## _wp1146 - Section III. In Section IV we consider the implications of rebalancing for exchange rates and

## Source details

**Canonical URL:** [_wp1146 - Section III. In Section IV we consider the implications of rebalancing for exchange rates and](https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2011/_wp1146.pdf)

## Other formats

- [Markdown version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2011/_wp1146.pdf.md)
- [Structured JSON version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2011/_wp1146.pdf.json)

---

### Model overview
- Model largely based on OR (Obstfeld and Rogoff).
- Two main structures:
  - Simplified two-country version with only tradable goods (two-period model) to explain mapping between trade balances and exchange rates.
  - Full three-country version including nontradable goods and input-output linkages (U.S., China, OEA).

### Simplified two-country model (only tradables)
- Time structure: two-period model (period t and t+1).
- Preferences and parameters:
  - Home utility: u(C_t︷︸︸︷(α 1/η C_H,t^{(η−1)/η} + (1−α) 1/η C_F,t^{(η−1)/η})^{η/(η−1)}) + β u(C_{t+1}︷︸︸︷(α 1/η C_{H,t+1}^{(η−1)/η} + (1−α) 1/η C_{F,t+1}^{(η−1)/η})^{η/(η−1)})
  - Parameters: β (intertemporal discount factor), η (elasticity of substitution), α (home bias).
- Key first-order conditions and definitions:
  - C_{F,t} / C_{H,t} = ((1−α)/α) φ_t^{−η}  (Equation (5))
  - P_t = P_{H,t} (α + (1−α) φ_t^{1−η})^{1/(1−η)}  (Equation (6))
  - Intertemporal Euler: C_{t+1} / C_t = [β R ( (α + (1−α) φ_t^{1−η}) / (α + (1−α) φ_{t+1}^{1−η}) )^{1/(1−η)} ]^{1/ρ}  (Equation (7))
  - Trade balance normalized: tb_{H,t} = 1 − φ_t (C_{F,t} / Y_{H,t}) + (C_{H,t} / Y_{H,t})  (Equation (8))
- Foreign country analogs provided (Equations (9) and (10)) and resource constraints (Equations (11) and (12)).

### Mapping between trade balances and relative prices (within-period equilibrium)
- Focus: within-period equilibrium mapping of φ_t to clear trade balance tb_{H,t}, abstracting from intertemporal determinants.
- Analytic mapping:
  - tb_{H,t} = 1 + [ (1−α^*) φ_t^{η} (Y^*_F,t / Y_{H,t}) − α^* ] [ α + (1−α) φ_t^{1−η} ]^{α^*+α−1}
- Qualitative result (under α and α^* > 0.5 and η ≥ 1):
  - Improvement of the home trade balance requires an increase in φ (worsening of terms of trade; domestic goods cheaper relative to foreign goods).
  - Intuition: with home bias, an improvement in home TB at fixed φ reduces home consumption more than it raises foreign demand for home goods → excess supply → home depreciation needed.
  - Higher η (greater substitutability) reduces required depreciation.

### Three-country version (OR (2007) extension)
- World: three endowment economies — U.S., China (CH), Other Emerging Asia (OEA).
- Households consume tradable and nontradable goods in all countries.
- Baseline trade network: U.S. trades with China and OEA; China and OEA do not trade among themselves (relaxed later).
- Substitutability assumptions:
  - Low substitutability between U.S.-produced and Asia-produced goods.
  - High substitutability between goods produced by China and OEA (small price change can induce large expenditure switching).
- U.S. household structure:
  - Aggregate consumption: C = [ γ^{1/θ} C_T^{(θ−1)/θ} + (1−γ)^{1/θ} C_N^{(θ−1)/θ} ]^{θ/(θ−1)}
  - Tradable aggregator: C_T = [ α^{1/η} C_H^{(η−1)/η} + (1−α)^{1/η} C_F^{(η−1)/η} ]^{η/(η−1)}
  - Imported tradables split: C_F = [ β^{1/ξ} C_{F,C}^{(ξ−1)/ξ} + (1−β)^{1/ξ} C_{F,O}^{(ξ−1)/ξ} ]^{ξ/(ξ−1)}
  - First-order price conditions:
    - P = [ γ P_T^{1−θ} + (1−γ) P_N^{1−θ} ]^{1/(1−θ)}
    - P_T = [ α P_H^{1−η} + (1−α) P_F^{1−η} ]^{1/(1−η)}
    - P_F = [ β P_{F,C}^{1−ξ} + (1−β) P_{F,O}^{1−ξ} ]^{1/(1−ξ)}
  - Consumption/price ratio identities (including φ_C = P_{F,C} / P_H ; φ_O = P_{F,O} / P_H).

### Market clearing (three-country equilibrium)
- Resource constraints:
  - Y_H = C_H + C*_H + C**_H
  - Y_F,C = C_F,C + C*_F,C
  - Y_F,O = C_F,O + C**_F,O
  - Y_N = C_N ; Y*_N = C*_N ; Y**_N = C**_N
- Aggregate external balance conditions:
  - CA_H + CA*_F,C Σ* + CA**_F,O Σ** = 0
  - F_H + F*_F,C Σ* + F*_F,O Σ** = 0
- Solve for:
  - optimal consumption allocations,
  - relative equilibrium prices x, x*, x** (tradable/nontradable),
  - terms of trade φ_C and φ_O,
  - U.S. terms of trade with emerging Asia: τ = P_F / P_H = (β φ_C^{1−ξ} + (1−β) φ_O^{1−ξ})^{1/(1−ξ)}
- Bilateral and trade-weighted real exchange rates:
  - R_C, R_O, and R defined as in the source expressions (depend on γ, θ, x, φ_C, τ, α, η, and country-specific parameters).
- Equilibrium responses depend on structural parameter calibration, shares of tradable/nontradable outputs, and initial external positions.

### III. Calibration — trade elasticities and parameters
- Elasticities:
  - Benchmark: η = 1.5 (implies elasticity of imports of −1.5).
  - η*, η** calibrated same as U.S. benchmark.
  - Robustness: experiment with η = 1 for the U.S. (implies elasticity of imports of −1).
  - Estimated ξ (CH vs OEA substitutability) using Feenstra (1994)/Broda and Weinstein (2006) sectoral aggregation:
    - ξ̂ = Σ_k w_k ξ̂_k → aggregate estimate = 3.98 ; Standard error = 0.39
    - Calibration uses ξ = 4.
- Other calibrated parameters (summary of Table 1):
  - θ, θ*, θ** = 2 (OR (2007))
  - ξ = 4 (our estimate)
  - γ, γ*, γ** = 0.25 (OR (2007))
  - α (U.S. home bias) = 0.85 (calibrated to Import/GDP from CH and OEA)
  - α*, α** = 0.925 (OR (2007))
  - β (U.S. import bias for Chinese goods) = 0.562% (U.S. import share from CH)
- Production share ratios (σ = Y_H / Y_N or equivalents):
  - σ (U.S. N/T real GDP) = 2.825
  - σ* (CH N/T real GDP) = 0.365
  - σ** (OEA N/T real GDP) = 0.345
  - σ_C (CH/U.S. tradable real GDP) = 0.853
  - σ_O (OEA/U.S. tradable real GDP) = 0.6827
- External positions and rates:
  - i_world interest rate = 5% (OR (2007))
  - f_U.S. NFA with CH and OEA (%GDP) = -12.4% (2009 bilateral data)
  - f*_CH NFA with U.S. (%GDP) = 27.3% (2009 bilateral data)
  - tb_U.S. TB with CH and OEA (%GDP) = -1.9% (2009 bilateral data)
  - tb*_CH TB with U.S. (%GDP) = 4.5% (2009 bilateral data)

### IV. Rebalancing and relative prices — scenarios and findings
- Experiment: reduce U.S. current account deficit vis-à-vis emerging Asia by 1 percent of U.S. GDP (from end-2009 bilateral deficit of 2.5 percent of U.S. GDP to 1.5 percent).
- Scenario A — Exchange rate adjustment (three cases):
  1. Symmetric appreciation (China and OEA export prices increase equally):
     - To reduce U.S. deficit by 1 percent of GDP: terms of trade in both China and OEA improve by 15 percent.
     - Emerging Asia bilateral CA surpluses with U.S. decline by about 2 percent of their respective GDPs:
       - China: from about 6 percent of GDP to 4 percent of GDP.
       - OEA: from 1.5 percent of GDP to a small deficit.
     - U.S. trade-weighted terms of trade (τ) worsen and U.S. real exchange rate (R) depreciates by similar amounts (increase denotes depreciation from U.S. point of view).
  2. China resists appreciation (all adjustment on OEA, φ_O):
     - OEA relative prices must increase by 32 percent.
     - China’s CA surplus increases (expenditure switching toward China).
     - OEA moves from surplus of about 1.5 percent of GDP to deficit of 2.5 percent of GDP.
     - Relative prices of nontradables fall in China and the U.S., increase in OEA.
     - U.S. real exchange rate depreciation smaller than terms-of-trade change.
  3. OEA resists appreciation (all adjustment on China, φ_C):
     - Chinese export prices increase by about 30 percent.
     - Chinese CA surplus almost vanishes vis-à-vis the U.S.
     - OEA surplus with the U.S. increases (from 1.5 percent of GDP to 2.9 percent of GDP).
- Scenario B — Robustness checks:
  - Lower U.S. η to 1 (η = 1, η* = η** = 1.5):
    - Required increase in emerging Asia export prices larger for same 1 percent GDP deficit reduction:
      - Symmetric improvement needed ≈ 23 percent.
      - If only China allows export prices to increase: required improvement ≈ 45 percent.
      - If only OEA appreciates: required improvement ≈ 42 percent.
  - Notes:
    - Model is endowment economy (no supply effects). Allowing factor mobility or production reallocation would reduce required relative price adjustments.
    - Including rest of world: if other regions also raise export prices, change required in emerging Asia smaller; if rest of world resists, emerging Asia terms of trade improve more and U.S. R appreciates more, implying larger contraction in emerging Asia CA surpluses.
- Scenario C — Change in home bias:
  - If China and OEA resist export-price changes, rebalancing could occur via reductions in consumption home bias (α* and α**).
  - Quantitative example:
    - If basket of Chinese and OEA tradables included about 3 percent more goods produced in the U.S. (decline in home bias ≈ 3 percentage points), bilateral TB effects similar to those from a 15 percent appreciation with no preference changes.
  - Even with no terms-of-trade change, U.S. real effective exchange rate still declines due to nontradable-to-tradable price changes.
  - Increased consumption of tradables in Asia raises nontradable demand; with fixed supply, nontradable prices rise in China.

### V. Introducing input-output (IO) linkages — evidence and model extension
- Empirical motivation:
  - Dean, Fung, and Wang (2007): estimate that 35 percent of the value of China’s aggregate exports is attributable to imported inputs (text truncated).
  - Hummels, Ishii and Yi (2001): vertical specialization grew ≈ 30 percent between 1970 and 1990, explaining > 30 percent of world export growth.
  - Koopman, Wang, and Wei (2008): when accounting for different production functions, intermediate inputs ≈ 50 percent of value of Chinese aggregate exports.
  - Bems, Johnson and Yi (2010): 42 percent of Chinese imports of intermediate inputs come from OEA; 8 percent from the U.S.
- Model augmentation (supply dimension and international segmentation):
  - Each country endowed with exogenous quantity of inputs used as the only productive factor; factors sector-specific (tradable inputs not usable for nontradables).
  - Nontraded good technology linear: one unit of good per unit of input.
  - Traded good sector: production internationally segmented; countries can trade in intermediate inputs.
  - Empirical GTAP-based import content (Hummels, Ishii, Yi methodology adapted):
    - Import content in U.S. tradables: 15 percent.
    - Import content in China tradables: 23 percent.
    - Import content in OEA tradables: 34 percent.
    - Aggregated into exports:
      - US: 16 percent
      - China: 33 percent
      - OEA: 40 percent
- Production functions for tradables with vertical specialization:
  - Y*_F,C = Q*_{C,C}^{μ*} Q*_{O,C}^{1−μ*}
  - Y**_F,O = Q**_{O,O}^{μ**} Q**_{C,O}^{1−μ**}
  - Calibrated μ parameters:
    - μ* = 0.902
    - μ** = 0.956
  - Interpretation: high share of domestic intermediate inputs; share of OEA inputs in Chinese tradable production ≈ 10 percent.
- Price pass-through and exchange-rate pass-through mechanics:
  - Prices of final goods in U.S. dollars are functions of intermediate input prices in the three countries.
  - If China appreciates by 1 percent (via Σ* or P*_{C,Q}), price of final Chinese goods increases by μ* percent.
  - Price of Chinese exports to the U.S. (from FOCs):
    - P_{F,C} = (Σ* P*_{C,Q})^{μ*} (Σ** P**_{O,Q})^{1−μ*} μ*^{μ*} (1−μ*)^{1−μ*}
  - With two-way IO linkages, Chinese appreciation affects OEA final goods prices shipped to the U.S., altering substitution patterns.
- Exchange rate adjustment quantitative implications:
  - One-way IO linkages (μ* = 0.902, μ** = 1):
    - Required Chinese intermediate goods price increase to reduce U.S. deficit by 1 percent of GDP = 33 percent (versus 30 percent in model without IO linkages).
    - Impact limited because OEA final export prices unaffected by Chinese appreciation, inducing substitution toward OEA.
  - Two-way IO linkages (μ* = 0.902, μ** = 0.956):
    - Required unilateral Chinese appreciation close to the one in model without IO linkages and smaller than in one-way case.
    - Intuition: OEA final goods prices also increase via input channels, reducing substitution away from Chinese goods.
  - Main message: IO linkages, especially empirically relevant two-way linkages, have only a very limited impact on required appreciation to accommodate a given reduction in the U.S. current account deficit.

### Key quantitative headline results
- Required joint improvement in terms of trade of all emerging Asia to accommodate a reduction in the U.S. current account of 1 percent of GDP: about 15 percent (when neglecting trade in intermediate inputs).
- One-way IO linkages example: required Chinese intermediate goods price increase = 33 percent (versus 30 percent without IO linkages) to reduce U.S. deficit by 1 percent of GDP.
- GTAP-based import content measures:
  - U.S. tradables import content: 15 percent.
  - China tradables import content: 23 percent.
  - OEA tradables import content: 34 percent.
  - Aggregated into exports: US 16 percent, China 33 percent, OEA 40 percent.
- Sources of Chinese intermediate imports (Bems, Johnson and Yi, 2010):
  - 42 percent from OEA
  - 8 percent from the U.S.
  - For emerging Asia aggregate: 13 percent from China, 16 percent from the U.S. (each ≈ 15 percent)

### Conclusions and directions for future research
- Main conclusions:
  - Neglecting intermediate inputs, emerging Asia jointly needs about a 15 percent terms-of-trade improvement to accommodate a 1 percent of GDP reduction in the U.S. current account.
  - If only China allows export prices to increase, a larger Chinese appreciation is required because U.S. consumers substitute toward OEA tradables.
  - One-way IO linkages modestly increase required Chinese appreciation; empirical evidence supports two-way IO linkages between China and OEA, which mute IO linkage impacts.
- Suggested research directions:
  - Move beyond endowment economy: allow supply responses to real exchange rate fluctuations (real quantity adjustments may reduce necessary relative price movements).
  - Expand beyond the U.S.–emerging Asia bilateral focus to incorporate other countries and study global sharing of rebalancing.
  - Study adjustments beyond the 1 percent of GDP shock to examine relative price adjustments in a fuller multi-country equilibrium.

*Source: _wp1146 - Section III. In Section IV we consider the implications of rebalancing for exchange rates and*

### Section III. In Section IV we consider the implications of rebalancing for exchange rates and

### _wp1146 - Section III. In Section IV we consider the implications of rebalancing for exchange rates and

### Model overview
- The model is largely based on OR (Obstfeld and Rogoff). It analyzes mapping between trade balances and exchange rates.
- Structure:
  - A simplified two-country version with only tradable goods to explain the mapping.
  - A full three-country version including nontradable goods and input-output linkages (discussed later in the paper).

### Simplified two-country model with only tradable goods
- Time structure: two-period model (period t and t+1).
- Home country utility (consuming domestic C_H,t and foreign goods C_F,t):
  - u(C_t︷︸︸︷(α 1/η C_H,t^{(η−1)/η} + (1−α) 1/η C_F,t^{(η−1)/η})^{η/(η−1)}) + β u(C_{t+1}︷︸︸︷(α 1/η C_{H,t+1}^{(η−1)/η} + (1−α) 1/η C_{F,t+1}^{(η−1)/η})^{η/(η−1)})
  - Parameters: β is the intertemporal discount factor, η is the elasticity of substitution between domestic and foreign goods, α controls home bias.
- Home budget constraint:
  - P_{H,t} Y_{H,t} − P_t C_t︷︸︸︷(P_{F,t} C_{F,t} + P_{H,t} C_{H,t}) = (1/I)[P_{t+1} C_{t+1}︷︸︸︷(P_{F,t+1} C_{F,t+1} + P_{H,t+1} C_{H,t+1}) − P_{H,t+1} Y_{H,t+1}]
  - I is the gross nominal interest rate; P_H and P_F are prices of home and foreign goods.
- Intratemporal optimality (consumption ratios and price definitions for period t and t+1):
  - C_{F,t} / C_{H,t} = ((1−α)/α) φ_t^{−η}  (Equation (5))
  - P_t = P_{H,t} (α + (1−α) φ_t^{1−η})^{1/(1−η)}  (Equation (6))
  - where φ_t = P_{F,t} / P_{H,t} are the terms of trade.
- Intertemporal Euler equation (with CRRA utility parameter ρ):
  - C_{t+1} / C_t = [β R ( (α + (1−α) φ_t^{1−η}) / (α + (1−α) φ_{t+1}^{1−η}) )^{1/(1−η)} ]^{1/ρ}  (Equation (7))
  - π = P_{H,t+1} / P_{H,t} is domestic inflation; R = I / π is the real interest rate.
- Trade balance definition and normalization:
  - TB_{H,t} = P_{H,t} Y_{H,t} − P_t C_t︷︸︸︷(P_{F,t} C_{F,t} + P_{H,t} C_{H,t})
  - Normalized by home GDP (P_{H,t} Y_{H,t}): tb_{H,t} = 1 − φ_t (C_{F,t} / Y_{H,t}) + (C_{H,t} / Y_{H,t})  (Equation (8))
- Foreign country first-order conditions:
  - C^*_H,t / C^*_F,t = ((1−α^*)/α^*) φ_t^{η}  (Equation (9))
  - C^*_{t+1} / C^*_t = [β^* I / π^* ( (α^* + (1−α^*) φ_t^{η−1}) / (α^* + (1−α^*) φ_{t+1}^{η−1}) )^{1/(1−η)} ]^{1/ρ}  (Equation (10))
- Resource constraints:
  - Y_{H,t} = C_{H,t} + C^*_H,t  (Equation (11))
  - Y^*_F,t = C_{F,t} + C^*_F,t  (Equation (12))

### Mapping between trade balances and relative prices (within-period equilibrium)
- The paper focuses on the within-period equilibrium mapping: how φ_t must adjust to clear the within-period equilibrium for a given trade balance tb_{H,t}, abstracting from intertemporal determinants.
- Analytic expression derived for the mapping (as presented in the text):
  - tb_{H,t} = 1 + [ (1−α^*) φ_t^{η} (Y^*_F,t / Y_{H,t}) − α^* ] [ α + (1−α) φ_t^{1−η} ]^{α^*+α−1}
- Qualitative result under assumptions α and α^* larger than 0.5 and η ≥ 1:
  - An improvement of the home trade balance requires an increase in φ (a worsening of the terms of trade, making domestic goods cheaper relative to foreign goods).
  - Intuition: With home bias, holding φ fixed an improvement in the home trade balance reduces home consumption more than foreign demand for home goods increases, generating net excess supply of home goods; home goods must depreciate to restore equilibrium.
  - The higher the substitutability between domestic and foreign goods (larger η), the lower the required depreciation.

### Three-country version of Obstfeld and Rogoff (2007)
- Key elements:
  - World composed of three endowment economies: the U.S., China, and OEA.
  - In all countries households consume nontradable and tradable goods.
  - The U.S. trades with both China and OEA; China and OEA do not trade among themselves (in the baseline).
  - Substitutability assumptions: low substitutability between U.S.-produced and Asia-produced goods; high substitutability between tradable goods produced by China and OEA. A small change in export prices between China and OEA can induce a large expenditure switching effect.
  - Section V relaxes the no-China-OEA trade assumption to allow trade in intermediate inputs.

### U.S. households (detailed structure)
- Aggregate consumption index:
  - C = [ γ^{1/θ} C_T^{(θ−1)/θ} + (1−γ)^{1/θ} C_N^{(θ−1)/θ} ]^{θ/(θ−1)}
  - θ is elasticity of substitution between tradable and nontradable goods; γ pins down the fraction of tradable goods.
- Tradable consumption aggregator:
  - C_T = [ α^{1/η} C_H^{(η−1)/η} + (1−α)^{1/η} C_F^{(η−1)/η} ]^{η/(η−1)}
  - η is elasticity between home and foreign goods; α is bias towards home-produced tradables.
- Imported tradables split between China and OEA:
  - C_F = [ β^{1/ξ} C_{F,C}^{(ξ−1)/ξ} + (1−β)^{1/ξ} C_{F,O}^{(ξ−1)/ξ} ]^{ξ/(ξ−1)}
  - β is the consumption bias for Chinese goods; ξ is elasticity between Chinese and OEA goods.
- Budget constraints and definitions:
  - P_H Y_H − TB_H︷︸︸︷(CA_H − i F_H) = P_H C_H + P_{F,C} C_{F,C} + P_{F,O} C_{F,O}
  - P_N Y_N = P_N C_N
  - Y_H is home endowment of tradables; i is the net world interest rate (I = 1 + i).
  - TB_H, CA_H, and F_H are trade balance, current account, and stock of net foreign assets vis-à-vis emerging Asia.
- First order conditions (price relationships):
  - P = [ γ P_T^{1−θ} + (1−γ) P_N^{1−θ} ]^{1/(1−θ)}
  - P_T = [ α P_H^{1−η} + (1−α) P_F^{1−η} ]^{1/(1−η)}
  - P_F = [ β P_{F,C}^{1−ξ} + (1−β) P_{F,O}^{1−ξ} ]^{1/(1−ξ)}
- Consumption ratios and price ratio definitions:
  - C_N / C_T = (1−γ)/γ (P_N / P_T)^{−θ} = (1−γ)/γ x^{−θ}  where x = P_N / P_T
  - C_F / C_H = (1−α)/α (P_F / P_H)^{−η} = (1−α)/α (β φ_C^{1−ξ} + (1−β) φ_O^{1−ξ})^{−η/(1−ξ)}
  - C_{F,O} / C_{F,C} = (1−β)/β (P_{F,O} / P_{F,C})^{−ξ} = (1−β)/β (φ_O / φ_C)^{−ξ}
  - φ_C = P_{F,C} / P_H ; φ_O = P_{F,O} / P_H

### Chinese and OEA households
- Chinese consumption aggregator:
  - C^* = [ (γ^*)^{1/θ^*} (C_T^*)^{(θ^*−1)/θ^*} + (1−γ^*)^{1/θ^*} (C_N^*)^{(θ^*−1)/θ^*} ]^{θ^*/(θ^*−1)}
- Chinese tradable consumption:
  - C_T^* = [ (α^*)^{1/η^*} (C_{F,C}^*)^{(η^*−1)/η^*} + (1−α^*)^{1/η^*} (C_H^*)^{(η^*−1)/η^*} ]^{η^*/(η^*−1)}
  - Chinese households do not consume OEA goods in the baseline.
- Chinese budget constraints:
  - P_{F,C}^* Y_H^* − (CA_{F,C}^* − i F_{F,C}^*) = P_{F,C}^* C_{F,C}^* + P_H^* C_H^*
  - P_N^* Y_N^* = P_N^* C_N^*
  - Y_{F,C}^* is endowment of tradables; prices with * are expressed in Chinese currency.
- Law of one price assumption for traded goods:
  - P_H^* = P_H Σ^*  where Σ^* is the U.S. Dollar per Renminbi nominal exchange rate.
- OEA households solve an equivalent problem; OEA prices of U.S. imports: P_H^{**} = P_H Σ^{**} where Σ^{**} is the nominal exchange rate for OEA (double asterisk denotes OEA variables).

*Source: _wp1146 - Section III. In Section IV we consider the implications of rebalancing for exchange rates and*

### 3.    Market clearing

### 3.    Market clearing

### Market clearing conditions
- Resource constraints imposed for nontradable and tradable goods:
  - Y_H = C_H + C*_H + C**_H
  - Y_F,C = C_F,C + C*_F,C
  - Y_F,O = C_F,O + C**_F,O
  - Y_N = C_N
  - Y*_N = C*_N
  - Y**_N = C**_N
- Aggregate external balance conditions:
  - CA_H + CA*_F,C Σ* + CA**_F,O Σ** = 0
  - F_H + F*_F,C Σ* + F*_F,O Σ** = 0

### Equilibrium prices and real exchange rates
- For given endowments and exogenous current accounts and net foreign asset positions, solve for:
  - optimal consumption allocations,
  - relative equilibrium prices between tradables and nontradables x, x*, x**,
  - terms of trade φ_C and φ_O,
  - U.S. terms of trade with respect to emerging Asia as a whole:
    - τ = P_F / P_H = (β φ_C^{1−ξ} + (1−β) φ_O^{1−ξ})^{1/(1−ξ)}
- Bilateral and trade-weighted real exchange rates of the U.S. vis-à-vis emerging Asia:
  - R_C = P*_Σ* / P = (γ* + (1−γ*)(x*)^{1−θ*})^{1/(1−θ*)} (γ + (1−γ)x^{1−θ})^{−1/(1−θ)} φ_C (α* + (1−α*)(τ*)^{1−η*})^{1/(1−η*)} (α + (1−α) τ^{1−η})^{−1/(1−η)}
  - R_O = P**_Σ** / P = (γ** + (1−γ**)(x**)^{1−θ**})^{1/(1−θ**)} (γ + (1−γ)x^{1−θ})^{−1/(1−θ)} φ_O (α** + (1−α**)(τ**)^{1−η**})^{1/(1−η**)} (α + (1−α) τ^{1−η})^{−1/(1−η)}
  - R = (β R_C^{1−ξ} + (1−β) R_O^{1−ξ})^{1/(1−ξ)}
- Equilibrium responses depend on calibration of structural parameters, shares of tradable and nontradable outputs, and initial external positions.

### III. CALIBRATION — Trade elasticities
- Two types of elasticities calibrated:
  - η, η*, η**: substitutability between home-produced and imported tradables (absolute value of price elasticity of real imports).
  - ξ: substitutability of Chinese and other Asian goods imported by the U.S.
- Literature context:
  - Goldstein and Kahn (1985): U.S. long-run price elasticities between -1.03 and -1.73.
  - Marquez (2002): reports price elasticities for the U.S. between 0 and -2.5.
  - Kwack et al. (2007): estimates between -0.50 and -1.06 for 8 Asian emerging countries (including China at -0.5); U.S. estimate -0.93 (not significantly different).
- Calibration choices:
  - Set η = 1.5 (implies elasticity of imports of −1.5) as benchmark.
  - Calibrate η* and η** the same as for the U.S.
  - Experiment with η = 1 (implies elasticity of imports of −1) for the U.S. in robustness checks.
- Estimation of ξ:
  - Use Feenstra (1994) structural method (as implemented by Broda and Weinstein (2006)) at ISIC sectoral level.
  - Aggregate sectoral estimates using sector shares in U.S. imports from Asia:
    - ξ̂ = Σ_k w_k ξ̂_k
  - Result: aggregate elasticity of substitution between Chinese and Asian exports = 3.98
    - Standard error = 0.39
  - Calibration uses ξ = 4 as benchmark.

### III.B Other parameters (summary of Table 1 calibration)
- Elasticities:
  - θ, θ*, θ** (tradables and nontradables) = 2 (Source: OR (2007))
  - η, η*, η** (domestic and foreign tradables) = 1.5 (Source: literature)
  - ξ (CH and OEA tradables) = 4 (Source: our estimate)
- Consumption weights:
  - γ, γ*, γ** (tradables consumption bias) = 0.25 (OR (2007))
  - α (home bias for the U.S.) = 0.85 (calibrated to Import/GDP from CH and OEA)
  - α*, α** (home bias for CH and OEA) = 0.925 (OR (2007))
  - β (U.S. import bias for Chinese goods) = 0.562% (U.S. import share from CH)
- Production share ratios (σ = Y_H / Y_N or equivalents):
  - σ (N/T real GDP in the U.S.) = 2.825 (0% nominal T/GDP in U.S. — as listed)
  - σ* (N/T real GDP CH) = 0.365 (0% nominal T/GDP in CH)
  - σ** (N/T real GDP OEA) = 0.345 (0% nominal T/GDP in OEA)
  - σ_C (CH/U.S. tradable real GDP) = 0.853 (0% CH share in total T GDP)
  - σ_O (OEA/U.S. tradable real GDP) = 0.6827 (0% OEA share in total T GDP)
- Bilateral net foreign asset positions and current accounts:
  - i_world interest rate = 5% (OR (2007))
  - f_U.S. NFA with CH and OEA (%GDP) = -12.4% (2009 bilateral data)
  - f*_CH NFA with U.S. (%GDP) = 27.3% (2009 bilateral data)
  - tb_U.S. TB with CH and OEA (%GDP) = -1.9% (2009 bilateral data)
  - tb*_CH TB with U.S. (%GDP) = 4.5% (2009 bilateral data)
- Abbreviations provided: CH China, OEA other emerging Asia, T tradables, N nontradables, NFA net foreign asset, TB trade balance.

### IV. REBALANCING AND RELATIVE PRICES — scenarios and findings
- Experiment setup:
  - Solve optimal consumption allocation and equilibrium prices given Table 1 calibration.
  - Consider adjustments required to reduce the U.S. current account deficit vis-à-vis emerging Asia.
  - As of end-2009, bilateral U.S. current account deficit with Asia = 2.5 percent of U.S. GDP.
  - Study reduction to 1.5 percent of GDP (i.e., decline by 1 percent of GDP).
- Scenario A — Exchange rate adjustment (three cases):
  1. Symmetric appreciation (both China and OEA export prices increase by same proportion):
     - When U.S. deficit falls by 1 percent of GDP, terms of trade in both China and OEA improve by 15 percent.
     - Emerging Asia bilateral current account surpluses with U.S. decline by about 2 percent of their respective GDPs:
       - China: from about 6 percent of GDP to 4 percent of GDP.
       - OEA: from 1.5 percent of GDP to a small deficit.
     - Result: U.S. trade-weighted terms of trade (τ) worsen and U.S. real exchange rate (R) depreciates by similar amounts (increase denotes depreciation from U.S. point of view).
  2. China resists appreciation (all adjustment falls on OEA, φ_O):
     - OEA relative prices must increase by 32 percent.
     - China’s current account surplus increases (due to expenditure switching — U.S. imports more Chinese tradables even while overall deficit falls).
     - OEA moves from surplus of about 1.5 percent of GDP to deficit of 2.5 percent of GDP.
     - Relative prices of nontradables fall in China and the U.S., increase in OEA.
     - U.S. real exchange rate depreciation is smaller than the terms of trade change.
  3. OEA resists appreciation (all adjustment falls on China, φ_C):
     - Chinese export prices increase by about 30 percent.
     - Chinese current account surplus almost vanishes vis-à-vis the U.S.
     - OEA surplus with the U.S. increases (from 1.5 percent of GDP to 2.9 percent of GDP).
- Scenario B — Robustness checks:
  - Lower U.S. elasticity of substitution between domestic and foreign goods: set η = 1, η* = η** = 1.5.
    - If U.S. import demand less sensitive to price changes, required increase in emerging Asia export prices is larger for same reduction in U.S. current account deficit.
    - Under η = 1, symmetric improvement in emerging Asia terms of trade needed ≈ 23 percent for 1 percent of GDP deficit reduction.
    - If only China lets export prices increase: required improvement ≈ 45 percent.
    - If only OEA appreciates: required improvement ≈ 42 percent.
  - Model is an endowment economy (no supply effects). Allowing factor mobility or production reallocation would reduce required relative price adjustments.
  - Including the rest of the world: if other regions also raise export prices, change required in emerging Asia would be smaller; if rest of world resists appreciation, emerging Asia terms of trade would improve more and U.S. real exchange rate would appreciate more, implying larger contraction in emerging Asia current account surpluses.
- Scenario C — Change in home bias:
  - If China and OEA resist export-price changes, rebalancing could occur only with substantial reduction in consumption home bias in emerging Asia (decline in α* and α**).
  - Quantitative example:
    - If the basket of Chinese and OEA tradables included about 3 percent more goods produced in the U.S. (i.e., decline in home bias ≈ 3 percentage points), the bilateral trade balance effects would be similar to those from a 15 percent appreciation with no change in preference parameters.
  - Even with no terms of trade change, U.S. real effective exchange rate still declines due to nontradable-to-tradable price changes.
  - Increased consumption of tradables in Asia leads to increased consumption of nontradables; with fixed supply, nontradable prices rise in China.

### V. Introducing input-output linkages — evidence (introductory note)
- Prior analysis focused on final goods trade and neglected trade in intermediate inputs.
- International fragmentation and vertical specialization have grown, particularly in Asia:
  - Dean, Fung, and Wang (2007): estimate that 35 percent of the value of China’s aggregate exports is attributable to imported inputs in [text truncated in source].
  - Hummels, Ishii and Yi (2001): estimate vertical specialization grew by about 30 percent between 1970 and 1990, explaining more than 30 percent of world growth of exports.

*Source: _wp1146 - 3.    Market clearing*

### 2002. Their results moreover suggest that OEA is a major supplier of intermediate inputs to

### _wp1146 - 2002. Their results moreover suggest that OEA is a major supplier of intermediate inputs to

### Evidence on vertical fragmentation and trade linkages
- More than half of the value of imported inputs in China’s exports comes from Japan, Hong Kong SAR, Taiwan POC, Republic of Korea, or Singapore (as reported by studies using input-output tables).
- Koopman, Wang, and Wei (2008) find that when accounting for different production functions for exported and domestic goods, the share of intermediate inputs in the value of Chinese aggregate exports is at about 50 percent.
- Empirical implications for exchange-rate pass-through and trade:
  - A unilateral Chinese appreciation has a smaller effect on the price of Chinese exports when production involves imported intermediate inputs whose costs remain constant in U.S. dollar terms.
  - Ahmed (2009): an appreciation of the Renminbi against the currencies of OEA’s trading partners has no impact on Chinese exports of processed goods, while it reduces exports of non-processed goods. An appreciation against developed countries reduces both types of exports.
  - Garćıa-Herrero and Koivu (2010) argue that use of Asian imported inputs explains why Chinese imports drop following a Renminbi appreciation.

### Extension of the model: supply dimension and international segmentation
- Model augmentation:
  - Each country endowed with an exogenous quantity of inputs used as the only productive factor.
  - Factors are sector-specific: inputs for tradables cannot be used for nontradables.
  - Non-traded good technology is linear: one unit of good per unit of input.
  - Traded good sector: production is internationally segmented; countries can trade in intermediate inputs.
- Empirical basis and measurement:
  - Use GTAP input-output tables across >100 countries to calculate import content in production and exports using Hummels, Ishii, and Yi (2001) methodology, adapted to aggregate by shares in tradable output (measuring imported inputs in tradable production rather than exports only).
  - Using GTAP data:
    - Import content in U.S. tradables: 15 percent.
    - Import content in China tradables: 23 percent.
    - Import content in OEA tradables: 34 percent.
  - When aggregating import content into aggregate exports (reproducing Hummels, Ishii, and Yi (2001) method):
    - US: 16 percent
    - China: 33 percent
    - OEA: 40 percent
- Key empirical findings used to shape model structure:
  - International fragmentation is more pronounced for Asian countries than for the U.S.; model includes only intermediate input linkages within Asia and assumes the U.S. does not use intermediate inputs from Asia for final goods production. U.S. tradable production equals the U.S. endowment of intermediate goods: Y_H = Q_H.
  - Vertical specialization is important in both China and OEA; production functions for tradables in China and OEA are specified as:
    - Y*_F,C = Q*_{C,C}^{μ*} Q*_{O,C}^{1−μ*}
    - Y**_F,O = Q**_{O,O}^{μ**} Q**_{C,O}^{1−μ**}
    - where Q_{i,j} denotes intermediate input from country i used in production of final good in country j, and μ* and μ** are shares of domestic intermediate inputs.
  - Two-way linkages between China and OEA are empirically important:
    - Bems, Johnson and Yi (2010) results: 42 percent of Chinese imports of intermediate inputs come from OEA; 8 percent come from the U.S.
    - For emerging Asia, relative share of China and the U.S. in intermediate inputs is approximately balanced: 13 percent from China and 16 percent from the U.S. (each country ≈ 15 percent of aggregate imports).
- Model closure for intermediate goods markets:
  - Q_C = Q_{C,C} + Q_{C,O}
  - Q_O = Q_{O,O} + Q_{O,C}

### Calibration and parameter values
- Calibration strategy:
  - Split value of tradable production into cost components from domestic inputs and foreign inputs coming from China, OEA, and the rest of the world using GTAP and Bems, Johnson and Yi (2010).
  - Rest-of-world intermediate inputs are assimilated to domestic inputs in the model.
- Calibrated parameter values reported:
  - μ* = 0.902
  - μ** = 0.956
- Interpretation:
  - These μ parameters imply that the share of domestic intermediate inputs in production is high for both China and OEA; results are virtually unchanged if inputs from the rest of the world are treated differently.
- Noted empirical check:
  - The share of OEA inputs in Chinese tradable production is about 10 percent (used in subsequent quantitative assessments).

### Price relationships and pass-through mechanics
- Prices of final goods in U.S. dollars exported by the U.S., China and OEA are functions of intermediate input prices in the three countries. Important implications:
  - If China appreciates by 1 percent (via Σ* or P*_{C,Q}), the price of final Chinese goods increases by μ* percent.
  - With two-way linkages, a Chinese appreciation also affects OEA final goods prices shipped to the U.S.
- Derived expression for price of Chinese exports to the U.S. (from first order conditions for intermediate input demand):
  - P_{F,C} = (Σ* P*_{C,Q})^{μ*} (Σ** P**_{O,Q})^{1−μ*} μ*^{μ*} (1−μ*)^{1−μ*}
  - This shows increases in costs of domestic inputs are passed to final tradable prices only in proportion to the share μ*.

### Exchange rate adjustment scenarios and quantitative implications
- One-way IO linkages scenario (μ* = 0.902 and μ** = 1):
  - Popular narrative: only Chinese exports to the U.S. are produced with foreign intermediate inputs; concern that Chinese appreciation would be ineffective because of limited pass-through.
  - Quantitative finding: the share of OEA inputs in China tradable production is about 10 percent; hence impact is limited.
  - Example calibration result:
    - To allow for a reduction in the U.S. deficit of 1 percent of U.S. GDP, Chinese intermediate goods prices should increase by 33 percent instead of 30 percent in the model without IO linkages.
  - Figure 5 (described): rebalancing with one-way IO linkages associated with only a slightly larger Chinese appreciation relative to the model without intermediate inputs.
- Two-way IO linkages scenario (μ* = 0.902 and μ** = 0.956):
  - Empirical two-way linkages imply OEA is affected by Chinese appreciation via input channels.
  - Quantitative finding: the required unilateral Chinese appreciation is close to the one in the model without IO linkages and smaller than in the one-way case.
  - Intuition:
    - One-way linkages: OEA final export prices not affected by Chinese appreciation, so U.S. consumers substitute away from Chinese goods toward OEA goods.
    - Two-way linkages: OEA final goods prices also increase when China raises the price of its intermediate goods, reducing substitution by U.S. consumers and leaving bilateral current accounts closer to the no-IO case.
  - Main message: presence of IO linkages, especially two-way, has only a very limited impact on the required appreciation to accommodate a reduction of the U.S. current account deficit.

### Key quantitative headline results
- Required joint improvement in terms of trade of all emerging Asia to accommodate a reduction in the U.S. current account of 1 percent of GDP: about 15 percent (when neglecting trade in intermediate inputs).
- One-way IO linkages case example: required Chinese intermediate goods price increase of 33 percent (versus 30 percent in model without IO linkages) to reduce U.S. deficit by 1 percent of GDP.
- GTAP-based import content measures:
  - U.S. tradables import content: 15 percent.
  - China tradables import content: 23 percent.
  - OEA tradables import content: 34 percent.
  - Alternative aggregation into exports: US 16 percent, China 33 percent, OEA 40 percent.
- Sources of Chinese intermediate imports (Bems, Johnson and Yi, 2010):
  - 42 percent from OEA
  - 8 percent from the U.S.
  - For emerging Asia aggregate: 13 percent from China, 16 percent from the U.S. (each ≈ 15 percent)

### Conclusions and directions for future research
- Main conclusions:
  - Neglecting intermediate inputs, a multi-country equilibrium implies emerging Asia jointly needs about a 15 percent terms-of-trade improvement to accommodate a 1 percent of GDP reduction in the U.S. current account.
  - If only China allows its export prices to increase, a larger Chinese appreciation is required because U.S. consumers substitute Chinese goods in favor of OEA tradables.
  - Incorporating one-way IO linkages modestly increases the required Chinese appreciation, but empirical evidence supports two-way IO linkages between China and OEA, which mute the impact of IO linkages on required terms-of-trade adjustments.
- Suggested promising research directions:
  - Move beyond endowment economy: allow supply of goods to react to real exchange rate fluctuations (real quantity adjustments may reduce necessary relative price movements).
  - Expand beyond the U.S.–emerging Asia bilateral focus to incorporate other countries and study how global rebalancing is shared among additional trading partners.
  - Study adjustments beyond the 1 percent of GDP shock considered here to examine how relative prices adjust in a fuller multi-country equilibrium.

*Source: IMF working paper content provided in the supplied PDF excerpt.*

---


_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2011/_wp1146.pdf_