## wpiea2024048-print-pdf — Geoeconomic Fragmentation and International Diversification Benefits (selected content units)

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### Geopolitical context, scope, and scenarios
- Geopolitical tensions: deterioration in U.S.–China ties and Russia’s invasion of Ukraine motivate assessment of geoeconomic fragmentation — policy-driven reversal of financial and economic integration.
- Bilateral geopolitical distance: degree of disagreement in UNGA voting patterns during 2012–2021 (S-score construction following Signorino and Ritter (1999); data sources Häge (2011) and Erik Voeten’s database).
- Coverage and baseline:
  - Model applied to each G7 country under four scenarios: full integration, autarky, moderate fragmentation (25 percent of partner countries excluded), and extreme fragmentation (50 percent of partner countries excluded).
  - Full integration global approximation: largest 60 countries (G7 + 53 non-G7) by nominal GDP as of 2021, accounting for 96 percent of world output.
- Fragmentation modeling:
  - G7 countries unable to engage in transactions with foreign countries with greater geopolitical distance; excluded imports are partly substituted by domestic production (local spending bias increases).

### Main quantitative findings: diversification benefits and welfare
- Diversification benefit definition: percentage decrease in macro-financial volatility, including consumption volatility, achieved through cross-border investment.
- Diversification benefit (full integration vs autarky, G7 countries): range of 5 percent to 15 percent.
- Loss of diversification under fragmentation:
  - Moderate fragmentation: G7 countries could lose about 20 percent of gains from full integration.
  - Extreme fragmentation: G7 countries could lose about 40–50 percent of gains from full integration.
- Macro-financial volatility changes (median, relative to full integration):
  - Moderate fragmentation (25 percent excluded): median volatility of output across G7 increases by 1 percentage point relative to full integration.
  - Extreme fragmentation (50 percent excluded): median volatility of output across G7 increases by 3 percentage points relative to full integration.
  - Median volatility of consumption, corporate profits, equity, and bond prices increases by about 2 to 8 percentage points (relative to full integration).
- Welfare translation (Appendix B; preserving reported values):
  - Welfare gain from financial integration (autarky → full integration), median = 0.21 percent increase of permanent consumption; first-to-third quantiles = 0.14–0.44.
  - Moderate fragmentation: median = 0.18; first-to-third quantiles = 0.13–0.38.
  - Extreme fragmentation: median = 0.13; first-to-third quantiles = 0.07–0.28.
  - Implication: welfare gains would reduce by around 20 percent (moderate) and 40 percent (extreme).

### Mechanisms driving increased volatility and lost diversification
- Three decomposed factors (replicated in Figure 4; methodology summarized):
  1. Increase in cross-country business cycle correlation:
     - Excluded countries under fragmentation tend to have business cycles less synchronized with G7 (e.g., China and major commodity exporters); their exclusion raises cross-country shock correlation among remaining partners and with G7.
     - Higher cross-country shock correlation increases common fluctuations and reduces terms-of-trade flexibility.
  2. Increase in volatility of foreign exogenous processes:
     - Partner composition under fragmentation can raise volatility of foreign aggregate TFP and investment-efficiency processes, especially in extreme fragmentation where commodity exporters are excluded and remaining partners are highly correlated European industrial countries.
  3. Increase in local spending bias (share of domestic production):
     - Substituting excluded imports with domestic production raises local spending bias for consumption and investment (a and aI), reducing smoothing via goods trade and increasing sensitivity to domestic cycles.
- Net effect under study parameters:
  - First factor (higher cross-country shock correlation) prevails in increasing consumption volatility because domestic business cycles are more volatile than foreign business cycles.
  - First two factors are particularly important and closely linked to geopolitical configuration; third factor contributes but its magnitude depends on substitutability assumptions.

### Model overview, equilibrium, and portfolio treatment
- Model: two-country open-economy DSGE with equities and bonds (based on Coeurdacier et al. (2010)); “home” = each G7 country; “foreign” = weighted average of partner countries remaining under scenario.
- Key preferences and production:
  - Representative household maximizes CRRA utility: E[Σ_{t=0}^∞ β^t (C_{i,t}^{1−σ}/(1−σ) − L_{i,t}^{1+ω}/(1+ω))], where σ > 1 and ω > 0.
  - Production: Y_{i,t} = θ_{i,t} K_{i,t}^κ L_{i,t}^{1−κ}.
  - Capital accumulation: K_{i,t+1} = (1−δ) K_{i,t} + χ_{i,t} I_{i,t}.
  - Consumption aggregator: C_{i,t} = [ a^{1/φ} C_{i,i,t}^{(φ−1)/φ} + (1−a)^{1/φ} C_{j,i,t}^{(φ−1)/φ} ]^{φ/(φ−1)} with a ∈ (1/2,1).
- Equilibrium and market clearing (selected exact identities):
  - Goods market: C_{H H,t} + C_{F H,t} + I_{H H,t} + I_{F H,t} = Y_{H,t} (equation (9)); symmetric for foreign (equation (10)).
  - Equity supply: S_{H H,t} + S_{F H,t} = S_{F F,t} + S_{H F,t} = 1 (equation (11)).
  - Bond market: B_{H H,t} + B_{F H,t} = B_{F F,t} + B_{H F,t} = 0 (equation (12)).
- Portfolio choice: zero-order portfolio used in log-linearized simulations
  - Closed-form equity home bias: S = 1/2 [ 1 + (2 a_I − 1)(1−κ) / (1 − (2 a_I − 1) κ) ] > 1/2 (equation (26)).
  - Bond position normalized by Y_H: b ≡ B / Y_H given by equation (27) (auxiliary definitions Λ, λ, λ^* provided in text).
  - Rationale: excess returns zero at steady state ⇒ first-order log-linearized conditions depend only on zero-order portfolio; simplifies computation while capturing first-order macroeconomic volatility implications.

### Benchmark parameterization and stochastic processes (selected calibrated/estimated values)
- Common parameters across G7 (i–iv):
  - β = 0.96; ω = 0.5; κ = 0.4; δ = 0.1.
- Local spending bias (consumption and investment) calibrated from historical import-to-GDP ratios (1992–2019):
  - United States: 0.87
  - Japan: 0.85
  - Germany: 0.70
  - United Kingdom: 0.76
  - France: 0.75
  - Italy: 0.77
  - Canada: 0.70
- Estimated elasticities (posterior means and 90 percent intervals; Table 3):
  - σ (inverse EIS) — posterior means and 90 percent intervals:
    - United States: 1.037, 1.004-1.085
    - Japan: 1.006, 1.001-1.014
    - Germany: 1.011, 1.001-1.026
    - United Kingdom: 1.034, 1.004-1.080
    - France: 1.016, 1.002-1.037
    - Italy: 1.009, 1.001-1.022
    - Canada: 1.056, 1.007-1.126
  - φ (consumption substitution) — posterior means and 90 percent intervals:
    - United States: 0.774, 0.617-1.021
    - Japan: 0.896, 0.643-1.249
    - Germany: 1.262, 0.972-1.467
    - United Kingdom: 0.746, 0.614-0.950
    - France: 0.761, 0.614-0.991
    - Italy: 0.656, 0.606-0.732
    - Canada: 0.954, 0.657-1.331
  - φI (investment substitution) — posterior means and 90 percent intervals:
    - United States: 0.898, 0.641-1.262
    - Japan: 1.006, 0.673-1.378
    - Germany: 1.137, 0.751-1.445
    - United Kingdom: 0.888, 0.637-1.262
    - France: 0.874, 0.630-1.241
    - Italy: 0.746, 0.615-0.944
    - Canada: 1.030, 0.674-1.408
- TFP and investment-efficiency processes (Table 4; selected reported ranges and country-specific values):
  - TFP persistence (home): 0.54–0.84; foreign: 0.69–0.72.
  - TFP std(ε) (home): 0.67–0.92; foreign: 0.51–0.61.
  - Cross-country correlations for TFP shocks: 0.17–0.67.
  - Investment-efficiency persistence (home): 0.58–0.87; foreign: 0.45–0.52.
  - Investment-efficiency std(ε) (home): 0.34–0.76; foreign: 0.87–0.88.
  - Cross-country correlations for investment-efficiency shocks: 0.19–0.34.
- Calibration frequency: annual. TFP from Penn World Table v10.0; investment-efficiency proxy = consumption deflator / investment deflator.

### Parameter changes across scenarios (local spending bias examples)
- Local spending bias (a and aI) under scenarios (Table 6, selected country values):
  - United States: full integration 0.87; moderate fragmentation 0.90; extreme fragmentation 0.93; autarky 1.00
  - Japan: full integration 0.85; moderate fragmentation 0.91; extreme fragmentation 0.94; autarky 1.00
  - Germany: full integration 0.70; moderate fragmentation 0.73; extreme fragmentation 0.75; autarky 1.00
  - United Kingdom: full integration 0.76; moderate fragmentation 0.79; extreme fragmentation 0.80; autarky 1.00
  - France: full integration 0.75; moderate fragmentation 0.78; extreme fragmentation 0.80; autarky 1.00
  - Italy: full integration 0.77; moderate fragmentation 0.80; extreme fragmentation 0.81; autarky 1.00
  - Canada: full integration 0.70; moderate fragmentation 0.73; extreme fragmentation 0.76; autarky 1.00
- Alternative calibration using export ratios (Table A2) yields similar values; robustness checks show small differences (Table A2 values listed in Appendix A2).

### Simulated macro-financial volatility (Appendix D — Table A1; standard deviation, unit: percent)
- United States (Full integration → Moderate → Extreme → Autarky):
  - Output: 1.99, 2.02, 2.05, 2.10
  - Consumption: 1.53, 1.57, 1.63, 1.70
  - Corporate profit: 1.83, 1.89, 1.98, 2.10
  - Equity price: 2.04, 2.08, 2.15, 2.25
  - Bond price: 1.12, 1.16, 1.21, 1.27
- Japan:
  - Output: 1.60, 1.63, 1.63, 1.65
  - Consumption: 1.05, 1.10, 1.12, 1.16
  - Corporate profit: 1.49, 1.57, 1.60, 1.65
  - Equity price: 1.49, 1.54, 1.56, 1.59
  - Bond price: 0.80, 0.84, 0.86, 0.89
- Germany:
  - Output: 1.43, 1.44, 1.44, 1.46
  - Consumption: 0.88, 0.89, 0.93, 1.03
  - Corporate profit: 1.28, 1.32, 1.35, 1.46
  - Equity price: 1.37, 1.39, 1.42, 1.47
  - Bond price: 0.68, 0.70, 0.73, 0.80
- United Kingdom:
  - Output: 2.51, 2.55, 2.61, 2.78
  - Consumption: 1.83, 1.91, 2.00, 2.30
  - Corporate profit: 2.12, 2.23, 2.36, 2.78
  - Equity price: 2.39, 2.48, 2.59, 2.94
  - Bond price: 1.32, 1.38, 1.45, 1.70
- France:
  - Output: 1.51, 1.53, 1.56, 1.60
  - Consumption: 1.04, 1.07, 1.12, 1.18
  - Corporate profit: 1.38, 1.43, 1.51, 1.60
  - Equity price: 1.46, 1.49, 1.56, 1.62
  - Bond price: 0.79, 0.82, 0.86, 0.91
- Italy:
  - Output: 2.15, 2.18, 2.23, 2.37
  - Consumption: 1.49, 1.53, 1.59, 1.76
  - Corporate profit: 1.86, 1.93, 2.04, 2.37
  - Equity price: 1.99, 2.03, 2.12, 2.34
  - Bond price: 1.10, 1.14, 1.18, 1.32
- Canada:
  - Output: 1.66, 1.66, 1.65, 1.68
  - Consumption: 1.03, 1.06, 1.08, 1.22
  - Corporate profit: 1.49, 1.54, 1.52, 1.68
  - Equity price: 1.71, 1.73, 1.74, 1.81
  - Bond price: 0.89, 0.92, 0.94, 1.06

### Robustness checks (Appendix E)
- Elasticities of substitution sweep (φ = φ^I = {0.6, 0.9, 1.2, 1.5}): impact on macro-financial volatility moderate; impact on percent loss of diversification benefit marginal.
- Alternative local spending bias calibration using export ratios and export partner shares (Table A2): results on macro-financial volatility and loss of diversification benefit barely change; findings robust to dataset used.

### Limitations and caveats
- Focus: loss of cross-border investment diversification benefits only; not a comprehensive assessment of all economic impacts of geopolitical fragmentation.
- Model simplifications:
  - Full substitutability of foreign goods production among G7 countries and partners.
  - Symmetry between home and foreign countries except for TFP and investment-efficiency processes.
  - Welfare translation uses r = 0.027 and μ = 0.017 (van Wincoop (1994)) and γ from Table 3.
- Results sensitive to assumption about substitutability of excluded imports: if lost imports can only be substituted by foreign countries (not domestic production), local spending bias would be unchanged and third factor would not increase volatility.

_Italic: Source — wpiea2024048-print-pdf (sections 1; 2.2–2.3; 4.1–4.2 beginning; Appendices A–E, D, and B excerpts)._

### 1. Introduction ........................................................................................................

### 1 Introduction

### Geopolitical context and research question
- Geopolitical tensions have increased globally amid deteriorating diplomatic ties between the United States and China, and Russia’s invasion of Ukraine.
- The paper assesses the impact of geoeconomic fragmentation — a policy-driven reversal of financial and economic integration — on diversification benefits for major advanced economies, specifically the Group of Seven (G7) countries.
- Bilateral geopolitical distance is defined as the degree of disagreement in countries’ voting patterns in the United Nations General Assembly (UNGA) during 2012-2021.

### Key scenarios and coverage
- The model is calibrated and simulated for each G7 country under four scenarios: a baseline full integration scenario, an autarky scenario, and two counterfactual fragmentation scenarios characterized by different degrees of fragmentation.
- The global economy under the full integration scenario is approximated by the largest 60 countries (G7 + 53 non-G7 countries), chosen by nominal GDP as of 2021 in the IMF World Economic Outlook database, accounting for 96 percent of world output.
- Under the fragmentation scenarios, G7 countries are assumed unable to engage in transactions with foreign countries with greater geopolitical distance and must partly substitute imported goods from those countries with domestic production.

### Main quantitative findings
- Diversification benefit (defined as the percentage decrease in macro-financial volatility, including consumption volatility, achieved through cross-border investment):
  - Under full integration compared to autarky, the diversification benefit for G7 countries is in the range of 5 percent to 15 percent.
  - Under fragmentation scenarios, G7 countries could lose 20 percent to 50 percent of the gains they obtain from full integration.
- Mechanisms driving the loss:
  - Countries excluded under fragmentation tend to be those with business cycles less synchronized with G7 cycles (e.g., China and major commodity-exporting countries), reducing opportunities for risk diversification.
  - Increasing the share of domestic production to substitute for excluded imports hampers risk sharing through goods trade and raises volatility of other macro-financial variables.

### Contribution to literature
- Adds to the literature on financial integration and international risk sharing by quantifying how changes in trading and investing partner countries, driven by geopolitical fragmentation, affect diversification benefits — emphasizing the role of cross-country business cycle synchronization.
- Contributes to the literature on geopolitics and cross-border economic and financial activity by linking geopolitical distance to changes in diversification benefits, an area not previously examined.

### Model overview and rationale
- Uses a two-country open-economy model with equities and bonds (based on Coeurdacier et al. (2010)), applied so that the “home country” corresponds to each G7 country and the “foreign country” is the weighted average of other countries with which trading is possible.
- The model is chosen because:
  - It generates plausible magnitudes of “equity home bias” for G7 countries, important to replicate international portfolio allocations.
  - It produces plausible macro-financial dynamics by including total factor productivity (TFP) and investment-specific technology shocks.

### Household and firm setup (model technical features)
- Representative household in country i∈{H,F} maximizes CRRA utility:
  - E[Σ_{t=0}^∞ β^t (C_{i,t}^{1−σ}/(1−σ) − L_{i,t}^{1+ω}/(1+ω))], where σ >1 and ω >0.
- Consumption aggregator for country i:
  - C_{i,t} = [ a^{1/φ} C_{i,i,t}^{(φ−1)/φ} + (1−a)^{1/φ} C_{j,i,t}^{(φ−1)/φ} ]^{φ/(φ−1)}, where φ >0 and in the symmetric deterministic steady state a∈(1/2,1) is the share of the local good in consumption spending (local spending bias).
- Consumer price index:
  - P_{i,t} = [ a P_{i,t}^{1−φ} + (1−a) P_{j,t}^{1−φ} ]^{1/(1−φ)}.
- International financial assets: real bonds denominated in each country’s good (zero net supply) and equities (supply of each share normalized at unity).
- Household budget constraint (period t) includes consumption spending and holdings/prices of equities and bonds (equation (4) in source).
- Firm production:
  - Y_{i,t} = θ_{i,t} K_{i,t}^κ L_{i,t}^{1−κ}, where κ∈(0,1) and θ_{i,t} is TFP.
- Capital accumulation:
  - K_{i,t+1} = (1−δ) K_{i,t} + χ_{i,t} I_{i,t}, where δ∈(0,1) is depreciation and χ_{i,t} is an investment-efficiency shock.
- Investment uses domestic and foreign goods:
  - I_{i,t} = [ a_I^{1/φ_I} I_{i,i,t}^{(φ_I−1)/φ_I} + (1−a_I)^{1/φ_I} I_{j,i,t}^{(φ_I−1)/φ_I} ]^{φ_I/(φ_I−1)}, where a_I∈(1/2,1) is the degree of local bias in investment and φ_I is the elasticity of substitution in investment.
- Firms maximize the present value of dividend payments, taking prices and wages as given.
- TFP and investment-efficiency processes and full parameterization are specified in Section 4 of the source; appendices provide welfare approximations, geopolitical distance construction, and robustness.

*Source: wpiea2024048-print-pdf — 1. Introduction*

### 2.2    Equilibrium

### 2.2    Equilibrium

### Definition of equilibrium and market clearing
- Equilibrium is defined as a set of prices {P_{t,i}, P_{i,t}, P^S_{i,t}, P^B_{i,t}, W_{i,t}} and allocations {C_{i,t}, C_{i i,t}, C_{j i,t}, L_{i,t}, S_{i i,t}, S_{i j,t}, B_{i i,t}, B_{i j,t}} and {I_{i,t}, I_{i i,t}, I_{j i,t}, K_{i,t+1}, Y_{i,t}, D_{i,t}, D_{j,t}} for households and firms in country i ∈ {H,F} with j ∈ {H,F} (j ̸= i), such that:
  - Household choices {C_{i,t}, C_{i i,t}, C_{j i,t}, L_{i,t}, S_{i i,t}, S_{i j,t}, B_{i i,t}, B_{i j,t}} solve the households’ problem (equations (1), (2), and (4)) given prices and firms’ choices.
  - Firms’ choices {I_{i,t}, I_{i i,t}, I_{j i,t}, K_{i,t+1}, Y_{i,t}, D_{i,t}, D_{j,t}} solve the firms’ problem (equations (5), (6), and (7)) given prices and wages.
  - Goods and asset markets clear:
    - C_{H H,t} + C_{F H,t} + I_{H H,t} + I_{F H,t} = Y_{H,t} (equation (9))
    - C_{F F,t} + C_{H F,t} + I_{F F,t} + I_{H F,t} = Y_{F,t} (equation (10))
    - S_{H H,t} + S_{F H,t} = S_{F F,t} + S_{H F,t} = 1 (equation (11))
    - B_{H H,t} + B_{F H,t} = B_{F F,t} + B_{H F,t} = 0 (equation (12))

### Household first-order conditions (excluding portfolio choice)
- Consumption allocations across home and foreign goods (for j ∈ {H,F}):
  - C_{i i,t} = a [P_{i t} / P_{i,t}]^{−φ} C_{i,t} (equation (13))
  - C_{j i,t} = (1−a) [P_{j t} / P_{i,t}]^{−φ} C_{i,t} (equation (14))
- Labor supply:
  - L_{ω i,t} = [W_{i,t} / P_{i,t}] C_{i,t}^{−σ} (equation (15))
- Euler equations for equities and bonds (j ∈ {H,F}):
  - 1 = E_{i t} Q_{t,t+1} R^S_{j,t+1} (equation (16))
  - 1 = E_{i t} Q_{t,t+1} R^B_{j,t+1} (equation (17))
  - Definitions:
    - R^S_{j,t+1} = (P^S_{j,t+1} + D_{j,t+1}) / P^S_{j,t}
    - R^B_{j,t+1} = (P^B_{j,t+1} + P_{j t+1}) / P^B_{j,t}
    - Q_{i t,t+1} ≡ β (C_{i,t+1} / C_{i,t})^{−σ} (P_{i,t} / P_{i,t+1}) is the period-t pricing kernel

### Firm first-order conditions and accounting identities
- Wage bill (Cobb-Douglas technology, share to workers 1−κ):
  - W_{i,t} L_{i,t} = (1−κ) P_{i t} Y_{i,t} (equation (18))
- Dividends (investment financed from retained earnings; dividend is κ share of output minus physical investment):
  - D_{i,t} = κ P_{i t} Y_{i,t} − P^I_{i,t} I_{i,t} (equation (19))
- Investment optimality condition:
  - 1 = E_{i t} Q_{i t,t+1} χ_{i,t} P^I_{i,t} [ (P_{i t+1}/P^I_{i,t}) (θ_{i,t+1} κ K_{i,t+1}^{κ−1} L_{i,t+1}^{1−κ}) + (1−δ) P^I_{i,t+1} / χ_{i,t+1} ] (equation (20))
- Cost-minimizing composition of investment (home and foreign goods, for j ∈ {H,F}):
  - I_{i i,t} = (1−a_I) [P_{i t} / P^I_{i,t}]^{−φ_I} I_{i,t} (equation (21))
  - I_{j i,t} = (1−a_I) [P_{j t} / P^I_{i,t}]^{−φ_I} I_{i,t} (equation (22))

### Terms of trade, risk sharing, and asset price definitions
- Terms of trade Q_t ≡ P_{H,t} / P_{F,t} are pinned down by a risk-sharing condition under complete markets (first-order): the ratio of home to foreign marginal utilities of aggregate consumption, C_{H,t}^{−σ} / C_{F,t}^{−σ}, is equated to the consumption-based real exchange rate RER_t ≡ P_{H,t} / P_{F,t} up to first order.
- Real variables of interest (home country):
  - Real profits: Π_{H,t} ≡ P_{H t} Y_{H,t} − W_{H,t} L_{H,t} / P_{H,t} (equation (23))
  - Real equity price: bP^S_{H,t} ≡ P^S_{H,t} / P_{H,t} (equation (24))
  - Real bond price: bP^B_{H,t} ≡ P^B_{H,t} / P_{H,t} (equation (25))

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### 2.3    Portfolio Choice (Zero-Order Portfolio)

### Definition and steady-state characterization
- Zero-order portfolio: portfolio decision rules evaluated at steady state values of state variables; steady-state equilibrium portfolio holdings (S_{H H,t}, S_{F H,t}, S_{F F,t}, S_{H F,t}, B_{H H,t}, B_{F H,t}, B_{F F,t}, B_{H F,t}) are functions of state variables in period t−1.
- In the symmetric deterministic steady state:
  - S_{H H} = 1 − S_{F H} = S_{F F} = 1 − S_{H F} ≡ S
  - B_{H H} = −B_{F H} = B_{F F} = −B_{H F} ≡ B
  - (S,B) denotes the zero-order equilibrium portfolio; S is country’s holdings of local equity, B is holdings of bonds denominated in the local good.

### Closed-form zero-order portfolio solution and parameter definitions
- Equity home bias result:
  - S = 1/2 [ 1 + (2 a_I − 1)(1−κ) / (1 − (2 a_I − 1) κ) ] > 1/2 (equation (26))
- Bond position normalized by Y_H:
  - b ≡ B / Y_H = 1/2 [ (1 − Λ)(1 − 1/σ)(2 a − 1) + (1 − κ)[λ^* − 1 + Λ(2 a_I − 1)^2] / 2 ] / [1 − (2 a_I − 1) κ] (equation (27))
- Auxiliary definitions:
  - Λ ≡ κ / [ (1/δ)(1 − β)/β + 1 ]
  - λ ≡ φ(1 − (2 a − 1)^2) + (2 a − 1)^2 σ > 0  (since a ∈ (1/2, 1) implies 1 − (2 a − 1)^2 > 0)
  - λ^* ≡ (1 − Λ) λ + Λ φ_I (1 − (2 a_I − 1)^2) > 0

### Mechanism and implications
- The closed-form S > 1/2 indicates an equity home bias in the model.
- Equity portfolio S depends only on local spending bias in investment a_I and capital share κ:
  - Degree of equity home bias increases with a_I (local spending bias in investment).
  - Higher κ (capital share) strengthens the link between domestic investment and output, reinforcing home bias.
- Economic intuition:
  - An increase in domestic physical investment reduces dividends to equity investors and lowers correlation between labor income and dividends; lower correlation improves diversification via local equity and induces stronger home bias.
  - Bonds denominated in domestic vs foreign goods hedge exposure to real exchange rate fluctuations; equities hedge labor income fluctuations.

### Use in model simulation
- The model simulations use the log-linearized (non-portfolio) first-order conditions from Subsection 2.2 together with the zero-order portfolio.
- Rationale: because excess returns of financial assets are zero at steady state, the log-linearized (non-portfolio) conditions depend only on the zero-order portfolio; higher-order portfolio behavior is irrelevant for the first-order approximated macroeconomic dynamics.
- This approach simplifies computation while capturing first-order macroeconomic volatility implications of the portfolio choice.

*Source: wpiea2024048-print-pdf (sections 2.2–2.3).*

### 4.1    Benchmark Parameterization

### 4.1    Benchmark Parameterization

### Model parameters and stochastic processes
- The model has nine types of parameters:
  - (i) subjective discount factor (β)
  - (ii) inverse of Frisch elasticity of labor supply (ω)
  - (iii) capital share (κ)
  - (iv) depreciation rate of capital (δ)
  - (v) local spending bias in consumption and investment (a and aI)
  - (vi) inverse elasticity of inter-temporal substitution (σ)
  - (vii) elasticity of substitution in consumption between domestic and foreign goods (φ)
  - (viii) elasticity of substitution in investment between them (φI)
  - (ix) the processes of TFP and investment efficiency (θH,t, θF,t, χH,t, χF,t)
- Log-deviations of TFP and investment efficiency from steady state (bθH,t, bθF,t, bχH,t, bχF,t) follow first-order autoregressive processes:
  - bθH,t = ρHθ bθH,t−1 + εHθ,t  (equation 28)
  - bθF,t = ρFθ bθF,t−1 + εFθ,t  (equation 29)
  - bχH,t = ρHχ bχH,t−1 + εHχ,t  (equation 30)
  - bχF,t = ρFχ bχF,t−1 + εFχ,t  (equation 31)
- Parameters relevant to these processes: persistence (ρHθ, ρFθ, ρHχ, ρFχ) and variance-covariance structure of shocks (std(εHθ), std(εFθ), corr(εHθ, εFθ), std(εHχ), std(εFχ), corr(εHχ, εFχ)). std denotes standard deviation and corr denotes correlation.
- Parameters (i)-(iv) are common across G7 countries; parameters (v)-(ix) are country-specific.
- Model frequency is annual.

### Common parameters for the G7 countries (parameters i–iv)
- Calibrated values for all G7 countries following Coeurdacier et al. (2010):
  - β = 0.96
  - ω = 0.5
  - κ = 0.4
  - δ = 0.1

### Country-specific parameters: local spending bias (v)
- Local spending biases in consumption and investment are updated from historical import-to-GDP ratios for 1992-2019:
  - United States: 0.87
  - Japan: 0.85
  - Germany: 0.70
  - United Kingdom: 0.76
  - France: 0.75
  - Italy: 0.77
  - Canada: 0.70

### Country-specific parameters: estimated elasticities (vi–viii)
- Estimation approach: Bayesian full information (Smets and Wouters 2003) using Metropolis-Hastings MCMC; posterior means used in simulations. Observed variables: yearly real consumption and output in home country (one-sided HP filtered, smoothing parameter = 100).
- Priors and estimation ranges:
  - σ (inverse elasticity of inter-temporal substitution): prior uniform [1, 2]; posterior means close to 1 in all countries.
  - φ (elasticity of substitution in consumption): prior uniform [0.6, 1.5]; posterior mean ranges across G7: 0.7–1.3.
  - φI (elasticity of substitution in investment): prior uniform [0.6, 1.5]; posterior mean ranges across G7: 0.7–1.1.
- Table 3 (estimation results) — posterior means and 90 percent intervals:
  - (a) σ — Posterior means and 90 percent intervals:
    - United States: 1.037, 1.004-1.085
    - Japan: 1.006, 1.001-1.014
    - Germany: 1.011, 1.001-1.026
    - United Kingdom: 1.034, 1.004-1.080
    - France: 1.016, 1.002-1.037
    - Italy: 1.009, 1.001-1.022
    - Canada: 1.056, 1.007-1.126
  - (b) φ — Posterior means and 90 percent intervals:
    - United States: 0.774, 0.617-1.021
    - Japan: 0.896, 0.643-1.249
    - Germany: 1.262, 0.972-1.467
    - United Kingdom: 0.746, 0.614-0.950
    - France: 0.761, 0.614-0.991
    - Italy: 0.656, 0.606-0.732
    - Canada: 0.954, 0.657-1.331
  - (c) φI — Posterior means and 90 percent intervals:
    - United States: 0.898, 0.641-1.262
    - Japan: 1.006, 0.673-1.378
    - Germany: 1.137, 0.751-1.445
    - United Kingdom: 0.888, 0.637-1.262
    - France: 0.874, 0.630-1.241
    - Italy: 0.746, 0.615-0.944
    - Canada: 1.030, 0.674-1.408

### Country-specific parameters: TFP and investment efficiency processes (ix)
- Calibration sample period: 1994-2019.
- TFP series from Penn World Table, version 10.0; TFP cycles = percent deviation from trend using one-sided HP filter (smoothing parameter = 100) on log TFP. First-order autoregression estimated to obtain persistence (ρHθ, ρFθ) and std(εHθ), std(εFθ) from residuals. Foreign aggregate TFP cycles are weighted averages of partner countries by real output (USD) in each year. Correlation corr(εHθ, εFθ) calculated from residuals.
- Investment efficiency series computed as consumption deflator divided by investment deflator (Justiniano et al. 2011). Persistence (ρHχ, ρFχ), std(εHχ), std(εFχ), and corr(εHχ, εFχ) calculated analogously to TFP.

### Estimation results for TFP and investment efficiency processes (Table 4)
- (a) TFP process in home and foreign country (θH,t, θF,t) — reported values by country:
  - United States: ρHθ 0.84, std(εHθ) 0.67, ρFθ 0.72, std(εFθ) 0.61, corr(εHθ, εFθ) 0.17
  - Japan: ρHθ 0.69, std(εHθ) 0.72, ρFθ 0.72, std(εFθ) 0.54, corr(εHθ, εFθ) 0.27
  - Germany: ρHθ 0.59, std(εHθ) 0.67, ρFθ 0.72, std(εFθ) 0.53, corr(εHθ, εFθ) 0.30
  - United Kingdom: ρHθ 0.85, std(εHθ) 0.86, ρFθ 0.70, std(εFθ) 0.52, corr(εHθ, εFθ) 0.39
  - France: ρHθ 0.74, std(εHθ) 0.63, ρFθ 0.69, std(εFθ) 0.52, corr(εHθ, εFθ) 0.58
  - Italy: ρHθ 0.76, std(εHθ) 0.92, ρFθ 0.71, std(εFθ) 0.52, corr(εHθ, εFθ) 0.47
  - Canada: ρHθ 0.54, std(εHθ) 0.78, ρFθ 0.69, std(εFθ) 0.51, corr(εHθ, εFθ) 0.67
- Reported ranges summarized in text:
  - Persistence of TFP: home 0.54-0.84, foreign 0.69-0.72
  - Standard deviations of TFP shocks: home 0.67-0.92, foreign 0.51-0.61
  - Cross-country correlations for TFP shocks: 0.17-0.67
- (b) Investment efficiency process in home and foreign country (χH,t, χF,t) — reported values by country:
  - United States: ρHχ 0.76, std(εHχ) 0.60, ρFχ 0.87, std(εFχ) 0.52, corr(εHχ, εFχ) 0.27
  - Japan: ρHχ 0.81, std(εHχ) 0.34, ρFχ 0.87, std(εFχ) 0.47, corr(εHχ, εFχ) 0.19
  - Germany: ρHχ 0.87, std(εHχ) 0.42, ρFχ 0.88, std(εFχ) 0.46, corr(εHχ, εFχ) 0.29
  - United Kingdom: ρHχ 0.58, std(εHχ) 0.90, ρFχ 0.87, std(εFχ) 0.46, corr(εHχ, εFχ) 0.34
  - France: ρHχ 0.81, std(εHχ) 0.40, ρFχ 0.87, std(εFχ) 0.46, corr(εHχ, εFχ) 0.29
  - Italy: ρHχ 0.69, std(εHχ) 0.50, ρFχ 0.87, std(εFχ) 0.46, corr(εHχ, εFχ) 0.20
  - Canada: ρHχ 0.78, std(εHχ) 0.76, ρFχ 0.87, std(εFχ) 0.45, corr(εHχ, εFχ) 0.28
- Reported ranges summarized in text:
  - Persistence of investment efficiency: home 0.58-0.87, foreign 0.45-0.52
  - Standard deviations of investment efficiency shocks: home 0.34-0.76, foreign 0.87-0.88
  - Cross-country correlations for investment efficiency shocks: 0.19-0.34

### Notes on estimation choices and data sources
- Correlation between TFP shock and investment efficiency shocks assumed zero following Coeurdacier et al. (2010).
- TFP data source: Penn World Table, version 10.0 (Feenstra et al. 2015).
- Import-to-GDP ratios used for local spending bias: United Nations “The National Accounts Main Aggregates Database.”
- Investment efficiency proxy: consumption deflator divided by investment deflator (Justiniano et al. 2011).
- One-sided Hodrick-Prescott filter used with smoothing parameter = 100 for cyclical decomposition.

### Connection to counterfactual scenarios (beginning of 4.2)
- Parameters set differently across scenarios to reflect narratives: (i) foreign-country processes of TFP and investment efficiency (ˆθF,t and ˆχF,t), and (ii) local spending bias in consumption and investment (a and aI).
- Under fragmentation scenarios, foreign-country aggregate processes differ because weights (based on real output in USD) for partner countries change; the exogenous processes at the individual partner-country level remain identical across scenarios.
- Under autarky: home country cannot engage in cross-border transactions; parameters related to foreign-country processes are abstracted from; local spending bias set to full bias with a = aI = 1.
- Local spending bias under full integration and fragmentation scenarios (Table 6):
  - United States: full integration 0.87; moderate fragmentation 0.90; extreme fragmentation 0.93; autarky 1.00
  - Japan: full integration 0.85; moderate fragmentation 0.91; extreme fragmentation 0.94; autarky 1.00
  - Germany: full integration 0.70; moderate fragmentation 0.73; extreme fragmentation 0.75; autarky 1.00
  - United Kingdom: full integration 0.76; moderate fragmentation 0.79; extreme fragmentation 0.80; autarky 1.00
  - France: full integration 0.75; moderate fragmentation 0.78; extreme fragmentation 0.80; autarky 1.00
  - Italy: full integration 0.77; moderate fragmentation 0.80; extreme fragmentation 0.81; autarky 1.00
  - Canada: full integration 0.70; moderate fragmentation 0.73; extreme fragmentation 0.76; autarky 1.00
- TFP and investment-efficiency foreign-process parameters are recalculated under moderate and extreme fragmentation scenarios to reflect changed partner weights (Tables 5a and 5b provide calibrated values for ρFθ, std(εFθ), corr(εHθ, εFθ), ρFχ, std(εFχ), corr(εHχ, εFχ) by country under each fragmentation scenario).

_Italic: Source — wpiea2024048-print-pdf, section 4.1 (Benchmark Parameterization) and beginning of 4.2 (Parameterization under Counterfactual Scenarios)._

### Appendix D shows the values of macro-financial volatility in four scenarios. Further, appendix B explains

### wpiea2024048-print-pdf - Appendix D shows the values of macro-financial volatility in four scenarios. Further, appendix B explains

### Key findings and quantitative impacts
- Appendix D shows the values of macro-financial volatility in four scenarios. Appendix B explains the consistency of the size of the estimated diversification benefit under the full integration scenario with the literature.
- Geopolitical fragmentation can significantly undermine international risk-sharing benefits for G7 countries.
- Under the moderate fragmentation scenario (25 percent of partner countries excluded):
  - The median volatility of output across G7 countries increases by 1 percentage point relative to the full integration scenario.
- Under the extreme fragmentation scenario (50 percent of partner countries excluded):
  - The median volatility of output across G7 countries increases by 3 percentage points relative to the full integration scenario.
- The median volatility of consumption, corporate profits, equity, and bond prices increases by a range of about 2 to 8 percentage points (relative to the full integration scenario).
- The loss of diversification benefits under fragmentation scenarios, compared to the full integration scenario:
  - About 20 percent in the moderate fragmentation scenario.
  - About 40-50 percent in the extreme fragmentation scenario.

### Robustness and parameter sensitivity
- Results on changes in macro-financial volatility and the loss of diversification benefits are robust to different sets of parameters, although the size of macro-financial volatility and diversification benefit varies.
- Appendices E.1 and E.2 present results under alternative parameter sets regarding:
  - The elasticity of substitution in consumption and investment between home and foreign goods (Appendix E.1).
  - The local spending bias in consumption and investment (Appendix E.2).

### Three driving factors behind higher macro-financial volatility
- The paper decomposes changes in volatility into three factors (decomposition replicated in Figure 4; methodology summarized below).
- Factor 1 — Increase in cross-country business cycle correlation:
  - Occurs because countries excluded under fragmentation scenarios have lower cross-country correlation with G7 than under full integration.
  - Represented by differences in cross-country correlation of TFP and investment efficiency shocks.
  - Higher cross-country shock correlation increases common fluctuations and reduces terms-of-trade flexibility, raising sensitivity of macro-financial variables to common shocks.
- Factor 2 — Increase in business cycle volatility in the foreign country:
  - Occurs because partner-country composition under fragmentation leads to higher cross-country business cycle correlations among remaining partners, increasing foreign country volatility.
  - Represented by differences in volatility of exogenous TFP and investment efficiency processes in foreign countries.
  - Particularly pronounced under the extreme fragmentation scenario because exclusion of commodity-exporting countries leaves mostly highly correlated European industrial countries as partners, making foreign country more volatile.
- Factor 3 — Increase in the share of domestic production in local goods markets (local spending bias):
  - Under fragmentation, domestic production partly substitutes imports from excluded partners, increasing local spending bias for consumption and investment.
  - Represented by differences in local spending bias of consumption and investment goods.
  - Higher local spending bias increases sensitivity of domestic consumption to domestic business cycles and reduces sensitivity to foreign cycles, hampering diversification via goods trade.
- Net effect under study parameters:
  - The first factor (higher cross-country shock correlation) prevails in increasing consumption volatility because domestic business cycles are more volatile than foreign business cycles.
  - The first two factors (cross-country shock correlation and foreign exogenous process volatility) are particularly noteworthy and closely linked to geopolitical configuration.

### Decomposition methodology (summary)
- The decomposition is performed by simulating the model and holding subsets of parameters at full integration values while changing others to fragmentation scenario values:
  1. Contribution of cross-country business cycle correlation: simulate with cross-country shock correlation parameters from fragmentation scenarios, keeping other parameters as in full integration; difference from full integration simulation is the contribution of cross-country correlation.
  2. Contribution of volatility of exogenous processes: simulate with volatility and persistence of TFP and investment efficiency (and cross-country shock correlation) from fragmentation scenarios, keeping local spending bias as in full integration; net difference (after removing cross-country correlation contribution) is the contribution of volatile foreign TFP and investment efficiency.
  3. Contribution of local spending bias: residual difference between simulated volatility under fragmentation scenarios and the sum of the first two contributions (second and third contributions include cross-term effects).

### Economic intuition and non-linearities
- Higher cross-country shock correlations reduce terms-of-trade adjustment that would otherwise cushion asymmetric shocks, increasing volatility.
- Higher foreign exogenous-process volatility raises foreign output volatility; when remaining partners are more correlated (extreme fragmentation), this effect is amplified.
- Increased local spending bias reduces import shares in consumption and investment, increasing sensitivity to domestic cycles and weakening cross-border smoothing.
- The non-linear contribution of the second factor arises from the changing composition of partner countries across moderate and extreme fragmentation scenarios.

### Limitations and caveats
- The study examines only the loss of cross-border investment diversification benefits; estimates are not a comprehensive assessment of all impacts of geopolitical fragmentation.
- The framework does not consider the impact of capital reallocation on growth.
- Model simplifications include:
  - Full substitutability of foreign goods production among G7 countries and partners.
  - Symmetry between home and foreign countries except for TFP and investment efficiency processes.
- The increase of local spending bias depends on the assumption that imports lost from excluded countries are substitutable by remaining countries including home country; if imports can only be substituted by foreign countries, local spending share would be unchanged and the third factor would not increase macro-financial volatility.

### Conclusion
- Geopolitical fragmentation between countries with asynchronous business cycles could imply a substantial loss of international diversification benefits for G7 countries, driven mainly by higher cross-country shock correlations and increased volatility of foreign exogenous processes; increased local spending bias also contributes.

*Source: wpiea2024048-print-pdf*

### References

### wpiea2024048-print-pdf - References and Appendices

### References (bibliographic scope)
- The reference list cites foundational and recent literature on international macroeconomics, financial integration, risk sharing, trade-policy pass-through, geopolitical measures based on UNGA voting, and DSGE estimation. Key recurring authors and works include Signorino and Ritter (1999); van Wincoop (1994, 1999); Coeurdacier et al.; Smets and Wouters (2003); and Feenstra, Inklaar, and Timmer (2015).
- The bibliography underpins the study’s empirical measures (UNGA voting-based foreign policy proximity), theoretical modeling (open-economy DSGE, international portfolios, risk sharing), and comparative welfare calculations (van Wincoop framework).

### Appendix A — Geopolitical Distance Measure
- Construction method:
  - Bilateral geopolitical distance S_t(a,b) = (−1) × foreign policy proximity (S-scores from Signorino and Ritter (1999)).
  - S-scores are based on average disagreement in UNGA roll-call voting using the squared sum of differences, normalized to take values from 1 (complete disagreement) to −1 (complete agreement).
  - Votes coded as: yea (for) = 1, abstain = 2, nay (against) = 3. d_max,t denotes the maximum possible distance within the year.
  - Example interpretation: a country pair voting yea vs nay in a session implies implied distance 1; identical votes imply distance −1.
- Data:
  - 2012–2015: geopolitical distance taken from Häge (2011) dataset (methodology following Signorino and Ritter (1999)).
  - 2016–2021: extended using Erik Voeten’s database of 196 economies’ roll-call votes in the UNGA from 1946 to 2021 (sessions 1–76).
- Alternative measures and robustness:
  - Alternatives: Häge (2011) π-measure and Bailey et al. (2017) ideal point distance (latent-preference discrete choice).
  - S-score is highly correlated with π-measure and ideal point distance.
  - Robustness of partner-grouping under fragmentation scenarios:
    - Using the π-measure: the list of countries excluded in the extreme fragmentation scenario is identical; some countries excluded in the moderate fragmentation scenario differ.
    - Using the ideal point distance: the extreme fragmentation exclusions are identical; some proportion excluded under the moderate fragmentation scenario differ.
  - Specific noted differences (relative to Table 2):
    - Footnote 42: India, Pakistan, China, and Hong Kong SAR are included in partners while Singapore, Morocco, Nigeria, and Malaysia are excluded from the partners.
    - Footnote 43: India, China, Hong Kong SAR, and Pakistan are included in partners while Nigeria, South Africa, Malaysia, and Morocco are excluded from the partners.
  - Conclusion: selection of partner countries under fragmentation scenarios is robust to the choice of geopolitical distance measure.

### Appendix B — Size of Diversification Benefits (welfare translation)
- Welfare gain formula (as reported):
  - Welfare gains from reduction of consumption volatility are calculated as −0.5γ r−μ ∆σ^2_c where γ is the inverse elasticity of inter-temporal substitution (corresponds to σ in the model), r is the risk-free interest rate, μ is the risk-adjusted growth rate, and ∆σ^2_c is the change in the variance of consumption from autarky to full integration.
- Calibration inputs used in the exercise:
  - γ is obtained from Table 3 (model parameter; exact γ value referenced to Table 3).
  - r = 0.027 and μ = 0.017 (borrowed from van Wincoop (1994)).
- Numerical welfare findings (preserving reported values exactly):
  - Median welfare gain from financial integration (transition from autarky to full integration) = 0.21 percent increase of the permanent consumption.
  - First-to-third quantiles of the estimates = 0.14–0.44.
  - Under the moderate fragmentation scenario:
    - Median = 0.18
    - First-to-third quantiles = 0.13–0.38
  - Under the extreme fragmentation scenario:
    - Median = 0.13
    - First-to-third quantiles = 0.07–0.28
  - Implication: under the moderate and extreme fragmentation scenarios, welfare gains from financial integration would reduce by around 20 and 40 percent, respectively.
- Comparison with literature:
  - Reported gains in the literature vary enormously (less than 0.1 percent to over 100 percent).
  - Comparison with Coeurdacier et al. (2020):
    - For country D (advanced economies) with CRRA utility and low risk aversion and no capital scarcity (degree of risk aversion = 4, corresponding with γ = 4), Coeurdacier et al. (2020) report estimates 0.39 and 0.25, which fall within the study’s first-to-third quantiles 0.14–0.44.
  - Notes on structural differences across studies:
    - van Wincoop (1994) considers endowment economies and reports larger diversification benefits (median around 0.9 percent).
    - Production-economy models with capital (this study and Coeurdacier et al. (2020)) yield smaller diversification benefits because capital provides consumption smoothing.

### Appendix C — Log-Linearization of Equilibrium Equations (summary of transformed conditions)
- Linearization setup:
  - Log-deviations indicated by lower-case letters; variables symmetric in steady state; price level, TFP, and investment efficiency normalized to unity.
- Key log-linearized conditions presented (equations preserved by theme):
  - Price index: p_H,t = a p_H t + (1−a) p_F t, p_F,t = a p_F t + (1−a) p_H t, p^I_H,t = a^I p_H t + (1−a^I) p_F t, p^I_F,t = a^I p_F t + (1−a^I) p_H t.
  - Consumption allocation: c^H_H,t = −φ (p_H t − p_H,t) + c_H,t; c^F_H,t = −φ (p_F,t − p_H,t) + c_H,t; c^H_F,t = −φ (p_H,t − p_F,t) + c_F,t; c^F_F,t = −φ (p_F,t − p_F,t) + c_F,t.
  - Investment allocation: analogous log-linear forms with φ^I and p^I terms.
  - Labor supply: ω l_H,t = w_H,t − p_H,t − σ c_H,t; ω l_F,t = w_F,t − p_F,t − σ c_F,t.
  - Wage bill: w_H,t + l_H,t = p_H t + y_H,t; w_F,t + l_F,t = p_F t + y_F,t.
  - Dividend: d_H,t = κ/(κ−Λ) (p_H t + y_H,t) − Λ/(κ−Λ) (p^I_H,t + i_H,t); symmetric for d_F,t.
  - Investment Euler: detailed linearized conditions for c_H,t and c_F,t involving expectations E_t[·], 1/σ terms, p^I, χ̂, θ̂, k, l, β, κ, δ, Λ.
  - Stock Euler and Bond Euler: four conditions each (noting two of the four conditions are redundant in both cases).
  - Production: y_H,t = b θ̂_H,t + κ k_H,t + (1−κ) l_H,t; symmetric for y_F,t.
  - Law of motion of capital: k_H,t+1 = (1−δ) k_H,t + δ(χ̂_H,t + i_H,t); symmetric for foreign.
  - Budget constraint: (1−Λ)(c_H,t + p_H,t) = (1−κ)(l_H,t + w_H,t) + (κ−Λ)(S d_H,t + (1−S) d_F,t) + b (p_H t − p_F t); symmetric for foreign.
  - Resource constraint: (1−Λ) a c^H_H,t + (1−Λ)(1−a) c^F_H,t + Λ a^I i^H_H,t + Λ(1−a^I) i^F_H,t = y_H,t; symmetric for foreign (Warlas’s Law note on redundancy with budget constraints).
  - Terms of trade: up to first order, −σ(c_H,t − c_F,t) = p_H,t − p_F,t ⇔ p_H t − p_F t = −σ/(2a−1) (c_H,t − c_F,t).
  - Real corporate profits and relative prices: π_H,t = p_H t + y_H,t − p_H,t; b p^S_H,t = p^S_H,t − p_H,t; b p^B_H,t = p^B_H,t − p_H,t.

### Appendix D — Simulated Macro-Financial Volatility in G7 Countries (standard deviation, unit: percent)
- Table A1: Macro-financial volatility in G7 countries — volatility measured as standard deviation (unit: percent). Values listed for Output, Consumption, Corporate profit, Equity price, Bond price under four scenarios: Full integration, Moderate fragmentation, Extreme fragmentation, Autarky.

- United States
  - Full integration: Output 1.99, Consumption 1.53, Corporate profit 1.83, Equity price 2.04, Bond price 1.12
  - Moderate fragmentation: Output 2.02, Consumption 1.57, Corporate profit 1.89, Equity price 2.08, Bond price 1.16
  - Extreme fragmentation: Output 2.05, Consumption 1.63, Corporate profit 1.98, Equity price 2.15, Bond price 1.21
  - Autarky: Output 2.10, Consumption 1.70, Corporate profit 2.10, Equity price 2.25, Bond price 1.27

- Japan
  - Full integration: Output 1.60, Consumption 1.05, Corporate profit 1.49, Equity price 1.49, Bond price 0.80
  - Moderate fragmentation: Output 1.63, Consumption 1.10, Corporate profit 1.57, Equity price 1.54, Bond price 0.84
  - Extreme fragmentation: Output 1.63, Consumption 1.12, Corporate profit 1.60, Equity price 1.56, Bond price 0.86
  - Autarky: Output 1.65, Consumption 1.16, Corporate profit 1.65, Equity price 1.59, Bond price 0.89

- Germany
  - Full integration: Output 1.43, Consumption 0.88, Corporate profit 1.28, Equity price 1.37, Bond price 0.68
  - Moderate fragmentation: Output 1.44, Consumption 0.89, Corporate profit 1.32, Equity price 1.39, Bond price 0.70
  - Extreme fragmentation: Output 1.44, Consumption 0.93, Corporate profit 1.35, Equity price 1.42, Bond price 0.73
  - Autarky: Output 1.46, Consumption 1.03, Corporate profit 1.46, Equity price 1.47, Bond price 0.80

- United Kingdom
  - Full integration: Output 2.51, Consumption 1.83, Corporate profit 2.12, Equity price 2.39, Bond price 1.32
  - Moderate fragmentation: Output 2.55, Consumption 1.91, Corporate profit 2.23, Equity price 2.48, Bond price 1.38
  - Extreme fragmentation: Output 2.61, Consumption 2.00, Corporate profit 2.36, Equity price 2.59, Bond price 1.45
  - Autarky: Output 2.78, Consumption 2.30, Corporate profit 2.78, Equity price 2.94, Bond price 1.70

- France
  - Full integration: Output 1.51, Consumption 1.04, Corporate profit 1.38, Equity price 1.46, Bond price 0.79
  - Moderate fragmentation: Output 1.53, Consumption 1.07, Corporate profit 1.43, Equity price 1.49, Bond price 0.82
  - Extreme fragmentation: Output 1.56, Consumption 1.12, Corporate profit 1.51, Equity price 1.56, Bond price 0.86
  - Autarky: Output 1.60, Consumption 1.18, Corporate profit 1.60, Equity price 1.62, Bond price 0.91

- Italy
  - Full integration: Output 2.15, Consumption 1.49, Corporate profit 1.86, Equity price 1.99, Bond price 1.10
  - Moderate fragmentation: Output 2.18, Consumption 1.53, Corporate profit 1.93, Equity price 2.03, Bond price 1.14
  - Extreme fragmentation: Output 2.23, Consumption 1.59, Corporate profit 2.04, Equity price 2.12, Bond price 1.18
  - Autarky: Output 2.37, Consumption 1.76, Corporate profit 2.37, Equity price 2.34, Bond price 1.32

- Canada
  - Full integration: Output 1.66, Consumption 1.03, Corporate profit 1.49, Equity price 1.71, Bond price 0.89
  - Moderate fragmentation: Output 1.66, Consumption 1.06, Corporate profit 1.54, Equity price 1.73, Bond price 0.92
  - Extreme fragmentation: Output 1.65, Consumption 1.08, Corporate profit 1.52, Equity price 1.74, Bond price 0.94
  - Autarky: Output 1.68, Consumption 1.22, Corporate profit 1.68, Equity price 1.81, Bond price 1.06

### Appendix E — Robustness
- E.1 Elasticity of Substitution between Home and Foreign Goods (φ, φ^I)
  - Parameter sweep: φ = φ^I = {0.6, 0.9, 1.2, 1.5} with the other estimated parameter σ re-estimated.
  - Main outcomes:
    - Impact on computed macro-financial volatility is moderate.
    - Impact on loss of diversification benefit is marginal; φ and φ^I barely affect percent changes in diversification benefit while they moderately affect the size of the benefit.
  - Visual aids referenced: Figure A1 (macro-financial volatility) and Figure A2 (loss of diversification benefit) showing medians and interquartile ranges across G7 countries.
- E.2 Local Spending Bias in Consumption and Investment (a, a^I)
  - Robustness check: calibrate local spending bias parameters using export ratios and export partner shares (instead of import and import partner shares) because model symmetry implies a and a^I determine the home country’s export ratio.
  - Method: apply the calculation formula in Section ... (text continues in source beyond provided excerpt).

*Italic: Content unit: wpiea2024048-print-pdf - References (selected references and appendices as provided).*

### 4.  Table A2 shows the calibrated parameters based on the export ratios and the export partner shares under

### 4. Table A2 shows the calibrated parameters based on the export ratios and the export partner shares under

### Calibrated parameters (Table A2)
- Table A2: Local spending bias in consumption and investment under four scenarios
- Scenarios: Full integration, Moderate fragmentation, Extreme fragmentation, Autarky
- Country parameter values (Full integration, Moderate fragmentation, Extreme fragmentation, Autarky):
  - United States — 0.90, 0.91, 0.94, 1.00
  - Japan — 0.87, 0.91, 0.93, 1.00
  - Germany — 0.66, 0.68, 0.70, 1.00
  - United Kingdom — 0.75, 0.78, 0.79, 1.00
  - France — 0.74, 0.77, 0.79, 1.00
  - Italy — 0.75, 0.77, 0.79, 1.00
  - Canada — 0.68, 0.70, 0.71, 1.00

### Robustness and comparative findings (Figures A3 and A4)
- Comparison of parameter sets:
  - Figure A3 compares macro-financial volatility estimates under the parameters in Table A2 with those in Table 6.
  - Figure A4 compares estimates of the loss of diversification benefit under the parameters in Table A2 with those in Table 6.
- Key findings:
  - The impact of the changes in these parameters (a, a_I) on estimates of macro-financial volatility is small.
  - The impact of the changes in these parameters on the estimates of loss of diversification benefit is tiny.
  - These results imply robustness of the findings with respect to the dataset used for calibrating local spending bias.
- Notes on figures:
  - Figure A3: Bars show the median volatility (standard deviation) of the variables in the home country under fragmentation scenarios. Whiskers indicate the interquartile range of the effect across the G7 countries.
  - Figure A4: Bars show the median of loss of diversification benefit under fragmentation scenarios. Whiskers indicate the interquartile range of the effect across the G7 countries.

### Data sources and calibration notes
- The export ratios are calculated based on the dataset by the United Nations “The National Accounts Main Aggregates Database.”
- The dataset of bilateral export partner share is obtained from World Bank, “World Integrated Trade Solution.”
- Calibrated parameters exhibit little changes from Table 6.

*Geoeconomic Fragmentation and International Diversification Benefits Working Paper No. WP/2024/048*

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_Source: https://www.imf.org/-/media/files/publications/wp/2024/english/wpiea2024048-print-pdf.pdf_