## Determinants of Bilateral Real Exchange Rate Volatility

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---

### I. Introduction — research question and contribution
- Research question:
  - What are the macroeconomic consequences of increased integration in international trade, with focus on determinants of long-run real exchange rate volatility and the effects of trade costs on volatility.
- Main contribution:
  - Introduces a multi-country channel: heterogeneity in suppliers of traded goods (common supplier structure) affects diffusion of technological shocks and thus bilateral real exchange rate volatility.
  - Builds a static multi-country Ricardian framework (based on Eaton and Kortum (2002)) with nontradables to show how trade costs shape dissimilarity in providers of traded goods.
  - Provides empirical tests using country-pair panel data over 1970–97 in five year periods and constructs a common supplier index from detailed trade data.

### II. Key conceptual mechanism
- Channel intuition:
  - If two countries share similar sets of suppliers, global technological shocks diffuse similarly to them via trade → similar movements in price indices → lower bilateral real exchange rate volatility.
- Relationship to literature:
  - Emphasizes multi-country interactions beyond bilateral frameworks and complements trade and international RBC literature.
- Empirical headline result (whole sample):
  - Using panel data (1970–97, five year periods), controlling for country-pair fixed effects and standard variables:
    - "the impact of a standard deviation decrease in the supplier index implies a 5 percentage point decrease in bilateral real exchange rate volatility over five years."
  - Effect described as significant, economically large, and robust across specifications and sub-samples.

### III. Model structure (multi-country Ricardian framework)
- Model features and primitives:
  - Static general equilibrium with nontradable and tradable sectors; preferences: U = Q_NT^μ Q_T^(1−μ) with Dixit-Stiglitz aggregators.
  - Nontradable sector: l_NT = F + c_NT q_NT; monopoly pricing p_NT = (η/(η−1)) c_NT w; zero-profit q*_NT = F(η−1)/c_NT; m* = L_NT / (Fη).
  - Tradable sector: Eaton–Kortum style with Fréchet productivity, delivered price p_T,ni(j) = (c_{T,i} / z_i(j))·τ_ni and price index (equation (9)):
    - P_{T,n} = γ Φ_n^{−1/θ} = γ (∑_{i=1}^N A_{T,i} (c_{T,i} τ_{ni})^{−θ})^{−1/θ},
    - γ = [Γ((θ+1−ρ)/θ)]^{1/(1−ρ)}.
  - Expenditure shares and global equilibrium:
    - Λ_ni = X_ni / X_n = A_{T,i} (τ_{nk} c_{T,i})^{−θ} / Φ_n.
    - Export value relation: w_k L_{T,k} = ∑_{n=1}^N Λ_{nk} (1−μ) Y_n = ∑_{n=1}^N A_{T,n} (γ τ_{nk} w_n / P_{T,n})^{−θ} (1−μ) Y_n.
    - Total income Y_k = L̄_k w_k with L̄_k = L_{NT,k} + L_{T,k}.
  - Global equilibrium yields 4N nonlinear equations in 4N unknowns (L_{T,k}, L_{NT,k}, Y_k, w_k), generally solved numerically.

### IV. Volatility derivation and intuition
- Shocks:
  - Technological shocks A_{T,i} = Ã_{T,i} exp(ε_i), ε_i ∼ N(0, σ_ε^2), Cov{ε_i, ε_j} = 0 for i ≠ j (base case).
- First-order approximation (equation (14)) — traded-price variance decomposition:
  - Var{ log [P_{T,1} / P_{T,2}] } ≈ Υ (Term[1] + Term[2]) − 2 Υ (Term[3]),
    - Υ = ( e^{σ_ε^2} [ e^{σ_ε^2} − 1 ]^θ ) > 0,
    - Term[1] = ∑_{i=1}^N Ã_{T,i}^2 (c_{T,i} τ_{1i})^{−2θ} [ ∑_{i=1}^N Ã_{T,i} (c_{T,i} τ_{1i})^{−θ} ]^{−2},
    - Term[2] analogous for country 2,
    - Term[3] = ∑_{i=1}^N Ã_{T,i}^2 (c_{T,i} τ_{1i} τ_{2i})^{−θ} [ ∑_{i=1}^N Ã_{T,i} (c_{T,i} τ_{1i})^{−θ} ]^{−1} [ ∑_{i=1}^N Ã_{T,i} (c_{T,i} τ_{2i})^{−θ} ]^{−1}.
- Interpretation of components:
  - Term[1] and Term[2]: country-specific pass-through of global shocks determined by consumption/supplier weights.
  - Term[3]: covariance from shared suppliers; greater supplier overlap (lower dissimilarity) raises Term[3] and reduces variance of the relative price.
- Analytical sign of derivative:
  - The derivative of real exchange rate variance with respect to bilateral trade costs τ_{12} is not unambiguously signed analytically; numerical examples show volatility typically increases with trade costs under reasonable parameters.

### V. Numerical examples and parameter sensitivity
- Experimental setup:
  - N varies between 30 and 150.
  - θ = 8.26.
  - A_{T,1} = 2; A_{T,2} = (1 + ∆A_T) A_{T,1}, ∆A_T > 0.1; A_{T,i} = A_{T,2} for i = 2, . . . , N.
  - c_{T,1} = 0.5; c_{T,2} = (1 + ∆c_T) c_{T,1}, ∆c_T > 0.1; c_{T,i} = c_{T,2} for i = 2, . . . , N.
  - τ varies between 1 and 4; τ = 1 corresponds to zero trade costs.
  - Trade-cost structure: τ_{1i} = τ_{i1} = τ ≥ 1 for i = 2, . . . , N; τ_{2i} = τ_{i2} = 1 for i = 2, . . . , N.
  - σ_ε considered with σ_ε ≥ 0.1; productivity and cost gaps increased in 10% increments; ∆A_T normalized to show a 10% increase.
- Main simulation findings (Figure 1 summaries):
  - Real exchange rate volatility is increasing in bilateral trade costs τ for all σ_ε values (Fig. 1(a)).
  - A rise in σ_ε increases real exchange rate volatility as σ_ε grows (Fig. 1(a)).
  - Volatility is increasing in τ for all ∆A_T values; an increase in the technological gap reduces volatility (Fig. 1(b)).
  - Volatility is increasing in τ for all ∆c_T values; the rate of increase is not monotonic and cost-gap changes have large impacts (Fig. 1(c)).
  - Volatility is increasing in τ for all N, but volatility decreases as N increases (diversification effect) (Fig. 1(d)).
- Decomposition (Figure 2, parameter example: σ_ε = 0.5, N = 150, A_{T,1} = 2, ∆A_T = 0, c_{T,1} = 1, ∆c_T = 0):
  - Most variation comes from Term[1] (Fig. 2(b)).
  - Covariance term [3] decreases with increasing trade costs; the negative of the covariance illustrated in Fig. 2(d).
  - Explanation: country 2’s price index stabilizes once its trade costs with country 1 are significantly > 2 while country 1’s price index continues to rise with τ.

### VI. Empirical strategy, index construction, and data
- Central empirical prediction:
  - Countries with more common suppliers of traded goods (ceteris paribus) have lower bilateral real exchange rate volatility.
- Common supplier index (CS_{ij}, equation (17)):
  - CS_{ij} = [∑_{k ≠ (i or j)} ∑_{m=1}^M 1(X_{kim} > 0, X_{kjm} > 0) [X_{kim} + X_{kjm}]] / [∑_{k ≠ (i or j)} ∑_{m=1}^M (X_{kim} + X_{kjm})]
  - Bounded between 0 and 1; denominator normalizes by i and j’s total trade with the world (except with each other).
- Reduced-form regression (equation (18)):
  - σ_{RER,ij,t} = β_0 + β_1 CS_{ij,t−1} + γ X + μ_{ij} + δ_t + ζ_{ij,t}
  - Prediction: β_1 < 0.
  - Controls X: ln(product real GDP_i × GDP_j), ln(product real GDP per capita), regional trade agreement indicator, ln(Herfindahl index), correlation of output shocks, exchange rate regime variables.
- Data and measurement:
  - World Trade Database (1970–97) at 4-digit SITC for CS index.
  - CS index sample Mean = 0.04; St. Dev. = 0.045.
  - Bilateral real exchange rates from Global Financial Database; volatility measured as standard deviation of rolling annual changes over five-year periods; HP (λ = 14400) and BK (band (18,96) months) filters used as robustness.
  - Herfindahl H_i = ∑_j (X_{ij}/X_i)^2 at 4-digit SITC.
  - Income from Penn World Tables (Heston, Summers, Aten 2002) with gaps filled from WDI and IFS; exchange rate regimes from Shambaugh (2004).

### VII. Empirical findings and robustness
- Whole-sample (Table 2) results:
  - CS index coefficient negative and statistically significant across pooled and fixed-effects specifications.
  - Quantitative interpretation: a one standard deviation increase in CS (4.5%) decreases bilateral long-run real exchange rate volatility by 5.1% (over a five-year period) (average estimate across specifications).
  - Export concentration (Herfindahl) coefficient negative and significant (more diversified exports → less volatile prices).
  - Gravity/income variables: mixed signs; GDP coefficients positive in pooled results but weaken or reverse with country-pair fixed effects.
  - Distance and border coefficients positive and significant in pooled regressions; border effects examined in subsamples.
  - Exchange rate regime variables jointly significant; individual regime indicators negative in pooled regressions.
- Subsample results:
  - Developed–Developed:
    - CS index significant in three of four specifications; stronger cross-section identification.
    - Country-pair fixed effects jointly not significant (P-value ≈ 0.94 and 0.99).
  - Developed–Less Developed:
    - CS index negative, large, significant in pooled regressions; positive but not significant in fixed-effects regressions.
    - Index captures cross-sectional heterogeneity well but weak over time; output shock correlations negative and significant in several specs.
  - Less Developed–Less Developed:
    - CS index larger and more significant in fixed-effects regressions than pooled regressions; explains within-pair time variation better.
    - Border coefficient positive and very significant in pooled results; drives counter-intuitive border effect in whole sample.
    - Exchange rate regime variables jointly significant.
- Robustness:
  - Results robust to HP and BK filtered measures (Table A2 shows negative CS coefficients under HP and BK).
  - World-average CS index shows secular increase starting in the 1980s (Figure 3).
  - CS index negatively correlated with distance; estimated coefficients on Log(Distance) in Fig. 4: Fig. 4(a): -0.025 (R^2 = 0.26); Fig. 4(b): -0.017 (R^2 = 0.21); Fig. 4(c): -0.020 (R^2 = 0.14); Fig. 4(d): -0.026 (R^2 = 0.35). Each coefficient significant at the 99% confidence level.

### VIII. Relaxing zero correlation of shocks (Appendix I)
- Generalization:
  - Shocks ε = {ε_1, . . . , ε_N} ∼ n(0, Σ) with Σ = σ_ε^2 [1 ρ_{ij} ...], ρ_{i,j} ∈ [−1,1].
  - Use multivariate normal MGF M_Y(t) = exp(t′ μ + t′ Σ t / 2) (equation (A.10)) to derive closed-form Var(Φ_1), Var(Φ_2), Cov(Φ_1, Φ_2) (equations (A.14)–(A.16)).
- Effects of correlation:
  - Var(Φ_1) and Var(Φ_2) include pairwise covariance terms proportional to e^{ρ_{ij}} − 1.
  - Cov(Φ_1, Φ_2) includes pairwise covariance terms involving combinations of τ_{1i}, τ_{2j}, scaled by e^{ρ_{ij}} − 1.
- Sign implications:
  - Impossible to sign unambiguously the derivative of real exchange rate volatility with respect to trade costs in full generality when shocks are correlated.
  - Negative correlation of shocks tends to reduce bilateral real exchange volatility via Var(Φ_1) and Var(Φ_2); Cov(Φ_1, Φ_2) may counteract this.

### IX. Policy-relevant implications and research directions
- Policy implications:
  - Reductions in trade costs that increase overlap in suppliers across countries can lower bilateral real exchange rate volatility by aligning countries’ price-index responses to global shocks.
  - Trade integration and policies reducing transport and other trade frictions can have macroeconomic stabilizing effects on bilateral real exchange rates via the common-supplier channel.
- Suggested extensions:
  - Embed the channel into a fully dynamic multi-country intertemporal general equilibrium model to analyze implications for macro volatility and international macro puzzles.
  - Endogenize nontradability and solve full global equilibrium numerically to simulate moments.
  - Explore alternative trade-cost formulations (e.g., fixed entry costs) while noting potential added complexity.

*Source: IMF Working Paper — "Determinants of Bilateral Real Exchange Rate Volatility" (chapter excerpt provided).*

### 1.    Determinants of Bilateral Real Exchange Rate Volatility:

### Determinants of Bilateral Real Exchange Rate Volatility:

### I. Introduction — research question and contribution
- Research question: What are the macroeconomic consequences of increased integration in international trade, with focus on determinants of long-run real exchange rate volatility and the effects of trade costs on volatility.
- Main contribution:
  - Emphasizes a new channel in a multi-country setting: heterogeneity in suppliers of traded goods (common supplier structure) affects diffusion of technological shocks across countries and thus bilateral real exchange rate volatility.
  - Builds a tractable static multi-country Ricardian framework (based on Eaton and Kortum (2002)) that incorporates nontradables and emphasizes how trade costs shape dissimilarity in providers of traded goods.
  - Provides empirical tests using panel data (country-pair as unit) over 1970–97 in five year periods and constructs a common supplier index from detailed trade data to proxy the channel.

### Key conceptual points
- Channel mechanism:
  - Given technological differences and trade barriers, the same good may be supplied to two countries by different foreign suppliers.
  - If two countries share similar sets of suppliers, global shocks diffuse to them similarly via trade, producing similar movements in price indices and lower bilateral real exchange rate volatility.
- Distinction from other literature:
  - Focus on multi-country interactions (beyond bilateral) complements trade and international RBC literature.
  - Uses a static modeling strategy to isolate and highlight the common-supplier channel; not intended as a fully specified dynamic model to simulate full moments.
- Relation to prior work:
  - Highlights relevance alongside works such as Obstfeld and Rogoff (2001), Eaton and Kortum (2002), Anderson and van Wincoop (2003, 2004), Kose and Yi (2004), Broda and Romalis (2004), Hau (2002), Naknoi (2004), Bergin and Glick (2003a, 2003b), Ghironi and Melitz (2004).

### Empirical headline result (from whole sample)
- Using panel data (1970–97, five year periods), controlling for country-pair fixed effects and other standard variables:
  - "the impact of a standard deviation decrease in the supplier index implies a 5 percentage point decrease in bilateral real exchange rate volatility over five years."
  - The effect is described as significant, economically large, and robust across specifications and sub-samples (developed-developed, developed-less developed, less developed-less developed).

---

### II. Model structure (multi-country Ricardian framework)
- Purpose: illustrate mechanism and derive a reduced-form expression motivating empirical specification.
- Model features:
  - Static general equilibrium model building on Eaton and Kortum (2002) and incorporating a nontradable sector (based on Fujita, Krugman, and Venables, 1999).
  - Preferences: Dixit-Stiglitz aggregator with nontradable and tradable aggregates:
    - U = Q_NT^μ Q_T^(1−μ)
    - Q_NT = (∫_0^m q_NT(j)^{(η−1)/η} dj)^{η/(η−1)}
    - Q_T = (∫_0^1 q_T(j)^{(ρ−1)/ρ} dj)^{ρ/(ρ−1)}
  - Nontradable sector:
    - Labor input l_NT = F + c_NT q_NT, monopoly pricing p_NT = (η/(η−1)) c_NT w.
    - Zero profit output q*_NT = F(η−1)/c_NT, labor per firm l*_NT = Fη, number of varieties m* = L_NT / (Fη).
    - Equilibrium wage expressed (equation (8)) as a function of μ, q*_NT, Y, p_NT, m*.
  - Tradable sector:
    - Eaton-Kortum style: country i efficiency z_i(j) follows Fréchet; cost of producing good j in i is c_T,i / z_i(j); iceberg trade costs τ_ni > 1.
    - Delivered price p_T,ni(j) = (c_T,i / z_i(j))·τ_ni. Price index (equation (9)):
      - P_T,n = γ Φ_n^(−1/θ) = γ (∑_{i=1}^N A_{T,i} (c_{T,i} τ_{ni})^{−θ})^(−1/θ),
      - where γ = [Γ((θ+1−ρ)/θ)]^{1/(1−ρ)}, A_{T,i} is technology, θ regulates comparative advantage.
  - Global equilibrium links sectoral labor and wages across countries (equations (10)–(12)):
    - Expenditure shares Λ_ni = X_ni / X_n = A_{T,i} (τ_{nk} c_{T,i})^{−θ} / Φ_n.
    - Trade balance / export value relation w_k L_{T,k} = ∑_{n=1}^N Λ_{nk} (1−μ) Y_n = ∑_{n=1}^N A_{T,n} (γ τ_{nk} w_n / P_{T,n})^{−θ} (1−μ) Y_n.
    - Total income Y_k = L̄_k w_k where L̄_k = L_{NT,k} + L_{T,k}.
  - The global equilibrium system (equations (8), (10), (11), (12)) yields 4N equations in 4N unknowns (L_{T,k}, L_{NT,k}, Y_k, w_k) and is non-linear (solved numerically in general).

### III. Volatility derivation and intuition
- Modeling shocks:
  - Technological shocks modeled as multiplicative lognormal shocks to A_{T,i}:
    - A_{T,i} =  Ã_{T,i} exp(ε_i), with ε_i ∼ N(0, σ_ε^2) and Cov{ε_i, ε_j} = 0 for i ≠ j.
- First-order approximation yields expression for variance of relative tradable price log ratio (equation (14)):
  - Var{ log [P_{T,1} / P_{T,2}] } ≈ Υ (Term[1] + Term[2]) − 2 Υ (Term[3]),
    - where Υ = ( e^{σ_ε^2} [ e^{σ_ε^2} − 1 ]^θ ) > 0,
    - Term[1] = ∑_{i=1}^N Ã_{T,i}^2 (c_{T,i} τ_{1i})^{−2θ} [ ∑_{i=1}^N Ã_{T,i} (c_{T,i} τ_{1i})^{−θ} ]^{−2},
    - Term[2] analogous for country 2 with τ_{2i},
    - Term[3] = ∑_{i=1}^N Ã_{T,i}^2 (c_{T,i} τ_{1i} τ_{2i})^{−θ} [ ∑_{i=1}^N Ã_{T,i} (c_{T,i} τ_{1i})^{−θ} ]^{−1} [ ∑_{i=1}^N Ã_{T,i} (c_{T,i} τ_{2i})^{−θ} ]^{−1}.
- Interpretation of components:
  - Terms [1] and [2] reflect how each country’s consumption composition (weights on suppliers) determines pass-through of global shocks to its price index; as trade costs τ_{1i} or τ_{2i} approach 1 (frictionless trade), these terms depend only on relative technology and costs and shocks pass one-for-one.
  - Term [3] captures covariance component from shared suppliers: higher overlap in suppliers (lower dissimilarity) increases Term[3], which reduces variance of the relative price.
- Sign of derivative:
  - The derivative of real exchange rate variance with respect to bilateral trade costs τ_{12}=τ_{21} is not unambiguously signed analytically (first-order derivative can have an inflection), so the paper presents a numerical example showing that bilateral real exchange rate volatility typically increases with trade costs under reasonable parameters.

---

### IV. Empirical strategy and evidence
- Data and identification:
  - Panel estimation across country-pairs over 1970–97 in five year periods; unit of observation: country-pair.
  - Constructs a common supplier index of traded goods from detailed trade data to proxy dissimilarity in suppliers (this index varies over time and is not absorbed by country-pair fixed effects like geographic distance).
  - Controls for standard economic variables and tests across sub-samples defined by level of development: whole sample (1970–97), Developed-Developed, Developed-Less Developed, Less Developed-Less Developed.
- Main empirical finding (repeated):
  - For the whole sample, a standard deviation decrease in the supplier index implies a 5 percentage point decrease in bilateral real exchange rate volatility over five years.
  - The supplier index is also significant in various sub-samples; results are robust to different specifications.
- Interpretation:
  - Empirical results are interpreted as supportive evidence for the model’s common-supplier channel and as a measure of why trade costs matter for bilateral real exchange rate volatility.

---

### V. Policy-relevant implications and research directions
- Policy implications (inferred from model emphasis):
  - Reductions in trade costs that increase overlap in suppliers across countries can lower bilateral real exchange rate volatility by making countries’ price indices respond more similarly to global shocks.
  - Trade integration and policies that reduce transport and other trade frictions can have macroeconomic stabilizing effects on bilateral real exchange rates via the common-supplier channel.
- Suggested further work (from text):
  - Extend analysis in fully dynamic frameworks, endogenize nontradability, and solve the full global equilibrium numerically to simulate moments.
  - Explore alternative trade-cost formulations (e.g., fixed entry costs) though authors note added complexity would obscure mechanism focus.

*Source: IMF Working Paper — "Determinants of Bilateral Real Exchange Rate Volatility" (chapter excerpt provided).*

### Appendix I presents the solution when we relax the assumption of zero correlation of shocks.

### Appendix I presents the solution when we relax the assumption of zero correlation of shocks

### Key theoretical result: how trade costs affect bilateral real exchange rate volatility
- Real exchange rate volatility decomposes into three terms (equation (14) / (A.9)): term [1], term [2], and covariance term [3], which together show how similarities in trade costs and technology with respect to the rest of the world affect bilateral real exchange rate volatility.
- Intuition from symmetry:
  - If two countries are very close and have similar technologies, terms [1]-[3] will be quite small and shocks will diffuse similarly, resulting in lower real exchange rate volatility.
  - For a set of countries on a straight line with equal spacing and identical technology and factor cost, real exchange rate volatility between extreme countries is zero because the sum of terms [1] and [2] equals term [3].
  - Introducing asymmetries in technologies or costs breaks symmetry and increases volatility, particularly through term [3].
- Aggregate real exchange rate (equation (15) and (16)):
  - P = P_T^{\mu} P_{NT}^{1−\mu} μ^{μ} (1−μ)^{1−μ} (equation (15), where P_T corresponds to P_{T,n} in (9)).
  - Log bilateral real exchange rate q = p_1 − p_2 = (1−μ)(p_{T,2} − p_{T,1}) + μ(p_{NT,1} − p_{NT,2}) (equation (16)).
  - The traded goods component tends to drive real exchange rate volatility; therefore analysis focuses on the traded goods component.

### Numerical example: sensitivity of traded-price volatility to parameters (Section III)
- Experimental setup and parameter choices:
  - Number of countries N varies between 30 and 150.
  - θ = 8.26.
  - Normalize A_{T,1} = 2; A_{T,2} = (1 + ∆A_T) A_{T,1}, ∆A_T > 0.1; A_{T,i} = A_{T,2} for i = 2, . . . , N.
  - c_{T,1} = 0.5; c_{T,2} = (1 + ∆c_T) c_{T,1}, ∆c_T > 0.1; c_{T,i} = c_{T,2} for i = 2, . . . , N.
  - τ varies between 1 and 4, with τ = 1 corresponding to zero trade costs (τ = 1/(1−τ_2) interpretation).
  - Trade cost structure in simulations: τ_{1i} = τ_{i1} = τ ≥ 1 for i = 2, . . . , N; τ_{2i} = τ_{i2} = 1 for i = 2, . . . , N.
  - Variance of productivity shocks σ_ε considered (σ_ε ≥ 0.1); productivity and cost gaps increased in 10% increments in simulations; ∆A_T normalized to show a 10% increase.
- Main simulation findings (Figure 1 results):
  - Real exchange rate volatility is increasing in bilateral trade costs τ for all σ_ε values (Fig. 1(a)).
  - A rise in σ_ε increases real exchange rate volatility as σ_ε grows (Fig. 1(a)).
  - Real exchange rate volatility is increasing in bilateral trade costs τ for all ∆A_T values; an increase in the technological gap reduces volatility (Fig. 1(b)).
  - Real exchange rate volatility is increasing in bilateral trade costs τ for all ∆c_T values; the rate of increase is not monotonic and changes in the cost gap have increasing and quite large impacts on volatility (Fig. 1(c)).
  - Real exchange rate volatility is increasing in bilateral trade costs τ for all N, but volatility decreases as the size of the group of countries increases (diversification effect) (Fig. 1(d)).
- Decomposition of volatility (Figure 2 with σ_ε = 0.5, N = 150, A_{T,1} = 2, ∆A_T = 0, c_{T,1} = 1, ∆c_T = 0):
  - Most of the action comes from term [1] (Fig. 2(b)).
  - Covariance term [3] decreases with increasing trade costs; Fig. 2(d) plots the negative of the covariance.
  - Explanation: country 2’s price index stabilizes once trade costs with country 1 are significantly greater than 2 while country 1’s price index keeps increasing with trade costs.

### Empirical strategy and index construction (Section IV and A)
- Central prediction tested: countries with more common suppliers of traded goods (ceteris paribus) should have lower bilateral real exchange rate volatility.
- Common supplier index construction (equation (17)):
  - CS_{ij} = [∑_{k ≠ (i or j)} ∑_{m=1}^M 1(X_{kim} > 0, X_{kjm} > 0) [X_{kim} + X_{kjm}]] / [∑_{k ≠ (i or j)} ∑_{m=1}^M (X_{kim} + X_{kjm})]
  - Indicator 1(·) captures whether country k exports good m to both i and j.
  - Denominator normalizes by i and j’s total trade with the world (except with each other), bounding CS_{ij} between 0 and 1 and controlling for country size.
- Reduced-form regression (equation (18)):
  - σ_{RER,ij,t} = β_0 + β_1 CS_{ij,t−1} + γ X + μ_{ij} + δ_t + ζ_{ij,t}
  - Prediction: β_1 < 0.
  - Controls X include: ln(product real GDP_i × GDP_j), ln(product real GDP per capita), regional trade agreement indicator, ln(Herfindahl index of export concentration), correlation of output shocks, exchange rate regime variables.
  - Estimation in five-year panels; both pooled and country-pair fixed effects specifications; subsamples by development status: (i) developed-developed, (ii) developed-less developed, (iii) less developed-less developed.
- Data sources and construction:
  - World Trade Database for 1970–97 at 4-digit SITC level used to compute CS index.
  - Means and standard deviations of CS index in estimation sample: Mean = 0.04; St. Dev. = 0.045.
  - Bilateral real exchange rates from Global Financial Database; volatility measured using rolling annual changes and computing standard deviation over five-year periods (alternative filters HP with λ = 14400 and BK with band (18,96) months were tested).
  - Herfindahl index H_i = ∑_j (X_{ij}/X_i)^2 at 4-digit SITC; income data from Penn World Tables (Heston, Summers, Aten 2002) with gaps filled from WDI and IFS; exchange rate regime variables from Shambaugh (2004).

### Empirical findings (Section IV.B and tables)
- Whole-sample results (Table 2):
  - Common supplier index coefficient negative and statistically significant across pooled and fixed-effects specifications.
  - Quantitative interpretation: a one standard deviation increase in the index (4.5%) will decrease bilateral long-run real exchange rate volatility by 5.1% (over a five-year period) (average estimate across specifications).
  - Export concentration (Herfindahl) coefficient is significant and negative across specifications (more diversified exports → less volatile prices).
  - Gravity/income variables show mixed signs; GDP coefficients positive in pooled results but weakened or reversed with country-pair fixed effects.
  - Distance and border coefficients positive and significant in pooled regressions; some counterintuitive signs (border) investigated in subsamples.
  - Exchange rate regime variables jointly significant; individual regime indicators negative in pooled regressions.
- Subsample results:
  - Developed-Developed (Table 3):
    - CS index significant in three of four specifications; relationship stronger in cross-section than within-country pair over time.
    - Country-pair fixed effects jointly not significant (P-value ≈ 0.94 and 0.99), suggesting cross-sectional identification.
  - Developed-Less Developed (Table 4):
    - CS index negative, large, and significant in pooled regressions; positive but not significant in fixed effects regressions.
    - Interpretation: index picks up cross-sectional heterogeneity well for this subsample but performs weakly over time; standard errors large relative to coefficients.
    - Output shock correlations negative and significant in several specifications.
  - Less Developed-Less Developed (Table 5):
    - CS index larger and more significant in fixed effects regressions than pooled regressions (reverse of developed-less developed results); index explains within-pair variation over time better in this subsample.
    - Border coefficient positive and very significant in pooled results; drives counter-intuitive border effect in whole sample and may reflect regional developing-country volatility patterns.
    - Exchange rate regime variables jointly significant across specifications.
- Robustness and auxiliary results:
  - Results robust to using HP and BK filtered measures of real exchange rate volatility (Table A2 shows negative CS coefficients under HP and BK filtering).
  - World-average CS index shows secular increase starting in the 1980s (Figure 3).
  - CS index negatively correlated with distance (Figure 4); estimated coefficients on Log(Distance) in Fig. 4 panels: Fig. 4(a): -0.025 (R^2 = 0.26); Fig. 4(b): -0.017 (R^2 = 0.21); Fig. 4(c): -0.020 (R^2 = 0.14); Fig. 4(d): -0.026 (R^2 = 0.35). Each coefficient significant at the 99% confidence level.

### Relaxing zero correlation of shocks: appendix derivations and implications (Section C)
- Assumption: production shocks ε = {ε_1, . . . , ε_N} distributed n(0, Σ) with Σ = σ_ε^2 [1 ρ_{ij} ...] where ρ_{i,j} ∈ [−1,1].
- Using multivariate normal moment generating function M_Y(t) = exp(t′ μ + t′ Σ t / 2) (equation (A.10)), derive closed-form contributions to Var(Φ_1), Var(Φ_2), and Cov(Φ_1, Φ_2) with correlated shocks (equations (A.14), (A.15), (A.16)).
- Key additional terms introduced by correlation ρ_{ij}:
  - Var(Φ_1) and Var(Φ_2) include pairwise covariance contributions proportional to e^{ρ_{ij}} − 1.
  - Cov(Φ_1, Φ_2) also includes pairwise covariance contributions involving combinations of τ_{1i}, τ_{2j}, etc., scaled by e^{ρ_{ij}} − 1.
- Sign implications:
  - It is impossible to sign unambiguously the derivative of real exchange rate volatility with respect to trade costs in full generality when shocks are correlated.
  - From inspection: negative correlation of shocks will decrease bilateral real exchange volatility via terms in (A.14) and (A.15); (A.16) implies the opposite effect may hold via the covariance term.

### Conclusions and research implications (Section V)
- Main conclusion: trade costs increase bilateral real exchange rate volatility through a channel that operates by affecting the heterogeneity of suppliers of traded goods; more common suppliers between two countries reduce bilateral volatility.
- The multi-country Ricardian model and empirical tests support the central prediction that a higher common supplier index (more common suppliers) associates with lower bilateral real exchange rate volatility.
- Suggested extensions and future research:
  - Incorporate the highlighted channel into a dynamic general equilibrium macroeconomic model (multi-country intertemporal environment) to analyze implications for macroeconomic volatility and other international macro puzzles/anomalies.

*Source: Appendix I and related sections of the provided IMF working paper content.*

### REFERENCES

### _wp0505 - REFERENCES

### International trade, geography, and firm heterogeneity
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- Yi, Kei-Mu, 2003, “Can Vertical Specialization Explain the Growth of World Trade?”Journal of Political Economy, Vol. 111 (February), pp. 52–102.
- Kose, M. Ayhan, and Kei-Mu Yi, 2001, “International Trade and Business Cycles: Is Vertical Specialization the Missing Link?”American Economic Review, Vol. 91 (May), pp. 371–75.
- Kose, M. Ayhan, and Kei-Mu Yi, 2004, “The Trade-Comovement Problem in International Macroeconomics” (unpublished; Washington: International Monetary Fund).

### Exchange rates, currency unions, and border effects
- Anderson, James E., and Eric van Wincoop, 2003, “Gravity with Gravitas: A Solution to the Border Puzzle,”American Economic Review, Vol. 93 (March), pp. 170–92.
- ———, 2004, “Trade Costs,”Journal of Economic Literature, Vol. 42 (September), pp. 691–751.
- Bayoumi, Tamim, and Barry Eichengreen, 1998, “Exchange Rate Volatility and Intervention: Implications of the Theory of Optimum Currency Area,”Journal of International Economics, Vol. 45 (August), pp. 191–209.
- Bergin, Paul R., and Reuven Glick, 2003, “Endogenous Nontradability and Macroeconomic Implications,” NBER Working Paper No. 9739 (Cambridge, Massachusetts: NBER).
- Bergin, Paul R., and Reuven Glick, 2003, “A Model of Endogenous Nontradability and its Implications for The Current Account” (unpublished; Davis, CA: University of Califronia; and San Fransisco: Federal Reserve Bank).
- Broda, Christian, and John Romalis, 2004, “Identifying the Effect of Exchange Rate Volatility on the Composition and Volume of Trade” (unpublished; New York: Federal Reserve Bank; and Chicago: Chicago Graduate School of Business).
- Devereux, Michael B., and Philip R. Lane, 2003, “Understanding Bilateral Exchange Rate Volatility,”Journal of International Economics, Vol. 60 (May), pp. 109–32.
- Engel, Charles, 1999, “Accounting for U.S. Real Exchange Rate changes,”Journal of Political Economy, Vol. 107 (June), pp. 507–38.
- Engel, Charles, and Andrew K. Rose, 2002, “Currency Unions and International Integration,” Journal of Money, Credit and Banking, Vol. 34 (November), pp. 1067–89.
- Engel, Charles, and John H. Rogers, 1996, “How Wide is the Border,”American Ecomomic Review, Vol. 86 (December), pp. 1112–25.
- Hau, Harald, 2002, “Real Exchange Rate Volatility and Economic Openness: Theory and Evidence,”Journal of Money, Credit and Banking, Vol. 34, (August), pp. 611–30.
- Naknoi, Kanda, 2004, “Real Exchange Rate Fluctuations and Endogenous Tradability” (unpublished; Palo Alto:  Stanford University).
- Obstfeld, Maurice, and Alan M. Taylor, 1997, “Nonlinear Aspects of Goods-Market Arbitrage and Adjustment: Heckscher’s Commodity Points Revisited,”Journal of the Japanese and International Economies, Vol. 11 (December), pp. 441–79.
- Obstfeld, Maurice, and Alan M. Taylor, 2001, “The Six Major Puzzles in International Finance: Is There a Common Cause?” inNBER Macroeconomics Annual 2000, ed. by Ben S. Bernanke and Kenneth S. Rogoff (Cambridge, Massachusetts: MIT Press), pp. 339–90.
- Reinhart, Carmen M., and Kenneth S. Rogoff, 2004, “The Modern History of Exchange Rate Arrangements: A Reinterpretation,”Quarterly Journal of Economics, Vol. 119 (February), pp. 1–48.
- Rose, Andrew K., and Eric van Wincoop, 2001, “National Money as a Barrier to International Trade: The Real Case for Currency Union,”American Economic Review, Vol. 91 (May), pp. 386–90.
- Shambaugh, Jay C., 2004, “The Effects of Fixed Exchange Rates on Monetary Policy,” Quarterly Journal of Economics, Vol. 119 (February), pp. 301–52.
- Bravo-Ortega, Claudio, and Julian di Giovanni, 2005, “Remoteness and Real Exchange Rate Volatility,” IMF Working Paper 05/1 (Washington: International Monetary Fund).

### International business cycles, macroeconomic dynamics, and productivity
- Backus, David K., Patrick J. Kehoe, and Finn E. Kydland, 1992, “International Real Business Cycles,”Journal of Political Economy, Vol. 100 (August), pp. 745–75.
- Backus, David K., Patrick J. Kehoe, and Finn E. Kydland, “International Business Cycles: Theory and Evidence,” 1995, inFrontiers of Business Cycle Research, ed. by Thomas F. Cooley (Princeton: Princeton University Press), pp. 331–56.
- Baxter, Marianne, and Robert G. King, 1999, “Measure Business Cycles: Approximate Band-Pass Filters for Economic Time Series,”Review of Economics and Statistics, Vol. 81 (November), pp. 575–93.
- Bergin, Paul R., and Reuven Glick, 2003, “Endogenous Nontradability and Macroeconomic Implications,” NBER Working Paper No. 9739 (Cambridge, Massachusetts: NBER).
- Ghironi, Fabio, and Marc J. Melitz, 2004, “International Trade and Macroeconomic Dynamics with Heterogeneous Firms,” NBER Working Paper No. 10540 (Cambridge, Massachussets: NBER).
- Heathcote, Johnathan, and Fabrizio Perri, 2002, “Financial Autarky and International Business Cycles,”Journal of Monetary Economics, Vol. 49 (April), pp. 601–27.
- Kose, M. Ayhan, and Roberto Cardarelli, 2004, “Economic Integration, Business Cycle, and Productivity in North America,” IMF Working Paper 04/138 (Washington: International Monetary Fund).
- Kose, M. Ayhan, Guy M. Meredith, and Christopher M. Towe, 2004, “How Has NAFTA Affected the Mexican Economy? Review and Evidence,” IMF Working Paper No. 04/59 (Washington: International Monetary Fund).
- Ravn, Morten O., and Elisabetta Mazzenga, 2004, “International Business Cycles: The Quantitative Role of Transportation Costs,”Journal of International Money and Finance, Vol. 23 (June), pp. 645–71.

### Data sources and statistical methods
- Anderson, T.W., 1958,An Introduction to Multivariate Statistical Analysis(New York: John Wiley & Sons).
- Casella, George, and Roger L. Berger, 2002,Statistical InferenceDuxbury Advance Series, 2 ed. (Pacific Grove, CA: Duxbury).
- Hodrick, Robert J., and Edward C. Prescott, 1997, “Postwar U.S. Business Cycles: An Empirical Investigation,”Journal of Money, Credit and Banking, Vol. 29 (February), pp. 1–16.
- Heston, Alan, Robert Summers, and Bettina Aten, 2002, “Penn World Table Version 6.1” (Philadelphia: Center for International Comparisons,University of Pennsylvania).

### Working papers and unpublished studies cited
- Bergin, Paul R., and Reuven Glick, 2003, “A Model of Endogenous Nontradability and its Implications for The Current Account” (unpublished; Davis, CA: University of Califronia; and San Fransisco: Federal Reserve Bank).
- Bravo-Ortega, Claudio, and Julian di Giovanni, 2005, “Remoteness and Real Exchange Rate Volatility,” IMF Working Paper 05/1 (Washington: International Monetary Fund).
- Broda, Christian, and John Romalis, 2004, “Identifying the Effect of Exchange Rate Volatility on the Composition and Volume of Trade” (unpublished; New York: Federal Reserve Bank; and Chicago: Chicago Graduate School of Business).
- Fitzgerald, Doireann, 2004, “Trade, Interdependence and Exchange Rates” (unpublished; Santa Cruz: University of California).
- Ghironi, Fabio, and Marc J. Melitz, 2004, “International Trade and Macroeconomic Dynamics with Heterogeneous Firms,” NBER Working Paper No. 10540 (Cambridge, Massachussets: NBER).
- Naknoi, Kanda, 2004, “Real Exchange Rate Fluctuations and Endogenous Tradability” (unpublished; Palo Alto:  Stanford University).
- Kose, M. Ayhan, and Kei-Mu Yi, 2004, “The Trade-Comovement Problem in International Macroeconomics” (unpublished; Washington: International Monetary Fund).
- Alvarez, Fernando, and Robert E. Lucas, 2004, “General Equilibrium Analysis of the Eaton-Kortum of International Trade” (unpublished; Chicago: University of Chicago).

*Source: _wp0505 - REFERENCES*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2005/_wp0505.pdf_