## wp17239

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### Conceptual framework
- Definitions and setup:
  - p_ij: log price of goods exported from country i to country j measured in currency j.
  - e_ij: log bilateral exchange rate between country i and country j (price of currency i in terms of currency j).
  - e_j$: log price of a U.S. dollar in currency j.
  - Invoicing shares: θ_i (producer currency), θ_j (local currency), θ_u (dominant currency/dollar), with ∑_{k∈{i,j,u}} θ_k = 1.
- Import price inflation decomposition:
  - ∆p_{ij,t} = θ_j ∆p^j_{ij,t} + θ_i [∆p^i_{ij,t} + ∆e_{ij,t}] + θ_u [∆p^u_{ij,t} + ∆e_{uj,t}]
  - Under Calvo pricing and substituting reset-price dynamics:
    - ∆p_{ij,t} = θ_i ∆e_{ij,t} + θ_u ∆e_{uj,t} + (1−δ_p) ∑_k θ_k ∆p̄^k_{ij,t}, where ∆p̄^k_{ij,t} ≡ p̄^k_{ij,t} − p^k_{ij,t−1}.
- Very short-run benchmarks (δ_p → 1):
  - Producer currency pricing (PCP): θ_i = 1 → ∆p_{ij,t} = 1·∆e_{ij,t}; tot_{ij,t} = 1·∆e_{ij,t}.
  - Local currency pricing (LCP): θ_j = 1 → ∆p_{ij,t} = 0·∆e_{ij,t}; tot_{ij,t} = −1·∆e_{ij,t}.
  - Dominant currency pricing (DCP): θ_u = 1 → ∆p_{ij,t} = 1·∆e_{uj,t}; tot_{ij,t} = 0·∆e_{ij,t}.
- Implications:
  - Predicted coefficients from regressions of import-price changes on bilateral and dollar exchange rates differ qualitatively across PCP, LCP, and DCP.
  - With endogenous currency choice and Calvo timing, divergent PCP/LCP/DCP predictions expected to hold at longer horizons (annual).

### Data
- Core datasets and construction:
  - Bilateral trade values and volumes: UN Comtrade (HS 6-digit); USD value, quantity, weight used to compute unit values and Laspeyres, Paasche, Fisher indices (fixed base and chained). Commodities defined as HS chapters 1–27 and 72–83. Chained Fisher indices used in main analysis.
  - Aggregations: commodities vs non-commodities (main results use non-commodities goods only).
  - Country aggregates: World Bank World Development Indicators.
  - Financial variables: Federal Reserve Bank of St. Louis FRED database.
  - Currency invoicing shares: Gopinath (2015); export and import invoicing share computed as simple average over years reported in 1999–2014.
  - U.S. monetary policy induced exchange rate changes: sum of daily exchange rate changes on scheduled FOMC announcement dates (1990–2015; 219 scheduled dates), daily series from FactSet; annual series = unweighted sum of log changes on FOMC dates in a year.
- Coverage and sample:
  - Annual frequency analyses, separate exporter- and importer-reported data.
  - Longest span: 1989–2015 (coverage varies by dyad). In 2015, 55 countries in sample account for 91.2% and 91.5% of world goods imports and exports recorded in Comtrade.
  - For each reporting country, indices constructed for both imports and exports (two sets per bilateral flow).
- Data challenges and mitigation:
  - Unit value bias: eliminate products whose unit values have variance higher than a threshold.
  - HS vintage changes: compute indices twice in transition years and switch to new vintage thereafter.
  - Validation: Comtrade unit value indices broadly aligned with BLS import price indices for the U.S.; favorable comparisons to WTO and IMF WEO.

### Exchange rate pass-through into prices — estimation and findings
- Estimation framework:
  - Dependent variable: ∆p_{ij,t} (log change in bilateral import price index).
  - Key regressors: ∆e_{ij,t} and ∆e_{j$,t}, up to two lags; controls: dyadic fixed effects λ_{ij}, time fixed effects δ_t, exporter PPI growth and two lags, other X_{i,t}.
  - Specifications:
    - Eq. (1): ∆p_{ij,t} = λ_{ij} + δ_t + ∑_{k=0}^2 α_k ∆e_{ij,t−k} + θ′X_{i,t} + ε_{ij,t}
    - Eq. (2): adds ∑_{k=0}^2 β_k ∆e_{j$,t−k}
    - Eq. (3): adds interactions with importer dollar invoicing share S_j
- Key empirical findings (Table 1 highlights):
  - Baseline bilateral-only pass-through (exporter-reported, column (1)):
    - Contemporaneous ∆e_{ij,t} coefficient = 0.801*** (s.e. 0.0113).
    - Interpretation: 10% depreciation of country j’s currency relative to i → import prices in j rise by 8%.
  - Including dollar exchange rate (exporter-reported, column (2)):
    - ∆e_{ij,t} coefficient falls from 0.80 to 0.315*** (s.e. 0.0127).
    - ∆e_{j$,t} contemporaneous coefficient = 0.656*** (s.e. 0.0142).
  - Including dollar exchange rate (importer-reported, column (5)):
    - ∆e_{ij,t} coefficient falls from 0.757*** to 0.164*** (s.e. 0.0126).
    - ∆e_{j$,t} contemporaneous coefficient = 0.565*** (s.e. 0.0143).
  - Interaction with importer dollar invoicing share S_j (columns (3) and (6)):
    - Increasing S_j by 10 percentage points raises contemporaneous dollar pass-through by 2.0–3.5 percentage points (range depends on exporter- vs importer-reported prices).
    - Coefficients on ∆e_{j$,t} × S_j: 0.196*** (s.e. 0.0320) and 0.348*** (s.e. 0.0326).
- Robustness and interpretation:
  - Time fixed effects included, so dollar dominance is not driven by global episodes when the dollar moves against all currencies.
  - Results robust to alternative time samples and data choices.
  - When weighting by trade value shares, bilateral pass-through can exceed dollar pass-through for low dollar invoicing share importers (e.g., S_j = 0.13), indicating country-level S_j proxies may understate bilateral heterogeneity.

### Terms of trade and exchange rates — findings
- Definitions:
  - tot_{ij} = p_{ij} − p_{ji} − e_{ij}.
  - ∆ppi_{ij}: log ratio of PPI in country i divided by PPI in country j; lags 0–2 included.
- Regression specifications:
  - Eq. (4): ∆tot_{ij,t} = λ_{ij} + δ_t + ∑_{k=0}^2 α_k ∆e_{ij,t−k} + ε_{ij,t}
  - Eq. (5): adds ∑_{k=0}^2 β_k ∆ppi_{ij,t−k}
- Empirical findings (Table 2 highlights):
  - Without controlling for relative PPI:
    - Exporter-reported (col (1)): contemporaneous ∆e_{ij,t} coefficient = −0.0881*** (s.e. 0.00941); 95% CI = [−0.11, −0.07].
    - Importer-reported (col (3)): contemporaneous ∆e_{ij,t} coefficient = −0.0369*** (s.e. 0.00863); 95% CI = [−0.05, −0.02].
    - These negative contemporaneous coefficients contradict PCP and are inconsistent with pure LCP magnitudes.
  - Controlling for relative PPI: coefficients on bilateral exchange rate shrink further toward zero.
  - Interpretation: bilateral exchange rates are virtually uncorrelated with bilateral terms of trade once relative PPI is accounted for; supports the dominant currency paradigm.
- Additional notes:
  - R-squared values are very small (e.g., 0.007–0.015).
  - Number of cross-sectional dyads: exporter columns use 1,322 and 1,172 dyads; importer columns use 1,347 and 1,200 dyads.

### Trade volume elasticity — methodology and key results
- Methodology and scope:
  - Dependent variable: ∆y_{ij,t} (log growth rate of bilateral trade volumes).
  - Regressions mirror price pass-through specs but replace dependent variable and controls X_{j,t} (log growth of real GDP and two lags for importer j).
  - Results are predictive (not structural): regressions conflate expenditure switching and aggregate import demand shifts.
  - Panel regressions include dyad and time fixed effects; standard errors clustered by dyad.
- Key regression results (Table 3: contemporaneous ∆e_{ij,t} coefficients preserved exactly):
  - Column (1): −0.148*** (s.e. 0.0148)
  - Column (2): −0.0384** (s.e. 0.0180)
  - Column (3): 0.0171 (s.e. 0.0403)
  - Column (4): −0.119*** (s.e. 0.0139)
  - Column (5): −0.0310* (s.e. 0.0160)
  - Column (6): −0.0765* (s.e. 0.0403)
- Dollar exchange rate contemporaneous elasticity (selected columns):
  - Column (2): −0.237*** (s.e. 0.0294)
  - Column (3): −0.188*** (s.e. 0.0587)
  - Column (5): −0.186*** (s.e. 0.0250)
  - Column (6): −0.140** (s.e. 0.0600)
- Lag dynamics:
  - Lagged bilateral terms show positive coefficients at t−1 and t−2 in some specifications (e.g., ∆e_{ij,t−1} = 0.0755*** (s.e. 0.0148) in (1)), implying partial reversal over 1–2 years.
- Fit and sample:
  - R-squared: 0.073, 0.075, 0.084, 0.069, 0.071, 0.074 for columns (1)–(6).
  - Observations: 50,761; 50,761; 36,757; 52,272; 52,272; 38,582.
  - Dyads: 2,773; 2,773; 1,982; 2,807; 2,807; 2,014.
  - Statistical significance: *** p<0.01, ** p<0.05, * p<0.1.
- Main substantive findings on trade elasticities and dynamics:
  - The U.S. dollar dominates prediction of bilateral trade volumes: adding the dollar exchange rate substantially reduces the bilateral rate coefficient.
  - Contemporaneous elasticity for the dollar exchange rate is around −0.2 across specifications and data sources; the bilateral elasticity is an order of magnitude smaller.
  - Impulse responses show the immediate negative impact of dollar or bilateral shocks on bilateral trade volume is essentially neutral at horizons of 1–2 years due to negative lagged terms.
  - Appendix B.2: the neutrality is driven by early years; the 2002–2015 subsample points toward a large, permanent negative effect of dollar appreciations on bilateral trade volumes.
  - Heterogeneity by importer dollar invoicing share S_j: point estimates suggest higher S_j associated with more negative trade elasticities, but confidence intervals are wide and estimates mostly imprecise.

### U.S. monetary policy induced exchange rate shocks (z_{j,t}) — construction and validation
- Construction:
  - z_{j,t} = sum of daily log exchange rate changes in year t for country j on scheduled FOMC announcement dates; exchange rate measured in units of country j currency per U.S. dollar.
  - Use of FOMC-date daily changes gives a specific interpretation but does not claim z_{j,t} is solely driven by U.S. monetary policy or that all fluctuations are surprises.
- Summary statistics and validation:
  - Daily correlation of log exchange rate changes with changes in U.S. 1-year Treasury bill rate on FOMC dates (1990–2007): 0.064.
  - Std. dev. of daily log exchange rate changes across all currencies on FOMC dates: 0.72%.
  - Std. dev. of daily log exchange rate changes across all days in 1990–2015: 0.92%.
  - Std. dev. of annual (summed) monetary shock series z_{j,t}: 2.6%.
  - Annual std. dev. of overall log exchange rate changes ∆e_{j$,t} on 1990–2015 sample: 31.6%.
  - Annual correlation of z_{j,t} and ∆e_{j$,t}: 0.17.
  - Conclusion: z_{j,t} captures a small but nontrivial fraction of shocks to exchange rates vis-à-vis the dollar.

### Pass-through and volumes for monetary shocks — summary
- Pass-through of U.S. monetary shocks to prices:
  - Impact effect of shocks to both bilateral and dollar exchange rates on bilateral import prices is about 0.3.
  - When both bilateral and dollar shocks included, dollar pass-through rises to about 0.6–1.0 in years 4–6 depending on specification; bilateral pass-through negligible in long run.
  - Pass-through of dollar shocks strongly positively associated with importer’s S_j:
    - For S_j = 0.13 (example Switzerland), long-run pass-through close to zero.
    - For S_j = 0.88 (example Argentina), long-run pass-through about 2.0–3.5 depending on specification.
  - Note: magnitudes not directly comparable with Section 4.1 pass-through because a 1% monetary shock z_{j,t} represents a rarer event than a 1% appreciation of ∆e_{j$,t}.
- Trade volumes and monetary shocks:
  - Regressions of trade volumes on U.S. monetary shocks are very noisy; low R-squared and limited variation in z_{j,t} lead to imprecise volume results; authors refrain from reporting volume regression results for monetary shocks.

### The dollar versus the euro
- Regression with bilateral, dollar, and euro exchange rates (sample 2002–2015; Eq. (6)):
  - Controls: global real GDP growth, global GDP deflator inflation, global export volume growth, growth in WTI oil price deflated by global GDP deflator, log VIX; time fixed effects omitted.
- Main findings:
  - Euro pass-through into prices negligible on average when controlling for the euro; dollar pass-through remains high when controlling for the euro.
  - In regressions including bilateral, dollar, and euro exchange rates, dollar pass-through quantitatively much larger than euro pass-through; euro pass-through small and slightly negative.
  - Difference between dollar and euro pass-through is statistically significant.
  - For trade volumes, dollar exchange rate has largest predictive power and is the only one with a quantitatively large negative association with trade volumes.
  - Euro trade elasticity estimated positive in short and long run, though confidence intervals consistent with economically small magnitudes; difference between dollar and euro trade elasticities statistically significant.

### Bayesian model of pass-through heterogeneity — structure and implementation
- Model structure and identification:
  - Bayesian hierarchical panel with cross-sectionally varying slopes for contemporaneous log changes in bilateral and U.S. dollar exchange rates Rij,t = (∆e_{ij,t}, ∆e_{j$,t})′; some coefficients γ_{ij} vary across dyads.
  - Dyad-specific effects λ_{ij} ∼ N(α, τ2); errors ε_{ij,t} ∼ N(0, σ2).
  - Priors: diffuse half-Cauchy on τ and σ; diffuse Cauchy on α, δ_t, θ.
  - Parameter reduction: impose γ_{ij,1} + γ_{ij,2} = γ̄ for all (i,j) so dollar and bilateral pass-through sums constant across dyads; rewrite with scalar γ_{ij} and Rij,t = ∆e_{j$,t} − ∆e_{ij,t}.
- Nonparametric prior for cross-sectional heterogeneity:
  - Conditional distribution (γ_{ij} | S_j) specified as Mixture of Gaussian Linear Regressions (MGLR): draw from one of K normals N(μ0,k + μ1,k S_j, ω_k2) with prob. π_k(S_j).
  - Mixture probabilities π_k(s) use probit stick-breaking; independent Gaussian process priors on ζ_k(·).
  - MGLR allows heavy-tailed, skewed, multimodal conditional densities; K selection via Bayesian Leave-One-Out (LOO) cross-validation.
- Posterior sampling and implementation:
  - Posterior draws obtained using Stan (No U-Turn Sampler).
  - Price pass-through implementation: Y_{ij,t} = ∆p_{ij,t}; X_{ij,t} includes exporter log PPI growth, and one lag each of log PPI growth, bilateral and dollar exchange rate log growth; sample: importer-reported Comtrade; 1856 dyads; 35,398 observations.
  - Trade elasticity implementation: Y_{ij,t} = ∆y_{ij,t}; controls: one lag of bilateral and dollar exchange rates, contemporaneous and lagged importer log real GDP growth; same dyad-year sample.
  - Model selection: price pass-through preferred K = 2 (LOO); trade elasticity reported with K = 4 (LOO favors K = 3,4,5; K = 4 slightly higher).

### Bayesian results — price pass-through heterogeneity
- Conditional densities and moments:
  - Higher importer S_j associated with rightward shift in cross-sectional density of dollar pass-through γ_{ij}.
  - Posterior median indicates mode of γ_{ij} distribution shifts by about 0.10 when S_j increases from illustrative low (Switzerland) to high (Argentina) levels.
  - Cross-dyad IQR of γ_{ij} = 0.13 (estimated).
- Summary statistics across 1856 dyads:
  - Sample median of γ_{ij} posterior median: 0.76.
  - Median IQR of γ_{ij}: 0.13.
  - Winsorized cross-dyad correlation of γ_{ij} and S_j: median correlation 0.39.
  - Implied R2: posterior median indicates S_j explains 15% of cross-dyad variance in dollar pass-through; 95% equal-tailed posterior credible interval = [7.1%, 24.6%].
- Conditional moments across S_j:
  - Conditional mean E[γ_{ij} | S_j] appears approximately linear in S_j.
  - Conditional std[γ_{ij} | S_j] fairly constant across S_j, though posterior uncertainty large.
- Model evidence: K = 2 strongly preferred over K = 1, indicating heavy-tailed conditional distributions and substantial heterogeneity.

### Bayesian results — trade elasticity heterogeneity
- Conditional densities and moments:
  - Dollar trade elasticity γ_{ij} (expected negative) shifts leftward (more negative) as importer S_j increases; credible bands wider than for price pass-through.
- Summary statistics across dyads:
  - Median median γ_{ij}: −0.11.
  - Median IQR of γ_{ij}: 0.09.
  - Winsorized cross-dyad correlation of γ_{ij} and S_j: median correlation −0.41.
  - 95% equal-tailed posterior credible interval for R2 in regression of winsorized dollar elasticity on S_j: [2.6%, 34.0%].
- Conditional moments: posterior medians indicate E[γ_{ij} | S_j] is downward-sloping over most of S_j range, with substantial uncertainty.
- Model evidence: K = 4 chosen; results robust for K ≥ 3.

### Aggregate implications: effect of U.S. dollar on rest-of-world trade
- Aggregation setup:
  - w_j: country j’s total non-commodity import value from all countries except the U.S., normalized so ∑_{j≠US} w_j = 1.
  - Rest-of-world aggregate as Cobb-Douglas of country imports. Weighted average importer dollar invoicing share ∑_{j≠US} w_j S_j ≈ 0.40 in 2002–2015 sample; exercise uses 0.40.
- Main predictive result:
  - A 1% U.S. dollar appreciation against all other currencies predicts a 0.6–0.8% decline within a year in the volume of total trade between countries in the rest of the world, holding constant proxies for the global business cycle.
    - Range 0.6–0.8% depends on exporter- vs importer-reported data.
  - This contractionary predictive effect persists out to two years.
- Interpretation:
  - Dominant currency paradigm materially affects aggregate trade outcomes ex-U.S.; the U.S. dollar has substantial predictive power for global trade even excluding direct U.S. trade.

### Spillovers from U.S. dollar to foreign inflation (Section 6.2)
- Mechanism:
  - U.S. dollar fluctuations pass strongly through to bilateral import prices in importer currency, especially where imports are heavily invoiced in dollars.
  - Non-negligible import content in consumption implies U.S. dollar movements directly affect foreign CPI inflation; producer prices may amplify these effects.
- Empirical approach (Eq. (10)):
  - ∆cpi_{j,t} = λ_j + δ_t + Σ_{k=0}^2 β_k ∆e'_{j,t−k} + Σ_{k=0}^2 ψ_k ∆e'_{j,t−k} × S_j + ε_{j,t}, where ∆cpi_{j,t} is log CPI change in currency j.
  - Focus on post-2002 sample; small-sample clustered CI corrections using Imbens and Kolesár (2016) “LZ2-BM”.
- Key empirical findings:
  - Average dollar pass-through to CPI and PPI (post-2002, no interaction):
    - CPI: 11% within the year; cumulative 23% after two years.
    - PPI: 28% within the year; cumulative 43% after two years.
  - Heterogeneity by S_j:
    - Dollar pass-through larger for countries with substantial S_j.
    - Contemporaneous interaction term ∆e' × S_j statistically significant at 10% for CPI and PPI, and at 5% for CPI (confidence intervals wide due to small number of clusters).
  - Trade-volume spillover reiterated: 1% USD appreciation predicts 0.6–0.8% decline in rest-of-world trade volume within a year.
  - Cross-sectional explanation: importer S_j explains 15% of variance of dollar pass-through/elasticity across country pairs.
  - Specifications using U.S. monetary policy–induced exchange rate fluctuations: point estimates consistent but variation in z_{j,t} insufficient for informative confidence statements.
- Interpretation and caveats:
  - Results support the dominant currency paradigm for international transmission of shocks.
  - Magnitudes imprecisely estimated when controlling for country and time fixed effects; wide confidence intervals.
  - Robust to sample choices (similar with full 1992–2015 sample when extreme inflation observations dropped).

### Data comparison, robustness, and additional diagnostics (NBER WP 11040 appendix material)
- Comtrade vs BLS import price indices:
  - Comtrade-based Laspeyres indices "track the BLS import price indices fairly well" for Canada, Japan, Mexico, and aggregated Latin America and Asia Near East; some Asian countries show greater volatility in Comtrade series.
  - High correlation between Comtrade and BLS growth rates for most groups and countries except Germany (2008 transport vehicle unit value decreases drove divergence).
- Panel regression robustness (post-2002 subsample):
  - Price pass-through impulse responses similar to full-sample.
  - Post-2002 USD cumulative trade elasticity substantially negative at lags 1 and 2 years; full-sample level effect close to zero at lags 1 and 2.
  - Interaction terms with importing-country euro and dollar invoicing shares statistically and economically significant in price pass-through regressions; imprecise in trade elasticity regressions.
- Representative coefficient magnitudes (preserved exactly):
  - Price pass-through (Table 9, Baseline, importer-reported):
    - ∆e_{ij,t} = 0.164*** (0.0126)
    - ∆e_{j,t} (USD) = 0.781*** (0.0143)
    - R-squared = 0.398
    - Observations = 46,820
    - Dyads = 2,647
  - Trade elasticity (Table 10, Baseline, importer-reported):
    - ∆e_{ij,t} = -0.0310* (0.0160)
    - ∆e_{j,t} (USD) = -0.186*** (0.0250)
    - R-squared = 0.071
    - Observations = 52,272
    - Dyads = 2,807
- Robustness to data choices:
  - Variations tested: raw vs cleaned data, total goods vs non-commodities, Laspeyres vs Fisher indices.
  - Across variations, USD exchange rate quantitatively dominates bilateral rate in price pass-through regressions; magnitudes similar to baseline for most variations.
  - Raw data reduce R-squared and can weaken estimated relationships; cleaned data preferred due to extreme outliers and non-random missingness in raw Comtrade.
- Bayesian MCMC settings and diagnostics:
  - No U-Turn Sampler run for 2,500 iterations after discarding 1,000 warm-up iterations, storing every 5th draw; initialization random; Stan default adaptive tuning in warm-up.
  - Stored posterior draws exhibit essentially zero serial correlation after a handful of lags; mixture components with low posterior π_k(·) may mix more slowly but negligibly influence main posterior features.
  - Run times: 2–60 hours per specification on a personal laptop (2.30 GHz, 8 GB RAM); often 2–4 hours sufficient to get sense of results.
  - Posterior for ̄γ concentrated close to 1 (near-complete total pass-through within a year) in price pass-through model (example K = 2); trade elasticity model posteriors consistent with panel regressions.
  - Robustness to larger K (K = 8): additional mixture components receive very low posterior probability; densities reported conditional on S = 0.13, 0.59, 0.88 for K = 8.

*Source: wp17239 - Section 6 shows that the strength of the U.S. dollar is a key predictor of rest-of-world trade vol- (IMF working paper content provided).*

### Section 6 shows that the strength of the U.S. dollar is a key predictor of rest-of-world trade vol-

### wp17239 - Section 6 shows that the strength of the U.S. dollar is a key predictor of rest-of-world trade vol-

### Conceptual framework
- Definitions and setup:
  - p_ij: log price of goods exported from country i to country j measured in currency j.
  - e_ij: log bilateral exchange rate between country i and country j (price of currency i in terms of currency j).
  - e_j$: log price of a U.S. dollar in currency j.
  - Invoicing shares: θ_i (producer currency), θ_j (local currency), θ_u (dominant currency/dollar), with ∑_{k∈{i,j,u}} θ_k = 1.
- Import price inflation decomposition:
  - ∆p_{ij,t} = θ_j ∆p^j_{ij,t} + θ_i [∆p^i_{ij,t} + ∆e_{ij,t}] + θ_u [∆p^u_{ij,t} + ∆e_{uj,t}]
  - Under Calvo pricing and substituting reset-price dynamics:
    - ∆p_{ij,t} = θ_i ∆e_{ij,t} + θ_u ∆e_{uj,t} + (1−δ_p) ∑_k θ_k ∆p̄^k_{ij,t}, where ∆p̄^k_{ij,t} ≡ p̄^k_{ij,t} − p^k_{ij,t−1}.
- Benchmarks in the very short run (δ_p → 1):
  - Producer currency pricing (PCP): θ_i = 1, θ_j = θ_u = 0
    - ∆p_{ij,t} = 1·∆e_{ij,t} + 0·∆e_{uj,t}
    - ∆p_{ji,t} = −1·∆e_{ij,t} + 0·∆e_{uj,t}
    - tot_{ij,t} = ∆p_{ij,t} − (∆p_{ji,t} + ∆e_{ij,t}) = 1·∆e_{ij,t}
  - Local currency pricing (LCP): θ_j = 1, θ_i = θ_u = 0
    - ∆p_{ij,t} = 0·∆e_{ij,t} + 0·∆e_{uj,t}
    - ∆p_{ji,t} = 0·∆e_{ij,t} + 0·∆e_{uj,t}
    - tot_{ij,t} = ∆p_{ij,t} − (∆p_{ji,t} + ∆e_{ij,t}) = −1·∆e_{ij,t}
  - Dominant currency pricing (DCP): θ_u = 1, θ_i = θ_j = 0
    - ∆p_{ij,t} = 0·∆e_{ij,t} + 1·∆e_{uj,t}
    - ∆p_{ji,t} = 0·∆e_{ij,t} + 1·∆e_{ui,t}
    - tot_{ij,t} = ∆p_{ij,t} − (∆p_{ji,t} + ∆e_{ij,t}) = 0·∆e_{ij,t}
- Implications:
  - Predicted coefficients from regressions of log changes in import prices on log changes in bilateral and dollar exchange rates differ qualitatively across PCP, LCP, and DCP benchmarks.
  - With endogenous currency choice and Calvo timing, firms choose invoicing currencies where reset price is most stable; divergent predictions across PCP, LCP, and DCP are expected to hold at longer horizons (annual).

### Data
- Core datasets and construction:
  - Bilateral trade values and volumes: UN Comtrade (HS 6-digit), with USD value, quantity, and weight used to compute unit values and Laspeyres, Paasche, Fisher indices (fixed base and chained). Commodities defined as HS chapters 1–27 and 72–83. Chained Fisher indices used in main analysis.
  - Aggregations done separately for commodities and noncommodities; main results use non-commodities goods only.
  - Country aggregates: World Bank World Development Indicators.
  - Financial variables: Federal Reserve Bank of St. Louis FRED database.
  - Currency invoicing shares: Gopinath (2015); export and import invoicing share for a country computed as simple average over years reported in 1999–2014.
  - U.S. monetary policy induced exchange rate changes: constructed by summing daily exchange rate changes on scheduled FOMC announcement dates (1990–2015; 219 scheduled announcement dates). Daily exchange rate series from FactSet (close mid price). Annual series obtained as unweighted sum of log exchange rate changes on FOMC dates in a given year.
- Coverage and sample:
  - Annual frequency analyses, separate exporter- and importer-reported data.
  - Longest time span: 1989–2015 (coverage varies by dyad). Appendix A.1 breaks down coverage by country.
  - In 2015, the 55 countries in sample account for 91.2% and 91.5% of the value of world goods imports and exports, respectively, as recorded in Comtrade.
  - For each reporting country, indices constructed for both imports and exports, yielding two sets of numbers per bilateral flow (importer- and exporter-reported) for robustness checks.
- Data challenges and mitigation:
  - Unit value bias (Silver, 2007): unit values (value/quantity) may not reflect true prices due to within-6-digit-category product heterogeneity and quantity composition shifts. Method corrects by eliminating products whose unit values have variance higher than a threshold.
  - HS vintage changes: for transition years compute indices twice (old vintage using concordances and new vintage) and switch to new vintage thereafter to minimize information loss and include new products.
  - Validation: comparison of unit value indices to BLS import price indices for the U.S. shows broadly aligned growth rates for most trading partners (Appendix B.1). Boz and Ceruši (2017) compare country-level indices to WTO and IMF WEO with favorable results.

### Exchange rate pass-through into prices
- Estimation framework:
  - Dependent variable: ∆p_{ij,t} (log change in bilateral import price index).
  - Key regressors: ∆e_{ij,t} (bilateral exchange rate changes) and ∆e_{j$,t} (dollar exchange rate vis-à-vis country j), with up to two lags included.
  - Controls: dyadic fixed effects λ_{ij}, time fixed effects δ_t, exporter PPI growth and two lags, and other X_{i,t}.
  - Estimated specifications:
    - Eq. (1): ∆p_{ij,t} = λ_{ij} + δ_t + ∑_{k=0}^2 α_k ∆e_{ij,t−k} + θ′X_{i,t} + ε_{ij,t}
    - Eq. (2): adds ∑_{k=0}^2 β_k ∆e_{j$,t−k}
    - Eq. (3): adds interactions of exchange rates with importer dollar invoicing share S_j
- Key empirical findings (Table 1 highlights):
  - Baseline bilateral-only pass-through (exporter-reported, column (1)):
    - Contemporaneous ∆e_{ij,t} coefficient = 0.801*** (s.e. 0.0113).
    - Interpretation: when country j’s currency depreciates relative to country i by 10%, import prices in country j rise by 8% (close to complete pass-through at one year horizon).
  - Including dollar exchange rate (exporter-reported, column (2)):
    - ∆e_{ij,t} coefficient falls from 0.80 to 0.315*** (s.e. 0.0127).
    - ∆e_{j$,t} contemporaneous coefficient = 0.656*** (s.e. 0.0142).
  - Including dollar exchange rate (importer-reported, column (5)):
    - ∆e_{ij,t} coefficient falls from 0.757*** to 0.164*** (s.e. 0.0126).
    - ∆e_{j$,t} contemporaneous coefficient = 0.565*** (s.e. 0.0143).
  - Interaction with importer dollar invoicing share S_j (columns (3) and (6)):
    - Dollar pass-through increases with S_j: increasing the dollar invoicing share by 10 percentage points raises contemporaneous dollar pass-through by 2.0–3.5 percentage points (range depends on exporter- vs importer-reported prices).
    - Coefficients on ∆e_{j$,t} × S_j: 0.196*** (s.e. 0.0320) and 0.348*** (s.e. 0.0326) in relevant columns.
- Robustness and interpretation:
  - Time fixed effects are included, so dollar dominance is not driven by global episodes when the dollar moves against all currencies (e.g., global recessions or flight to safety).
  - Results robust to alternative time samples (Appendix B.2) and alternative data choices (Appendix B.2).
  - When weighting by trade value shares, bilateral pass-through can exceed dollar pass-through for low dollar invoicing share importers (e.g., S_j = 0.13), indicating country-level S_j proxies may understate bilateral heterogeneity.

### Terms of trade and exchange rates
- Definitions and setup:
  - Bilateral log terms of trade: tot_{ij} = p_{ij} − p_{ji} − e_{ij}.
  - ∆ppi_{ij}: log ratio of PPI in country i divided by PPI in country j (indices expressed in same currency); lags 0–2 included as controls.
  - Cross-sectional unit: unordered country pair {i,j} (both directions collapsed).
- Regression specifications:
  - Eq. (4): ∆tot_{ij,t} = λ_{ij} + δ_t + ∑_{k=0}^2 α_k ∆e_{ij,t−k} + ε_{ij,t}
  - Eq. (5): adds ∑_{k=0}^2 β_k ∆ppi_{ij,t−k}
- Empirical findings (Table 2 highlights):
  - Without controlling for relative PPI:
    - Exporter-reported data (column (1)): contemporaneous ∆e_{ij,t} coefficient = −0.0881*** (s.e. 0.00941); 95% confidence interval = [−0.11, −0.07].
    - Importer-reported data (column (3)): contemporaneous ∆e_{ij,t} coefficient = −0.0369*** (s.e. 0.00863); 95% confidence interval = [−0.05, −0.02].
    - These negative contemporaneous coefficients contradict PCP and are inconsistent in magnitude with pure LCP.
  - Controlling for relative PPI (columns (2) and (4)):
    - Coefficients on bilateral exchange rate shrink further toward zero; confidence intervals remain narrow.
  - Interpretation:
    - Bilateral exchange rates are virtually uncorrelated with bilateral terms of trade once relative PPI is accounted for.
    - Results lend strong support to the dominant currency paradigm: terms of trade are unresponsive to bilateral exchange rates.
- Additional notes:
  - R-squared values are very small (e.g., 0.007–0.015 across columns), indicating limited explanatory power of bilateral exchange rates for changes in terms of trade in this sample.
  - Number of cross-sectional dyads: exporter columns use 1,322 and 1,172 dyads; importer columns use 1,347 and 1,200 dyads (about half the dyads in Table 1 due to collapsing ordered pairs).

*Source: wp17239 - Section 6 shows that the strength of the U.S. dollar is a key predictor of rest-of-world trade vol- (IMF working paper content provided).*

### 4.3  Trade volume elasticity

### wp17239 - 4.3  Trade volume elasticity

### Methodology and scope
- Dependent variable: log growth rate ∆yij,t of bilateral trade volumes (log volume Lij).
- Regressions mirror price pass-through specifications (Eqs. (1)–(3)) but replace dependent variable and controls Xj,t (log growth rate of real GDP and two lags for importer j).
- Results are predictive (not structural): regressions conflate expenditure switching and aggregate import demand shifts and use importer GDP growth as an imperfect proxy for import demand.
- Panel regressions include dyad and time fixed effects where specified; standard errors clustered by dyad.

### Key regression results (Table 3)
- Contemporaneous coefficient on bilateral exchange rate ∆eij,t:
  - Column (1): −0.148*** (s.e. 0.0148)
  - Column (2): −0.0384** (s.e. 0.0180)
  - Column (3): 0.0171 (s.e. 0.0403)
  - Column (4): −0.119*** (s.e. 0.0139)
  - Column (5): −0.0310* (s.e. 0.0160)
  - Column (6): −0.0765* (s.e. 0.0403)
- Lagged bilateral terms:
  - ∆eij,t−1: 0.0755*** (s.e. 0.0148) in (1); 0.00728 (s.e. 0.0198) in (2); −0.0682 (s.e. 0.0485) in (3); 0.0757*** (s.e. 0.0126) in (4); −0.00245 (s.e. 0.0165) in (5); 0.00742 (s.e. 0.0354) in (6).
  - ∆eij,t−2: 0.0416*** (s.e. 0.0102) in (1); 0.0128 (s.e. 0.0141) in (2); 0.0495 (s.e. 0.0311) in (3); 0.0393*** (s.e. 0.00919) in (4); 0.0235** (s.e. 0.0115) in (5); 0.00410 (s.e. 0.0241) in (6).
- Interaction terms with importer dollar invoicing share Sj (selected):
  - ∆eij,t × Sj: −0.0606 (s.e. 0.0655) in exporter panel; 0.118* (s.e. 0.0684) in importer panel.
  - ∆eij,t−1 × Sj: 0.0976 (s.e. 0.0746) in exporter panel; −0.0433 (s.e. 0.0640) in importer panel.
  - ∆eij,t−2 × Sj: −0.0441 (s.e. 0.0494) in exporter panel; 0.0419 (s.e. 0.0428) in importer panel.
- Contemporaneous coefficient on dollar exchange rate ∆e$j,t:
  - Column (2): −0.237*** (s.e. 0.0294)
  - Column (3): −0.188*** (s.e. 0.0587)
  - Column (5): −0.186*** (s.e. 0.0250)
  - Column (6): −0.140** (s.e. 0.0600)
- Lagged dollar exchange rate terms:
  - ∆e$j,t−1: 0.148*** (s.e. 0.0278) in (2); 0.359*** (s.e. 0.0666) in (3); 0.168*** (s.e. 0.0248) in (5); 0.221*** (s.e. 0.0635) in (6).
  - ∆e$j,t−2: 0.0542*** (s.e. 0.0201) in (2); −0.114** (s.e. 0.0580) in (3); 0.0365* (s.e. 0.0198) in (5); 0.111** (s.e. 0.0525) in (6).
- Interactions of dollar shocks with Sj (selected):
  - ∆e$j,t × Sj: −0.0104 (s.e. 0.0906) in exporter panel; −0.0903 (s.e. 0.0871) in importer panel.
  - ∆e$j,t−1 × Sj: −0.244** (s.e. 0.100) in exporter panel; −0.0465 (s.e. 0.0922) in importer panel.
  - ∆e$j,t−2 × Sj: 0.192** (s.e. 0.0797) in exporter panel; −0.0952 (s.e. 0.0706) in importer panel.
- Goodness-of-fit and sample:
  - R-squared: 0.073, 0.075, 0.084, 0.069, 0.071, 0.074 for columns (1)–(6) respectively.
  - Observations: 50,761; 50,761; 36,757; 52,272; 52,272; 38,582 for columns (1)–(6) respectively.
  - Dyads: 2,773; 2,773; 1,982; 2,807; 2,807; 2,014 for columns (1)–(6) respectively.
- Statistical significance notation: *** p<0.01, ** p<0.05, * p<0.1.

### Main substantive findings on trade elasticities and dynamics
- The U.S. dollar dominates prediction of bilateral trade volumes:
  - Adding the dollar exchange rate substantially reduces the coefficient on the bilateral exchange rate.
  - The contemporaneous elasticity for the dollar exchange rate is around −0.2 across specifications and data sources.
  - The elasticity for the bilateral exchange rate is an order of magnitude smaller.
- Lag dynamics and reversal:
  - Data show an increase in import volumes one year after a ceteris paribus depreciation of the importer currency rate vis-à-vis the dollar.
  - Impulse responses (Figure 3) show that the immediate negative impact of dollar or bilateral shocks on the level of bilateral trade volume is essentially neutral at horizons of 1–2 years due to negative lagged terms.
  - Appendix B.2 indicates that the neutrality is driven by early years; the 2002–2015 subsample points toward a large, permanent negative effect of dollar appreciations on bilateral trade volumes.
- Heterogeneity by importer dollar invoicing share Sj:
  - Point estimates suggest association between higher dollar invoicing shares and more negative trade elasticities (Figure 4), but confidence intervals are wider and estimates are mostly imprecise for volumes.
  - Interactions of exchange rate changes with the importer’s dollar invoicing share are mostly imprecisely estimated in volume regressions.

### U.S. monetary policy induced exchange rate shocks (zj,t)
- Construction:
  - zj,t = sum of daily log exchange rate changes in year t for country j on dates with scheduled FOMC announcements, exchange rate measured in units of country j currency per U.S. dollar.
  - Use of FOMC-date daily changes gives a specific interpretation but does not claim zj,t is solely driven by U.S. monetary policy or that all fluctuations are surprises.
- Summary statistics and validation:
  - Daily correlation of log exchange rate changes (across all currencies) with changes in U.S. 1-year Treasury bill rate on FOMC dates (1990–2007): 0.064.
  - Standard deviation of daily log exchange rate changes across all currencies on FOMC dates: 0.72%.
  - Standard deviation of daily log exchange rate changes across all days in 1990–2015 sample: 0.92%.
  - Standard deviation of the annual (summed) monetary shock series zj,t: 2.6%.
  - Annual standard deviation of overall log exchange rate changes ∆e$j,t on 1990–2015 sample: 31.6%.
  - Annual correlation of zj,t and ∆e$j,t: 0.17.
  - Conclusion: the monetary shock series captures a small but nontrivial fraction of shocks to exchange rates vis-à-vis the dollar.
- Pass-through of U.S. monetary shocks to prices (Figures 5–6):
  - Impact effect of shocks to both bilateral and dollar exchange rates on bilateral import prices is about 0.3.
  - When both bilateral and dollar shocks included, dollar pass-through rises to about 0.6–1.0 in years 4–6 depending on specification; bilateral pass-through is negligible in the long run.
  - Pass-through of dollar shocks is strongly positively associated with importer’s dollar invoicing share Sj:
    - For Sj = 0.13 (example: Switzerland), estimated long-run pass-through close to zero.
    - For Sj = 0.88 (example: Argentina), estimated long-run pass-through about 2.0–3.5 depending on specification.
  - Note: magnitudes are not directly comparable with Section 4.1 pass-through because a 1% monetary shock zj,t represents a rarer event than a 1% appreciation of the dollar exchange rate ∆e$j,t.
- Trade volumes and monetary shocks:
  - Regressions of trade volumes on U.S. monetary shocks are very noisy.
  - Low R-squared values for volume regressions and limited variation in measured monetary shocks relative to overall exchange rate variation lead to imprecise volume results.
  - Authors refrain from reporting volume regression results for monetary shocks.

### The dollar versus the euro
- Regression framework (Eq. (6)): ∆pij,t = λij + Σk=0^2 αk ∆eij,t−k + Σk=0^2 βk ∆e$j,t−k + Σk=0^2 ξk ∆eej,t−k + θ′Xij,t + εij,t, where eej,t is log euro exchange rate in units of currency j per euro; time fixed effects omitted and global controls included (global real GDP growth, global GDP deflator inflation, global export volume growth, growth in WTI oil price deflated by global GDP deflator, and log VIX); sample 2002–2015.
- Main findings:
  - Euro pass-through into prices is negligible on average when controlling for the euro; dollar pass-through remains high when controlling for the euro (Figure 7).
  - In regressions that include bilateral, dollar, and euro exchange rates, dollar pass-through is quantitatively much larger than euro pass-through; the euro pass-through is small and slightly negative.
  - Difference between dollar and euro pass-through is statistically significant at conventional significance levels.
  - For trade volumes (Figure 8), dollar exchange rate has the largest predictive power and is the only one of the three with a quantitatively large negative association with trade volumes.
  - The euro trade elasticity is estimated to be positive in short and long run, though confidence intervals are consistent with economically small magnitudes; the difference between dollar and euro trade elasticities is statistically significant.

### Implications and interpretation
- The U.S. dollar is the dominant predictor of bilateral trade volumes and prices in the sample and specifications analyzed.
- Dollar-dominated pass-through and trade elasticities imply that dollar fluctuations (including those induced by U.S. monetary policy) can generate significant international spillovers in prices and, to a more uncertain extent, volumes.
- Heterogeneity across importers is linked to the importer’s dollar invoicing share Sj, especially for price pass-through; for volumes the heterogeneity evidence is weaker and less precise.
- Future work suggested: develop more comprehensive measures of U.S. monetary policy shocks to better relate monetary shocks to trade volumes, and investigate mechanisms behind the positive predictive effect of euro appreciations on bilateral import volume (e.g., valuation effects on net foreign assets).

*Source: wp17239 - 4.3  Trade volume elasticity*

### 5.1  Bayesian model of pass-through heterogeneity

### 5.1  Bayesian model of pass-through heterogeneity

### Model structure and identification
- Bayesian hierarchical panel data model with cross-sectionally varying slopes that models heterogeneity of pass-through across trade dyads.
- Outcome equation is a linear panel with dyad and time fixed effects; some coefficients vary across dyads:
  - Outcome Yij,t is price or quantity log growth.
  - Cross-sectionally varying coefficients γij apply to contemporaneous log growth rates of the bilateral and U.S. dollar exchange rates Rij,t = (∆eij,t, ∆e$j,t)′.
  - Cross-sectionally constant coefficients θ apply to covariates Xij,t (including lags of exchange rates and other exogenous controls used in Section 4).
- Random effects assumptions:
  - Dyad-specific effects λij ∼ N(α, τ2) i.i.d. across dyads.
  - Errors εij,t ∼ N(0, σ2) i.i.d. across dyads and time.
- Priors:
  - Independent diffuse half-Cauchy priors on τ and σ.
  - Independent diffuse Cauchy priors on intercept α, time fixed effects δt, and cross-sectionally constant coefficients θ.
- Parameter reduction restriction:
  - Imposed γij,1 + γij,2 = γ̄ for all (i,j) so that dollar and bilateral pass-through sums are constant across dyads; motivated by invoicing in either dollars or local currency.
  - This implies the outcome can be written in restricted form with scalar γij and Rij,t = ∆e$j,t − ∆eij,t and the term γ̄∆eij,t absorbed into Xij,t.

### Nonparametric prior for cross-sectional heterogeneity
- Conditional distribution of dollar pass-through γij given importer dollar invoicing share Sj is specified nonparametrically as a Mixture of Gaussian Linear Regressions (MGLR):
  - (γij | Sj) is drawn from one of K normal distributions N(μ0,k + μ1,k Sj, ωk2) with prob. πk(Sj), independent across dyads.
  - Mixture probabilities use the probit stick-breaking specification:
    - πk(s) = Φ(ζk(s)) ∏k−1 j=1 (1−Φ(ζj(s))) for k = 1,...,K−1, and remainder for k = K, s ∈ [0,1].
  - Independent nonparametric Gaussian process priors are placed on functions ζk(·) for k = 1,...,K−1.
- Rationale and properties:
  - MGLR allows flexible conditional densities (heavy-tailed, skewed, multimodal) and permits the conditional distribution to change with Sj.
  - If K = ∞, Pati et al. (2013) show posterior consistency for nonparametric conditional density estimation under weak assumptions.
  - Choice of K is informed by Bayesian Leave-One-Out (LOO) cross-validation.

### Posterior sampling
- Posterior draws obtained using Stan (No U-Turn Sampler, Hamiltonian Monte Carlo variant).
- Stan automates posterior density computation and MCMC tuning, enabling robust and rapid mixing in the high-dimensional hierarchical model without requiring conjugate priors.
- Appendix B.3 (in source) details MCMC performance.

### Empirical implementation specifics
- For price pass-through applications:
  - Yij,t = ∆pij,t (price log growth).
  - Xij,t includes exporter log PPI growth, and one lag each of log PPI growth, bilateral exchange rate log growth, and dollar exchange rate log growth.
  - Data: Comtrade data reported by importers; sample of 1856 dyads; total 35,398 observations (average of 19.1 years per dyad).
  - Dyads with gaps removed; require importer’s dollar invoicing share Sj.
- For trade elasticity applications:
  - Yij,t = ∆yij,t (quantity log growth).
  - Controls: one lag of bilateral and dollar exchange rates, contemporaneous and lagged importer log real GDP growth.
  - Same dyad-year sample as price pass-through results.

### Model selection for K (mixture components)
- Price pass-through preferred specification: K = 2.
  - LOO indicates strong support for K ≥ 2 against K = 1; LOO mostly flat for K = 2,3,...,8; posterior summaries virtually unchanged across these values.
- Trade elasticity reported with K = 4.
  - LOO strongly favors K = 3,4,5 against K ≤ 2 or K = 6,7,8; K = 4 has slightly higher LOO than K = 3,5.
  - Results are little changed for K ≥ 3; Appendix B.4.2 reports K = 8 results.

---

### Results: price pass-through — key findings
- Conditional densities:
  - Higher importer dollar invoicing share Sj is associated with a rightward shift in the cross-sectional density of dollar pass-through γij.
  - Posterior median indicates the mode of γij distribution shifts by about 0.10 when Sj increases from Switzerland to Argentina levels (illustrative invoicing shares used in figures).
  - Cross-dyad interquartile range (IQR) of γij is 0.13 (estimated).
- Summary statistics across dyads (1856 dyads):
  - Sample median of γij posterior median: 0.76 (median median 0.76).
  - Median IQR of γij: 0.13 (median IQR 0.13).
  - Winsorized cross-dyad correlation of γij and Sj (winsorized γij by 5% each tail): median correlation 0.39.
  - Implied R2 (squared winsorized correlation): posterior median indicates importer dollar invoicing share explains 15% of cross-dyad variance in dollar pass-through, with 95% equal-tailed posterior credible interval [7.1%, 24.6%].
- Conditional moments across Sj:
  - Conditional mean E[γij | Sj] appears approximately linear in Sj though not imposed a priori.
  - Conditional standard deviation std[γij | Sj] appears fairly constant across Sj values, but posterior uncertainty is large.
- Model evidence:
  - K = 2 mixture strongly preferred over K = 1, indicating heavy-tailed conditional distributions and substantial heterogeneity.

### Results: trade elasticity — key findings
- Conditional densities:
  - Dollar trade elasticity γij (expected negative) shifts leftward (more negative) as importer Sj increases; higher Sj associated with larger-in-magnitude dollar trade elasticities on average.
  - Credible bands much wider than for price pass-through (higher posterior uncertainty).
- Summary statistics across dyads:
  - Median median γij: −0.11 (median median −0.11).
  - Median IQR of γij: 0.09 (median IQR 0.09).
  - Winsorized cross-dyad correlation of γij and Sj: median correlation −0.41 (winsorized γij at 5% each tail).
  - 95% equal-tailed posterior credible interval for R2 in cross-dyad regression of winsorized dollar elasticity on Sj: [2.6%, 34.0%].
- Conditional moments across Sj:
  - Posterior medians indicate conditional mean E[γij | Sj] is downward-sloping over most of Sj range, but with substantial uncertainty.
- Model evidence:
  - K = 4 chosen based on LOO; results are qualitatively robust for K ≥ 3.

---

### Aggregate implications: effect of U.S. dollar on rest-of-world trade
- Objective: measure elasticity of rest-of-world (ex-U.S.) trade volume to a 1% U.S. dollar appreciation against all other currencies, using aggregation from bilateral interactive panel regressions that include dollar and euro exchange rates and interactions with importer invoicing shares.
- Aggregation setup:
  - Let wj denote country j’s total non-commodity import value from all countries except the U.S. in a reference year, normalized so that ∑j≠US wj = 1.
  - Rest-of-world aggregate trade conceptualized as Cobb-Douglas aggregate of country imports with weights wj.
  - Weighted average importer dollar invoicing share across ex-U.S. import values:
    - In the 2002–2015 sample, ∑j≠US wj Sj fluctuates tightly around a mean of 0.40; the exercise uses the 0.40 value.
- Main quantitative predictive result:
  - A 1% U.S. dollar appreciation against all other currencies predicts a 0.6–0.8% decline within a year in the volume of total trade between countries in the rest of the world, holding constant proxies for the global business cycle.
    - The range 0.6–0.8% depends on whether exporter- or importer-reported data is used.
  - This contractionary predictive effect persists out to two years.
- Interpretation:
  - The dominant currency paradigm materially affects aggregate trade outcomes in the rest of the world; the U.S. dollar has substantial predictive power for global trade even when excluding direct U.S. trade.
  - By contrast, the Mundell-Fleming framework does not imply a role for the strength of the U.S. dollar in influencing trade volumes among countries in the rest of the world.

*Source: IMF Working Paper section 5.1 and linked results (wp17239).*

### 6.2  Spillovers from U.S. dollar to foreign inƒation

### 6.2  Spillovers from U.S. dollar to foreign inƒation

### Mechanism and economic logic
- Fluctuations in the strength of the U.S. dollar (for example those caused by U.S. monetary policy actions) have spillover effects on foreign inflation.
- The U.S. dollar exchange rate passes strongly through to bilateral import prices measured in the importer’s currency, especially for countries whose imports are heavily invoiced in dollars.
- Given a non-negligible import content in consumption, U.S. dollar movements will directly affect foreign CPI inflation.
- If foreign firms behave in a monopolistically competitive way, foreign producer prices will react to changes in foreign import prices, although perhaps with a lag; hence, direct effects of U.S. dollar movements on foreign CPI inflation may be amplified by endogenous producer responses.

### Empirical approach
- Country-level panel regression estimated (Eq. (10)):
  - ∆cpi_{j,t} = λ_j + δ_t + Σ_{k=0}^2 β_k ∆e'_{j,t−k} + Σ_{k=0}^2 ψ_k ∆e'_{j,t−k} × S_j + ε_{j,t}
  - Where ∆cpi_{j,t} is the change in the log CPI in the currency of country j; λ_j and δ_t are country and year fixed effects.
- Also estimated specifications with ∆ppi_{j,t} on the left-hand side and specifications restricting ψ_k = 0 for all k.
- Focus on the post-2002 (post-euro) sample to avoid undue influence from 1990s inflation/depreciation episodes.
- Small-sample corrections applied to clustered confidence intervals using Imbens and Kolesár (2016) “LZ2-BM” adjustment; details and regression tables in Appendix B.2.

### Key empirical findings (pass-through magnitudes and heterogeneity)
- Average dollar pass-through to CPI and PPI (no interaction, post-2002):
  - Average pass-through of the dollar into CPI is 11% within the year, rising to a cumulative pass-through of 23% after two years.
  - Average pass-through of the dollar into PPI is 28% within the year, rising to a cumulative pass-through of 43% after two years.
- Heterogeneity by dollar invoicing share S_j:
  - Dollar pass-through is larger for countries with a substantial fraction of imports invoiced in dollars.
  - The contemporaneous interaction term (∆e' × S_j) is statistically significant at the 10% level for both CPI and PPI specifications, and at the 5% level for the CPI specification (confidence intervals are wide due to small number of country clusters).
- Trade-volume spillover (rest-of-world aggregate):
  - A 1% U.S. dollar appreciation against all other currencies predicts a 0.6–0.8% decline within a year in the volume of total trade between countries in the rest of the world, controlling for the global business cycle.
- Cross-sectional explanation:
  - The importing country’s share of imports invoiced in dollars explains 15% of the variance of dollar pass-through/elasticity across country pairs.
- Specifications using U.S. monetary policy–induced exchange rate fluctuations:
  - Point estimates are consistent with patterns for raw exchange rate pass-through, but the variation in the monetary policy series z_{j,t} is insufficient to deliver informative confidence statements.

### Interpretation and caveats
- Findings support the dominant currency paradigm as the empirically relevant framework for understanding international transmission of shocks and for policy analysis (i.e., the dollar, not bilateral exchange rates, is often the relevant predictor).
- The magnitude of pass-through is imprecisely estimated when controlling for country and time fixed effects; confidence intervals are wide.
- Results are robust to sample choices: very similar results if the full 1992–2015 sample is used but country-year observations with arithmetic CPI inflation rate exceeding 30% annually (0.26 log inflation rate) are dropped.

### Methodological notes relevant for interpretation
- Regression specifications control for country and year fixed effects and allow interaction with dollar import invoicing share.
- Small-sample clustered confidence-interval corrections applied as recommended in Imbens and Kolesár (2016).
- Bayesian hierarchical modeling and semiparametric components are used elsewhere in the paper; see Appendix B.2 for regression tables and Appendix A for data sources.

*Source: wp17239 - 6.2  Spillovers from U.S. dollar to foreign inƒation.*

### 2000. NBER Working Paper 11040.

### wp17239 - 2000. NBER Working Paper 11040

### Data comparison: Comtrade unit values vs BLS import price indices
- Method: Constructed Laspeyres indices of total goods (commodities and non-commodities) from Comtrade unit values to compare with BLS locality-of-origin import price indices; aggregated country-level growth rates using Comtrade import values with a two year lag.
- Key qualitative findings:
  - The Comtrade-based indices "track the BLS import price indices fairly well" for Canada, Japan, Mexico, and aggregated Latin America and Asia Near East.
  - Some Asian countries show greater volatility in the Comtrade series, suggesting residual unit value bias.
  - For every country group and individual country except Germany, the correlation coefficient between Comtrade and BLS growth rates is high.
  - Germany: Comtrade shows large unit value decreases in 2008 for a couple of products (transport vehicles) that drove divergence from BLS.

### Panel regression results: pass-through and trade elasticities
- Post-2002 subsample (2002–2015):
  - Price pass-through impulse responses for bilateral and dollar exchange rates similar to full-sample results.
  - "Post-2002 USD cumulative trade elasticity is substantially negative at lags of 1 and 2 years, whereas the level effect is close to zero at lags 1 and 2 on the full sample."
- Euro vs. dollar regressions (selected findings and diagnostics):
  - Interaction terms with importing-country euro and dollar invoicing shares (S_j and S^e_j) are "statistically and economically significant and mostly have the expected signs" in the price pass-through regressions: higher euro (resp., dollar) invoicing share implies higher pass-through from the euro (resp., dollar) exchange rate.
  - Interaction terms are imprecisely estimated in the trade elasticity regressions.
  - Representative estimation sizes (from Tables 6 and 7; importer-reported and exporter-reported panels reported separately):
    - Price pass-through sample sizes: Observations 32,825; 32,825; 23,668; 33,802; 33,802; 24,463 (across columns). Dyads 2,611; 2,611; 1,867; 2,647; 2,647; 1,900.
    - Trade elasticity sample sizes: Observations 36,269; 36,269; 26,129; 37,437; 37,437; 27,109. Dyads 2,773; 2,773; 1,982; 2,807; 2,807; 2,014.
- Representative coefficient magnitudes (baseline and robustness; exact values preserved):
  - Price pass-through (Table 9, Baseline, importer-reported):
    - ∆e_ij,t = 0.164*** (0.0126)
    - ∆e_j,t (USD) = 0.781*** (0.0143)
    - R-squared = 0.398
    - Observations = 46,820
    - Dyads = 2,647
  - Trade elasticity (Table 10, Baseline, importer-reported):
    - ∆e_ij,t = -0.0310* (0.0160)
    - ∆e_j,t (USD) = -0.186*** (0.0250)
    - R-squared = 0.071
    - Observations = 52,272
    - Dyads = 2,807
- CPI and PPI country-level regressions (2002–2015; Table 8, selected coefficients and sample sizes):
  - CPI regressions (columns vary by specification):
    - ∆e$_{j,t} = 0.106** (95% CI [0.04, 0.18]) in column (1).
    - Other coefficients and lags reported with 95% confidence intervals; Countries = 55 (column 1) and 39 (column 2) for CPI specifications.
    - Observations = 766 and 544 for CPI columns shown.
  - PPI regressions:
    - ∆e$_{j,t} = 0.284** (95% CI [0.14, 0.43]) in column (3).
    - Countries = 52 and 38 for PPI specifications shown.
    - Observations = 697 and 525 for PPI columns shown.
  - Note: 95% confidence intervals clustered by country and corrected using the “LZ2-BM” method (Imbens and Kolesár, 2016).

### Dollar invoicing share and aggregation
- Weighted average dollar import invoicing share (used in Section 6.1):
  - Weighted average ∑_{j≠US} w_j S_j fluctuates tightly around a mean of 0.40.
  - Figure 21 plots the series over 1990–2015 with horizontal lines showing the mean on the 1992–2015 and 2002–2015 samples.

### Robustness tests and data choices
- Robustness to data choices (Tables 9 and 10):
  - Variations tested: raw data (no imputation/outlier adjustment), total goods vs non-commodities, Laspeyres vs Fisher price indices.
  - Main messages:
    - Across variations, the USD exchange rate quantitatively dominates the bilateral exchange rate in price pass-through regressions.
    - Magnitudes of contemporaneous and lagged coefficients similar to baseline for most variations.
    - Using raw (unadjusted) data reduces R-squared and can weaken estimated relationships—e.g., trade volumes in raw data appear uncorrelated with the dollar exchange rate conditional on bilateral exchange rate.
    - The authors "strongly prefer the cleaned data set" because raw Comtrade exhibits extreme outliers and non-randomly missing data.

### Bayesian analysis: MCMC settings, diagnostics, and posterior summaries
- MCMC settings (Stan via MatlabStan/CmdStan):
  - No U-Turn Sampler run for 2,500 iterations after discarding 1,000 warm-up iterations, storing every 5th draw.
  - MCMC routine initialized at parameter values drawn uniformly at random (after transformation to unconstrained support).
  - Stan’s default settings used for adaptive tuning in warm-up.
  - Results insensitive to initialization.
- Computational performance and diagnostics:
  - Stored posterior draws of most parameters exhibit essentially zero serial correlation after a handful of lags.
  - Parameters corresponding to mixture components k with low posterior probability π_k(·) may mix more slowly but negligibly influence main posterior features.
  - Run times: depending on K and initialization, 2–60 hours per specification on a personal laptop (2.30 GHz, 8 GB RAM); often sufficient to run 2–4 hours to get a sense of results.
- Posterior summaries and robustness to number of mixture components:
  - Price pass-through model (example K = 2):
    - Posterior for ̄γ (the sum of the dollar and bilateral pass-throughs) "is concentrated close to 1", indicating near-complete total pass-through within a year.
    - Posterior histograms reported for cross-sectionally constant regression coefficients, and for α, τ, σ (random effects mean, SD, and idiosyncratic SD).
  - Trade elasticity model (example K = 4) posterior summaries consistent with panel regressions.
  - Robustness to larger K (K = 8):
    - Additional mixture components in K = 8 specifications receive very low posterior probability.
    - Figures report densities of dollar price pass-through and dollar trade elasticity conditional on dollar invoicing share S at S = 0.13, 0.59, 0.88 for K = 8; sample distributions shown for the K = 8 case.

*Source: wp17239 - 2000. NBER Working Paper 11040 (online appendix and tables as provided).*

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_Source: https://www.imf.org/-/media/files/publications/wp/2017/wp17239.pdf_