## 2.1 Currency Returns (excerpt)

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### Dataset and definitions
- Primary dataset: monthly data for 25 countries from 02/2003 to 11/2018, sourced from FX4casts; sample expanded with 7 additional countries using forward returns (Romania, Iceland, Kenya, Israel, Tunisia, Morocco, and Pakistan).
- Realized excess currency return for a USD-based investor:
  - RX_{t+1} ≡ R^L_t S_t / S_{t+1} − R^{US}_t, where S_t is spot (LCU per USD); R^L_t and R^{US}_t are local and US gross short-term interest rates.
- Currency risk premium of interest:
  - E[RX_{t+1}] ≡ E[R^L_t S_t / S_{t+1} − R^{US}_t].

### Global risk factors and pricing
- PCA on panel of currency returns yields two priced components:
  - Component 1: "Dollar Risk Factor"
  - Component 2: "Carry Trade Risk Factor"
- Cross-sectional pricing (Table 1, full specification Column 3):
  - Dollar Risk Exposure: 0.136 ∗∗
  - Carry trade Risk Exposure: 0.076 ∗∗∗
  - Constant: 0.003
  - Observations: 32; R^2: 0.585; Adjusted R^2: 0.556; Residual Std. Error: 0.015 (df = 29)
- Interpretation: both factors positively and statistically significantly related to average excess returns — both are priced.

### Time-series explanatory power (selected countries, Table 2)
- Regressions of excess returns on the two factors (coefficients marked by significance):
  - Turkey: Dollar 0.258 ∗∗∗; Carry 0.406 ∗∗∗; Observations 190; R^2 0.599; Adj. R^2 0.595; Residual Std. Error 0.033 (df = 187)
  - Chile: Dollar 0.167 ∗∗∗; Carry 0.118 ∗∗∗; Observations 190; R^2 0.460; Adj. R^2 0.454; Residual Std. Error 0.024 (df = 187)
  - Mexico: Dollar 0.167 ∗∗∗; Carry 0.156 ∗∗∗; Observations 190; R^2 0.553; Adj. R^2 0.548; Residual Std. Error 0.021 (df = 187)
  - Euro Area: Dollar 0.191 ∗∗∗; Carry −0.219 ∗∗∗; Observations 190; R^2 0.876; Adj. R^2 0.874; Residual Std. Error 0.010 (df = 187)
  - Japan: Dollar 0.035; Carry −0.130 ∗∗; Observations 190; R^2 0.097; Adj. R^2 0.087; Residual Std. Error 0.027 (df = 187)
- Notable: high R^2 for Turkey, Chile, Mexico, Euro Area; low R^2 for Japan consistent with safe-haven dynamics.

### Economic interpretation of factors (Table 3)
- Component 1 (Dollar Risk Factor) regressors:
  - S&P500 Returns: 1.533 ∗∗∗ (0.341)
  - ∆log(VIX): −0.070 (0.053)
  - ∆GFC: −0.013 (0.009)
  - Observations 190; R^2 0.306; Adj. R^2 0.299; Residual Std. Error 0.105 (df = 187)
  - Interpretation: strongly and positively correlated with S&P 500 returns — Component 1 is a global equity factor.
- Component 2 (Carry Trade Risk Factor) regressors:
  - S&P500 Returns: −0.080 (0.110)
  - ∆log(VIX): −0.085 ∗∗∗ (0.032)
  - ∆GFC: 0.001 (0.004)
  - Observations 190; R^2 0.045; Adj. R^2 0.035; Residual Std. Error 0.058 (df = 187)
  - Interpretation: significantly and negatively correlated with changes in the VIX — Component 2 is global risk aversion (carry trade risk).

### Determinants of exposures (Table 4)
- Dollar Risk Exposure (full specification, Column 2):
  - FL/FA: 0.043 ∗∗ (0.019)
  - Dollar Invoicing: −0.095 ∗∗ (0.040)
  - Constant: 0.228 ∗∗∗ (0.076)
  - Observations: 20; R^2 0.743; Adj. R^2 0.582; Residual Std. Error 0.047 (df = 8)
  - Interpretation: exposure driven by financial leverage (FL/FA) and trade invoicing; higher FL/FA → greater vulnerability; higher dollar invoicing → lower exposure to Dollar Risk Factor when controlling for financial vulnerabilities.
- Carry Risk Exposure (full specification, Column 4):
  - Dollar Invoicing: 0.457 ∗∗∗ (0.075)
  - Net Foreign Assets/GDP: −0.090 (0.060) in Column 4; baseline Column 3 shows −0.190 ∗∗∗
  - Constant: −0.280 ∗∗ (0.119)
  - Observations: 20; R^2 0.533; Adj. R^2 0.242; Residual Std. Error 0.167 (df = 8)
  - Interpretation: Dollar invoicing is the strongest predictor (positive and highly significant); net debtor position associated with higher carry exposure in baseline.

### GDP–exchange-rate comovement and expected returns
- Measure: correlation ρ between log real GDP growth and log real exchange rate (RER = S_t / P_t).
- Empirical relationship: average excess returns vs GDP–ER correlation shows a strong negative relationship (R² = 0.172).
  - More negative GDP–ER correlation associated with higher excess returns: examples include Brazil, Turkey, Chile, Peru.
  - Positive correlation and near-zero or negative excess returns: Japan, Switzerland, Denmark.
- Drivers of GDP–ER correlation (Table 5):
  - Dollar Invoicing: −0.396 ∗∗∗ (0.138)
  - FL/FA: −0.033 (0.030)
  - Net Foreign Assets/GDP: 0.203 ∗∗ (0.093)
  - Observations: 19; R^2 0.430; Adj. R^2 0.316; Residual Std. Error 0.194 (df = 15)
  - Interpretation: higher dollar invoicing and net debtor position associated with more negative GDP–ER correlation (exchange rate more countercyclical).

### Expected returns and professional forecasts (Table 6)
- Expected excess return using quarterly professional forecasts (2003Q1–2018Q4):
  - E_t^{UIP}_t = R^L_t S_t / E_t(S_{t+1}) − R^{US}_t.
- PCA on expected returns; cross-sectional regression (Table 6, Column 3):
  - Dollar Risk Factor: −0.007 (0.008) (not significant)
  - Carry Trade Risk Factor: 0.031 ∗∗∗ (0.005)
  - Constant: 0.004 ∗∗ (0.002)
  - Observations: 26; R^2 0.484; Adj. R^2 0.439; Residual Std. Error 0.006 (df = 23)
  - Interpretation: professional forecasts associate higher carry-trade exposure with higher average expected returns; carry trade loading is positive and highly significant.

_Italic source attribution: Content unit: wpiea2026158-source-pdf - 2.1    Currency Returns (excerpt)._

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### 3.2 Domestic Production and Price Setting (model structure)

### Production, pricing, and demand aggregates
- Domestic aggregator:
  - Yt = [∫0^1 Yi,t^(ε−1)/ε di]^(ε/(ε−1)), ε > 1.
  - Yi,t = Yt (Pi,t / Pt)^−ε.
  - Pt = [∫0^1 Pi,t^(1−ε) di]^(1/(1−ε)).
- Market clearing:
  - Yt = Cdt + Idt + Xdt.
- Intermediate-firm production:
  - Yi,t = Ki,t−1^α (At li,t)^(1−α); real marginal cost = mct.
- Calvo price stickiness:
  - Firms reset domestic prices with probability 1−θp; keep price with probability θp.
  - Optimal reset price ep_t = Kp_t / Fp_t with Kp_t and Fp_t defined in (16)–(17).

### Final consumption and investment goods
- Consumption CES aggregator:
  - Ct = { (1−ωc)^(1/ηc) Cdt^((ηc−1)/ηc) + ωc^(1/ηc) Cmt^((ηc−1)/ηc) }^(ηc/(ηc−1)).
  - Pc_t = [ (1−ωc) Pt^(1−ηc) + ωc (Pm_t)^(1−ηc) ]^(1/(1−ηc)), with Pm_t = St Pf_t.
  - Cdt = (1−ωc) (Pt / Pc_t)^−ηc Ct.
  - Cmt = ωc (Pm_t / Pc_t)^−ηc Ct.
- Investment aggregator and capital accumulation:
  - It = { γI^(1/νI) Idt^((νI−1)/νI) + (1−γI)^(1/νI) Imt^((νI−1)/νI) }^(νI/(νI−1)).
  - Kt = (1−δ) Kt−1 + [1 − S(It / It−1)] It.

### Exports and dominant-currency pricing
- Export production and foreign demand:
  - Xt = { γx^(1/ηx) Xdt^((ηx−1)/ηx) + (1−γx)^(1/ηx) Xmt^((ηx−1)/ηx) }^(ηx/(ηx−1)).
  - Xt = (Px_t / Pf_t)^−ηf Yt^∗.
- Export-input producers set Pd,x_i,t in dollars and face Calvo stickiness with probability θx of keeping dollar price.
  - Reset dollar price epd,x_t = Kx_t / Fx_t.
  - Export price index evolves as in (30).
- Dominant-currency pricing implications:
  - High θx (sticky dollar export prices) → depreciation does not quickly lower dollar export prices → weak expenditure-switching; adjustment shifts toward import compression and sharper depreciation.

### Financial intermediation and currency mismatch
- Bank net worth and currency composition:
  - Nj,t+1 = Rk_{t+1} Qt Aj,t − Rt BLC_{j,t} − R∗_t St+1 / St BFC_{j,t}.
  - Currency-specific borrowing: BFC_{j,t} = (LFC_{j,t−1}) φ_{j,t} Nj,t; BLC_{j,t} = (LLC_{j,t−1}) (1−φ_{j,t}) Nj,t.
  - Bank net-worth growth and survival (θb) determine continuation value and incentive constraints; when binding, ψ_{k,t} = λb L_{k,t}.
  - Bank chooses φ_t solving ψFC_t − ψLC_t = χφ (φ_t − φ̄); solved relation φ_t − φ̄ = λb / χφ (LFC_t − LLC_t).
  - Interpretation: banks tilt toward dollar liabilities when foreign-currency funding is more valuable; regulatory or institutional constraints may limit actual mismatch—φ interpreted broadly as combined financial & non-financial mismatch.

### Financial market clearing and balance of payments
- Foreign financiers and supply of local-currency lending:
  - B∗_t − B̄∗ = Et[ Rt St / St+1 ] − R∗_t λf(Var_t(s_{t+1})).
- Market clearing:
  - BF_t + Dt = BLC_t.
  - BF,∗_t + D∗_t = BFC_t.
- Net foreign assets and net exports:
  - NFA_t = −[ BF_t + BF,∗_t ].
  - Xt − Mt = −[ BF,∗_t − R∗_{t−1} St / St−1 BF,∗_{t−1} ] − [ BF_t − Rt−1 BF_{t−1} ].
- Dominant-currency pricing slows export margin, pushing external adjustment toward import compression and sharper depreciation when external financing deteriorates.

_Italic source attribution: Content unit: wpiea2026158-source-pdf - 3.2    Domestic Production and Price Setting (excerpt)._

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### 3.8 Monetary Policy and Shocks (mechanism and calibration)

### Policy rule and foreign shock processes
- Central bank inertial Taylor rule:
  - log(R_t / ̄R) = ρ_R log(R_{t−1} / ̄R) + r_π log(π_t / ̄π) + r_y log(y_t / ̄y) + ε_{R,t}. (Equation 48)
  - Policy targets domestic-good inflation.
- Foreign processes:
  - R^*_t = (1−ρ_{R^*}) ̄R^* + ρ_{R^*} R^*_{t−1} + σ_{R^*} ε_{R^*,t}. (Equation 49)
  - Y^*_t = (1−ρ_{Y^*}) ̄Y^* + ρ_{Y^*} Y^*_{t−1} + γ_R (R^*_t − ̄R^*) + σ_{Y^*} ε_{Y^*,t}. (Equation 50)

### Core mechanism connecting dollar liabilities, export-price stickiness, and UIP deviations
- Key objects:
  - Gross depreciation s_{t+1} ≡ S_{t+1}/S_t. (Equation 51)
  - Simple local-currency premium p^{LC}_t ≡ R_t − R^*_t E_t s_{t+1}. (Equation 52)
  - Banker-weighted SDFs M^k_{t+1} ≡ β Λ_{t,t+1} Ω^k_{t+1}. (Equation 53)
  - Bank-valued funding wedge U^B_t ≡ ν^{LC}_t − ν^{FC}_t = E_t[M^{LC}_{t+1} R_t] − E_t[M^{FC}_{t+1} R^*_t s_{t+1}]. (Equation 54)
- Unconditional premium decomposition (Equation 65):
  - p^{LC}_t = U^B_t / E_t[M^{LC}_{t+1}] + R^*_t E_t s_{t+1} (E_t[M^{FC}_{t+1}] − E_t[M^{LC}_{t+1}]) / E_t[M^{LC}_{t+1}] + R^*_t E_t[M^{LC}_{t+1}] Cov_t(M^{FC}_{t+1}, s_{t+1}).
- Interpretation:
  - First term: conditional bank funding wedge (currency-choice margin).
  - Second term: average LC–FC valuation differences.
  - Third term: risk-premium component — covariance between depreciation and banker-weighted SDF.
- Covariance drivers:
  - Net-worth exposure: direct effect of depreciation on net-worth growth ∂(N_{t+1}/N_t)/∂ s_{t+1} |_direct = − R^*_t (L^{FC}_t − 1) φ_t. (Equation 69)
  - Steady-state loading ζ_N(θ_x, φ̄) captures scaling (Equation 70).
  - Household SDF channel: b Λ_{t,t+1} ≈ −σ (b C_{t+1} − b C_t) − b Π^c_{t+1}; coefficients χ_C and χ_π capture comovements with s_{t+1}. (Equations 74–76)
  - Export-price stickiness θ_x raises exchange-rate volatility and strengthens household-SDF channel by making depreciation less stabilizing.

### Local representation of unconditional currency premium (Equation 78)
- ̄p^{LC} ≈
  - E[ Γ(θ_x, φ̄) (φ_t − φ̄) ] / ̄M^{LC} | conditional bank funding margin
  - + ̄R^* ̄s (σ χ_C(θ_x, φ̄) − χ_π(θ_x, φ̄)) V_s(θ_x, φ̄) | household-SDF channel
  - + ̄R^* ̄s κ_N ( ζ_N(θ_x, φ̄) V_s(θ_x, φ̄) + B_N(θ_x, φ̄) ) | bank net-worth and continuation-value channel
  - + ̄A_M(θ_x, φ̄) + ̄R^* ̄s ( R_Ω(θ_x, φ̄) + T(θ_x, φ̄) ) | average-kernel and higher-order terms.
- Comparative statics:
  - Direct effect of dollar liabilities on premium positive:
    - ∂̄p^{LC} / ∂ φ̄ |_direct ≈ ̄R^* ̄s κ_N ∂ ζ_N(θ_x, φ̄) / ∂ φ̄ V_s(θ_x, φ̄) > 0. (Equation 80)
  - Interaction of φ̄ and θ_x positive in calibrated region: dollar debt is costlier when export-price stickiness raises exchange-rate volatility and countercyclicality.

### Baseline calibration (selected parameters, Table 7)
- β Discount Factor: 0.995
- α Capital Share: 0.340
- δ Depreciation: 0.020
- φ Inverse Frisch: 1.000
- σ Relative risk aversion: 2.000
- r_π Taylor Inflation Coefficient: 1.500
- r_y Taylor Output Coefficient: 0.100
- r_S Taylor Exchange Rate Coefficient: 0.020
- ε Elasticity of Substitution, intermediate goods: 6.000
- θ Calvo Parameter, intermediate goods: 0.750
- ε_x Elasticity of Substitution, export goods: 6.000
- γ Target Portfolio Cost (UIP Friction): 2.560
- θ_x Export Calvo Stickiness: 0.800
- κ Investment Adjustment Cost: 5.850
- η_c C, Elasticity of Substitution: 0.410
- 1−ω_c Home Bias, C: 0.830
- ω_i Home Bias, I: 0.290
- γ_x Home Bias, X: 0.500
- η_f Elasticity of Demand, Exports: 1.530
- η_i I, Elasticity of Substitution: 0.910
- η_x X, Elasticity of Substitution: 0.700
- ρ_R MP Persistence: 0.900
- φ Target Credit Dollarization: 0.250
- Υ Target Deposit Dollarization: 0.200
- d^*_Y Dollar Deposit/GDP: 0.500
- γ_R Export Demand Shifter: -20.000
- θ_b Banker survival: 0.972
- W_b Banker startup: 0.030
- λ Banker constraint: 0.300
- λ_f Financier Constraint: 1.000
- Calibration notes:
  - θ_x = 0.800 baseline (dollar export prices adjust slowly).
  - λ_b = 0.300 implying steady-state leverage ≈ eight.
  - Steady-state foreign-currency liability share φ̄ = 0.250.

_Italic source attribution: Content unit: wpiea2026158-source-pdf - 3.8    Monetary Policy and Shocks (excerpt)._

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### 5.2 Response to a Foreign Interest Rate Shock (quantitative results and policy)

### Comparative impulse-response patterns (four economy profiles)
- Key drivers of cross-country differences: degree of dollar export invoicing and share of bank liabilities denominated in dollars.
- Main quantitative pattern (Figure 3 summary):
  - Largest UIP deviation when high dollar export invoicing is combined with high dollar liabilities.
  - High USD debt is the direct balance-sheet exposure; dollar invoicing amplifies the real payoff by weakening expenditure switching.
- UIP-spread outcomes:
  - High invoicing + high debt: largest currency-risk premium.
  - High debt + low invoicing: sizable but smaller spread.
  - Low-debt economies: only small UIP deviations.
- Real effects in high-invoicing, high-debt economy:
  - Largest depreciation.
  - Sharpest decline in consumption.
  - Most severe initial contraction in investment and output.
  - Mechanism: depreciation raises import prices and revalues dollar liabilities → weaker bank net worth → tighter credit → lower investment and consumption.

### Export response nuance and external adjustment
- Exports may rise on impact in high-debt economies, but via a costly adjustment:
  - Larger depreciation required; dollar-priced exports adjust slowly under high invoicing.
  - Low-invoicing economies obtain larger immediate declines in dollar export prices; high-invoicing economies adjust dollar export prices sluggishly.
  - Result: for a given exchange-rate movement, dollar invoicing weakens improvement in export competitiveness.

### Monetary-policy trade-off under a fixed Taylor rule
- Depreciation raises CPI inflation via import-price pass-through while output and investment contract.
- Under a fixed-intercept Taylor rule:
  - Stronger anti-inflation response tightens domestic financial conditions further.
  - More accommodative response validates part of depreciation.
- Structural nature: monetary policy cannot remove the source of the UIP premium; the exchange rate prices trade and financial frictions.

### Mechanism amplification and financial flows
- Transmission: foreign tightening → higher dollar funding costs → depreciation → valuation losses on dollar liabilities → reduced bank net worth → higher UIP spread and tighter credit.
- Dollar invoicing amplifies leverage increase and macro volatility.
- Households reduce local deposits and foreign assets; banks shift funding currency composition, often increasing dollar borrowing in equilibrium.
- Result: rising dollar debt combined with declining dollar assets → higher systemic dollar exposure.

### Stochastic steady-state and comparative statics
- Solution method: third-order approximation around non-stochastic steady state to capture risk effects on averages.
- Main findings:
  - Increasing θ_x raises exchange-rate volatility and strengthens negative comovement between output and the exchange rate.
  - UIP premium rises with export-price stickiness θ_x and with higher steady-state dollar liabilities φ̄.
  - Quantitative preview: largest UIP spreads when high dollar liabilities combine with high dollar export invoicing.
  - Raising θ_x increases exchange-rate volatility, makes depreciation more countercyclical, and raises unconditional UIP premium.
  - Varying φ̄ increases exchange-rate volatility, UIP premium, and average inflation.

### Monetary-policy rules and robustness
- Conventional Taylor rule with fixed intercept cannot internalize rising currency risk premia; equilibrium inflation tends to rise.
- Alternative robust rule (Orphanides and Williams (2006) style):
  - Rt − Rt−1 = rπ log(πt / π̄). (Equation 82)
  - Robust rule anchors inflation across θ_x values at the cost of higher average real rates and interest-rate spreads.
- Trade-off: standard rule → premium shows up as higher average inflation; robust rule → inflation anchored but economy bears higher real rates and tighter conditions.

### Policy recommendations and conclusions
- Core interaction: dominant-currency pricing and foreign-currency liabilities jointly create currency risk premia by making depreciation both costly for intermediaries and less effective for expenditure switching.
- Policy implications:
  - Monetary policy alone cannot undo structural currency risk.
  - Macroprudential policies limiting unhedged foreign-currency borrowing can reduce balance-sheet amplification.
  - Policies encouraging more flexible or local-currency export pricing can restore expenditure-switching benefits of depreciation.
- Suggested future work: explore how allocation of credit (beyond currency denomination and trade invoicing)—for example, dependence of nontradable sectors on bank credit—can further amplify exchange-rate volatility.

_Italic source attribution: Content unit: wpiea2026158-source-pdf - 5.2    Response to a Foreign Interest Rate Shock (excerpt)._

### 2.1    Currency Returns

### 2.1    Currency Returns

### Currency returns definition and dataset
- Primary dataset: monthly data for 25 countries from 02/2003 to 11/2018, sourced from FX4casts.
- Realized excess currency return for a USD-based investor:
  - RX_{t+1} ≡ R^L_t S_t / S_{t+1} − R^{US}_t
  - S_t is the spot exchange rate (LCU per USD); R^L_t and R^{US}_t are local and US gross short-term interest rates from t to t+1.
  - Interpretation: ex-post profit from borrowing in USD, investing in local currency, converting back to USD one period later.
- Currency risk premium of interest:
  - E[RX_{t+1}] ≡ E[R^L_t S_t / S_{t+1} − R^{US}_t]
- Sample expansion for cross-sectional analysis: augmented with 7 additional countries using forward returns (Romania, Iceland, Kenya, Israel, Tunisia, Morocco, and Pakistan). Derivation of forward-contract returns in Appendix Section C.

### Global risk factors (principal component analysis)
- PCA on panel of currency returns identifies two key components:
  - Component 1: "Dollar Risk Factor"
  - Component 2: "Carry Trade Risk Factor"
- Table 1 (cross-sectional pricing of risk exposures, full specification = Column 3):
  - Dollar Risk Exposure: 0.136 ∗∗
  - Carry trade Risk Exposure: 0.076 ∗∗∗
  - Constant (Column 3): 0.003
  - Observations: 32
  - R^2 (Column 3): 0.585
  - Adjusted R^2 (Column 3): 0.556
  - Residual Std. Error (Column 3): 0.015 (df = 29)
  - Significance notation: ∗ p<0.1; ∗∗ p<0.05; ∗∗∗ p<0.01
- Interpretation: both Dollar Risk Exposure and Carry Trade Risk Exposure show positive and statistically significant relationships with average excess returns — both factors are priced in the currency market.

### Time-series explanatory power across selected countries (Table 2)
- Regressions of excess returns on the two factors for five countries; reported coefficients and R^2:
  - Turkey: Dollar Risk Exposure 0.258 ∗∗∗; Carry trade Risk Exposure 0.406 ∗∗∗; Observations 190; R^2 0.599; Adjusted R^2 0.595; Residual Std. Error 0.033 (df = 187)
  - Chile: Dollar Risk Exposure 0.167 ∗∗∗; Carry trade Risk Exposure 0.118 ∗∗∗; Observations 190; R^2 0.460; Adjusted R^2 0.454; Residual Std. Error 0.024 (df = 187)
  - Mexico: Dollar Risk Exposure 0.167 ∗∗∗; Carry trade Risk Exposure 0.156 ∗∗∗; Observations 190; R^2 0.553; Adjusted R^2 0.548; Residual Std. Error 0.021 (df = 187)
  - Euro Area: Dollar Risk Exposure 0.191 ∗∗∗; Carry trade Risk Exposure −0.219 ∗∗∗; Observations 190; R^2 0.876; Adjusted R^2 0.874; Residual Std. Error 0.010 (df = 187)
  - Japan: Dollar Risk Exposure 0.035; Carry trade Risk Exposure −0.130 ∗∗; Observations 190; R^2 0.097; Adjusted R^2 0.087; Residual Std. Error 0.027 (df = 187)
- Notable: high R^2 for Turkey, Chile, Mexico, Euro Area; low R^2 for Japan (R^2 = 0.097) consistent with safe-haven dynamics.

### Economic interpretation of factors (Table 3)
- Regress Dollar Risk Factor (Component 1) and Carry Trade Risk Factor (Component 2) on macro-financial variables:
  - Component 1:
    - S&P500 Returns: 1.533 ∗∗∗ (0.341)
    - ∆log(VIX): −0.070 (0.053)
    - ∆GFC: −0.013 (0.009)
    - Observations: 190; R^2 0.306; Adjusted R^2 0.299; Residual Std. Error 0.105 (df = 187)
    - Interpretation: Strongly and positively correlated with S&P 500 returns — identifies Component 1 as a global equity factor.
  - Component 2:
    - S&P500 Returns: −0.080 (0.110)
    - ∆log(VIX): −0.085 ∗∗∗ (0.032)
    - ∆GFC: 0.001 (0.004)
    - Observations: 190; R^2 0.045; Adjusted R^2 0.035; Residual Std. Error 0.058 (df = 187)
    - Interpretation: Significantly and negatively correlated with changes in the VIX — identifies Component 2 as global risk aversion (carry trade risk).

### Determinants of component exposures (Table 4)
- Objective: regress estimated risk exposures (component loadings) on established determinants: FL/FA, Net Foreign Assets/GDP, Reserves/GDP, Dollar Invoicing, GDP (Nominal USD), Average Centrality.
- Key results (selected coefficients and significance):
  - Dollar Risk Exposure (full specification, Column 2):
    - FL/FA: 0.043 ∗∗ (0.019)
    - Dollar Invoicing: −0.095 ∗∗ (0.040)
    - Constant: 0.228 ∗∗∗ (0.076)
    - Observations: 20; R^2 0.743; Adjusted R^2 0.582; Residual Std. Error 0.047 (df = 8)
    - Interpretation: exposure driven by financial leverage (FL/FA) and trade invoicing; higher FL/FA → greater vulnerability; higher dollar invoicing → lower exposure to Dollar Risk Factor when controlling for financial vulnerabilities.
  - Carry Risk Exposure (full specification, Column 4):
    - Carry trade Risk Exposure drivers:
      - Dollar Invoicing: 0.457 ∗∗∗ (0.075)
      - Net Foreign Assets/GDP: −0.090 (0.060) in Column 4, but baseline shows −0.190 ∗∗∗ (Column 3)
      - Constant: −0.280 ∗∗ (0.119)
      - Observations: 20; R^2 0.533; Adjusted R^2 0.242; Residual Std. Error 0.167 (df = 8)
    - Interpretation: Dollar invoicing is the strongest predictor (positive and highly significant), implying high-invoicing countries' currencies are more exposed to global risk-off shocks; net debtor position (lower NFA/GDP) associated with higher exposure in baseline specification.
- Overall conclusion: observable frictions—dollar-denominated debt and dollar invoicing—jointly shape vulnerability to global shocks.

### Comovement between GDP and exchange rate
- Measure: correlation ρ between log real GDP growth and log real exchange rate (RER changes), where RER = nominal dollar exchange rate divided by CPI (S_t / P_t).
- Estimation approach: regression of standardized variables yields estimate ρˆ as the correlation coefficient:
  - ∆ log(GDP_t) / σ_{∆ log(GDP)} = α + ρ ∆ log(S_t / P_t) / σ_{∆ log(S/P)} + ε_t
- Economic interpretation:
  - Negative correlation (ρ < 0) implies currency depreciates when economy is in recession → local currency is a poor hedge → local residents demand a risk premium (higher expected returns) to hold local currency assets.
  - Figure 2: plot of average excess returns vs GDP-ER correlation shows strong negative relationship (R² = 0.172).
  - Examples:
    - More negative correlation and higher excess returns: Brazil, Turkey, Chile, Peru.
    - Positive correlation and near-zero or negative excess returns: Japan, Switzerland, Denmark.

### Macroeconomic transmission channel (drivers of GDP-ER comovement, Table 5)
- Regression of GDP-ER correlation on dollar frictions:
  - Dollar Invoicing: −0.396 ∗∗∗ (0.138)
  - FL/FA: −0.033 (0.030)
  - Net Foreign Assets/GDP: 0.203 ∗∗ (0.093)
  - Constant: −0.023 (0.149)
  - Observations: 19; R^2 0.430; Adjusted R^2 0.316; Residual Std. Error 0.194 (df = 15)
- Interpretation:
  - Higher dollar invoicing strongly associated with more countercyclical exchange rate (more negative GDP-ER correlation).
  - Net foreign assets/GDP positive coefficient implies net debtor countries (low or negative NFA/GDP) are associated with more negative GDP-ER correlation.
  - Conclusion: high dollar invoicing and net debtor position make the exchange rate fundamentally riskier.

### Currency return expectations (expected excess returns and PCA, Table 6)
- Expected excess currency return using quarterly exchange rate expectations from FX4Casts, sample 2003Q1-2018Q4:
  - E_t^{UIP}_t = R^L_t S_t / E_t(S_{t+1}) − R^{US}_t
  - E_t(S_{t+1}) is the one-quarter-ahead professional forecast for the spot rate.
- PCA applied to panel of expected returns; regress average expected excess returns on first two factor loadings:
  - Table 6 (Column 3, full specification):
    - Dollar Risk Factor: −0.007 (0.008) (not statistically significant)
    - Carry Trade Risk Factor: 0.031 ∗∗∗ (0.005)
    - Constant: 0.004 ∗∗ (0.002)
    - Observations: 26; R^2 0.484; Adjusted R^2 0.439; Residual Std. Error 0.006 (df = 23)
  - Interpretation: professional forecasts associate higher carry-trade factor exposure with higher average expected returns; carry trade loading is positive and highly significant.

### Model: rationale and key mechanisms
- Framework: small open-economy New Keynesian model with:
  - dominant-currency pricing in trade (export prices set in dollars),
  - foreign-currency borrowing by financial intermediaries,
  - segmented international asset markets.
- Two central mechanisms:
  1. Export price stickiness in dollars:
     - θ_x denotes Calvo probability that an export-price setter cannot adjust its dollar price in a given period.
     - High θ_x → export dollar prices are sticky → depreciation does not quickly lower the dollar price paid by foreign buyers → weak expenditure-switching channel.
  2. Dollar-denominated bank liabilities:
     - φ_t denotes the share of bank liabilities denominated in dollars; φ̄ is the target dollar-liability share.
     - High φ_t → depreciation raises local-currency value of dollar liabilities → reduces intermediary net worth → tightens credit.
- Interaction determines whether depreciation is stabilizing or contractionary:
  - Flexible export prices and little dollar debt → depreciation can support exports and absorb shocks.
  - Sticky dollar export prices and high dollar debt → depreciation fails to boost exports quickly and weakens bank balance sheets → local-currency assets pay off poorly in bad states → investors require endogenous risk premium.
- Households (model details):
  - Preferences: E_0 Σ_{t=0}^∞ β^t [u(C_t) − ξ_l l_t^{1+φ_l}/(1+φ_l) − γ/2 (Θ_t − Υ_t)^2]; Γ captures preferred-habitat cost of deviating dollar-asset share from target.
  - Budget constraint: D_t + S_t D^*_t + P^c_t C_t = R_{t-1} D_{t-1} + S_t R^*_{t-1} D^*_{t-1} + W_t l_t + T_t
  - Real stochastic discount factor: m_{t+1} ≡ β u_C(C_{t+1}) / u_C(C_t) 1 / Π^c_{t+1}
  - Euler equations:
    - 1 = R_t E_t[m_{t+1}]
    - 1 = R^*_t E_t[m_{t+1} S_{t+1} / S_t]
  - Portfolio-share condition:
    - γ_Θ (Θ_t − Υ_t) = β A_t E_t[ u_C(C_{t+1}) / Π^c_{t+1} (R_t − s_{t+1} R^*_t) ]
    - When dollar assets hedge bad states, households tilt toward dollar assets.

_Italic source attribution: Content unit: wpiea2026158-source-pdf - 2.1    Currency Returns (excerpt)._

### 3.2    Domestic Production and Price Setting

### 3.2    Domestic Production and Price Setting

### Domestic production and price setting
- Domestic homogeneous good Yt is produced by a competitive aggregator using differentiated intermediate varieties Yi,t:
  - Yt = [∫0^1 Yi,t^(ε−1)/ε di]^(ε/(ε−1)), ε > 1. (10)
- Cost minimization implies:
  - Yi,t = Yt (Pi,t / Pt)^−ε. (11)
  - Pt = [∫0^1 Pi,t^(1−ε) di]^(1/(1−ε)). (12)
- Elasticity of substitution across varieties is ε; a higher relative price reduces firm sales with sensitivity governed by ε.
- Market-clearing for the domestic homogeneous good:
  - Yt = Cdt + Idt + Xdt. (13)
  - Cdt, Idt, and Xdt are domestic inputs used in consumption, investment, and exports.
- Intermediate-firm production function:
  - Yi,t = Ki,t−1^α (At li,t)^(1−α). (14)
  - Ki,t−1 is predetermined capital; At is technology; α is capital’s share.
- Real marginal cost in units of the domestic good is mct.
- Calvo price stickiness for domestic intermediate firms:
  - With probability 1−θp a firm can reset its price; with probability θp it keeps previous price.
- Optimal reset price (relative):
  - ep_t ≡ eP_t / Pt = Kp_t / Fp_t. (15)
  - Kp_t = uC(Ct) / Pc_t * Yt^(ε/(ε−1)) * mct + β θp Et[(Πt+1)^ε Kp_{t+1}]. (16)
  - Fp_t = uC(Ct) / Pc_t * Yt + β θp Et[(Πt+1)^(ε−1) Fp_{t+1}]. (17)
  - Πt+1 ≡ Pt+1 / Pt.
- Interpretation:
  - Kp_t is the discounted value of expected marginal costs, adjusted by desired markup ε/(ε−1).
  - Fp_t is the discounted value of expected demand.
  - Firms choose a price balancing today’s markup against the probability the price persists.

### Final consumption and investment goods
- Final consumption combines domestic and imported goods:
  - Ct = { (1−ωc)^(1/ηc) (Cdt)^( (ηc−1)/ηc ) + ωc^(1/ηc) (Cmt)^( (ηc−1)/ηc ) }^( ηc/(ηc−1) ). (18)
  - ωc is import share in consumption; ηc is substitution elasticity between domestic and imported consumption goods.
- Associated CPI:
  - Pc_t = [ (1−ωc) Pt^(1−ηc) + ωc (Pm_t)^(1−ηc) ]^(1/(1−ηc)), Pm_t = St Pf_t. (19)
  - Imported goods priced in dollars Pf_t; local-currency price Pm_t = St Pf_t. Depreciation raises local-currency import prices.
- Input demands:
  - Cdt = (1−ωc) (Pt / Pc_t)^−ηc Ct. (20)
  - Cmt = ωc (Pm_t / Pc_t)^−ηc Ct. (21)
- Final investment produced analogously:
  - It = { γI^(1/νI) (Idt)^((νI−1)/νI) + (1−γI)^(1/νI) (Imt)^((νI−1)/νI) }^( νI/(νI−1) ). (22)
  - γI is domestic share in investment; νI is substitution elasticity between domestic and imported investment inputs.
- Capital accumulation:
  - Kt = (1−δ) Kt−1 + [1 − S(It / It−1)] It. (23)
  - δ is depreciation; S(·) is investment adjustment-cost function.
- Exchange-rate movements affect cost of building capital via imported inputs; adjustment costs make investment responses gradual.

### Exports and dominant-currency pricing
- Final exports combine domestic export input Xdt and imported input Xmt:
  - Xt = { γx^(1/ηx) (Xdt)^((ηx−1)/ηx) + (1−γx)^(1/ηx) (Xmt)^((ηx−1)/ηx) }^( ηx/(ηx−1) ). (24)
  - γx is domestic-input share in exports; ηx is substitution elasticity between domestic and imported export inputs.
- Foreign demand for final export good:
  - Xt = (Px_t / Pf_t)^−ηf Yt^∗. (25)
  - Px_t is dollar price of final export good; Pf_t is dollar price of foreign goods; Yt^∗ is foreign demand; ηf is foreign demand elasticity.
- Domestic export input assembled from differentiated export varieties:
  - Xdt = [∫0^1 Xi,t^( (εx−1)/εx ) di]^( εx/(εx−1) ). (26)
  - Xi,t = Xdt (Pd,x_i,t / Pd,x_t)^−εx. (27)
  - Pd,x_t = [∫0^1 (Pd,x_i,t)^(1−εx) di]^(1/(1−εx)). (28)
- Key feature: Pd,x_i,t is set in dollars. Export-input producers face Calvo stickiness in dollar prices:
  - With probability 1−θx a firm resets its dollar price; with probability θx it keeps the previous dollar price.
- Resetting exporter chooses relative dollar price:
  - epd,x_t ≡ ePd,x_t / Pd,x_t = Kx_t / Fx_t. (29)
- Export price index evolves:
  - (Pd,x_t)^(1−εx) = (1−θx) (epd,x_t)^(1−εx) + θx (Pd,x_{t−1})^(1−εx). (30)
- Dominant-currency pricing implications:
  - If θx = 0, firms reset dollar prices every period; depreciation lowers dollar price implied by domestic costs and supports export demand.
  - If θx is high, export dollar prices move little on impact; depreciation improves competitiveness only slowly, shifting adjustment toward import compression and sharper depreciation.

### Bankers and financial intermediation
- Banks borrow from households and foreign financiers in local currency and dollars, purchase capital claims, and earn gross return Rk_{t+1}.
- Bank j end-of-period net worth:
  - Nj,t+1 = Rk_{t+1} Qt Aj,t − Rt BLC_{j,t} − R∗_t St+1 / St BFC_{j,t}. (31)
  - BLC_{j,t} is local-currency borrowing; BFC_{j,t} is dollar borrowing measured in local-currency units at t.
  - A depreciation raises St+1 / St, increasing local-currency burden of dollar debt and reducing bank net worth.
- Dollar-liability share is φ_{j,t}. Leverage allowed to differ by funding currency:
  - BFC_{j,t} = (LFC_{j,t−1}) φ_{j,t} Nj,t. (32)
  - BLC_{j,t} = (LLC_{j,t−1}) (1−φ_{j,t}) Nj,t. (33)
- Growth rate of bank net worth:
  - Nj,t+1 / Nj,t = LLC_{j,t} (1−φ_{j,t}) (Rk_{t+1} − Rt) + LFC_{j,t} φ_{j,t} [ Rk_{t+1} − R∗_t St+1 / St ] + (1−φ_{j,t}) Rt + φ_{j,t} R∗_t St+1 / St. (34)
- Bankers survive with probability θb. Bank value:
  - Vj,t = Et ∑_{i=0}^∞ (1−θb) θb^i β^{i+1} Λ_{t,t+i+1} Nj,t+i+1. (35)
  - Recursive form: Vj,t = Et[ β(1−θb) Nj,t+1 + β θb Λ_{t,t+1} Vj,t+1 ]. (36)
- Incentive constraint: if a banker can divert fraction λb of assets, lenders provide funds only if continuation value is large enough.
  - Define value per unit of allocated net worth ψ_{k,t} ≡ Vk,t / Nk,t for funding currency k ∈ {LC, FC}.
  - When constraint binds: ψ_{k,t} = λb L_{k,t}. (37)
- Solved leverage:
  - LFC_t = νFC_t λb^{−ηFC_t}. (38)
  - LLC_t = νLC_t λb^{−ηLC_t}. (39)
  - η_{k,t} and ν_{k,t} are discounted continuation-value terms; higher continuation values relax leverage constraints; greater exchange-rate risk makes foreign-currency leverage more fragile.
- Bank chooses currency composition φ_t solving:
  - max_{φ_t} (1−φ_t) ψLC_t + φ_t ψFC_t − χφ^2 (φ_t − φ̄)^2. (40)
  - First-order condition: ψFC_t − ψLC_t = χφ (φ_t − φ̄). (41)
  - Using ψ_{k,t} = λb L_{k,t}: φ_t − φ̄ = λb / χφ (LFC_t − LLC_t). (42)
  - Banks shift toward dollar liabilities when value of foreign-currency funding rises relative to local-currency funding; quadratic cost prevents corner jumps.
- Note: In many small open economies banks are not allowed by regulation to hold currency mismatch. In the model φ should be interpreted as combined financial & non-financial currency mismatch.

### Foreign financiers and financial market clearing
- Foreign financiers borrow in dollars and lend to domestic economy in local currency.
  - B∗_t is dollar amount invested in local-currency assets; BF_t ≡ St B∗_t is its local-currency value.
- Foreign supply of local-currency lending:
  - B∗_t − B̄∗ = Et[ Rt St / St+1 ] − R∗_t λf(Var_t(s_{t+1})). (43)
  - λf(Var_t(s_{t+1})) is increasing in exchange-rate risk; foreigners require larger expected return to hold more local-currency assets when exchange-rate is volatile.
- Financial market clearing:
  - BF_t + Dt = BLC_t. (44)
  - BF,∗_t + D∗_t = BFC_t. (45)
  - First condition: bank local-currency borrowing funded by household local-currency deposits and foreign local-currency lending.
  - Second condition: bank dollar borrowing funded by domestic and foreign dollar positions.

### Balance of payments
- Net foreign asset position:
  - NFA_t = −[ BF_t + BF,∗_t ]. (46)
- Net exports equal change in NFA after interest payments:
  - Xt − Mt = −[ BF,∗_t − R∗_{t−1} St / St−1 BF,∗_{t−1} ] − [ BF_t − Rt−1 BF_{t−1} ]. (47)
- Central identity implications:
  - If the economy loses external financing or must repay more because dollar liabilities become expensive, external adjustment must occur through higher exports, lower imports, a larger depreciation, or a combination.
  - Dominant-currency pricing makes the export margin slow, so adjustment is pushed toward import compression and a sharper depreciation.

*Source: https://www.imf.org/-/media/files/publications/wp/2026/english/wpiea2026158-source-pdf.pdf*

### 3.8    Monetary Policy and Shocks

### wpiea2026158-source-pdf - 3.8    Monetary Policy and Shocks

### Monetary-policy rules and external shocks
- Central bank follows an inertial Taylor rule:
  - log(R_t / ̄R) = ρ_R log(R_{t−1} / ̄R) + r_π log(π_t / ̄π) + r_y log(y_t / ̄y) + ε_{R,t}. (Equation 48)
  - Coefficients r_π and r_y govern responses to inflation and output; ρ_R captures interest-rate smoothing.
  - Target is domestic-good inflation rather than CPI inflation.
- Foreign interest-rate process and export-demand response:
  - R^*_t = (1−ρ_{R^*}) ̄R^* + ρ_{R^*} R^*_{t−1} + σ_{R^*} ε_{R^*,t}. (Equation 49)
  - Y^*_t = (1−ρ_{Y^*}) ̄Y^* + ρ_{Y^*} Y^*_{t−1} + γ_R (R^*_t − ̄R^*) + σ_{Y^*} ε_{Y^*,t}. (Equation 50)
  - Foreign tightening works through financial (dollar funding costs) and trade channels (reduces external demand).

### Dollar liabilities, export-price stickiness, and deviations from UIP — core mechanism
- Object of interest: unconditional premium on local-currency assets (distinct from conditional bank funding wedge).
- Key components:
  - Dollar liabilities determine sensitivity of bank net worth to depreciation.
  - Sticky dollar export prices (high θ_x) weaken immediate export response to depreciation, increasing required exchange-rate movements and domestic absorption adjustments.
- Definitions and central expressions:
  - Gross depreciation: s_{t+1} ≡ S_{t+1}/S_t. (Equation 51)
  - Simple local-currency premium (domestic-return units): p^{LC}_t ≡ R_t − R^*_t E_t s_{t+1}. (Equation 52)
  - Banker-weighted stochastic discount factor for funding currency k∈{LC,FC}: M^k_{t+1} ≡ β Λ_{t,t+1} Ω^k_{t+1}. (Equation 53)
  - Bank-valued funding wedge: U^B_t ≡ ν^{LC}_t − ν^{FC}_t = E_t[M^{LC}_{t+1} R_t] − E_t[M^{FC}_{t+1} R^*_t s_{t+1}]. (Equation 54)
  - Currency-choice condition with quadratic cost around reference φ̄:
    - ψ^{FC}_t − ψ^{LC}_t = χ_φ (φ_t − φ̄). (Equation 55)
    - When incentive constraint binds: ψ^k_t = λ_b L^k_t, k∈{LC,FC}. (Equation 56)
    - Implied revealed leverage advantage: L^{FC}_t − L^{LC}_t = χ_φ/λ_b (φ_t − φ̄). (Equation 57)
  - Approximate leverage spread around symmetric reference:
    - L^{FC}_t − L^{LC}_t ≈ (L^{−1} / (λ_b − η)) U^B_t. (Equation 59)
  - Conditional bank-side wedge:
    - U^B_t = χ_φ (λ_b − η)/[λ_b (L − 1)] (φ_t − φ̄). (Equation 60)
  - Conditional margin depends on φ_t − φ̄; export-price stickiness θ_x affects slope via general-equilibrium objects η, ν, L = ν/(λ_b − η). (Equations 61–63)
- Unconditional premium decomposition (key pricing/covariance terms):
  - U^B_t decomposed to isolate p^{LC}_t; solved expression:
    - p^{LC}_t = U^B_t / E_t[M^{LC}_{t+1}] + R^*_t E_t s_{t+1} (E_t[M^{FC}_{t+1}] − E_t[M^{LC}_{t+1}]) / E_t[M^{LC}_{t+1}] + R^*_t E_t[M^{LC}_{t+1}] Cov_t(M^{FC}_{t+1}, s_{t+1}). (Equation 65)
  - Interpretation of terms:
    - First term: conditional bank funding wedge (currency-choice margin).
    - Second term: average LC–FC valuation differences.
    - Third term: risk-premium component — key covariance between depreciation and banker-weighted SDF.
- Covariance channel and net-worth exposure:
  - Approximation (log deviations) isolates household SDF, bank continuation values, and higher-order interactions:
    - Cov(M^{FC}_{t+1}, s_{t+1}) / [E_t[M^{FC}_{t+1}] E_t[s_{t+1}]] ≈ Cov(bΛ_{t,t+1}, b s_{t+1}) + Cov(bΩ^{FC}_{t+1}, b s_{t+1}) + T_t(θ_x, φ̄). (Equation 66)
  - Aggregate bank net worth evolution:
    - N_{t+1} = R^k_{t+1} Q_t A_t − R_t B^{LC}_t − R^*_t s_{t+1} B^{FC}_t. (Equation 67)
    - B^{FC}_t = (L^{FC}_t − 1) φ_t N_t. (Equation 68)
  - Direct effect of depreciation on net-worth growth (holding balance-sheet positions fixed):
    - ∂(N_{t+1}/N_t)/∂ s_{t+1} |_direct = − R^*_t (L^{FC}_t − 1) φ_t. (Equation 69)
  - Steady-state direct log-linear loading:
    - ∂ b N_{t+1} / ∂ b s_{t+1} |_ss,direct = − ζ_N(θ_x, φ̄),
      ζ_N(θ_x, φ̄) ≡ ̄R^* ̄s [ ̄L^{FC}(θ_x, φ̄) − 1 ] ̄φ / ̄g_N(θ_x, φ̄). (Equation 70)
  - Net-worth covariance decomposition:
    - −Cov(b N_{t+1}, b s_{t+1}) = ζ_N(θ_x, φ̄) V_{s,t}(θ_x, φ̄) + B_{N,t}(θ_x, φ̄). (Equation 71)
  - Continuation value linkage:
    - b Ω^{FC}_{t+1} ≈ − κ_N b N_{t+1} + b R^{FC}_{t+1}, κ_N > 0. (Equation 72)
    - Cov(b Ω^{FC}_{t+1}, b s_{t+1}) ≈ κ_N [ ζ_N(θ_x, φ̄) V_s,t(θ_x, φ̄) + B_{N,t}(θ_x, φ̄) ] + R_{Ω,t}(θ_x, φ̄). (Equation 73)
- Household-SDF component and role of export-price stickiness:
  - b Λ_{t,t+1} ≈ −σ (b C_{t+1} − b C_t) − b Π^c_{t+1}. (Equation 74)
  - Define correlations scaled by Var(bs_{t+1}):
    - χ_C(θ_x, φ̄) ≡ − Cov(b C_{t+1} − b C_t, b s_{t+1}) / Var(b s_{t+1})
    - χ_π(θ_x, φ̄) ≡ Cov(b Π^c_{t+1}, b s_{t+1}) / Var(b s_{t+1}). (Equation 75)
  - Then Cov(b Λ_{t,t+1}, b s_{t+1}) = (σ χ_C(θ_x, φ̄) − χ_π(θ_x, φ̄)) V_s(θ_x, φ̄). (Equation 76)
  - Higher θ_x (stickier dollar export prices) strengthens the household-SDF channel because depreciation provides less immediate export support and is associated with weaker real activity.
- Local representation of unconditional currency premium (unconditional mean):
  - ̄p^{LC} ≡ E[p^{LC}_t] ≈
    - E[ Γ(θ_x, φ̄) (φ_t − φ̄) ] / ̄M^{LC} | conditional bank funding margin
    - + ̄R^* ̄s (σ χ_C(θ_x, φ̄) − χ_π(θ_x, φ̄)) V_s(θ_x, φ̄) | household-SDF channel
    - + ̄R^* ̄s κ_N ( ζ_N(θ_x, φ̄) V_s(θ_x, φ̄) + B_N(θ_x, φ̄) ) | bank-net-worth and continuation-value channel
    - + ̄A_M(θ_x, φ̄) + ̄R^* ̄s ( R_Ω(θ_x, φ̄) + T(θ_x, φ̄) ) | average-kernel and higher-order valuation terms. (Equation 78)
  - Interpretation:
    - Level of steady-state dollar liabilities φ̄ scales direct covariance via ζ_N(θ_x, φ̄).
    - Export-price stickiness θ_x affects how much stabilization exchange-rate movements provide; higher θ_x raises exchange-rate volatility, makes depreciation more associated with weak output, and raises the unconditional UIP premium.
- Comparative statics (direct effects):
  - ∂ ζ_N(θ_x, φ̄) / ∂ φ̄ ≈ ̄R^* ̄s [ ̄L^{FC}(θ_x, φ̄) − 1 ] / ̄g_N(θ_x, φ̄) > 0. (Equation 79)
  - Direct effect of dollar liabilities on unconditional premium:
    - ∂ ̄p^{LC} / ∂ φ̄ |_direct ≈ ̄R^* ̄s κ_N ∂ ζ_N(θ_x, φ̄) / ∂ φ̄ V_s(θ_x, φ̄) > 0. (Equation 80)
  - Interaction with export-price stickiness:
    - ∂^2 ̄p^{LC} / ∂ φ̄ ∂ θ_x ≈ ̄R^* ̄s κ_N [ ∂ ζ_N(θ_x, φ̄) / ∂ φ̄ ∂ V_s(θ_x, φ̄) / ∂ θ_x + ∂^2 B_N(θ_x, φ̄) / ∂ φ̄ ∂ θ_x ] + household-SDF, average-kernel, and higher-order interaction terms. (Equation 81)
    - In the calibrated region, this derivative is positive: dollar debt is more costly when export-price stickiness raises exchange-rate volatility and when the macro-financial feedback amplifies net-worth losses.

### Quantitative implications summarized
- Complementary margins:
  - Conditional bank wedge: depends on deviations of endogenous dollar share φ_t from φ̄ (currency-choice margin).
  - Unconditional premium: depends on the level of dollar liabilities φ̄ (direct revaluation when currency depreciates).
- Dominant-currency pricing (high θ_x) alone is insufficient for a large premium unless steady-state dollar-liability share φ̄ is large; the revaluation channel scales with φ̄.
- Quantitative patterns (previewed):
  - Largest UIP spreads when high dollar liabilities are combined with high dollar export invoicing.
  - Raising θ_x increases exchange-rate volatility, makes depreciation more countercyclical, and raises the unconditional UIP premium.
  - Varying φ̄ in appendix simulations yields higher exchange-rate volatility, higher UIP premium, and higher average inflation.

### Model calibration — baseline parameter values (Table 7)
- Parameters central to trade, financial exposure, and nominal rigidities (selected entries shown exactly as in source):
  - β Discount Factor: 0.995
  - α Capital Share: 0.340
  - δ Depreciation: 0.020
  - φ Inverse Frisch: 1.000
  - σ Relative risk aversion: 2.000
  - r_π Taylor Inflation Coefficient: 1.500
  - r_y Taylor Output Coefficient: 0.100
  - r_S Taylor Exchange Rate Coefficient: 0.020
  - ε Elasticity of Substitution, intermediate goods: 6.000
  - θ Calvo Parameter, intermediate goods: 0.750
  - ε_x Elasticity of Substitution, export goods: 6.000
  - γ Target Portfolio Cost (UIP Friction): 2.560
  - θ_x Export Calvo Stickiness: 0.800
  - κ Investment Adjustment Cost: 5.850
  - η_c C, Elasticity of Substitution: 0.410
  - 1−ω_c Home Bias, C: 0.830
  - ω_i Home Bias, I: 0.290
  - γ_x Home Bias, X: 0.500
  - η_f Elasticity of Demand, Exports: 1.530
  - η_i I, Elasticity of Substitution: 0.910
  - η_x X, Elasticity of Substitution: 0.700
  - ρ_R MP Persistence: 0.900
  - φ Target Credit Dollarization: 0.250
  - Υ Target Deposit Dollarization: 0.200
  - d^*_Y Dollar Deposit/GDP: 0.500
  - γ_R Export Demand Shifter: -20.000
  - θ_b Banker survival: 0.972
  - W_b Banker startup: 0.030
  - λ Banker constraint: 0.300
  - λ_f Financier Constraint: 1.000
- Calibration notes from source text:
  - Investment home-bias parameter γ_I = 0.290 and domestic-input share in exports γ_x = 0.500 (reflects high exposure to foreign prices and demand).
  - Elasticity of substitution between domestic and imported consumption η_c = 0.410 (η_c < 1 implies complements).
  - Export-demand shifter γ_R = −20 captures foreign tightening reducing external demand.
  - Export-price stickiness θ_x = 0.800 in baseline (dollar export prices adjust slowly).
  - Banker incentive parameter λ_b = 0.300 implying steady-state leverage of approximately eight.
  - Steady-state foreign-currency liability share φ̄ = 0.250 (moderate liability dollarization).

*Source: wpiea2026158-source-pdf - 3.8    Monetary Policy and Shocks*

### 5.2    Response to a Foreign Interest Rate Shock

### 5.2    Response to a Foreign Interest Rate Shock

### Impulse-response comparison across four economies
- Framework: the monetary policy rule and the foreign interest-rate shock are held fixed across economies; differences in domestic interest rates, exchange rates, output, and UIP spreads are equilibrium outcomes driven by:
  - degree of dollar export invoicing (high invoicing = dollar export prices sticky; low invoicing = producer-currency pricing)
  - share of bank liabilities denominated in dollars (high USD debt vs low USD debt)
- Key quantitative pattern (Figure 3):
  - The largest UIP deviation arises when high dollar export invoicing is combined with high dollar liabilities.
  - High USD debt is the direct source of balance-sheet exposure: a depreciation raises the local-currency value of intermediaries’ dollar debt and lowers bank net worth.
  - Dollar export invoicing changes the real payoff to that balance-sheet exposure by weakening expenditure switching when dollar export prices are sticky.
- UIP-spread panel outcomes:
  - High invoicing + high debt: largest currency-risk premium.
  - High debt + low invoicing: sizable but smaller spread.
  - Low-debt economies: only small UIP deviations.
- Real effects in the high-invoicing, high-debt economy:
  - Largest depreciation.
  - Sharpest decline in consumption.
  - Most severe initial contraction in investment and output.
  - Depreciation raises domestic prices of imported consumption goods and imported investment inputs, reducing real purchasing power and effective return to capital accumulation.
  - Revaluation of dollar liabilities weakens intermediary net worth and tightens credit, raising UIP spread.

### Export response nuance
- Exports rise on impact in high-debt economies (including high-invoicing), but:
  - This is a costly external adjustment driven by a much larger depreciation and sharp external-account movements—not the benign textbook expenditure-switching channel.
  - Low-invoicing economies obtain a larger immediate decline in dollar export prices; high-invoicing economies adjust dollar export prices more sluggishly.
  - For a given exchange-rate movement, dollar invoicing weakens improvement in export competitiveness; observed export expansion in vulnerable economies occurs because the exchange rate and risk premium move much more.

### Monetary-policy trade-off under common Taylor rule
- Depreciation raises CPI inflation via import-price pass-through while output and investment contract due to balance-sheet losses and costly external adjustment.
- Central bank cannot remove structural source of the UIP premium under a fixed Taylor rule:
  - Stronger anti-inflation response tightens domestic financial conditions further.
  - More accommodative response validates part of the depreciation.
- The policy problem is endogenous to trade and financial structure: the exchange rate prices the risk created by the joint presence of dollar liabilities and sticky dollar export prices.

*Italicized figure notes and panel labels describing high/low invoicing and USD debt appear in the source figures.*

### Mechanism (Section 5.3)
- Transmission steps:
  - A foreign interest-rate shock raises dollar funding costs and pressures the domestic currency downward.
  - With dollar liabilities, depreciation increases local-currency value of debt → valuation losses → reduced bank net worth → higher leverage → tightened credit.
  - Dollar export invoicing determines whether the trade account can absorb financial loss:
    - Under producer-currency pricing or flexible dollar export prices: depreciation lowers foreign-currency export prices and stimulates foreign demand, helping offset balance-sheet loss.
    - Under sticky dollar export pricing: relative-price channel is weaker; same depreciation produces less immediate export competitiveness improvement → external adjustment requires larger depreciation, import compression, and lower domestic absorption.
- Current-account dynamics (Figure 4) in high-invoicing, high USD debt:
  - Current account sharply deteriorates on impact and then reverses into surplus.
  - Initial deterioration reflects financial pressure and burden of dollar liabilities.
  - Subsequent surplus reflects forced external adjustment: strong trade balance improvement achieved via large depreciation, high UIP premium, and sharp contraction in domestic demand.

### Currency returns and export-price adjustment (Figure 5)
- UIP spread largest when high dollar debt combines with high dollar export invoicing.
- High dollar debt alone generates substantial spread; high invoicing amplifies it.
- Low-invoicing economies see larger initial declines in dollar export prices (depreciation works more directly through competitiveness).
- High-invoicing economies: muted and delayed dollar-price adjustment → exchange rate must move more → in high-debt setting this worsens intermediary balance sheets.
- Conclusion: dollar-liability share is the direct balance-sheet exposure; export-price stickiness raises the marginal riskiness of that exposure.

### UIP Premium and marginal-utility co-movement (Figure 6)
- UIP spread relates to covariance between marginal utility and the exchange rate.
- This covariance rises following foreign interest-rate shocks in economies with high financial dollarization.
- When balance sheets are damaged, further shocks are more destabilizing → aggregate volatility rises → agents prefer dollar assets and banks prefer local-currency borrowing → equilibrium reached at higher local interest rates.

### Financial flows (Figure 7)
- Presence of dollar debt → balance-sheet damage → bank leverage increases to repair net worth.
- Dollar invoicing heavily amplifies increase in leverage, driving macro volatility and marginal-utility/exchange-rate co-movement.
- Households:
  - Decrease local deposits and foreign assets.
  - Use foreign assets as a buffer but mainly liquidate local-currency deposits to avoid local assets.
- Rising UIP premium disincentivizes banks from borrowing in local currency; they borrow in dollars instead.
- Result: rising dollar debt combined with declining dollar assets → economy accumulates higher dollar debt.

### Stochastic steady-state results (Section 5.4)
- Solution method: third-order approximation around non-stochastic steady state to allow risk to affect simulation averages.
- Main result: greater export-price stickiness (θ_x increases) makes the currency both more volatile and more countercyclical.
  - When dollar export prices adjust slowly, external shocks require larger exchange-rate movements to satisfy balance-of-payments constraint.
  - These depreciations occur when output is weak because dollar liabilities reduce intermediary net worth and import prices compress domestic absorption.
  - Exchange rate becomes a poor hedge for domestic activity.

#### Volatility, cyclicality, and UIP premium
- Figure 8:
  - Increasing θ_x raises exchange-rate volatility and strengthens negative comovement between output and the exchange rate.
  - Stickier dollar export prices weaken expenditure switching; larger depreciations worsen financial conditions and make output fall as currency depreciates.
- Asset-pricing implication:
  - Dollar assets appreciate in domestic downturns and provide insurance to domestic agents; local-currency assets lose value in low-income states.
  - Households demand compensation to hold local-currency exposure.
  - Foreign financiers require larger expected excess return when exchange-rate volatility rises (see Equation 43 in source).
- Figure 9:
  - Stochastic steady-state UIP premium rises with export-price stickiness (θ_x).
  - Dollar debt creates direct exposure; dominant-currency pricing raises the price of that exposure by making exchange rate less stabilizing.

#### Inflation and monetary-policy implications
- UIP premium rise has monetary implications:
  - In open economy with segmented international asset markets, domestic nominal interest rate must compensate investors for currency risk.
  - When premium rises, the risk-adjusted neutral interest rate rises.
  - A conventional Taylor rule with a fixed intercept (e.g., Equation 48) does not internalize this shift; at the inflation target the policy rate is too low relative to return required to clear currency markets → equilibrium inflation rises above target so that Taylor rule generates a higher nominal and real interest rate.
- Alternative rule considered (robust rule responding to inflation changes, following Orphanides and Williams (2006)):
  - Rt − Rt−1 = rπ log(πt / π̄). (Equation 82 in source)
  - This rule allows long-run level of nominal interest rate to adjust to the risk premium while still anchoring inflation around target.
- Figure 11 outcomes:
  - Robust rule stabilizes inflation across θ_x values (Figure 11a).
  - Cost: domestic economy sustains a higher interest-rate spread when currency risk premium is high (Figure 11b).
  - Trade-off: standard rule → premium shows up as higher average inflation; robust rule → inflation anchored but economy absorbs premium through higher real rates and tighter financial conditions.
  - Structural conclusion: as long as dollar pricing and dollar liabilities make exchange rate risky, monetary policy must either accommodate part of the premium or impose the real-rate adjustment required to offset it.

### Policy implications and conclusion
- Core mechanism: dominant-currency pricing and foreign-currency liabilities are mutually reinforcing frictions.
  - Dollar export pricing weakens expenditure-switching benefit of depreciation.
  - Dollar liabilities make depreciation costly for financial intermediaries.
  - Joint operation: exchange rate ceases to be stabilizing; depreciations occur in bad states, tighten balance sheets, compress domestic absorption, and make local-currency assets risky.
- Quantitative findings:
  - Following a foreign monetary tightening, the vulnerable economy (high dollar invoicing + high dollar debt) experiences a larger depreciation, sharper declines in consumption and investment, and a higher UIP spread than a benchmark economy without these frictions.
  - The interaction—not any single friction in isolation—is the main driver: depreciation fails to stimulate exports quickly while immediately worsening balance sheets.
- Policy recommendations:
  - Monetary policy alone cannot undo structural source of currency risk.
  - Macroprudential policies that limit unhedged foreign-currency borrowing can reduce balance-sheet amplification of depreciations.
  - Policies encouraging more flexible or local-currency export pricing can restore part of the expenditure-switching role of the exchange rate.
  - More generally, currency risk is an equilibrium outcome shaped by goods pricing, liability denomination, and how international investors absorb currency exposure.
- Suggestion for future work:
  - Investigate whether exchange-rate risk also depends on domestic allocation of credit beyond foreign-currency denomination and trade invoicing—e.g., stronger dependence of nontradable sectors on bank credit could create additional feedback amplifying exchange-rate volatility.

*Source: IMF working-paper content unit "5.2 Response to a Foreign Interest Rate Shock" (source PDF provided).*

### References

### References and Appendices (wpiea2026158-source-pdf)

### Major bibliographic sources
- Comprehensive reference list includes empirical and theoretical contributions on currency invoicing, dollarization, exchange-rate dynamics, financial intermediation, and international monetary transmission. Representative entries:
  - Amiti, Mary, Oleg Itskhoki, and Jozef Konings, “Dominant currencies: How firms choose currency invoicing and why it matters,” The Quarterly Journal of Economics, 2022, 137(3), 1435–1493.
  - Gopinath, Gita and Jeremy C. Stein, “Banking, Trade, and the Making of a Dominant Currency,” The Quarterly Journal of Economics, 2021, 136(2), 783–830.
  - Gopinath, et al., “Dominant Currency Paradigm,” American Economic Review, March 2020, 110(3), 677–719.
  - Maggiori, Matteo, “Financial Intermediation, International Risk Sharing, and Reserve Currencies,” American Economic Review, October 2017, 107(10), 3038–3071.
- Data sources cited for empirical analysis: IFS, Datastream, FX4Casts, Gopinath, Boz, Casas, Díez, Gourinchas and Plagborg-Møller (2020), Richmond (2019).

### Appendix A — Determinants of Currency Returns (empirical findings)
- Variables considered: external balance (Della Corte, Riddiough and Sarno (2016)), foreign assets/liabilities in banking system (Yeyati (2006); Christiano, Dalgic and Nurbekyan (2021)), Dollar invoicing (Gopinath et al. (2020)), country size (Hassan (2013)), trade network centrality (Richmond (2019)).
- Robust determinants across currencies:
  - Foreign liabilities (external debt, NFA) and export dollar invoicing emerge as robustly significant determinants of currency returns.
- Regression results (Table 8: Determinants of Returns). Dependent variable: Average Return. Coefficient estimates (standard errors in parentheses) and model fit:
  - FL/FA: 0.010 ∗∗∗ (0.004) in column (1); 0.009 ∗∗ (0.004) in (2); 0.008 ∗∗ (0.004) in (3).
  - Net Foreign Assets/GDP: −0.031 ∗∗∗ (0.009) in (1); −0.027 ∗∗∗ (0.003) in (2); −0.028 ∗∗∗ (0.005) in (3).
  - GDP (Share of US): 0.006 (0.005) in (3); 0.003 (0.007) in (4).
  - Reserves/GDP: 0.060 (0.048) in (1); 0.003 (0.026) in (2); 0.015 (0.025) in (3); 0.033 (0.042) in (4).
  - Export USD Invoicing: 0.036 ∗ (0.019) in (1); 0.018 ∗∗ (0.008) in (2); 0.017 ∗∗∗ (0.006) in (3); 0.019 ∗∗ (0.009) in (4).
  - Trade Centrality: −4.304 ∗∗ (2.011) in (1); −0.983 (1.088) in (2); −2.774 (4.387) in (3).
  - Constant terms and diagnostics:
    - Observations: 20, 17, 14, 14 (columns (1)–(4) respectively).
    - R2: 0.560, 0.335, 0.805, 0.810 (columns (1)–(4)).
    - Adjusted R2: 0.402, 0.182, 0.683, 0.648.
    - Residual Std. Error: 0.020 (df = 14), 0.016 (df = 13), 0.010 (df = 8), 0.011 (df = 7).
  - Note: ∗ p<0.1; ∗∗ p<0.05; ∗∗∗ p<0.01.
- Empirical visual relationships (figures described):
  - FL/FA and excess returns: higher banking-system foreign liabilities imply higher expected currency returns.
  - Reserves/GDP and excess returns: no significant relationship observed.
  - NFA (Net external balance) and excess returns: clear negative relationship.
  - Size and trade centrality: larger and/or more central economies have lower currency returns (assets provide insurance).
  - Financial depth (total foreign assets + liabilities as share of GDP) correlates strongly with net external balance and relates to excess returns.
  - Dollar invoicing:
    - Panel (a): negative relationship between Dollar Invoicing and GDP-ER correlation (R² = 0.198) — higher invoicing → exchange rate becomes more countercyclical.
    - Panel (b): positive relationship between Export Invoicing and average Excess Returns (R² = 0.143).

### Appendix B — Inflation and GDP-ER co-movement (empirical patterns)
- Mechanism: High USD invoicing mutes expenditure-switching; economies with sticky export prices face contractionary external shocks because depreciation does not raise export demand.
- Empirical scatterplots and patterns:
  - Figure 18: Average inflation vs GDP-ER correlation — countries with high inflation tend to exhibit countercyclical exchange rates.
  - Figure 19: Average inflation vs average excess returns — high average inflation associated with higher average excess returns (lower demand for local currency assets).
  - Figure 20: Average inflation vs dollar invoicing in exports — high dollar invoicing associated with higher average inflation.
  - Price level volatility (standard deviation of log(P_t)) produces similar results (Figures 21–23).

### Appendix C — Forward Returns
- Covered interest rate parity gives an alternative measure for currency returns:
  - Equation relation: S_t / F_t R^L_t = R^US_t (equation (83) in text).
  - Forward returns are valid returns even with documented CIP deviations; buying forward contracts is the most straightforward strategy to invest in other currencies.

### Appendix D — Details of the Model (key equations and mechanisms)
- Household FOCs and portfolio choice:
  - Real budget constraint (85); consumption FOC (86); labor FOC (87) leading to real wage relation (88).
  - Portfolio return and FOC for total savings (89)–(94).
  - Dollar share choice involves penalty/adjustment γ_Θ(Θ_t − Υ_t) and expected return differences (equations (93)–(94)).
- CES demand systems and price indices (95)–(103).
- Domestic Calvo pricing: reset-price condition (104)–(107).
- Export pricing in dollars: reset-price condition for dollar export price (109)–(112); θ_x governs degree of dominant-currency pricing.
- Banker leverage and currency choice:
  - Banker value function and incentive constraints (113)–(126).
  - Bank chooses dollar-liability share φ_t by maximizing (123), with FOC (124)–(126).

### Appendix E — From dollar liabilities and export pricing to the unconditional UIP premium (analytical decomposition)
- Five-step derivation connects bank’s conditional funding wedge to unconditional currency risk premium; key definitions and decompositions:
  - Bank-weighted funding wedge: U^B_t ≡ ν^LC_t − ν^FC_t (130).
  - Exact decomposition of simple local-currency premium p^LC_t ≡ R_t − R^*_t E_t s_{t+1} (144):
    - p^LC_t = U^B_t E_t[M^LC_{t+1}] + R^*_t E_t s_{t+1} (E_t[M^FC_{t+1}] − E_t[M^LC_{t+1}]) / E_t[M^LC_{t+1}] + R^*_t E_t[M^LC_{t+1}] Cov_t(M^FC_{t+1}, s_{t+1}) / E_t[M^LC_{t+1}] (equation (147)).
  - Around symmetric reference point (M^LC ≃ M^FC ≡ M^B), reduced form (148):
    - p^LC_t ≈ U^B_t E_t[M^B_{t+1}] + R^*_t E_t[M^B_{t+1}] Cov_t(M^B_{t+1}, s_{t+1}).
- Scaling of bank net-worth exposure to depreciation:
  - Direct log-linear loading ζ_N(θ_x, ̄φ) ≡ ̄R^* ̄s [ ̄L^FC(θ_x, ̄φ) − 1 ] ̄φ / ̄g_N(θ_x, ̄φ) (equation (154)).
  - Log-linear net-worth decomposition: b_N_{t+1} = b_N^{GE}_{t+1} − ζ_N(θ_x, ̄φ) b_s_{t+1} (155).
  - Covariance with depreciation decomposes into direct balance-sheet effect ζ_N V_s and general-equilibrium amplification B_N (156).
- Continuation-value and household SDF covariances:
  - Banker continuation-value linearization (157) and resulting covariance expression (158).
  - Household SDF covariance expressed via consumption and inflation co-movements; key coefficients χ_C(θ_x, ̄φ) and χ_π(θ_x, ̄φ) defined in (162)–(163) and combined in (164).
- Combined approximation for unconditional mean premium (equation (167)):
  - ̄p^LC ≡ E[p^LC_t] ≈ E[ Γ(θ_x, ̄φ)(φ_t − ̄φ) ] ̄M^LC + ̄R^* ̄s [ σχ_C(θ_x, ̄φ) − χ_π(θ_x, ̄φ) ] V_s(θ_x, ̄φ) + ̄R^* ̄s κ_N [ ζ_N(θ_x, ̄φ)V_s(θ_x, ̄φ) + B_N(θ_x, ̄φ) ] + ̄R^* ̄s [ R_Ω(θ_x, ̄φ) + T(θ_x, ̄φ) ].
- Comparative statics:
  - Direct effect of dollar liabilities on premium (168):
    - ∂̄p^LC / ∂̄φ |_{direct} ≈ ̄R^* ̄s κ_N ∂ζ_N(θ_x, ̄φ) / ∂̄φ V_s(θ_x, ̄φ) > 0.
  - Interaction of dollar liabilities and export-price stickiness (170) is positive in calibrated economy: higher ̄φ increases balance-sheet exposure; higher θ_x raises the price of that exposure via increased exchange-rate volatility and countercyclicality of depreciation.

### Appendix F — Additional quantitative results (model simulations)
- Response to foreign interest rate shocks (Figure 24):
  - Four economy profiles varying level of dollar-denominated debt and degree of dollar invoicing.
  - Key observation: amplification effect of trade frictions (dollar invoicing) is highly contingent on presence of financial frictions (dollar debt).
    - When foreign currency debt is low, choice of invoicing currency has negligible impact on real macro outcomes.
    - When foreign currency debt is high and dollar invoicing is high, downturns are drastically amplified — roughly doubling peak declines in investment and GDP versus low-dollar-debt with low invoicing.
- Financial flows after foreign interest rate shock (Figure 25):
  - Under high dollar debt, leverage rises to rebuild balance sheets; local residents decrease savings and economy attracts foreign capital in both local currency and foreign currency.
- Steady-state variation with respect to target dollar ratio ̄φ (Figure 26):
  - Increasing ̄φ raises exchange-rate volatility, UIP premium, and steady-state inflation.
  - Panels illustrated (a) Exchange rate volatility (φ), (b) Output and exchange rate comovement (φ), (c) UIP premium (φ), (d) Steady state inflation.
- Inflation and GDP-ER comovement (Figure 27):
  - Negative relationship between average inflation and comovement between output and exchange rate observed along both export-price stickiness (θ_x) and dollar debt (̄φ) margins.
- Equity premium (Figure 28):
  - Equity premium defined as E_t(R^k_{t+1}) − R_t.
  - Simulation result: equity premium falls as dollar invoicing and dollar debt increase because both R^k_t and R_t increase but R_t increases more.

*Dominant Currency Pricing and Currency Risk Premia — Working Paper No. WP/2026/158*

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_Source: https://www.imf.org/-/media/files/publications/wp/2026/english/wpiea2026158-source-pdf.pdf_