Long-run dynamics driven by firms’ investment responses to increased distortions from tariffs, affecting external demand and firms’ profitability and leading to lower capital stock, lower marginal product of labor, lower labor demand, and lower labor supply.
  - Tariff wedge lowers firms’ profitability in both markets: U.S. markets become less profitable for Chinese firms and Chinese markets less profitable for U.S. firms.
  - Armington preferences limit perfect substitution of foreign goods with domestic production, so higher import prices create a wedge in production costs and contraction pressures on capital and labor utilization.
  - In the long run, changes in the nominal exchange rate are fully passed on to trade prices:
    - For China, renminbi depreciation partly offsets the stronger negative impulse to investment but raises import costs.
    - For the U.S., dollar appreciation hurts exports to other destinations though it reduces import costs.
  - On net, Chinese and U.S. long-run investment declines are quite comparable, in contrast to larger short-run divergence.
- Investment and labor supply dynamics (Figure 4 summary):
  - Investment and labor responses are steep in the short run and milder in the long run.
  - Tariffs have the strongest short-run impact on firms’ investment in China.
  - In the medium and long run, expenditure switching and increased exports to other destinations (via currency depreciation) help support Chinese investment relative to the short run.
  - For the U.S., differences between short and long run are less stark; short-run dollar appreciation attenuates higher import costs, whereas full long-run pass-through weighs negatively on firms’ sales and investment, partially offset by expenditure switching.
  - Investment and labor supply closely track real GDP paths in both countries.

### 3.1.2    Spillovers to third countries
- Mechanism and timing:
  - Trade diversion is the main source of spillovers to third countries, especially in the short run.
  - Nominal and real rigidities, and changes in bilateral exchange rates, govern the magnitude of trade diversion.
- Short run:
  - China and U.S. total imports show a sluggish response to import tariffs because of import adjustment costs and gradual pass-through of the exchange rate to import prices.
  - This sluggishness generates diversion of U.S. and China imports toward countries not involved in the tariff dispute.
  - The U.S. and China intensify imports from other partners while total demand for foreign goods adjusts slowly, leading to an increase in exports and GDP of third countries in the short run.
  - Trade diversion is very pronounced in the short run but fades toward the medium run.
- Long run:
  - In the long run there is no significant increase in total exports for countries not involved in the dispute.
  - Reasons: rigidities dissipate so trade partners can fully adjust domestic demand and aggregate imports; full exchange-rate pass-through to trade prices acts as either a rebalancing or an additional negative force for the disputing countries.
  - Trade diversion toward third countries is typically weaker in the long run (example: euro area).
- Bilateral trade flow matrix (Figure 6):
  - Figure 6 reports all changes in bilateral trade flows in the long run, showing:
    - The model predicts a fall in U.S. exports toward all destinations as a direct effect of dollar appreciation and full pass-through to import prices.
    - U.S. bilateral trade balance with China improves somewhat, but aggregate U.S. trade balance remains broadly unchanged because of offsetting losses in other markets due to the dollar appreciation.
    - Exports to China experience the largest contraction because of the increase in bilateral tariffs, and the appreciation of the dollar adds to this contraction.
    - China’s exports to the U.S. display a very significant fall and are the only reason why China’s total exports contract; China’s exports to partners other than the U.S. increase as a result of renminbi depreciation.
    - On net, China’s export losses appear more muted in the long run relative to the U.S., but this occurs at the expense of other trade partners.
    - The U.S. is the only market where third countries maintain some gain in market share.
- Numerical highlights preserved from the analysis:
  - 10-percentage-point increase in bilateral import tariffs.
  - Short-run total export changes: -2.1 percent (U.S.), -2.2 (China).
  - Short-run GDP changes: -0.19 percent (U.S.), -0.66 percent (China).

*Source: GIMF simulations and IMF calculation. In percentage deviation from steady state.*

### 3.2    The channels in GTAP

### 3.2 The channels in GTAP

### Effects on the countries involved in the trade war
- Experiment: 10-percentage-point increase in U.S. and China bilateral import tariffs.
- Mechanism in GTAP:
  - GTAP does not model nominal exchange rates explicitly. The model focuses on changes in the relative price of goods and production factors.
  - Production factors are in fixed net supply at the regional level; changes in factor prices reflect reallocation across sectors rather than changes in total factor supplies.
  - Input-output linkages transmit relative price (cost) changes along production chains across sectors and between countries, inducing firms and households to substitute toward domestically produced goods or imports from third countries whose goods become relatively more competitive.
- Sectoral outcomes:
  - Reallocation observed across sectors; the largest moves occur in electronics, agriculture, and automotive.
  - Electronics: China’s production and exports of electronics fall (due to higher U.S. import tariffs and an increase in its price relative to similar sectors elsewhere); U.S. electronics production increases.
  - Agriculture: U.S. agricultural production and exports decline; Chinese agricultural production increases as agricultural imports become more expensive.
  - Automotive (cars and car parts): Production declines in the U.S. and increases (more modestly) in China.
  - These three sectors (electronics, agriculture, automotive) also show the largest production reductions in countries not involved in the dispute, likely due to disruption of global trade.
- Factor prices and aggregate efficiency:
  - Demand for production factors in trade-exposed sectors falls, causing downward pressure on factor prices under the hard constraint of fixed regional endowments/employment.
  - Reallocation of primary factors toward less trade-exposed sectors generates a loss of aggregate efficiency that materializes as a decline in factor real returns (measured as deviation from the model numeraire).
- GDP impacts (GTAP):
  - China: GDP falls 0.23 percent.
  - U.S.: GDP falls 0.09 percent.
  - Interpretation: Greater loss in China driven by the importance of electronics in Chinese exports and GDP and the reallocation away from electronics.
- Terms of trade:
  - Changes in terms of trade are larger in GTAP than in GIMF.
  - China: export prices decline relative to import prices, leading to a worsening of the terms of trade in both models.
  - U.S.: GTAP delivers a mild decline in U.S. terms of trade (ex-tariff export prices fall), whereas GIMF produces an increase in U.S. relative export prices (mostly owing to exchange rate appreciation). The difference may reflect the absence of an exchange-rate rebalancing role in GTAP and factor-price driven lower export prices.

### Spillovers to third countries
- Net trade spillovers in GTAP are dominated by the impact of tariffs on the external positions of China and the U.S., given absent movements in bilateral nominal exchange rates in GTAP.
- Key patterns in GTAP:
  - The increase in trade flows from Asia to third countries present in GIMF disappears in GTAP; total flows are dominated by an increase in exports to the U.S.
  - Trade diversion in GTAP can arise from:
    - (i) the complex sectoral input-output structure, and
    - (ii) a larger expansion of domestic production (than in GIMF) resulting from fixed net employment of production factors.
  - Example interpretation: diversion of U.S. imports from China towards Asia in specific sectors (electronics) and increased U.S. domestic production of those goods can generate higher U.S. imports from Asia and higher Chinese exports to Asian markets through supply-chain linkages.
- Bilateral export changes (percent deviation from steady state) reported in GTAP (excerpted matrix format):
  - To Asia:  -1.2, 6.7, -0.8, -1.7, -0.7, 7.5  (row label formatting in source)
  - To China: -1.0, -0.7, -1.6, -0.6, -43.8
  - To Euro:  -0.7, 7.6, -0.4, -1.0, -0.6, 1.4
  - To Japan: -1.2, 6.1, -1.1, -0.7, 0.8
  - To RestWorld: -0.8, 7.2, -0.7, -1.0, -0.8, 1.1
  - To USA: 7.5, -39.2, 4.4, 4.6, 3.0
  - (Source: IMF calculation. In percentage deviation from steady state.)

### Sensitivity analysis in GTAP
- Elasticities and calibration:
  - Benchmark: sector-specific elasticity of substitution between domestic and foreign goods, εγj, estimated from data; simple average across sectors yields a value just above 3.
  - Elasticity of substitution between imported goods from different source countries, θj, is set to double the elasticity between domestic and foreign goods.
- Experiments: multiply both εγj and θj by 0.5 and by 2 to obtain low and high elasticity scenarios (low roughly equivalent to GIMF’s domestic-foreign elasticity).
- Key sensitivities and channels:
  - In GTAP with full employment and absent investment dynamics, real GDP response is primarily influenced by changes in allocative efficiency.
  - Higher elasticities of substitution amplify the shock’s impact on exports and GDP because expenditure switching and reallocation across sectors are stronger.
  - Terms of trade are very sensitive to the elasticity of substitution.
  - China: decrease in terms of trade can generate a positive impulse to exports that is higher (lower) when the elasticity of substitution is lower (higher).
- Quantitative ranges and findings:
  - Despite high sensitivity of exports and welfare measures, the range of GDP results lies in a very small neighborhood: 0.1 for the U.S. and 0.2-0.3 for China.
  - The full employment condition in GTAP explains the limited variance in GDP: domestic production is more stable since resources are invariant and relative prices/terms of trade adjust to maintain regional constraints.

### Combining insights from both models (GTAP → GIMF mapping)
- Complementarity:
  - GTAP captures sectoral reallocation and implied losses in aggregate efficiency from misallocation across sectors.
  - GIMF captures dynamics of investment, utilization of labor and capital, and exchange-rate driven rebalancing absent in standard GTAP.
  - Using GTAP results as estimates of productivity losses from reallocation can augment GIMF’s aggregate representation to produce a more complete macroeconomic impact assessment.
- Mapping approach:
  - Aggregate factor endowments in GTAP are fixed; percentage changes in sectoral GDP from GTAP can be viewed as percentage changes in productivity (a residual of an aggregate production function).
  - The percentage changes in GDP from GTAP are applied as shocks to labor-augmenting productivity and to TFP in GIMF, in addition to the bilateral tariff increase.
  - Calibration: shocks to long-run productivity are set to match GTAP GDP changes of -0.09 percent for the U.S. and -0.23 percent for China; productivity shock unfolds gradually, reaching the long-run level after 5 years.
- Combined-model quantitative results (percent deviation from baseline of real GDP in GIMF):
  - Mapping GTAP GDP changes into a TFP shock:
    - China: accounting for the productivity loss from resource reallocation leads to about 0.5 percentage point worse GDP contraction in the long run.
    - The larger relative impact in China reflects a higher baseline investment share of GDP in China versus the U.S.
  - Mapping GTAP GDP changes into a labor-specific productivity shock:
    - China: leads to a more contained response, about just over 0.1 percentage point worse GDP loss in the long run, given a more muted investment reaction.
- Caveats:
  - Using GTAP-derived productivity shocks in GIMF may overestimate the overall effect because frameworks that allow factor contraction would produce lower estimates of lost productivity from reallocation.
  - Shocks to TFP generate much larger GDP responses in DSGE models (especially where investment/GDP shares are high) than shocks to labor-specific productivity.

### Concluding remarks
- Two complementary perspectives on tariffs:
  - GIMF: tariff increases generate exchange-rate appreciation for the imposing country, falls in investment, labor utilization, and exports, in short and long run.
  - GTAP: tariff increases produce reallocation of resources across sectors and associated aggregate productivity losses when less efficient domestic production replaces previously cheaper imports.
- Policy-relevant synthesis:
  - Combining GTAP’s sectoral estimates of productivity loss with GIMF’s macro-dynamics can more than double GIMF’s long-run GDP effects in some cases, illustrating that accounting for resource reallocation materially affects macro estimates of tariff impacts.
- Overall finding: unilateral or bilateral increases in import tariffs produce sectoral resource reallocation and an aggregate loss in productivity in countries involved in the dispute; the macroeconomic magnitude depends crucially on model features (full employment vs. factor utilization, elasticities of substitution, investment shares).

*Source: IMF calculation. In percentage deviation from steady state.*

### References

### References and Technical Appendices (wpiea2020279-print-pdf - References)

### References
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- [19] Hertel W.T., A.R. McDougall, G.B. Narayanan, H.A. Aguiar (2009), GTAP 10 data base documentation - chapter 14: behavioral parameters. Available at: https://www.gtap.agecon.purdue.edu/resources/download/4184.pdf.
- [20] Kambourov G. (2009), Labour Market Regulations and the Sectoral Reallocation of Workers: The Case of Trade Reforms, The Review of Economic Studies 76(4), pp. 1321-1358.
- [21] Kumhof M., D. Muir, S. Mursula, D. Laxton (2010), Global Integrated Monetary and Fiscal Model, IMF Working Paper 10/34.
- [22] Lerner A. P. (1936), The Symmetry Between Import and Export Taxes, Economica 3(11), pp. 306-313.
- [23] Linde J. and A. Pescatori (2017), The Macroeconomic Effects of Trade Tariffs: Revisiting the Lerner Symmetry Result, IMF Working Paper 17/151.
- [24] McDaniel C. A. and E. J. Balistreri (2003), A Discussion on Armington Trade Substitution Elasticities, U.S. International Trade Commission Working Paper No. 2002-01-A.
- [25] McKibbin W. J. and P. J. Wilcoxen (1999), The Theoretical and Empirical Structure of the G-Cubed Model, Economic Modelling 16(1), pp. 123-148.
- [26] Restuccia D. (2019), Misallocation and Aggregate Productivity Across Time and Space, Canadian Journal of Economics 52(1), pp. 5-32.
- [27] Restuccia D. and R. Rogerson (2017), The Causes and Costs of Misallocation, Journal of Economic Perspectives 31(3), pp. 151-174.
- [28] Walmsley T. and P. Minor (2017), Supply Chains and Tariff Rates: The Impact of Reversing NAFTA, GTAP Working Paper, March 2017.

### Appendix A: A description of GTAP algorithm — key equations and solution steps
- Model solved in linearized version; variables of interest solved as percentage changes.
- Notation:
  - superscript j indicates a sector producing commodity j; superscript i the commodity or primary factor inputs.
  - Lower case letters indicate proportional (percentage) changes; values Vx = Px Qx and dV/V = p + q.
- Market clearing conditions:
  - Non-tradable goods and primary factors: ∑_j Q^S,i,j = ∑_j Q^D,i,j + Q^H,i (equation (A.1)); linearized to (A.4): ∑_j V^S,i,j q^S,i,j = ∑_j V^D,i,j q^D,i,j + V^H,i q^H,i.
  - For primary factor supply (fully employed, net fixed supply): 0 = ∑_j V^D,i,j q^D,i,j (equation (A.5)).
  - Tradable goods global clearing: ∑_r ∑_j Q^S,i,j,r = ∑_r ∑_j Q^D,i,j,r + ∑_r Q^H,i,r (equation (A.6)); linearized (A.7) with world prices P^w_i.
- Price transmission channels (equation (A.8)):
  - p^m_i,r = t_i,r + p^w_i
  - p^D,i,j,r = t^D,i,j,r + p^m_i,r
  - p^S,i,j,r = t^S,i,j,r + p^m_i,r
  - where t_i,r is the (percentage) change in import tariff on commodity i in region r; t^D,i,j,r, t^S,i,j,r are taxes/subsidies.
- Zero-profit condition (perfect competition) (A.9)/(A.10): sum of value of sales equals sum of value of demanded inputs in each sector j and region r; expressed using cost and revenue shares S^D and S^S.
- Income in each region (A.11)/(A.12): Y_r = ∑_E ∑_j P^E_S,i,j,r Q^E_S,i,j,r + taxes; linearized: Y_r y_r = ∑_E ∑_j V^E_S,i,j,r [ p^E_S,i,j,r + q^E_S,i,j,r ] + taxes.
- Behavioral equations — firms and households:
  - Industry demand uses nested CES technology; firm minimizes ∑_i P^D,i,j,r Q^D,i,j,r subject to Z_j,r defined by CES with elasticity σ_j (equation (A.13) and following).
  - Optimal demand linearized to q^D,i,j,r = −σ_j S^D,i,j,r p^D,i,j,r + z_j,r (equation (A.21)), where −σ_j S^D,i,j,r is jointly estimated from data.
  - Supply: q^S,i,j,r = φ_i,k p^S,k,j,r + z_j,r (equation (A.23)), where φ_i,k is a conditional supply elasticity.
  - Household utility is Cobb-Douglas across sub-utilities (A.24); allocations to savings and government spending follow shares β_x,r (A.25) and linearized u_x,r = y_r − p_H,x (A.26).
  - Household consumption demand linearized: q^H,i,r = ∑_k η^H,i,k,r p_H,i,r + η^H,i,r y_r (A.27).
- Effect of a tariff increase — multi-step simulation using Gragg’s method (Harrison and Pearson, 1994):
  - Model solved as system of differential equations for proportional changes; shocks broken into smaller steps.
  - Illustrative two-region example (r = U.S., ROW) with U.S. import tariff increase t_i,US on all imported commodities and single sector j = electronics importing from ROW:
    1. From (A.8), prices of imported goods increase; p^S,i,j,US = p^D,i,j,US > 0 for sector j and U.S. household.
    2. Quantities demanded by household, government and firms of sector j goods fall per (A.21) and (A.27).
    3. Total activity in sector j importing intermediate goods from abroad falls, z_j < 0 (equation (A.22)).
    4. Demand for primary factors and nontradable services falls as per (A.21).
    5. Market clearing conditions for primary factors and tradable goods are not satisfied.
    6. In particular, the full employment condition for primary factors in the U.S. from (A.5) is not satisfied.
    7. Algorithm calculates percentage changes in prices compatible with returning these equations to equilibrium by steps.
    8. Prices of primary factors fall to reestablish equilibrium (demand in other sectors increases).
    9. Commodities supplied by all sectors increase via (A.22) as domestic goods become cheaper.
    10. Armington assumption implies these domestic responses do not fully compensate for fall in imports of commodity j.
    11. To satisfy global clearing (A.7), prices in the ROW decrease so supply of goods imported by the U.S. decreases.
    12. This may imply U.S. prices increase relative to ROW, improving U.S. terms of trade (implicit exchange rate appreciation).
  - Note: these steps are illustrative; full model includes sectoral linkages and more complex price/quantity interactions.

### Appendix B: International trade in GIMF — structure and tariff transmission
- Regions produce tradable final (D) and intermediate (T) goods and nontradable (N) goods.
- Import agents for intermediate and final goods are domestically owned but located in export destination countries; import agents sell output to foreign distributors or goods producers at prices rigid in foreign currencies in short run (local currency pricing).
- Distributors combine imported final goods from import agents using nested CES technology with elasticity of substitution σ_j, j ∈ {D, T}.
- Distributors then combine foreign (TF) with domestic (TH) intermediate tradable goods using elasticity of substitution ϵ_T; consumption and investment goods producers combine DF with DH with elasticity ϵ_D.
- Import adjustment costs are quadratic to prevent instantaneous responsiveness to relative price changes.
- Prices of imported goods are weighted averages by destination, converted to local currency, augmented by tariffs imposed by import region.
- Key tariff transmission equations and balance of payments:
  - Relative demand for imported versus domestic goods: Y^M_t / Y^H_t = f(Θ; τ_m, φ_t, P^*_t / P_t), where Θ contains parameters including elasticities.
  - Short run: full pass-through of exchange rate to import prices assumed (PCP). If imperfect pass-through, P^M_t replaces φ_t and P^*_t / P_t.
  - Law of one price for domestic goods consumed abroad: P^X_t = P_t (1 + τ^*_m) φ_t (notation as in text).
  - Balance of payments (nominal): B^F_t = B^F_{t−1} R^*_t + P^X_t (1 + τ^*_m) Y^X_t − P^M_t (1 + τ_m) φ_t Y^M_t.
  - Intertemporal condition for foreign bond holdings (Euler): 1 = β E_t [ Λ_{t,t+1} P_t / P_{t+1} φ_{t+1} / φ_t R^*_t ].
  - Domestic bond Euler: 1 = β E_t [ Λ_{t,t+1} P_t / P_{t+1} R_t ].
  - Combination leads to uncovered interest rate parity (UIP) under incomplete markets; tariffs generate shocks that interact with nominal and real rigidities and policy reaction functions, affecting interest rates and exchange rates, thereby amplifying tariff impacts on resources and exports.

### Appendix C: Details on parameterization — GTAP and GIMF parameter values and trade flows
- GTAP elasticity of substitution table (values are the same by region but differ by sector/commodity i):
  - Crops: ϵ_i = 2.5, θ_i = 4.9
  - Meat and livestock: ϵ_i = 3.2, θ_i = 7.4
  - Extraction: ϵ_i = 4.9, θ_i = 11.9
  - Processed food: ϵ_i = 2.1, θ_i = 4.4
  - Textile and apparel: ϵ_i = 3.7, θ_i = 7.4
  - Light manufacturing: ϵ_i = 3.6, θ_i = 7.6
  - Iron and steel: ϵ_i = 3.0, θ_i = 5.9
  - Aluminum and other metals: ϵ_i = 4.2, θ_i = 8.4
  - Auto and parts: ϵ_i = 2.8, θ_i = 5.6
  - Heavy manufacturing: ϵ_i = 3.2, θ_i = 6.7
  - Electronics: ϵ_i = 4.4, θ_i = 8.8
  - Transportation services: ϵ_i = 2.1, θ_i = 4.6
  - Other services: ϵ_i = 1.9, θ_i = 3.8

- GTAP trade flows between partner regions (in percent of total exports):
  - To Asia: Asia 22.8, China 22.4, Euro 5.5, Japan 27.8, RestWorld 12.2, USA 12.1
  - To China: Asia 20.9, China 4.5, Euro 25.9, Japan 9.0, RestWorld 8.7
  - To Euro: Asia 10.2, China 13.2, Euro 41.5, Japan 9.0, RestWorld 25.3, USA 17.4
  - To Japan: Asia 7.1, China 8.2, Euro 1.5, Japan 4.4, RestWorld 5.2
  - To RestWorld: Asia 26.4, China 37.5, Euro 39.4, Japan 21.5, RestWorld 31.6, USA 56.7
  - To USA: Asia 12.5, China 18.7, Euro 7.5, Japan 15.8, RestWorld 17.4

- GIMF key parameter values (one model period = one year):
  - USA / China
    - Real adjustment costs of imports: 1.0 / 1.0
    - Capital as share of GDP: 39.5 / 45.1
    - Investment as share of GDP: 16.9 / 26.1
    - Discount factor (β): 0.982 / 0.973
    - Share of liquidity-constrained households (ψ): 0.25 / 0.25
    - Frisch elasticity of labor supply: 0.5 / 0.5
    - Elasticity of substitution btw domestic and foreign goods: 1.5 / 1.5
    - Elasticity of substitution among foreign goods: 1.5 / 1.5
    - Coeff. on deviation from inflation target (monetary rule): 1.0 / 1.0
    - Coeff. on deviation from output target (monetary rule): 0.0 / 0.0

- GIMF trade flows between partner regions (in percent of total exports):
  - To Asia: Asia 25.4, China 7.8, Euro 26.6, Japan 19.6, RestWorld 12.4
  - To China: Asia 19.5, China 8.2, Euro 22.8, Japan 20.4, RestWorld 10.3
  - To Euro: Asia 8.5, China 17.1, Euro 8.9, Japan 32.6, RestWorld 14.0
  - To Japan: Asia 5.9, China 8.8, Euro 2.6, Japan 5.1, RestWorld 4.9
  - To RestWorld: Asia 54.9, China 24.2, Euro 68.0, Japan 23.3, RestWorld 58.4
  - To USA: Asia 11.3, China 24.4, Euro 13.4, Japan 18.3, RestWorld 22.3

*Source: wpiea2020279-print-pdf - References (Appendices A–C).*

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_Source: https://www.imf.org/-/media/files/publications/wp/2020/english/wpiea2020279-print-pdf.pdf_