## wpiea2026056-source-pdf

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---

### Data and definitions
- Data and coverage:
  - Primary data: CryptoCompare exchange-level daily data from the secondary market for cryptoassets (including stablecoins).
  - Sample: 64 centralized exchanges (CEXs), including Binance, Coinbase, and Kraken.
  - Stablecoins analyzed: USDT, USDC, DAI, and BUSD.
  - Currencies: traded against 27 fiat currencies.
  - Sample period: January 2021 to November 2025.
  - For each stablecoin–fiat pair on each exchange collected: daily closing prices, trading volumes, and gross flows (inflows from fiat to stablecoin and outflows from stablecoin to fiat). Currency-level aggregates are volume-weighted averages of prices and sums of flows across exchanges.
- Key variable definitions and formulas:
  - Parity deviation D_{s,f,t} (equation (1)):
    - D_{s,f,t} ≡ (P_{s,f,t} / (P_{s,USD,t} e_{USD,f,t})) × 100.
    - Interpretation: D_{s,f,t} = 1 implies no arbitrage between direct and indirect routes; D_{s,f,t} > 1 implies stablecoin s is relatively expensive in fiat f; D_{s,f,t} < 1 implies relatively cheap.
  - Net inflow rate g_{f,s,t} (equation (2)):
    - g_{f,s,t} = (inflows_{f,s,t} − outflows_{f,s,t}) / market size_{f,s,t−1}, expressed in percentage terms and winsorized at the 1/99th percentile.
  - CIP deviation δ:
    - δ ≡ (F − S)/S − (i_H − i_USD); δ < 0 indicates a dollar premium (synthetic dollar funding more expensive than direct dollar borrowing).
- Special handling:
  - For ARS, NGN, and UAH, parallel exchange rates from Haver and IMF country desks are used to capture effective trading conditions for agents without access to rationed official rates.

### Descriptive statistics (selected Table 1 highlights for USDT across 27 fiats)
- Selected currency rows (currency — N — Volume — Volatility — Mean — Median — Max):
  - USD — 20 — 333.13 — 0.76% — 0.05% — 0.03% — 0.80%
  - KRW — 4 — 123.73 — 11.50% — 2.51% — 1.90% — 10.53%
  - EUR — 15 — 123.27 — 10.81% — 0.31% — 0.23% — 2.21%
  - TRY — 6 — 77.07 — 6.28% — 1.08% — 0.68% — 20.98%
  - BRL — 10 — 16.02 — 13.80% — 0.81% — 0.71% — 3.80%
  - ARS — 2 — 2.59 — 23.10% — 1.06% — 0.61% — 14.80%
  - NGN — 2 — 0.04 — 13.68% — 4.54% — 3.44% — 24.39%
  - KES — 1 — 0.00 — 83.38% — 3.25% — 1.26% — 13.74%
- Observations from Table 1:
  - Trades quoted in USD show the largest volume (333.13 million USD) and the lowest volatility (0.76%).
  - Several emerging-market currencies (e.g., ARS 23.10%, NGN 13.68%, KES 83.38%) show much higher volatility and larger average parity deviations.

### Stylized empirical findings (Section 5 summary)
- Stylized fact #1: sizable parity deviations between stablecoin and traditional FX markets, heterogeneous across currencies:
  - Major liquid currencies (USD, EUR, GBP): small parity deviations clustered around zero.
  - Other currencies (COP, ZAR, BRL, TRY, ARS, NGN, UAH): larger and more dispersed parity deviations (up to one order of magnitude in some cases).
- Stylized fact #2: net inflows into stablecoins correlated with three outcomes:
  - (2a) Parity deviations: positive and contemporaneous association — increases in net stablecoin inflows associated with immediate and statistically significant rises in parity deviations.
  - (2b) Spot FX depreciation: net stablecoin inflows associated with subsequent depreciation of the domestic currency in traditional spot FX markets.
  - (2c) CIP deviations (deterioration in synthetic dollar funding): stablecoin inflows correlated with declines in CIP deviations (greater dollar premium), stronger at short maturities.
- Estimation approach:
  - Linear projection regressions pooling four USD-pegged stablecoins:
    - Y_{f,s,t+h} = β_h g_{f,s,t} + γ X_{f,s,t} + δ_{f,s} + ζ_{f,s,t+h} for horizons h = 0,...,10.
  - Figure 3 (described): cumulative impact of a one-standard deviation increase in net inflows on parity deviations, exchange rates, and CIP over horizons h = 0,...,15 days.

### Structural model: mechanism, equilibrium, and comparative statics (Section 4.1–4.2)
- Environment and actors:
  - Two-country static model (Home currency H and USD); prices y (stablecoin parity deviation) and δ (CIP deviation) are central.
  - Households demand stablecoins and synthetic dollars with linear demand:
    - D_s c = ̄D_s c − α_s c y; D_s y n = ̄D_s y n + α_δ δ.
  - Intermediary incurs quadratic costs with cross-market term:
    - C(B_s y n, B_s c) = Γ_δ/2 (B_s y n)^2 + Γ_s c/2 (B_s c)^2 + Γ_×/2 (B_s y n + B_s c)^2.
  - Γ_× captures cross-market cost; when Γ_× = 0 markets decouple.
- Equilibrium analytical expressions:
  - y^* = (1/Δ)[ N_y · ̄ρ_s c + Γ_× · ̄ρ_s y n ].
  - −δ^* = (1/Δ)[ N_δ · ̄ρ_s y n + Γ_× · ̄ρ_s c ].
  - s^* = (1/ν_s)(−η_δ δ^* + η_y y^* + ̄Q).
  - Comparative statics to a marginal increase in stablecoin net demand ̄ρ_s c:
    - ∂ y^* / ∂ ̄ρ_s c = N_y / Δ > 0.
    - ∂ δ^* / ∂ ̄ρ_s c = − Γ_× / Δ ≤ 0 (strict if Γ_× > 0).
    - ∂ s^* / ∂ ̄ρ_s c = (1/ν_s)[ −η_δ (∂ δ^* / ∂ ̄ρ_s c) + η_y (∂ y^* / ∂ ̄ρ_s c) ] > 0.
- Multi-country extension and identification intuition:
  - Cross-book participants allocate a finite conversion budget W across countries: Σ_f S_s c_f = W.
  - Idiosyncratic reallocation v_f with Σ_f v_f = 0 links countries; reallocation shocks elsewhere provide instruments for local flows.

### Granular Instrumental Variable (GIV) identification and implementation (Section 4.3, Appendix A, G)
- GIV construction (two-step purging and aggregation):
  - Step 1: purge net inflow g_f,s,t of common global factors:
    - g_f,s,t = λ'_f,s F_t + FE_s,t + FE_f,s + u_f,s,t; retain residual u_f,s,t.
  - Step 2: construct Z_GIV_j,s,t = Σ_{k≠j} ω_k,s · u_k,s,t with weights ω_k,s equal to market shares.
- Two-stage estimation:
  - First stage: g_j,s,t = θ Z_GIV_j,s,t + κ' X_j,t + ν_j,s,t (controls include log VIX, log nominal broad dollar index, monthly bitcoin return, USDT price in USD lags, factors, coin-currency fixed effects).
  - Second stage: Y_j,s,t+h = β_h · ĝ_j,s,t + γ X_j,s,t + φ_j,s + ζ_j,s,t+h.
- Instrument validity logic:
  - Relevance: shocks elsewhere reallocate cross-book capacity and affect local flows (Cov(g_f, Z_f) ≠ 0).
  - Exogeneity/exclusion: idiosyncratic shocks in other countries are independent of local unobservables conditional on controls.

### First-stage and instrument strength (selected results from Table 3)
- GIV coefficients across specifications: −0.153***, −0.111***, −0.067***, −0.152***, −0.113***, −0.070*** (standard errors: (0.0160), (0.0151), (0.0164), (0.0169), (0.0160), (0.0169)).
- Fiat-specific factor 1 estimates: 1.054***, 1.051***, 1.036***, 1.049***, 1.049***, 1.036***.
- Observations: 42,142 (columns 1–3) and 40,160 (columns 4–6).
- R-squared: 0.215, 0.312, 0.358, 0.219, 0.315, 0.362.
- Robust F-statistics: 4353.5, 24058.2, 15647.6, 2839.0, 6324.9, 4759.7.
- Interpretation: granular instrument is strong and highly significant across specifications; robust F-statistics well above conventional thresholds.

### Empirical IV estimates (dynamic responses and mapping to structural parameters)
- Dynamic IV responses to a one standard deviation instrumented net inflow shock (Figure 5 summary):
  - Parity deviations: immediate sharp increase of approximately 40 basis points on impact; highly persistent, decaying over ten days.
  - Cumulative FX depreciation: positive, statistically significant depreciation; magnitude declines over time.
  - CIP deviations:
    - 3-month CIP: significant decline (higher dollar premium) at short horizons.
    - 12-month CIP: negligible and statistically insignificant in short-term.
- Structural interpretation (Proposition 4 and Appendix A mappings):
  - Estimated parity deviation response: ˆβ_IV_y ≈ 40 basis points per one percent flow shock — interpreted as marginal cost of stablecoin intermediation.
  - Estimated CIP response: ˆβ_IV_δ reported as ≈ −17.5 basis points in discussion (with an empirical mapping focus on −6 bps in calibration/summary moments); calibration reports |ˆβ_IV_δ| ≈ 6 bps in baseline supply-response perspective.
  - Estimated exchange rate response: ˆβ_IV_s ≈ 5–10 basis points.
  - Reported ratio measures:
    - |ˆβ_IV_δ| / ˆβ_IV_y ≈ 0.44 reported in one discussion (roughly 44 percent).
    - Quantitative summary reports an estimated spillover ratio approximately 0.15 indicating roughly one-sixth of stablecoin price pressure transmits to synthetic dollar funding costs.
  - Note: the document reports both ratio estimates in different contexts (empirical mapping vs. calibration/supply-response panels); both figures are preserved as reported.

### Structural calibration and counterfactuals (Section 6.1–6.2, Table 4 and Table 5)
- Calibration targets and fixed parameters:
  - α_sc = 0.55; ̃α_δ = 0.50; η_δ ≈ 0.48; ν_s = 1 normalization; Γ_δ calibrated to match N_δ / A_sc = 15.5 basis points.
- Calibrated supply-side parameters (Panel A Table 4):
  - Γ_sc = 0.337 (stablecoin intermediation cost) — consistent with GIV β_IV_y = 40 bps.
  - Γ_× = 0.065 (cross-market intermediation cost) — consistent with GIV |β_IV_δ| = 6 bps.
  - η_y = 0.078 (SC-to-spot substitution) — consistent with β_IV_s ≈ 6 bps.
- Swap intermediation and normalizations (Panel B & C):
  - Γ_δ = 0.093; ν_s = 1.00.
  - Comparison: Γ_sc = 0.337 is about 3.6 times Γ_δ = 0.093; Γ_× = 0.065 < Γ_sc and Γ_δ but Γ_× / Γ_δ ≈ 0.70.
- Counterfactual price responses to a 1% stablecoin demand shock (Table 5 selected entries):
  - Panel A (equilibrium ∂price/∂ ̄ρ_sc per 1% demand shock):
    - Baseline: Δy = 32.8 bps, Δδ = −4.9 bps, Δs = 4.9 bps.
    - 2×Γ_×: Δy = 36.7 bps, Δδ = −9.3 bps, Δs = 7.3 bps.
    - 0.5×Γ_×: Δy = 30.7 bps, Δδ = −2.5 bps, Δs = 3.6 bps.
    - Γ_× = 0: Δy = 28.4 bps, Δδ = 0.0 bps, Δs = 2.2 bps.
  - Panel B (supply-response / β_IV per 1% instrumented flow):
    - Baseline: β_IV_y = 40.0 bps, β_IV_δ = −6.0 bps, β_IV_s = 6.0 bps, |β_δ|/β_y = 0.151.
    - 2×Γ_×: β_IV_y = 45.9 bps, β_IV_δ = −11.7 bps, β_IV_s = 9.2 bps, |β_δ|/β_y = 0.255.
    - 0.5×Γ_×: β_IV_y = 36.9 bps, β_IV_δ = −3.1 bps, β_IV_s = 4.3 bps, |β_δ|/β_y = 0.083.
    - Γ_× = 0: β_IV_y = 33.7 bps, β_IV_δ = 0.0 bps, β_IV_s = 2.6 bps, |β_δ|/β_y = 0.000.
- Counterfactual insights:
  - Γ_× is the primary driver of spillovers to traditional FX markets; increasing Γ_× amplifies CIP spillovers and exchange rate responses.
  - If Γ_× → 0 (market segmentation) CIP spillovers vanish and exchange rate spillovers roughly halve.
  - Policy interpretation: tighter capital treatment or restricted netting that raises Γ_× increases transmission; environments allowing international offsetting lower Γ_× and dampen spillovers.

### Dynamic extension and amplification (Section 6.3, Appendix F)
- Dynamic model features:
  - Stablecoin demand ̄D_sc,t follows AR(1) with ρ = 0.8 (half-life ~ three days).
  - Intermediary wealth W_t scales quadratic costs; costs scaled by W_t in objective.
- Representative dynamic impulse responses (static-steady-state and dynamic calibrations):
  - Static/dynamic steady-state impact (steady state wealth):
    - Stablecoin parity deviation y: 34 basis points (impact).
    - CIP deviation δ: −5 basis points (impact) in one reported dynamic summary.
    - Exchange rate depreciation s: 5 basis points (impact).
  - Appendix F calibrated dynamic impulse response (alternate calibration table):
    - One percent shock (from steady state): y = 34 bps, δ = −15 bps, s = 3.5 bps; immediate wealth drop ≈ 5 percent; decay half-life ≈ four days.
    - Cumulative amplification: A_y = 5.4; CIP cumulative amplification = 5.6; persistence-only amplification 1/(1−ρ) = 5 with additional 8–12% from wealth channel.
- State-dependence and amplification:
  - When initial wealth falls, identical shocks produce larger responses:
    - Initial Wealth = ̄W: Δy = 34 bps, Δδ = −15 bps, Δs = 3.5 bps (Amplification = 1.0×).
    - Initial Wealth = 0.75 ̄W: Δy = 45 bps, Δδ = −20 bps, Δs = 4.7 bps (Amplification = 1.3×).
    - Initial Wealth = 0.50 ̄W: Δy = 68 bps, Δδ = −30 bps, Δs = 7.0 bps (Amplification = 2.0×).
  - Doubling Γ_× in dynamic model:
    - y impact increases (example: from 34 to 78 basis points in one counterfactual), CIP spillover can increase substantially (e.g., −15 to −58 basis points in reported counterfactual).
- Redemption frictions and run dynamics (Appendix F.8):
  - Haircut specification h_t = 1 − η · |B_s c_t| / W_t; run threshold ̄η = W_t / (shock size).
  - Amplification convex in η; at η = 0.9 ̄η impact effects roughly ten times larger than frictionless baseline in described illustrations.
  - Combined flow and redemption-friction shocks can multiply baseline spillovers (example: baseline flow shock 40 bps parity and 17.5 bps CIP; moderate friction raises impacts by factor 1.7; severe friction up to factor 5).

### Policy implications and recommendations (Section 6 and Appendix E, conclusion)
- Core policy messages:
  - Magnitude of spillovers critically depends on intermediary balance sheet linkages (Γ_×). Policies affecting Γ_× (capital requirements that treat stablecoin and swap exposures as substitutes) will influence transmission to FX markets.
  - Capital frameworks that permit netting of stablecoin and FX swap exposures lower effective Γ_× and dampen spillovers; ring-fencing crypto activities eliminates the balance-sheet channel but may reduce cross-market liquidity.
  - Prudential measures on stablecoin intermediaries (capital buffers, reserve liquidity mandates, limits on concentrated currency exposures) shrink spillover channels by preserving risk-bearing capacity.
  - Reserve liquidity requirements (reducing η) and intermediary capital requirements (raising W_t) are complementary in mitigating run risk and amplification.
  - Monitoring the spillover ratio as stablecoin markets grow provides an early-warning indicator of increasing crypto–FX integration.
- Suggested avenues for future research (verbatim themes preserved):
  - Investigate how spillover magnitudes vary with capital account openness, exchange rate regime, and local FX market depth.
  - Analyze how stablecoin design features (algorithmic vs. reserve-backed vs. CBDC) map into intermediation costs and spillover profiles.
  - Track the spillover ratio over time as a gauge of crypto–FX integration.
  - Study whether stablecoin flows weaken the effectiveness of monetary policy and capital flow management measures in economies where they offer an alternative channel for cross-border capital movements.

*Italicized source: Authors’ calculations based on CryptoCompare exchange-level trading data; material from wpiea2026056-source-pdf.*

### Section 5 presents the empirical specification, our empirical approach, our main results, and

### wpiea2026056-source-pdf - Section 5 presents the empirical specification, our empirical approach, our main results, and

### Data and definitions
- Data sources and coverage
  - Primary data: CryptoCompare exchange-level daily data from the secondary market for cryptoassets (including stablecoins).
  - Sample: 64 centralized exchanges (CEXs), including Binance, Coinbase, and Kraken.
  - Stablecoins analyzed: USDT, USDC, DAI, and BUSD (four major USD-pegged stablecoins).
  - Currencies: traded against a broad set of 27 fiat currencies.
  - Sample period: January 2021 to November 2025.
  - For each stablecoin–fiat pair on each exchange we collect: daily closing prices, trading volumes, and gross flows (inflows from fiat to stablecoin and outflows from stablecoin to fiat).
  - Currency-level aggregates: volume-weighted averages of prices and sums of flows across exchanges.

- Institutional observation
  - Stablecoin inflows from non-USD currencies embed an implicit FX conversion, creating a parallel, stablecoin-based FX ecosystem distinct from traditional, "off-chain" FX markets.

- Table 1: Descriptive statistics for USDT (traded against 27 fiat currencies)
  - Note: N denotes the number of exchanges included in the sample. Volume refers to daily trading volume measured in million USD, averaged over 2025Q2. Volatility is reported for 2025Q2, expressed at an annualized percentage rate. The mean, median, and maximum of parity deviations are computed using observations after 2021, following equation (1). All series are constructed from exchange-level data. Parity deviations for ARS, NGN, and UAH are measured based on parallel rates estimated by Graf von Luckner et al. (2024).
  - Selected rows (currency — N — Volume — Volatility — Mean — Median — Max):
    - USD — 20 — 333.13 — 0.76% — 0.05% — 0.03% — 0.80%
    - KRW — 4 — 123.73 — 11.50% — 2.51% — 1.90% — 10.53%
    - EUR — 15 — 123.27 — 10.81% — 0.31% — 0.23% — 2.21%
    - TRY — 6 — 77.07 — 6.28% — 1.08% — 0.68% — 20.98%
    - BRL — 10 — 16.02 — 13.80% — 0.81% — 0.71% — 3.80%
    - THB — 1 — 14.16 — 11.02% — 0.77% — 0.43% — 8.50%
    - GBP — 8 — 12.24 — 9.16% — 0.30% — 0.22% — 2.99%
    - MXN — 2 — 7.48 — 11.36% — 0.48% — 0.37% — 2.97%
    - TWD — 1 — 5.60 — 15.60% — 0.52% — 0.43% — 2.52%
    - IDR — 2 — 3.56 — 8.55% — 0.36% — 0.28% — 2.70%
    - ARS — 2 — 2.59 — 23.10% — 1.06% — 0.61% — 14.80%
    - CHF — 1 — 2.27 — 14.68% — 0.31% — 0.23% — 3.35%
    - HKD — 1 — 2.20 — 2.26% — 0.20% — 0.15% — 1.26%
    - AUD — 5 — 2.07 — 14.45% — 0.40% — 0.29% — 8.05%
    - PHP — 1 — 1.45 — 5.21% — 0.27% — 0.22% — 1.80%
    - UAH — 2 — 1.18 — 9.59% — 1.67% — 0.85% — 10.28%
    - COP — 2 — 1.15 — 12.25% — 1.49% — 1.44% — 5.56%
    - CAD — 2 — 0.89 — 7.27% — 0.34% — 0.25% — 8.37%
    - PLN — 3 — 0.72 — 13.92% — 2.32% — 0.64% — 40.94%
    - AED — 1 — 0.71 — 1.82% — 0.14% — 0.12% — 0.92%
    - INR — 3 — 0.63 — 14.09% — 4.83% — 4.78% — 13.19%
    - ZAR — 2 — 0.23 — 12.06% — 2.05% — 1.96% — 11.38%
    - SGD — 2 — 0.12 — 6.68% — 1.59% — 0.26% — 24.11%
    - JPY — 2 — 0.09 — 29.12% — 0.41% — 0.23% — 13.81%
    - NZD — 1 — 0.05 — 15.63% — 1.59% — 0.46% — 16.51%
    - NGN — 2 — 0.04 — 13.68% — 4.54% — 3.44% — 24.39%
    - KES — 1 — 0.00 — 83.38% — 3.25% — 1.26% — 13.74%
  - Observations from Table 1:
    - Trades quoted in USD show the largest volume (333.13 million USD) and the lowest volatility (0.76%).
    - Currencies such as ARS and NGN show lower volumes but much higher volatility (e.g., ARS 23.10%, NGN 13.68%) and larger average parity deviations.

- Key variable definitions and formulas
  - Parity deviation D_{s,f,t} (equation (1)):
    - D_{s,f,t} ≡ (P_{s,f,t} / (P_{s,USD,t} e_{USD,f,t})) × 100
    - Interpretation:
      - D_{s,f,t} = 1 implies no arbitrage between the direct and indirect routes.
      - D_{s,f,t} > 1: stablecoin s is relatively expensive in fiat f (arbitrage: buy in USD, sell in f).
      - D_{s,f,t} < 1: stablecoin s is relatively cheap in fiat f (arbitrage: buy in f, sell in USD).
  - Net inflow rate g_{f,s,t} (equation (2)):
    - g_{f,s,t} = (inflows_{f,s,t} − outflows_{f,s,t}) / market size_{f,s,t−1}
    - Expressed in percentage terms and winsorized at the 1/99th percentile.
    - Interpretation: net new funding from fiat f into the stablecoin ecosystem (fiat-to-stablecoin conversion).
  - CIP deviation δ:
    - Matches the empirical definition in Section 4: δ ≡ (F − S)/S − (i_H − i_USD), where i_H and i_USD are interest rates and F is the forward rate.
    - Interpretation: when δ < 0, synthetic dollar funding (via FX swaps) is more expensive than direct dollar borrowing (a dollar premium).

- Special handling
  - For currencies with active on-shore parallel exchange-rate markets (ARS, NGN, UAH), parallel exchange rates from Haver and IMF country desks are used to capture effective trading conditions for agents without access to rationed official exchange rates.

### Stylized facts (reduced-form findings)
- Stylized fact #1: Sizable parity deviations between stablecoin and traditional FX markets, with heterogeneity across currencies
  - Evidence: distribution of time-averaged parity deviations for USDT across fiat currencies (2021–2025).
  - For major, highly liquid currencies (USD, EUR, GBP): small parity deviations clustered around zero.
  - For other currencies (COP, ZAR, BRL, TRY, ARS, NGN, UAH): larger and more dispersed parity deviations (up to one order of magnitude in some cases).

- Stylized fact #2: Net inflows into stablecoins are correlated with three outcomes
  - (2a) Parity deviations:
    - Positive and contemporaneous association: a positive increase in net stablecoin inflows is associated with an immediate and statistically significant rise in parity deviations.
  - (2b) (Non-crypto) exchange rate depreciation:
    - Net stablecoin inflows are associated with a subsequent depreciation of the domestic currency in the traditional spot FX market, consistent with increased local-currency selling to buy stablecoins.
  - (2c) Decline in CIP deviations (a higher dollar premium):
    - Stablecoin inflows are correlated with a decline in CIP deviations, indicating increased dollar premium; effects stronger at short maturities consistent with binding balance-sheet constraints.

- Estimation approach for stylized fact #2
  - Linear projection regressions pooling all four USD-pegged stablecoins.
  - Baseline specification for horizons h = 0, 1, ..., 10 (equation (3)):
    - Y_{f,s,t+h} = β_h g_{f,s,t} + γ X_{f,s,t} + δ_{f,s} + ζ_{f,s,t+h}
    - Y_{f,s,t+h} are outcome variables (parity deviations, change in exchange rates, CIP deviations).
    - g_{f,s,t} is net inflows (scaled in percentage terms and winsorized at the 1st and 99th percentiles).
    - δ_{f,s} are stablecoin–fiat fixed effects; X contains controls.
    - β_h traces the conditional projection of the horizon-h response to a unit inflow change.
  - Figure 3 results (described):
    - Shows cumulative impact of a one-standard deviation increase in stablecoin net inflows on parity deviations, exchange rates (cumulative FX depreciation), and CIP deviations over horizons h = 0, ..., 15 days (dots with 95% confidence intervals).

- Endogeneity concern
  - Anticipated depreciation could drive both increased stablecoin demand and the observed exchange rate/CIP movements, complicating causal interpretation; motivates structural model for identification.

### Structural model and identification (overview and key implications)
- Purpose
  - Provide structural foundations for identification and counterfactuals (Section 6), and map reduced-form IV coefficients to structural parameters.

- Four-step argument
  1. Single Home-country setting:
     - An intermediary connecting the stablecoin and FX swap markets generates the triad of effects documented in Section 3: higher stablecoin demand raises parity deviations, widens CIP deviations (a higher dollar premium), and depreciates the local currency (Sections 4.1–4.2).
  2. Cross-market cost parameter Γ_×:
     - Γ_× (the cost the intermediary faces on its total currency exposure) is the sole channel through which stablecoin stress spills over to CIP deviations. When Γ_× = 0, the two markets decouple entirely.
  3. Multi-country extension:
     - Cross-book participants active on several fiat–stablecoin exchange books allocate a finite conversion budget across countries; their reallocation in response to local shocks elsewhere creates cross-country linkages used for identification (Section 4.2).
  4. Identification of structural parameters:
     - The IV coefficients identify: the marginal cost of intermediation, the cross-market spillover intensity, and provide a direct test of market integration (Section 4.2).

- Model implications for empirical work
  - Provides a structural interpretation for the reduced-form correlations and motivates counterfactual exercises (Section 6) including a dynamic extension that characterizes impulse responses and balance-sheet amplification.

_Italicized source: Authors’ calculations based on CryptoCompare exchange-level trading data; material from the specified content unit._

### 4.1 The model

### 4.1 The model

### Environment
- Two-country static economy: Home (currency 퐻) and the United States (USD). Spot exchange rate S quoted as units of 퐻 per USD; normalization S = 1. Analysis in log deviations s = log S (s > 0: depreciation; s < 0: appreciation).
- Two central prices:
  - Stablecoin parity deviation: y ≡ p_s c − s, where p_s c = log P_s c (log stablecoin price in currency 퐻). y > 0: stablecoins trade at a premium relative to spot FX. (Equation (4))
  - CIP deviation: δ ≡ (F − S)/S − (i_H − i_USD). δ < 0 indicates a dollar premium in the swap market (synthetic dollar funding more expensive than direct dollar borrowing). (Equation (5))
- Model is static; extensions to persistent shocks and intermediary balance sheet dynamics noted (references to Section 6.3 and the literature).

### Home households
- Households demand stablecoins and synthetic dollars (via FX swaps); imperfect substitutes with linear demand in cost:
  - D_s c = ̄D_s c − α_s c y (Equation (6))
  - D_s y n = ̄D_s y n + α_δ δ (Equation (7))
- Baseline demands ̄D_s c and ̄D_s y n; elasticities α_s c, α_δ > 0.
- Baseline stablecoin demand ̄D_s c captures shocks (capital flight, crypto commerce growth, regulatory changes) that drive empirical analysis.

### Global stablecoin supply and relative supply
- Stablecoins issued against dollar-denominated reserves. At the daily frequency, stablecoin supply is highly elastic; set P_s,USD_t = 1 (perfect elasticity assumption and empirical note that USDT/USD deviates from par by only 0.05% on average).

### US dollar supply to FX swap markets
- US dollar supply to Home FX swap markets modeled as:
  - L_US = ̄L − α_L δ (Equation (8))
- ̄L > 0 baseline supply; α_L > 0 supply elasticity (supply increases when dollar premium widens).

### Intermediary (dealers, market makers, arbitrageurs)
- Intermediary roles:
  - Stablecoin market: intermediary acquires stablecoins from global pool (trade near par USD) and sells to Home households for local currency; intermediary’s stablecoin position B_s c and earns y per unit.
  - FX swap market: intermediary intermediates FX swaps; swap position B_s y n and earns |δ| as compensation for balance sheet costs / counterparty risk.
- Cost structure: quadratic convex costs dependent on both positions with cross-market term:
  - C(B_s y n, B_s c) = Γ_δ/2 (B_s y n)^2 + Γ_s c/2 (B_s c)^2 + Γ_×/2 (B_s y n + B_s c)^2 (Equation (9))
  - Γ_δ, Γ_s c, Γ_× ≥ 0. Γ_× captures cross-market cost: total currency 퐻 exposure raises marginal costs across markets and generates spillovers when Γ_× > 0.
- Intermediary profit maximization:
  - max_{B_s y n, B_s c} (−δ)·B_s y n + y·B_s c − C(B_s y n, B_s c) (Equation (10))
  - Note: δ < 0 in equilibrium → intermediary revenue from swaps is (−δ)·B_s y n = |δ|·B_s y n > 0.

### Market clearing
- Stablecoin market clearing:
  - B_s c = D_s c + S_s c (Equation (11))
  - Define net demand pressure ̄ρ_s c ≡ ̄D_s c + S_s c → B_s c = ̄ρ_s c − α_s c y.
- FX swap market clearing:
  - D_s y n = L_US + B_s y n (Equation (12))
  - Define ̄ρ_s y n ≡ ̄D_s y n − ̄L and ̃α_δ ≡ α_δ + α_L → B_s y n = ̄ρ_s y n + ̃α_δ δ.
- Spot market determination:
  - Q_spot = ̄Q − η_δ δ + η_y y + ν_s s, with s = 0 (?) (text gives relation: Q_spot = ̄Q − η_δ/ν_s δ + η_y/ν_s y + ̄Q; reduced-form specification (Equation (13) and discussion))
  - ̄Q baseline net dollar demand independent of stablecoin/swap conditions; η_δ, η_y > 0 capture substitution toward spot when swaps or stablecoins become expensive; ν_s > 0 standard exchange rate elasticity.
  - When δ becomes more negative (dollar premium widens), households substitute toward spot dollar purchases (η_δ sign convention noted).

### Equilibrium and comparative statics
- Intermediary first-order conditions (marginal revenue = marginal cost):
  - −δ = (Γ_δ + Γ_×) B_s y n + Γ_× B_s c (Equation (14))
  - y = Γ_× B_s y n + (Γ_s c + Γ_×) B_s c (Equation (15))
  - Left-hand side of (14) is −δ > 0 since δ < 0 in equilibrium.
- Equilibrium characterization (unique equilibrium in (−δ, y, s)):
  - y^* = (1/Δ)[ N_y · ̄ρ_s c + Γ_× · ̄ρ_s y n ] (Equation (16))
  - −δ^* = (1/Δ)[ N_δ · ̄ρ_s y n + Γ_× · ̄ρ_s c ] (Equation (17))
  - s^* = (1/ν_s)(−η_δ δ^* + η_y y^* + ̄Q) (Equation (18))
  - Definitions: A_δ ≡ 1 + ̃α_δ (Γ_δ + Γ_×), A_s c ≡ 1 + α_s c (Γ_s c + Γ_×), B ≡ α_s c Γ_×, C ≡ ̃α_δ Γ_×, N_y ≡ A_δ (Γ_s c + Γ_×) − ̃α_δ Γ_×^2, N_δ ≡ A_s c (Γ_δ + Γ_×) − α_s c Γ_×^2, Δ ≡ A_δ A_s c − B C > 0.
- Interpretation:
  - Each price driven by own-market demand pressure (weighted by N_y or N_δ) and by cross-market spillover via Γ_×.
  - If Γ_× = 0, markets decouple.
- Comparative statics (Proposition 2) for an increase in stablecoin net demand ̄ρ_s c:
  - (i) Own-market effect: ∂ y^* / ∂ ̄ρ_s c = N_y / Δ > 0. (Equation (19))
  - (ii) Cross-market spillover to CIP: ∂ δ^* / ∂ ̄ρ_s c = − Γ_× / Δ ≤ 0, strict if Γ_× > 0, zero when Γ_× = 0. (Equation (20))
  - (iii) Total FX impact (depreciation): ∂ s^* / ∂ ̄ρ_s c = (1/ν_s)[ −η_δ (∂ δ^* / ∂ ̄ρ_s c) + η_y (∂ y^* / ∂ ̄ρ_s c) ] > 0. (Equation (21))
- Corollary 1 (Segmentation): When Γ_× = 0, CIP spillover vanishes and markets decouple (∂ δ^* / ∂ ̄ρ_s c = 0).
- Mechanism summary:
  - Higher stablecoin demand → intermediary expands B_s c → marginal costs rise → parity deviation y increases.
  - If Γ_× > 0, expanded B_s c raises marginal cost of swap provision → widens CIP deviation δ (balance sheet externality).
  - Both channels cause substitution to spot and cause local currency depreciation; CIP spillovers provide direct evidence of balance sheet linkages.

### Multiple currencies and identification (Section 4.2 preview)
- Extension to F home countries indexed f ∈ {1,...,F} to study cross-country spillovers and to build a structural Granular Instrumental Variable (GIV).
- Each country follows the single-country equilibrium (Proposition 1) with net demand pressure ̄ρ_s c_f = ̄D_s c_f + S_s c_f.
- Cross-book participants (traders active across multiple fiat-stablecoin books) introduce S_s c_f. They face a finite total conversion budget:
  - Σ_{f=1}^F S_s c_f = W (Equation (22))
  - Budget constraint implies cross-country linkages: reallocation to one country reduces participation in others.
- Cross-book participant allocation summarized by conversion urgency parameter θ_f > 0; optimal allocation yields:
  - S_s c_f = ̄S_s c_f + v_f, with Σ_f v_f = 0 (Equation (23))
  - v_f is idiosyncratic reallocation driven by urgency shocks elsewhere.
- Cross-country transmission (Proposition 3): Reallocation from country B to country A (S_s c_A up, S_s c_B down) implies for country B (A ≠ B):
  - ∂ y_B / ∂ S_s c_B > 0,
  - ∂ δ_B / ∂ S_s c_B < 0,
  - ∂ s_B / ∂ S_s c_B > 0. (Equation (24))
- This establishes that demand shocks elsewhere are relevant for local prices and underpin the identification strategy.

### Identification strategy with Granular Instrumental Variables (GIV) (Section 4.3 summary)
- OLS bias: local stablecoin demand shocks correlate with unobserved local factors that affect parity deviations, CIP, and exchange rates (e.g., anticipated depreciation drives both capital flight into stablecoins and depreciation itself).
- GIV construction:
  - Total demand on book f: ̃D_s c_f ≡ ̄D_s c_f + S_s c_f. Decompose:
    - ̃D_s c_f = ̄D_0 + ̄S_s c_f + φ μ + u_D_f + v_f ≡ ̃u_f (Equation (25))
    - ̃u_f combines local household shocks (u_D_f) and cross-book reallocation (v_f); estimated as residuals from a factor model applied to observed net inflow rates.
  - Instrument for country f:
    - Z_f ≡ Σ_{f′ ≠ f} w_{f′} ˆ̃u_{f′} (Equation (26))
    - Weights w_{f′} ≡ ̄D_s c_{f′} / Σ_{k ≠ f} ̄D_s c_k (demand-weighted shares). Instrument aggregates idiosyncratic total demand shocks from other countries, excluding f.
- Instrument validity intuition:
  - Relevance: demand shocks elsewhere reduce demand to f (Cov(g_f, Z_f) ≠ 0).
  - Exogeneity: idiosyncratic shocks in other countries are uncorrelated with local unobservables (Cov(Z_f, ε_f) = 0).
  - Exclusion: Z_f affects outcomes only through the stablecoin channel.
- Proposition 4 (preview): IV coefficients identify structural objects such as the marginal cost of intermediation, cross-market spillover intensity (Γ_×), and provide a test of market integration.

*Source: IMF working paper section 4.1–4.3 (model, multicurrency extension, and GIV identification).*

### Appendix A formalizes this.

### Appendix A formalizes this.

### IV identification (Proposition 4)
- Under Assumption 1, the IV coefficients identify the causal effects of stablecoin flows on prices:
  - (i) Stablecoin parity deviation coefficient 훽_IV_y — marginal cost of intermediation (Table 2, row (i)):
    - 훽_IV_y = Cov(y_f, Z_f) / Cov(g_f, Z_f) = 휕y_sc / 휕 ̄휌_sc · γ_g = N_y / A_δ  (equation (27))
  - (ii) CIP spillover coefficient 훽_IV_δ — cross-market externality (Table 2, row (ii)):
    - 훽_IV_δ = Cov(δ_f, Z_f) / Cov(g_f, Z_f) = 휕δ_sc / 휕 ̄휌_sc · γ_g = − Γ_× · A_δ  (equation (28))
  - (iii) Exchange rate coefficient 훽_IV_s — total FX impact (Table 2, row (iii)):
    - 훽_IV_s = 휕s_sc / 휕 ̄휌_sc · γ_g = 1/ν_s [ −η_δ 훽_IV_δ + η_y 훽_IV_y ] = η_δ Γ_× + η_y N_y / ν_s A_δ  (equation (29))
  - (iv) Spillover ratio |훽_IV_δ|/훽_IV_y — market integration test (Table 2, row (iv)):
    - |훽_IV_δ| / 훽_IV_y = |휕δ_sc / 휕 ̄휌_sc| / 휕y_sc / 휕 ̄휌_sc = Γ_× · N_y ∈ (0, 1)  (equation (30))
- Notes and identification mechanics:
  - Under perfectly elastic supply, instrument variation arises from cross-book demand reallocation. With finite supply elasticity, idiosyncratic household shocks u_D_f' provide additional variation through the dollar price P_s,USD_t.
  - Appendix G shows the IV coefficient identifies N_y / A_δ under both mechanisms; only instrument statistical power differs.
  - Given that USDT/USD deviates from par by only 0.05% on average, the cross-book reallocation channel is likely dominant.

### Implementing the Granular Instrument (GIV)
- Construction steps:
  - Step 1: Purge net inflow rate g_f,s,t of common global factors by estimating, for each stablecoin s:
    - g_f,s,t = λ'_f,s F_t + FE_s,t + FE_f,s + u_f,s,t  (equation (31))
    - F_t: vector of common factors (e.g., global risk appetite, broad crypto market trends)
    - FE_s,t: stablecoin-time fixed effects
    - FE_f,s: currency-coin fixed effects
    - Residual u_f,s,t is the idiosyncratic component orthogonal to global and coin-wide factors.
  - Step 2: Construct the granular instrument for currency j and stablecoin s:
    - Z_GIV_j,s,t = Σ_{k≠j} ω_k,s · u_k,s,t  (equation (32))
    - Weights ω_k,s are market shares of currency k for stablecoin s, measured by market capitalization.
    - Excluding currency j’s own shocks supports the exclusion restriction.
- Two-stage least squares procedure:
  - First stage:
    - g_j,s,t = θ Z_GIV_j,s,t + κ' X_j,t + ν_j,s,t  (equation (33))
    - Controls X_j,t include log VIX, log nominal broad dollar index, monthly bitcoin return (30-day change), USDT price in USD (with 5 days of lags), estimated factors, and coin-currency fixed effects.
  - Second stage:
    - Y_j,s,t+h = β_h · ĝ_j,s,t + γ X_j,s,t + φ_j,s + ζ_j,s,t+h  (equation (34))
  - Key identifying assumption: Z_GIV_j,s,t affects local outcome Y_j,s,t+h only through local stablecoin inflow g_j,s,t, conditional on controls.
  - Robustness: assess first-stage F-statistics, vary instrument construction (leave-one-out by coin or region), control for potential endogenous local flow responses.

### First-stage results and instrument strength
- Findings (Table 3 highlights):
  - GIV coefficients across specifications: −0.153***, −0.111***, −0.067***, −0.152***, −0.113***, −0.070*** (standard errors in parentheses: (0.0160), (0.0151), (0.0164), (0.0169), (0.0160), (0.0169)).
  - Fiat-specific factor 1 estimates: 1.054***, 1.051***, 1.036***, 1.049***, 1.049***, 1.036*** (standard errors reported).
  - Observations: 42,142 (columns 1–3) and 40,160 (columns 4–6).
  - R-squared: 0.215, 0.312, 0.358, 0.219, 0.315, 0.362 (per column).
  - Robust F-statistics: 4353.5, 24058.2, 15647.6, 2839.0, 6324.9, 4759.7.
  - K-P rk Wald F and Cragg-Donald F16 reported per column (values in table).
  - Adj. R^2: 0.214, 0.311, 0.357, 0.218, 0.314, 0.361.
- Interpretation:
  - The granular instrument is a strong and highly significant predictor of net stablecoin inflows across specifications.
  - Robust F-statistics are well above conventional thresholds, mitigating weak identification concerns.

### Estimation of causal effects (empirical IV results)
- Dynamic responses to a one standard deviation shock to instrumented net stablecoin inflow (Figure 5 summary):
  - Parity deviations: immediate, sharp increase of approximately 40 basis points on impact; highly persistent, decaying gradually over ten days.
  - Cumulative FX depreciation: positive, statistically significant depreciation of local currency in spot; magnitude declines over time and loses significance after a few days.
  - CIP deviations:
    - 3-month CIP deviations: significant decline (higher dollar premium) — short-term deterioration in synthetic funding conditions.
    - 12-month CIP deviations: negligible and statistically insignificant in short-term.
  - Tenor-specific pattern implies arbitrage constraints more binding at shorter horizons.
- Structural interpretation via Proposition 4:
  - Estimated parity deviation response: ˆ훽_IV_y ≈ 40 basis points per one percent flow shock — measures marginal cost of stablecoin intermediation.
  - Estimated CIP response: ˆ훽_IV_δ ≈ −17.5 basis points (reported elsewhere in discussion; empirical mapping focuses on −6bps in calibration/summary moments) — measures cross-market externality, evidence against full market segmentation.
  - Estimated exchange rate response: ˆ훽_IV_s ≈ 5–10 basis points — captures total FX impact combining direct substitution (η_y) and indirect CIP channel (η_δ).
  - Ratio test of market integration:
    - |ˆ훽_IV_δ| / ˆ훽_IV_y ≈ 0.44 — roughly 44 percent of parity deviation response transmits to CIP deviations via balance sheet channel.
    - Interpretation: intermediate value between fully segmented (0) and fully integrated (≈1), indicating meaningful but partial cross-market frictions.
- Dynamics:
  - The static model maps to impact effects (h = 0); observed persistence is consistent with autocorrelation in stablecoin demand shocks and intermediary balance sheet dynamics.
  - Dynamic extension in Section 6.3 generates impulse responses with shapes and half-lives closely matching empirical patterns.

### Calibration (Section 6.1)
- Targets and fixed parameters:
  - GIV empirical moments used: parity deviation, CIP deviation, and exchange rate responses to instrumented flow shocks.
  - Literature-based targets for swap market intermediation frictions used to pin Γ_δ.
- Demand-side and pass-through parameters (fixed from literature):
  - α_sc = 0.55 (midpoint of own-price elasticities −0.29 to −0.83).
  - ̃α_δ ≡ α_δ + α_L = 0.50.
  - η_δ ≈ 0.48 (swap-to-spot pass-through), with ν_s = 1 normalization.
  - Sensitivity note: varying ̃α_δ across [0.25, 0.75] shifts 훽_IV_δ by less than half a basis point.
- Swap market intermediation cost:
  - Calibrated Γ_δ using Rime et al. (2022) microstructure estimates: target semi-elasticity N_δ / A_sc = 15.5 basis points.
- Supply-side parameters identified from GIV coefficients (Panel A Table 4):
  - Γ_sc (Stablecoin intermediation cost) = 0.337 — GIV 훽_IV_y = 40 bps.
  - Γ_× (Cross-market intermediation cost) = 0.065 — GIV |훽_IV_δ| = 6 bps.
  - η_y (SC-to-spot substitution) = 0.078 — GIV 훽_IV_s ≈ 6 bps.
- Additional calibration notes (Table 4 Panel B & C):
  - Γ_δ = 0.093 (Swap interm. cost) — RSS22 target N_δ / A_sc = 15.5 bps.
  - ν_s = 1.00 (Spot market depth) — normalization.
  - Interpretation of calibrated values:
    - Γ_sc = 0.337 is roughly 3.6 times larger than Γ_δ = 0.093, reflecting larger frictions in stablecoin intermediation (on-ramps/off-ramps, blockchain fees, issuer counterparty risk).
    - Γ_× = 0.065 < Γ_sc and Γ_δ, but Γ_× / Γ_δ ≈ 0.70 indicates meaningful cross-market spillovers.
    - η_y = 0.078 is an order of magnitude smaller than η_δ, consistent with stablecoin markets having much smaller footprint in spot FX turnover.

### Counterfactual analysis (Section 6.2)
- Exercise design:
  - Vary one parameter (primarily Γ_×) while holding others at calibrated values.
  - Compute price responses to a 1% stablecoin flow shock.
- Baseline calibrated model responses (per 1% shock):
  - Parity deviation Δy = 32.8 bps (Panel A baseline reported 32.8 in Table 5; Panel B baseline reports IV per unit flow 훽_IV_y = 40.0 bps).
  - CIP deviation Δδ = −4.9 bps (Panel A baseline), or −6.0 bps (Panel B 훽_IV_δ).
  - Exchange rate depreciation Δs = 4.9 bps (Panel A baseline) or 6.0 bps (Panel B 훽_IV_s).
- Table 5 (selected counterfactuals for Γ_× variations):
  - Panel A: Equilibrium (휕price/휕 ̄휌_sc, per 1% demand shock)
    - Baseline: Δy = 32.8 bps, Δδ = −4.9 bps, Δs = 4.9 bps.
    - 2×Γ_×: Δy = 36.7 bps, Δδ = −9.3 bps, Δs = 7.3 bps.
    - 0.5×Γ_×: Δy = 30.7 bps, Δδ = −2.5 bps, Δs = 3.6 bps.
    - Γ_× = 0: Δy = 28.4 bps, Δδ = 0.0 bps, Δs = 2.2 bps (segmented markets).
  - Panel B: Supply response (훽_IV, per 1% instrumented flow)
    - Baseline: 훽_IV_y = 40.0 bps, 훽_IV_δ = −6.0 bps, 훽_IV_s = 6.0 bps, |훽_δ|/훽_y = 0.151.
    - 2×Γ_×: 훽_IV_y = 45.9 bps, 훽_IV_δ = −11.7 bps, 훽_IV_s = 9.2 bps, |훽_δ|/훽_y = 0.255.
    - 0.5×Γ_×: 훽_IV_y = 36.9 bps, 훽_IV_δ = −3.1 bps, 훽_IV_s = 4.3 bps, |훽_δ|/훽_y = 0.083.
    - Γ_× = 0: 훽_IV_y = 33.7 bps, 훽_IV_δ = 0.0 bps, 훽_IV_s = 2.6 bps, |훽_δ|/훽_y = 0.000.
- Key counterfactual insights:
  - Cross-market costs Γ_× are the primary driver of spillovers to traditional FX markets.
  - Doubling Γ_× nearly doubles the CIP spillover and substantially increases parity and exchange rate responses:
    - Example: doubling Γ_× raises Δy from 40 to 46 basis points (supply-response perspective), Δδ from −6 to −12 basis points, Δs from 6 to 9 basis points.
  - If markets are fully segmented (Γ_× → 0), CIP spillover vanishes and exchange rate spillover roughly halves.
  - Economic interpretations of Γ_× variations:
    - Higher Γ_× can represent tighter regulatory capital rules treating stablecoin and FX swap exposures as additive, or deterioration in counterparty credit raising netting costs.
    - Lower effective Γ_× corresponds to environments where global intermediaries can offset local currency exposures via international operations (open capital accounts).
    - Binding capital controls raise effective Γ_× by preventing international diversification of intermediary balance sheets.
  - Policy-relevant implication: moving from low-Γ_× (open capital account) to high-Γ_× (binding capital controls) can more than double the CIP spillover from stablecoin shocks.

*Source: wpiea2026056-source-pdf - Appendix A formalizes this.*

### Appendix E discusses the effects of increasing stablecoin-specific costs (Γ

### Appendix E discusses the effects of increasing stablecoin-specific costs (Γ_sc) and of increasing stablecoin demand elasticity (α_sc)

### Policy implications
- Magnitude of spillovers depends critically on intermediary balance sheet linkages.
- Policies that affect Γ_×, such as capital requirements that treat stablecoin and swap exposures as substitutes, will directly influence how stablecoin market stress transmits to traditional foreign exchange markets.
  - Capital frameworks that permit netting of stablecoin and FX swap exposures would lower the effective Γ_× and dampen spillovers.
  - Ring-fencing crypto activities into separately capitalized entities would eliminate the balance sheet link altogether (at the cost of reducing cross-market liquidity provision).
- The finding that CIP spillovers nearly vanish when Γ_× → 0 suggests that market segmentation, while potentially costly in terms of allocative efficiency, would limit contagion from stablecoin markets to traditional FX markets.

### 6.3 Dynamic counterfactuals — Dynamic model and main results
- The dynamic extension incorporates demand persistence and intermediary balance sheet dynamics and delivers three results:
  - The dynamic model generates impulse responses whose shape and persistence closely match empirical estimates.
  - Spillovers are state-dependent: identical shocks produce larger effects when intermediary balance sheets are impaired.
  - Doubling cross-market frictions amplifies spillovers more than proportionally through a feedback loop between prices and wealth.
- Two new assumptions:
  - Stablecoin demand ̄D_sc,t follows an AR(1) process generating autocorrelation so shocks decay gradually.
  - Wealth (W_t) is a key state variable: the intermediary evaluates portfolio composition in synthetic dollars and stablecoins relative to capital and constrained by the law of motion of wealth.

### Intermediary problem with wealth-dependent risk capacity
- Representative intermediary chooses positions in synthetic dollar intermediation (B_syn,t) and stablecoin intermediation (B_sc,t) entering period t with wealth W_t.
- Objective function (exact formulation):
  - max_{B_syn,t, B_sc,t} δ_t B_syn,t + y_t B_sc,t − Γ_δ 2 W_t (B_syn,t)^2 − Γ_sc 2 W_t (B_sc,t)^2 − Γ_× 2 W_t (B_syn,t + B_sc,t)^2
- Interpretation of scaling by W_t:
  - A given dollar position represents greater risk exposure when measured against a smaller capital base (example given: $1 billion position vs. $10 billion vs. $2 billion capital).
  - Analogous to measuring portfolio risk relative to equity (VaR-constraint literature).

### Wealth dynamics and amplification mechanism
- Wealth evolves with portfolio returns (exact law of motion):
  - W_{t+1} = W_t [ 1 + (B_syn,t / W_t) δ_t + (B_sc,t / W_t) y_t − φ · Δs_t ] = W_t [ 1 + b_syn,t δ_t + b_sc,t y_t − φ · Δs_t ]
- φ captures intermediary’s net foreign exchange exposure; Δs_t is rate of exchange rate depreciation.
- Position-to-wealth ratios b_syn,t and b_sc,t determine how portfolio returns translate into wealth growth.
- Amplification channel:
  - Adverse shocks that raise y_t and lower δ_t may generate mark-to-market losses that deplete wealth.
  - Reduced wealth lowers risk-bearing capacity, positions contract, and prices adjust further to clear markets.
  - This feedback loop sustains elevated prices and generates persistence.

### Equilibrium comparative statics
- Prices (y_t, δ_t, s_t) are functions of W_t and ̄D_sc,t given cost parameters Γ.
- Key comparative statics (exact signs):
  - ∂y_t / ∂W_t < 0
  - ∂δ_t / ∂W_t > 0
- Interpretation:
  - Lower intermediary wealth implies higher stablecoin parity deviations and lower CIP deviations (a higher dollar premium).
  - With reduced supply of intermediation, prices must adjust to equilibrate demand.

### Impulse response to a one percent stablecoin demand shock (from steady state)
- Impact effects (exact values):
  - Stablecoin parity deviation y: 34 basis points
  - CIP deviation δ (a higher dollar premium): −5 basis points
  - Exchange rate depreciation s: 5 basis points
- These impact effects equal those of the static model at steady-state wealth.

### State-dependence and amplification under impaired balance sheets
- Identical shocks generate larger price responses when intermediary balance sheets are impaired because:
  - Stablecoin parity deviation scales as 1 / W_t
  - CIP deviation scales as W_t
  - Lower wealth mechanically translates into higher parity deviations, larger dollar premia, and further FX depreciation
- Endogenous wealth depletion introduces further persistence of demand shocks and spillovers.

### Dynamic response to higher cross-market frictions
- Doubling Γ_× (2×Γ_×) results (exact reported effects):
  - Increases the impact effect on the stablecoin parity deviation by about 5 basis points.
  - CIP spillover increases from −6 to −9 basis points, nearly a 50 percent increase in the dollar premium.
- More-than-proportional increase in CIP spillovers reflects compounding through the balance sheet channel:
  - Higher Γ_× → larger initial price responses → greater wealth depletion → further amplifies subsequent price dynamics.
- Policy implication:
  - Reducing cross-market frictions yields compounding benefits: smaller spillovers preserve intermediary capital, which sustains risk-bearing capacity, which further damps price responses to future shocks.

### Run dynamics and amplification with redemption frictions
- Additional extension (Appendix F.8) incorporates redemption frictions that amplify during stress.
- When flow shocks coincide with friction shocks (examples referenced: Terra/Luna collapse, SVB-induced USDC depeg), interaction between redemption costs and balance sheet depletion can multiply baseline spillover effects severalfold.
- Implication: stablecoin-to-FX transmission can escalate sharply during crisis episodes.

### Conclusion — empirical findings, structural interpretation, and policy recommendations
- Empirical findings:
  - Causal link between crypto-based financial system and traditional foreign exchange markets using granular data on four USD-pegged stablecoins and 27 fiat currencies.
  - Exogenous shocks to stablecoin inflows cause parity deviations to widen, local currency depreciation, and impairment of synthetic dollar funding conditions.
- Structural interpretation:
  - A model of segmented arbitrage rationalizes findings; IV coefficients map to marginal cost of intermediation, cross-market spillover intensity, and a market integration test.
- Quantitative summary (exact figures and characterizations):
  - Estimated spillover ratio approximately 0.15 indicating roughly one-sixth of stablecoin price pressure transmits to synthetic dollar funding costs.
- Policy recommendations (exact directions):
  - Prudential requirements on stablecoin intermediaries, such as capital buffers, reserve liquidity mandates, and limits on concentrated currency exposures, would shrink the spillover channel by reducing cross-market frictions and preserving risk-bearing capacity.
  - Policymakers responsible for currency stability, particularly in emerging markets, could consider incorporating stablecoin market monitoring into macroprudential surveillance because the transmission mechanism runs through balance sheets that also serve traditional FX swap markets.
  - Monitoring the evolution of the spillover ratio as stablecoin markets grow would provide an early warning indicator of increasing interconnectedness.
- Suggested avenues for future research (verbatim themes):
  - Investigate how spillover magnitudes vary with capital account openness, exchange rate regime, and local FX market depth.
  - Analyze how stablecoin design features (algorithmic vs. reserve-backed vs. CBDC) map into different intermediation costs and spillover profiles.
  - Track the spillover ratio over time as a gauge of crypto–FX integration.
  - Study whether stablecoin flows weaken the effectiveness of monetary policy and capital flow management measures in economies where they offer an alternative channel for cross-border capital movements.

*Source: Appendix E and Section 6.3 (dynamic counterfactuals) of the provided document.*

### References

### References

### Key bibliographic inputs
- Comprehensive citation list spanning empirical and theoretical literature on stablecoins, cryptocurrency markets, covered interest parity (CIP) deviations, intermediary asset pricing, and international finance. Notable entries include:
  - Adrian, T. and H. S. Shin (2014): “Procyclical Leverage and Value-at-Risk,” Review of Financial Studies, 27, 373–403.
  - Brunnermeier, M. K. and L. H. Pedersen (2009): “Market Liquidity and Funding Liquidity,” Review of Financial Studies, 22, 2201–2238.
  - He, Z. and A. Krishnamurthy (2013): “Intermediary Asset Pricing,” American Economic Review, 103, 732–770.
  - Gabaix, X. and M. Maggiori (2015): “International Liquidity and Exchange Rate Dynamics,” The Quarterly Journal of Economics, 130, 1369–1420.
  - Selected recent working papers and BIS/IMF pieces on stablecoins and crypto spillovers (2023–2026).

### Shock structure and endogeneity (Appendix A)
- Demand decomposition for a stablecoin book f:
  - Total net demand ̄ρ_s c_f = ̄D_s c_f + S_s c_f.
  - Local household demand: ̄D_s c_f = ̄D_0 + φμ + u_D_f.
  - Cross-book participant demand: S_s c_f = ̄S_s c_f + v_f with ∑_f v_f = 0.
  - Total demand: ̃D_s c_f ≡ ̄D_s c_f + S_s c_f = (̄D_0 + ̄S_s c_f) + φμ + ̃u_f where ̃u_f ≡ u_D_f + v_f.
- Price equations show three channels affecting outcomes y_f, δ_f, s_f:
  - stablecoin channel (function of ̄ρ_s c_f),
  - direct global shock term (proportional to μ),
  - local factors (ε terms).
- Assumption 1 (Shock structure) — three conditions preserved exactly:
  - (i) Idiosyncratic total demand shocks are independent across countries: Cov(̃u_f, ̃u_f′)=0 for f≠f′.
  - (ii) Idiosyncratic total demand shocks are correlated with local unobservables: Cov(̃u_f, ε^y_f)=σ^y_{̃uε}≠0, and similarly for δ and s.
  - (iii) Idiosyncratic total demand shocks in country f are uncorrelated with unobservables in other countries: Cov(̃u_f, ε^y_f′)=0 for f≠f′.

### OLS bias and instrumental identification (Appendix B)
- Flows relation from market clearing: g_f ≡ B_s c_f = ̄ρ_s c_f − α_s c y_f.
- OLS is biased because flows g_f inherit variation from:
  - idiosyncratic demand shocks ̃u_f,
  - global shocks μ,
  - local price determinants ε^y_f.
- Proposition 5 (OLS bias) — key displayed structure preserved:
  - β_OLS^δ = − Γ × A_δ |β_IV^δ + [−φ ξ^δ σ_μ^2 − σ^δ_{̃uε}] · Var(g_f)/γ_g (bias)
  - where σ_μ^2 = Var(μ), σ^δ_{̃uε} = Cov(̃u_f, ε^δ_f), and γ_g = A_δ/Δ.
- Two distinct bias sources:
  - Global shock bias: −φ ξ^δ σ_μ^2.
  - Local confounding bias: −σ^δ_{̃uε}.
- Directional implications preserved exactly:
  - Crisis episodes (φ>0, ξ^δ>0, σ^δ_{̃uε}>0) tend to push OLS more negative than true causal effect (OLS likely overstates spillovers to CIP).
  - Alternative contexts (e.g., fintech-driven adoption with ε^δ_f<0) could reverse bias sign (OLS could understate causal effect).
- Instrumental variable strategy: construct instrument excluding common shock and own shock (GIV Z_f = ∑_{f′≠f} w_{f′} ̃u_{f′}) to isolate exogenous cross-country variation (Appendix C.4 details).

### Proofs and equilibrium properties (Appendix C)
- Proposition 1: Analytical equilibrium expressions derived via market clearing and first-order conditions; determinant Δ = A_δ A_s c − B C > 0.
- Proposition 2 (comparative statics):
  - ∂y∗/∂̄ρ_s c = N_y / Δ with N_y > 0.
  - ∂δ∗/∂̄ρ_s c = − Γ × / Δ (strictly negative when Γ × > 0).
  - Exchange rate response ∂s∗/∂̄ρ_s c = (η_δ Γ × + η_y N_y) / (ν_s Δ) > 0.
- Proposition 3: Reallocation across books (S_s c^B) has symmetric comparative statics: increases in S_s c^B raise y^B, lower δ^B, and appreciate the currency s^B.
- Appendix provides full algebraic derivations and identities used in IV results.

### Alternative specification: Segmented households (Appendix D)
- Two household types:
  - Traditional households (mass μ_T): access spot and swap only. Demand D_T = ̄D_T + α_T δ with α_T > 0.
  - Crypto-native households (mass μ_C): access spot and stablecoins only. Demand D_C = ̄D_C − α_C y.
- Market clearing yields identical reduced-form equilibrium to the integrated specification when composite elasticities map as:
  - α_s c = α_C, ̃α_δ = α_T + α_L.
- Comparative statics conclusions from main text carry over:
  - Stablecoin demand shocks raise stablecoin parity deviations, lower CIP deviations (increase dollar premium when Γ × > 0), and depreciate the local currency.
- Empirical interpretation guidance:
  - Integrated specification more appropriate for agents with access to multiple channels (large corporates, developed markets).
  - Segmented specification may be more appropriate for emerging markets or retail contexts where access constraints bind; leads to larger price movements for same shocks.

### Additional counterfactuals (Appendix E)
- Stablecoin-specific costs (Γ_s c):
  - Doubling Γ_s c more than doubles parity-deviation elasticity; effect on CIP is muted.
  - Policy implication: improving stablecoin market efficiency may primarily affect own-market stability but not strongly reduce spillovers to traditional markets.
- Stablecoin demand elasticity (α_s c):
  - Lower elasticities yield larger equilibrium responses; parity-deviation response range noted in text goes from 40 to 26 under alternative parameterizations.
  - Spillovers remain in a tight range across parameterizations.

### Dynamic model extension (Appendix F)
- Time extension: discrete time t = 0, 1, 2, ... with persistent demand shocks and wealth-dependent intermediary capacity.
- Demand AR(1): ̄D_s c_t = ρ ̄D_s c_{t−1} + ε_t, ε_t ∼ N(0, σ_ε^2) with calibration ρ = 0.8 (half-life of approximately three days).
- Intermediary problem: costs scaled by wealth W_t so positions scale linearly with wealth:
  - B_s y n_t = W_t · b_s y n(δ_t, y_t; Γ)
  - B_s c_t = W_t · b_s c(δ_t, y_t; Γ)
- Wealth dynamics include portfolio returns and FX exposure φ:
  - W_{t+1} = W_t [1 + b_s y n_t δ_t + b_s c_t y_t − φ · Δs_t].
- Key calibrated dynamic parameters (Table 6 preserved values):
  - Γ_δ (Swap market cost) = 0.023
  - Γ_s c (Stablecoin market cost) = 0.194
  - Γ × (Cross-market cost) = 0.148
  - ρ (Demand persistence) = 0.80
  - φ (FX exposure) = 150
  - ̄W (Steady-state wealth) = 1
- Impulse response summary:
  - One percent stablecoin demand shock (from steady state) - impact effects:
    - stablecoin parity deviation y: 34 basis points
    - CIP deviation δ: −15 basis points (more negative = higher dollar premium)
    - exchange rate depreciation s: 3.5 basis points
  - Immediate wealth drop on impact: approximately 5 percent.
  - Decay half-life of prices: roughly four days (longer than three-day AR(1) half-life due to balance-sheet channel).
  - Cumulative amplification factors:
    - A_y (stablecoin parity deviation) = 5.4
    - CIP cumulative amplification = 5.6
  - Persistence-only amplification: 1/(1−ρ) = 5; additional 8–12 percent amplification arises from the wealth (balance-sheet) channel.
- State-dependent amplification (Table 7 preserved entries):
  - Initial Wealth = ̄W (steady state): Δy = 34 bps, Δδ = −15 bps, Δs = 3.5 bps, Amplification = 1.0×
  - Initial Wealth = 0.75 ̄W: Δy = 45 bps, Δδ = −20 bps, Δs = 4.7 bps, Amplification = 1.3×
  - Initial Wealth = 0.50 ̄W (stressed): Δy = 68 bps, Δδ = −30 bps, Δs = 7.0 bps, Amplification = 2.0×
  - When intermediary wealth is 50 percent below steady state, impact effects double relative to baseline.
- Counterfactual: Doubling Γ ×
  - Impact effect on y increases from 34 to 78 basis points (factor 2.3).
  - CIP spillover increases from −15 to −58 basis points (nearly fourfold).
  - Amplification through balance-sheet depletion yields more-than-proportional increases in spillovers.
- Mechanism and literature linkages:
  - Dynamic channel implements the intermediary asset pricing mechanism (He and Krishnamurthy, 2013; Gabaix and Maggiori, 2015).
  - The term Γ / W_t acts as the shadow price of deploying balance-sheet capacity; lower W_t raises risk premia and sustains CIP deviations despite apparent arbitrage opportunities.
  - Policy implication: prudential capital buffers can dampen state-dependent amplification but may reduce intermediation in normal times.

### Redemption frictions and run dynamics (Appendix F.8)
- Introduced redemption haircut h_t ∈ (0, 1] reducing effective recovery on stablecoin positions during large redemptions.
- Parameterization:
  - h_t = 1 − η · |B_s c_t| / W_t with η ≥ 0 governing severity of redemption frictions.
  - η = 0 recovers baseline no-haircut case.
- Modified wealth dynamics:
  - W_{t+1} = W_t [1 + b_s y n_t δ_t + b_s c_t y_t · h_t − φ Δs_t].
- Run threshold and solvency constraint:
  - Constraint: η · |b_s c_t| < 1 ⇐⇒ η < W_t / |B_s c_t|.
  - Define critical threshold ̄η = W_t / (shock size). If redemption frictions exceed ̄η, haircuts render the intermediary unable to honor redemptions at positive value (system failure).
- Feedback mechanism: haircuts amplify losses during redemptions, deplete wealth, reduce capacity, and can trigger self-reinforcing run dynamics.

*Source: wpiea2026056-source-pdf - References — https://www.imf.org/-/media/files/publications/wp/2026/english/wpiea2026056-source-pdf.pdf*

### 1. A redemption shock increases|푏

### 1. A redemption shock increases|푏

### Mechanism: how a redemption shock propagates
- A redemption shock increases |푏 푠푐 푡 | (text as in source).
- The haircut rises (lower ℎ푡), reducing value recovered.
- Wealth 푊푡+1 falls more than in the baseline model.
- Lower wealth raises effective costs (Γ/푊푡+1), widening spreads.
- The run threshold ̄휂 = 푊푡+1/shock falls, making the system more fragile.
- The mechanism captures classic bank-run ingredients applied to stablecoin intermediation:
  - sequential service constraints (early redeemers get better terms),
  - strategic complementarities (my incentive to redeem rises if others redeem),
  - possibility of self-fulfilling crises.

### Counterfactual analysis (Figure 11): redemption frictions amplify price responses
- Each curve shows the impact effect of a 1% redemption shock as a function of 휂, with vertical dotted lines marking the run threshold ̄휂 = 푊0 for each case.
- Three features highlighted:
  - Amplification is convex: price responses increase slowly for low 휂 but accelerate sharply as frictions approach the threshold. At 휂 = 0.9 ̄휂, impact effects are roughly ten times larger than in the frictionless baseline.
  - Capitalization determines fragility: a well-capitalized intermediary (푊0 = 1) can tolerate frictions up to 휂 = 1, while a stressed intermediary (푊0 = 0.5) hits the run region at 휂 = 0.5. The same level of reserve illiquidity that is manageable in normal times becomes catastrophic when balance sheets are impaired.
  - Spillovers scale proportionally: the ratio of CIP response to stablecoin parity deviation response remains approximately constant as 휂 varies, implying the cross-market spillover channel operates similarly across the friction spectrum.
- Figure 11 panels:
  - stablecoin parity deviation (left),
  - CIP deviation (middle),
  - exchange rate depreciation (right).
- Dotted vertical lines mark the run threshold ̄휂 = 푊0 for each case; effects diverge to infinity as 휂 approaches the threshold.

### Policy implications
- Reserve liquidity requirements (reducing 휂) provide a buffer against runs by keeping the system away from the threshold. Mandating that stablecoin issuers hold liquid reserves, such as Treasury bills rather than commercial paper or crypto assets, directly lowers 휂 and expands the stable region.
- Intermediary capital requirements (raising 푊푡) increase the run threshold ̄휂, allowing the system to tolerate higher frictions without destabilizing.
- The two policies are complementary:
  - liquid reserves reduce the severity of redemption costs conditional on a run,
  - adequate capital reduces the probability of approaching run conditions.

### Combined shocks and crisis amplification (Figure 12)
- Amplifying role of redemption frictions is most apparent when flow shocks and friction shocks occur simultaneously.
- Comparison of impulse response to a 1% flow shock under three scenarios:
  - no friction (휂 = 0),
  - moderate friction (휂 = 0.4),
  - severe friction (휂 = 0.8).
- Quantitative impacts reported:
  - In the frictionless baseline, the flow shock generates a 40 basis point increase in the stablecoin parity deviation and a 17.5 basis point widening of the CIP deviation.
  - When the same flow shock is accompanied by a moderate friction shock, impact effects rise by a factor of 1.7.
  - Under severe frictions, the amplification reaches 5 times the baseline.
- Interpretation: crisis episodes (e.g., Terra/Luna collapse or SVB-induced USDC depeg) involve simultaneous bad news that triggers redemptions and raises redemption costs, as counterparties become cautious, liquidity evaporates, and reserve assets face fire-sale discounts.
- Lower panels in Figure 12 illustrate intermediary wealth, the haircut factor, and the friction path; both shocks decay over time.

### Appendix G — Finite supply elasticity: identification robustness
- Main claim: relaxing perfectly elastic supply does not affect the identified structural object.
- Setup:
  - Stablecoin supply responds to the dollar price deviation 휇 ≡ P_{s,USD}_t − 1:
    - S_{sc} = S_0 + κ 휇 (equation (73)).
  - Household demand in country f depends on absolute price P_f = 1 + 휇 + y_f:
    - D_{sc}^f = ̄D_{sc}^f − α_{sc}(1 + 휇 + y_f) (equation (74)).
- Local equilibrium given 휇:
  - Define effective local demand ̄ρ_{sc}^f(휇) ≡ ̃D_{sc}^f − α_{sc} 휇, where ̃D_{sc}^f ≡ ̄D_{sc}^f − α_{sc}.
  - Market clearing on book f requires B_{sc}^f = ̄ρ_{sc}^f(휇) − α_{sc} y_f.
  - Substituting into intermediary first-order conditions yields:
    - y_f = N_y ̄ρ_{sc}^f(휇) + N_synn ̄ρ_{ssyn} / Δ (equation (75)),
    - −δ_f = Γ × ̄ρ_{sc}^f(휇) + M_δ ̄ρ_{ssyn} / Δ (equation (76)),
    - where N_y, N_synn, M_δ, and Δ are as defined in the main text.
- Global clearing:
  - Aggregate condition ∑_f B_{sc}^f + D_US = S_0 + κ 휇 pins 휇 as a function of all demand shocks {̃D_{sc}^f}.
- Cross-country transmission and IV coefficient:
  - An idiosyncratic shock u_A in country A affects country B by raising 휇. With ̃D_{sc}^B unchanged, let m ≡ ∂휇/∂u_A > 0:
    - ∂y_B/∂u_A = −N_y α_{sc} m / Δ (equation (77)).
    - ∂B_{sc}^B/∂u_A = −α_{sc} m − α_{sc} ∂y_B/∂u_A (equation (78)).
  - Taking the ratio yields β_IV^y = N_y / A_δ (equation (81)), identical to the coefficient identified under the cross-book participant specification in the main text. The result holds for any κ ∈ (0,∞): supply elasticity does not enter the identified object.
- Instrument power:
  - First-stage coefficient proportional to:
    - Cov(g_B, Z) ∝ ∂B_{sc}^B/∂u_A = −α_{sc} m [1 + N_y α_{sc} / Δ] (equation (82)).
  - As κ → ∞, m = ∂휇/∂u_A → 0, and the first stage vanishes. In this limit, the P_{s,USD}_t channel provides no identifying variation; only cross-book participant reallocation can generate a non-degenerate first stage.
- Equivalence result (Proposition 7):
  - Two specifications identify the same structural object N_y / A_δ:
    - (i) Elastic supply (P_{s,USD}_t = 1) with cross-book participant demand (S_{sc}^f, ∑_f S_{sc}^f = W);
    - (ii) Finite supply elasticity (κ < ∞) with price-sensitive demand D_{sc}^f(P_f) and no cross-book participants.
  - When both channels operate simultaneously, the identified object remains N_y / A_δ, with instrument power reflecting the sum of both channels.

### Appendix H — Microfoundation for cross-book participants
- H.1 Agent problem:
  - Representative cross-book participant holds fiat balances {N_0^f}_f=1^F across F currencies.
  - Each currency f subject to stochastic local shock with conversion urgency θ_f > 0.
  - Residual fiat position variance σ_f^2.
  - Agent converts c_f units of currency f into USDT at cost y_f per unit.
  - Total conversion limited by operational capacity: ∑_f c_f ≤ W (equation (83)).
  - Agent maximizes expected wealth net of residual risk:
    - max_{c_f ≥ 0} ∑_f c_f θ_f − ∑_f c_f y_f − (γ/2) ∑_f (N_0^f − c_f)^2 / σ_f^2 subject to ∑_f c_f ≤ W (equation (84)).
- H.2 Optimal allocation:
  - First-order condition with Lagrange multiplier λ yields:
    - c_f = N_0^f + (θ_f − y_f − λ) / (γ σ_f^2) (equation (85)).
  - Imposing ∑_f c_f = W and defining Φ ≡ ∑_f (γ σ_f^2)^{-1} and risk-weighted average θ − y:
    - S_{sc}^f ≡ c_f = ̄S_{sc}^f + (1 / (γ σ_f^2)) [ (θ_f − y_f) − (θ − y) ] (equation (86)).
- H.3 Cross-country transmission:
  - Own effect of idiosyncratic shock increasing θ_A:
    - ∂S_{sc}^A / ∂θ_A = (1 / (γ σ_A^2)) [1 − (γ σ_A^2)^{-1} Φ] > 0 (equation (87)).
  - Cross-country effect (B ≠ A):
    - ∂S_{sc}^B / ∂θ_A = −(1 / (γ σ_B^2)) · (γ σ_A^2)^{-1} Φ < 0 (equation (88)).
  - Budget constraint forces reallocation; spillover magnitude proportional to (γ^2 σ_A^2 σ_B^2 Φ)^{-1}.
- H.4 Urgency versus premium-chasing:
  - Allocation responds to both urgency θ_f and premium y_f, which work in opposite directions during crises.
  - Urgency channel typically dominates because expected losses from holding a depreciating or at-risk currency can be tens of percentage points, while stablecoin premia are typically a few percentage points even under stress.
  - Empirical implication: observed negative first stage confirms urgency-driven reallocation is primary.
- H.5 Reduced form:
  - S_{sc}^f = ̄S_{sc}^f + v_f, with ∑_f v_f = 0 (equation (89)). v_f captures idiosyncratic reallocation driven by local conversion urgency.
- H.6 Connection to identification:
  - The GIV Z_f = ∑_{f' ≠ f} w_{f'} ˆ̃u_{f'} captures idiosyncratic urgency shocks θ_{f'} in other countries (after factor purging). These affect country f’s book through the budget constraint: higher θ_{f'} draws conversion activity from f, lowering S_{sc}^f. The exclusion restriction requires θ_{f'} uncorrelated with country f’s local fundamentals.

_Stablecoin Flows and Spillovers to FX Markets — Working Paper No. WP/2026/056_

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_Source: https://www.imf.org/-/media/files/publications/wp/2026/english/wpiea2026056-source-pdf.pdf_