## wpiea2020101-print-pdf — Section V and forecasting relationships in Section VI

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### B. Causal Relationship (IV strategy and 2SLS evidence)
- Objective: identify causal effect of demand for USD safe assets from non-U.S. banks on exchange rates using instrumental variables to separate supply and demand.
- Instruments proposed:
  - Safety of substitute currencies (simple averages across six non-USD G10 currencies: Canadian Dollar, Euro, Japanese Yen, Pound Sterling, Swedish Krona, Swiss Franc):
    - i. Treasury premium of substitute economies, Φ̅sub,t = (y̅j,tGovt − ρj,t − y̅sub,tGovt).
    - ii. Sovereign CDS spread of substitute Treasury securities (5-year maturity from Markit).
  - Balance sheet constraint instrument:
    - Logarithm of the book leverage ratio from Fitchconnect orthogonalized with respect to U.S. bank leverage.
- First-stage (Equation (2); dependent = ∆D̅$,t) — upper panel of Table 4:
  - Coefficient signs and significance:
    - ∆Φ̅sub,t: negative point estimates across columns (1)–(5); significant at the 10% level or above in 3 out of 5 specifications.
    - ∆Sovereign CDS̅sub,t: positive and significant at the 1% level across specifications.
    - ∆Leverage̅t: positive and significant at the 1% level across specifications.
  - Economic significance:
    - Variation from those three IVs alone accounts for around 20% of the variation in contemporaneous changes of USD asset demand from non-U.S. banks.
  - Weak IV test:
    - Stock-Yogo F Statistics (columns (1)–(5)): 15.59**, 18.58**, 24.61**, 27.87**, 32.38**.
  - Sample and fit:
    - N = 67; R2 = 0.18, 0.25, 0.18, 0.25, 0.26 across columns (1)–(5).
- Second-stage (Equation (3); dependent = ∆s̅t [Annualized %], using fitted ∆D̅̂$,t) — lower panel of Table 4:
  - Fitted ∆D̅̂$,t coefficients (columns (1)–(5)):
    - 51.54*** (std. err. 14.57)
    - 51.55*** (13.40)
    - 51.74*** (14.04)
    - 50.28*** (13.28)
    - 41.76*** (9.74)
  - R2 and explanatory power:
    - R2 = 0.07, 0.07, 0.07, 0.11, 0.36 across columns (1)–(5).
    - Predicted changes in USD asset share alone account for 7% of variation in contemporaneous changes in USD exchange rate (Column 1); OLS comparison shows 36% in Table 3, Column 1.
    - Column (4): R2 rises to 11% when including ∆Φ̅t and ∆(y̅tGovt − y$,tGovt); both are insignificant.
    - Column (5): including one-quarter lags raises R2 to 36%; point estimate on ∆D̅̂$,t ≈ 41.8.
  - Endogeneity and overidentification:
    - Durbin-Wu-Hausman F Statistics: 8.18***, 3.60*, 8.72***, 3.73*, 3.10* across columns (1)–(5).
    - Sargan χ2 Statistics: 2.45, 2.36, 2.57, 2.48, 1.23 across columns (1)–(5) — supports instrument exogeneity.
  - Interpretation:
    - 2SLS coefficients on fitted USD asset share are positive and significant at the 1% level across specifications.
    - 2SLS magnitudes are about two times larger than OLS estimates, suggesting OLS underestimates the slope of the supply curve due to simultaneous supply and demand shifts.
    - IV strategy identifies supply curve using demand shifters exogenous to supply.

### C. Transmission Channels (safe asset demand vs financial intermediation)
- Goal: relate U.S. Treasury premium, LIBOR cross-currency basis, and USD asset demand using IV strategy to distinguish channels.
- Second-stage results (Table 5) — dependent variables ∆ΦTreasury,t and ∆ΦLibor,t = (-1)*cross-currency basis:
  - Sample periods: Full (2001q2–2017q4) and Post-GFC (2010q1–2017q4).
  - Fitted ∆D̅̂$,t coefficients:
    - ∆ΦTreasury,t:
      - Full sample (Column 1): 0.46*** (0.15); R2 = 0.18; N = 67.
      - Post-GFC (Column 2): 0.58** (0.24); R2 = 0.19; N = 32.
    - ∆ΦLibor,t:
      - Full sample (Column 3): 0.29 (0.19); R2 = 0.06; N = 67 (not significant).
      - Post-GFC (Column 4): 0.20** (0.10); R2 = 0.20; N = 32 (positive and significant).
- Interpretation:
  - U.S. Treasury premium regressions: fitted USD asset share positive and statistically significant for full sample and larger post-GFC — supply curve in Treasury market is upward sloping.
  - LIBOR cross-currency basis regressions: fitted USD asset share not significant pre-GFC, but positive and significant post-GFC — supply curve became upward-sloping after GFC.
  - Economic message:
    - “Safe asset demand channel” affects both LIBOR swap market and U.S. Treasury market.
    - “Financial intermediation channel” became important in U.S. LIBOR cross-currency swap market post-GFC due to reduced balance sheet capacity limiting CIP arbitrage.
    - Financial intermediation channel is less critical in U.S. Treasury market because U.S. Treasury does not arbitrage away Treasury premium.
  - Overall: IV strategy provides causal evidence differentiating roles of safe asset demand and intermediation channels across markets.

### V. Cross-Sectional Asset Pricing (global USD asset demand as priced factor)
- Risk factor:
  - Global USD asset demand factor = cross-sectional average of annualized quarterly changes in USD asset share of non-U.S. banks across 16 economies.
- Currency excess return:
  - Rj,t ≜ yj,t−1Govt − ∆sj,t − y$,t−1Govt.
- Methodology:
  - Two-stage Fama and MacBeth (1973) regressions to estimate loadings (betas) on global USD asset demand factor.
- Key findings:
  - Time-series loadings (β̂j) on ∆D$,t are negative and significant at the 5% level or above for individual currencies.
  - Higher interest rate currencies (e.g., BRL and ZAR) have larger (in absolute value) negative loadings than lower interest rate currencies (e.g., JPY and GBP).
  - Currency portfolios ranked by interest rate show higher interest rate portfolios tend to have higher loadings.
  - Cross-sectional correlation between average excess returns and USD demand betas:
    - Bivariate correlation = -58% for individual currencies.
    - Bivariate correlation = -76% for currency portfolios.
- Economic interpretation:
  - USD asset demand of non-U.S. banks is a global risk factor priced in currency excess returns.
  - High interest rate currencies have larger negative exposure and require higher expected excess returns to compensate for “currency crash” risk when USD safe asset demand spikes.
  - Low interest rate currencies provide a hedge against USD asset demand risk.

### VI. Predictability (VAR evidence, in-sample and out-of-sample forecasting)
- VAR impulse responses (Figure 5; sample 2001q2–2017q4):
  - Positive shock to USD asset share contemporaneously appreciates the USD; appreciation nearly entirely undone after five years (overshooting and time-varying risk premia).
  - U.S. Treasury premium shock: contemporaneous USD appreciation, short-lived momentum one quarter, then depreciation over one-to-five years.
  - Interest differential (home – U.S.) shock: USD appreciates in first two years, then wanes over next three years.
  - VAR: four variables — exchange rate, U.S. Treasury premium, interest differential, USD asset share; Cholesky ordering as listed.
- A. In-sample forecasting (Equation (6)):
  - Regression: ∆sj,t^h = α1 + β1 Dj,$,t + β2 Φj,t + β3 (yj,tGovt − y$,tGovt) + εt+h; horizons h = 1 quarter, 1 year, 2 years, 3 years, 5 years.
  - Main in-sample results (Table 6; dependent = ∆s_h_t [Annualized %]; horizons h = 1, 4, 8, 12, 20):
    - Regressor D_j,$,t [%] coefficients (Newey-West SEs):
      - h=1: -0.27 (1.59)
      - h=4: -2.22** (0.92)
      - h=8: -2.75*** (0.55)
      - h=12: -2.54*** (0.38)
      - h=20: -2.02*** (0.30)
    - Regressor Φ_t [%] coefficients:
      - h=1: 4.66 (8.56)
      - h=4: -4.34 (3.72)
      - h=8: -5.16** (2.37)
      - h=12: -1.67 (1.48)
      - h=20: 0.49 (1.39)
    - Regressor (y_t − y$_t) [%] coefficients:
      - h=1: 2.57 (1.92)
      - h=4: 2.69** (1.16)
      - h=8: 1.74** (0.71)
      - h=12: 0.73 (0.50)
      - h=20: 0.65* (0.37)
    - Sample sizes (N): 67, 64, 60, 56, 48 for h=1,4,8,12,20 respectively.
    - R^2 by horizon:
      - h=1: 0.06
      - h=4: 0.20
      - h=8: 0.36
      - h=12: 0.45
      - h=20: 0.67
  - Main interpretation:
    - USD asset share has little predictive power at short horizon but strong predictive power over longer horizons — consistent with time variation in exchange rate risk premia and persistent deviations from UIP.
- Table 6 specific shock example:
  - A positive shock to USD asset share by one-standard deviation (0.33% from Table 1) is contemporaneously correlated with USD appreciation of 8.1% per annum in that year (Column 5 of Table 3) and forecasts depreciation of 0.67% per annum over the next five years (Column 5 of Table 6).
- Table 7 — Five-year bilateral forecasting (univariate regressions ∆s_j,t^20 = α1 + β1 D_j,$,t + ε_t+20):
  - Panel A (individual D_j,$,t): selected coefficients and R^2:
    - AUD: -1.58*** (0.24), N=48, R^2=0.24
    - BRL: -4.55*** (0.85), N=43, R^2=0.57
    - CAD: 0.67* (0.34), N=48, R^2=0.04
    - JPY: 1.25*** (0.41), N=48, R^2=0.11
    - MXN: -0.77*** (0.19), N=43, R^2=0.27
    - MYR: 2.33*** (0.67), N=21, R^2=0.33
    - SGD: 2.23*** (0.23), N=36, R^2=0.63
    - ZAR: -1.86** (0.84), N=14, R^2=0.33
  - Panel B (cross-sectional average D̅$,t): examples:
    - ALL: -2.87*** (0.36), N=48, R^2=0.52
    - MXN: -0.59** (0.26), N=48, R^2=0.10
    - MYR: -5.46*** (0.71), N=30, R^2=0.56
  - Forecasting conclusion:
    - USD asset share predicts USD exchange rate at the 5% significance level or above for 10 out of 16 currencies (Panel A).
    - Cross-sectional average D̅$,t predicts bilateral exchange rates at the 5% significance level or above for all 16 currencies (Panel B).
- Out-of-sample forecasting (five-year horizon, h=20):
  - Rolling-window OOS forecasts compared to random walk; Diebold-Mariano and Clark-West adjustments used.
  - Baseline: P = round(T/2); alternative P = round(T*2/3) robust.
  - Table 8 highlights:
    - Panel A: MSE_r − MSE_u for ALL = 13.49; OOS-T statistic = 2.40***.
    - Panel A OOS-T statistics significant at 1% for columns: ALL (2.40***), AUD (2.89***), CAD (1.65**), CHF (2.31***), EUR (2.34***), INR (4.37***), MYR (2.18**), NOK (2.42***), SEK (2.39***), TRY (4.33***), ZAR (2.68***); others mixed.
    - Panel B: MSE_r − (MSE_u − Adj.) for ALL = 19.70; C-W statistic = 2.47***.
    - Forecasting model outperforms random walk for 11 out of 16 currencies at 10% significance (Diebold-Mariano), and in 15 out of 16 after Clark-West adjustment at 10% significance.
  - Overall OOS conclusion:
    - Model using USD asset share significantly outperforms random walk benchmark for USD exchange rate against a basket of 16 currencies (1% significance for cross-sectional average) and for the majority of individual currencies.

### Robustness, refined IVs, and horse-race forecasting
- Appendix Table 2 — refined 2SLS (six EMs: Brazil, India, Malaysia, Mexico, South Africa, Turkey):
  - First-stage: ∆Sovereign CDS_{sub,t} [bps] coefficients (columns (1)–(5)): 0.01*** (0.00), 0.01*** (0.00), 0.01*** (0.00), 0.01*** (0.00), 0.01** (0.00).
  - Stock-Yogo F Statistics: 19.34**, 31.10**, 27.00**, 26.17**, 5.66.
  - Second-stage — Fitted ∆D_{$,t} [%] coefficients:
    - (1) 90.58*** (9.82)
    - (2) 91.47*** (12.03)
    - (3) 87.84*** (7.86)
    - (4) 89.31*** (11.77)
    - (5) 99.80*** (36.22)
  - Durbin-Wu-Hausman F statistics (endogeneity): 44.34***, 68.49***, 51.79***, 63.99***, 43.67***.
  - Interpretation: refined 2SLS coefficients are positive, significant at 1%, and around three times as large as OLS in Appendix Table 3; reinforces causal link.
- Forecastability horse race (Appendix Table 3):
  - Augmenting 9 exchange rate models with USD asset share improves OOS performance in all comparisons.
  - Diebold-Mariano MSE_existing − MSE_augmented positive across all models; OOS-T significant at 10% or better across all 9 comparisons.
  - Selected results (MSE difference ; OOS-T):
    - UIP: 6.19 ; 2.32***.
    - Monetary flexible prices: 0.69 ; 0.84*.
    - Monetary sticky prices: 0.82 ; 1.14**.
    - Productivity differentials: 1.17 ; 2.01***.
    - Taylor rule: 4.63 ; 3.85***.
    - Net foreign asset: 8.15 ; 2.61***.
    - U.S. dollar liquidity: 7.53 ; 2.41***.
    - U.S. Treasury premium: 10.84 ; 3.56***.
    - U.S. foreign bond flow: 10.27 ; 3.19***.
  - Conclusion: including USD asset share improves out-of-sample forecasting performance for each model.

### Robustness and measurement caveats
- Measurement caveat:
  - Data measure aggregated value of USD assets over aggregated values of total assets of non-U.S. banks at nationality level; cannot fully separate quantity from exchange rate and price effects.
  - Adjustments using BIS LBS and bottom-up consolidated approach; contemporaneous analysis does not adjust local currency positions for exchange rate movements to avoid bias.
  - After adjusting local positions for exchange rate movements (Appendix Table 1), contemporaneous relationship persists for cross-sectional average but magnitudes decline by around 30% relative to unadjusted series; pre-GFC relationship becomes insignificant; for individual currencies holds at 10% significance or above for 8 out of 16 currencies.
- IV validity concerns and proposed refinements:
  - Validity depends on exogeneity to USD asset supply; concerns include correlation between non-U.S. banks’ balance sheet capacity and USD lending propensity, and FX swap supply affecting Treasury premium.
  - Proposed refinements:
    - Restrict 2SLS sample to smaller countries acting as price takers.
    - Use sovereign CDS only as IV.
    - Focus safety measures on Canadian Dollar, Swiss Franc, and Swedish Krona as substitutes.

### Key quantitative findings and magnitudes
- One-standard-deviation shock:
  - One-standard-deviation positive shock to USD asset share ≈ 0.33% (Table 1).
  - Associated contemporaneous USD appreciation: 8.1% per annum on average in that year (Column 5 of Table 3).
  - Forecasted subsequent depreciation: 0.67% per annum over the next five years (Column 5 of Table 6).
- Forecasting R2:
  - In-sample R2: 36 percent at two-year horizon; 67 percent at five-year horizon.
- 2SLS magnitudes:
  - Table 4 second-stage fitted ∆D̅̂$,t coefficients ~ 41.76 to 51.74 (***).
  - Appendix Table 2 second-stage fitted ∆D_{$,t} [%] coefficients ~ 87.84 to 99.80 (***).
- Predictability significance:
  - In-sample: D_j,$,t coefficients significant at 5% or 1% for horizons ≥ one year.
  - Out-of-sample: augmented models outperform random walk in majority of currencies and across benchmark models.

### Economic interpretation and implications for literature
- Mechanism:
  - Evidence supports an overshooting mechanism (Dornbusch (1976) style): strong USD asset demand by non-U.S. banks contemporaneously appreciates the USD and induces expected future depreciation through time-varying risk premia.
  - Intermediary asset pricing perspective: non-U.S. banks as marginal investors; their leverage and balance sheet capacity influence USD safe asset scarcity and FX risk premia.
- Implications across four strands:
  - United States as provider of world safe assets: RoW intermediaries accumulate USD safe assets counter-cyclically, paying safety premium and driving contemporaneous USD appreciation.
  - Exchange rate disconnect and quantity measures: quantity-based USD asset share measure captures foreign safe asset demand relevant for marginal investors.
  - Global financial cycle and USD cycle: causal links among USD asset demand, USD exchange rate, U.S. Treasury premium, and LIBOR CIP deviation; balance sheet constraints matter for interbank but less for Treasury market.
  - Intermediary asset pricing: non-U.S. banks’ leverage significantly accounts for changes in demand for USD denominated assets; average USD asset shares help explain cross-sectional currency excess returns.

*Italic: Source — wpiea2020101-print-pdf - Section V and forecasting relationships in Section VI.*

### Section V and to forecasting relationships in Section VI.

### Section V and to forecasting relationships in Section VI.

### B. Causal Relationship
- Objective: establish causal interpretation between demand for USD safe assets from non-U.S. banks and exchange rates using instrumental variables to separate supply and demand.
- Instrumental variable groups proposed:
  - Safety of substitute currencies (simple averages across six non-USD G10 currencies: Canadian Dollar, Euro, Japanese Yen, Pound Sterling, Swedish Krona, Swiss Franc):
    - i. Treasury premium of substitute economies, Φ̅sub,t, equal to (y̅j,tGovt − ρj,t − y̅sub,tGovt), capturing convenience yield on substitute safe assets.
    - ii. Sovereign CDS spread of substitute Treasury securities (5-year maturity from Markit), capturing sovereign risk of substitute safe assets.
  - Balance sheet constraints of non-U.S. banks:
    - Logarithm of the book leverage ratio from Fitchconnect orthogonalized with respect to U.S. bank leverage; higher (orthogonalized) leverage → balance sheet capacity deteriorates → demand for USD assets increases.
- First-stage (Equation (2)) findings (upper panel of Table 4; dependent variable = ∆D̅$,t):
  - Coefficient signs and significance:
    - ∆Φ̅sub,t: coefficient point estimates negative across columns (1)–(5); significant at the 10% level or above for 3 out of 5 specifications.
    - ∆Sovereign CDS̅sub,t: coefficient point estimates positive and significant at the 1% level across specifications.
    - ∆Leverage̅t: coefficient point estimates positive and significant at the 1% level across specifications.
  - Economic significance:
    - Variation from those three instrumental variables alone accounts for around 20% of the variation in contemporaneous changes of USD asset demand from non-U.S. banks.
  - Weak IV test:
    - Stock-Yogo F Statistics (columns (1)–(5)): 15.59**, 18.58**, 24.61**, 27.87**, 32.38**.
  - Sample size and goodness of fit:
    - N = 67; R2 = 0.18, 0.25, 0.18, 0.25, 0.26 across columns (1)–(5).
- Second-stage (Equation (3)) findings (lower panel of Table 4; dependent variable = ∆s̅t [Annualized %], using fitted ∆D̅̂$,t):
  - Fitted ∆D̅̂$,t coefficients (columns (1)–(5)):
    - 51.54*** (std. err. 14.57)
    - 51.55*** (13.40)
    - 51.74*** (14.04)
    - 50.28*** (13.28)
    - 41.76*** (9.74)
  - R2 and explanatory power:
    - R2 = 0.07, 0.07, 0.07, 0.11, 0.36 across columns (1)–(5).
    - Variation from predicted changes in USD asset share alone accounts for 7% of variation in contemporaneous changes in USD exchange rate (Column 1), compared with 36% from OLS (Table 3, Column 1).
    - Column (4): R2 rises marginally to 11% when including ∆Φ̅t and ∆(y̅tGovt − y$,tGovt); both are insignificant.
    - Column (5): including one-quarter lags raises R2 to 36%; point estimate on ∆D̅̂$,t drops to around 41.8 (still almost two times OLS estimate).
  - Endogeneity and overidentification:
    - Durbin-Wu-Hausman F Statistics: 8.18***, 3.60*, 8.72***, 3.73*, 3.10* across columns (1)–(5).
    - Sargan χ2 Statistics: 2.45, 2.36, 2.57, 2.48, 1.23 across columns (1)–(5) — inference supports instruments exogeneity.
  - Interpretation:
    - 2SLS coefficients on fitted USD asset share are positive and significant at the 1% level across specifications.
    - Magnitudes from 2SLS are about two times larger than OLS estimates, suggesting OLS underestimates the slope of the supply curve due to simultaneous supply and demand shifts.
    - The IV strategy identifies the supply curve by using demand shifters exogenous to supply conditions.

### C. Transmission Channels
- Goal: investigate relationships between U.S. Treasury premium, LIBOR cross-currency basis, and USD asset demand from non-U.S. banks using the IV strategy to distinguish “safe asset demand channel” (demand shifters) and “financial intermediation channel” (supply shifters).
- Second-stage results (Table 5; dependent variables: ∆ΦTreasury,t and ∆ΦLibor,t = (-1)*cross-currency basis):
  - Sample periods: Full (2001q2–2017q4) and Post-GFC (2010q1–2017q4).
  - Fitted ∆D̅̂$,t coefficients:
    - ∆ΦTreasury,t:
      - Full sample (Column 1): 0.46*** (0.15); R2 = 0.18; N = 67.
      - Post-GFC (Column 2): 0.58** (0.24); R2 = 0.19; N = 32.
    - ∆ΦLibor,t:
      - Full sample (Column 3): 0.29 (0.19); R2 = 0.06; N = 67 (not significant).
      - Post-GFC (Column 4): 0.20** (0.10); R2 = 0.20; N = 32 (positive and significant).
- Interpretation:
  - U.S. Treasury premium regressions: fitted USD asset share positive and statistically significant for full sample and larger post-GFC — supply curve in U.S. Treasury market identified as upward sloping in both samples.
  - LIBOR cross-currency basis regressions: fitted USD asset share not significant in full sample (supply curve may be flat pre-GFC), but positive and significant post-GFC — supply curve became upward-sloping after GFC.
  - Economic message:
    - “Safe asset demand channel” affects both LIBOR cross-currency swap market and U.S. Treasury market.
    - “Financial intermediation channel” has become important in the U.S. LIBOR cross-currency swap market post-GFC — U.S. financial intermediaries’ reduced balance sheet capacity limits CIP arbitrage since the GFC.
    - The financial intermediation channel is less critical in the U.S. Treasury market because the U.S. Treasury does not actively arbitrage away Treasury premium due to fiscal mandate.
  - Overall conclusion: IV strategy provides causal evidence differentiating roles of safe asset demand and financial intermediation channels across markets.

### V. CROSS-SECTIONAL ASSET PRICING
- Risk factor definition:
  - Global USD asset demand factor = cross-sectional average of annualized quarterly changes in USD asset share of non-U.S. banks across 16 economies.
- Currency excess return definition (Equation (5)):
  - Rj,t ≜ yj,t−1Govt − ∆sj,t − y$,t−1Govt.
- Methodology:
  - Two-stage Fama and MacBeth (1973) regression to estimate loadings (betas) on global USD asset demand (time-series first stage; cross-sectional second stage).
- Key findings:
  - Time-series regressions: loadings (β̂j) on ∆D$,t are negative and significant at the 5% level or above for individual currencies.
  - Higher interest rate currencies (e.g., BRL and ZAR) have larger (in absolute value) negative loadings than lower interest rate currencies (e.g., JPY and GBP).
  - Currency portfolios ranked by interest rate (Lustig, Roussanov, Verdelhan (2011), drop last portfolio) show higher interest rate portfolios tend to have higher loadings.
  - Cross-sectional relationship (Figure 4):
    - Strong negative correlation between average excess returns and USD demand betas:
      - Bivariate correlation = -58% for individual currencies.
      - Bivariate correlation = -76% for currency portfolios.
- Economic interpretation:
  - USD asset demand of non-U.S. banks acts as a global risk factor priced in the cross section of currency excess returns.
  - High interest rate currencies have larger negative exposure to USD asset demand factor, requiring higher expected excess returns to compensate for “currency crash” risk when global volatility spikes and demand for USD safe assets is strong.
  - Low interest rate currencies provide a hedge against USD asset demand risk.
- Linkages:
  - Consistent with evidence that currencies with more exposure to broad U.S. dollar index have higher excess returns from CIP trade.
  - Aligns with theories linking global imbalances, capital flows, and currency premia (e.g., Gourinchas and Rey 2007).

### VI. PREDICTABILITY
- VAR impulse response evidence (Figure 5):
  - A positive shock to USD asset share contemporaneously appreciates the USD exchange rate; the appreciation is nearly entirely undone after five years — consistent with overshooting and time-varying risk premia.
  - U.S. Treasury premium shock: contemporaneous USD appreciation, short-lived momentum for another quarter, then depreciation over one-to-five years.
  - Interest differential (home – U.S.) shock: USD appreciates in first two years, then wanes over next three years.
  - VAR details: four-variable VAR in USD asset share, U.S. Treasury premium, interest rate differential (home – U.S.), and exchange rate; Cholesky ordering: exchange rate, U.S. Treasury premium, interest rate differential, USD asset share; sample 2001q2–2017q4.
- A. In-sample Forecasting (Equation (6)):
  - Regression: ∆sj,t^h = α1 + β1 Dj,$,t + β2 Φj,t + β3 (yj,tGovt − y$,tGovt) + εt+h, horizons h = 1 quarter, 1 year, 2 years, 3 years, 5 years.
  - Main result summary (Table 6 referenced):
    - USD asset share has little predictive power at short horizon but strong predictive power over longer horizons — consistent with time variation in exchange rate risk premia and persistent deviations from uncovered interest parity.
    - Coefficient point estimates on USD asset share (D̅$,t) "start from -0.27 (not significant) at the one-quarter horizon, and then stabilizes to a level between" (text ends here).

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### 2.02 and 2.75 per annum from one-year to five-year horizon at 5% significance level or above.

### wpiea2020101-print-pdf - 2.02 and 2.75 per annum from one-year to five-year horizon at 5% significance level or above.

### Main empirical findings on USD asset share and exchange rates
- A positive shock to USD asset share by one-standard deviation (0.33% from Table 1) is contemporaneously correlated with an appreciation of the U.S dollar by 8.1% (Column 5 of Table 3) per annum in that year on average, but it is expected to depreciate by 0.67% (Column 5 of Table 6) per annum over the next five years on average to wane down the overshooting.
- Results indicate an overshooting pattern: demand for USD assets leads to a sharp contemporaneous appreciation of the USD, which is reverted slowly over time.
- Time-varying USD risk premia covary with demand for USD denominated safe assets by non-U.S. banks; the scarcity of safe USD assets is driven in part by risk-taking capacity of non-U.S. banks, which enters the pricing kernel of marginal FX investors.

### Table 6 — In-sample forecasting of annualized % change in USD (∆s_h_t) (key coefficients and summary)
- Dependent variable = ∆s_h_t [Annualized %]; horizons h = 1, 4, 8, 12, 20 (one-quarter, one-year, two-year, three-year, five-year).
- Regressor D_j,$,t [%] coefficients (with Newey-West SEs in parentheses):
  - h=1: -0.27 (1.59)
  - h=4: -2.22** (0.92)
  - h=8: -2.75*** (0.55)
  - h=12: -2.54*** (0.38)
  - h=20: -2.02*** (0.30)
- Regressor Φ_t [%] coefficients:
  - h=1: 4.66 (8.56)
  - h=4: -4.34 (3.72)
  - h=8: -5.16** (2.37)
  - h=12: -1.67 (1.48)
  - h=20: 0.49 (1.39)
- Regressor (y_t − y$_t) [%] coefficients:
  - h=1: 2.57 (1.92)
  - h=4: 2.69** (1.16)
  - h=8: 1.74** (0.71)
  - h=12: 0.73 (0.50)
  - h=20: 0.65* (0.37)
- Sample sizes (N): 67, 64, 60, 56, 48 for h=1,4,8,12,20 respectively.
- R^2 by horizon:
  - h=1: 0.06
  - h=4: 0.20
  - h=8: 0.36
  - h=12: 0.45
  - h=20: 0.67
- Notes:
  - Specification: ∆s_j,t^h = α1 + β1 D_j,$,t + β2 Φ_j,t + β3 (y_j,t^Govt − y$,t^Govt) + ε_t+h.
  - Series are cross-sectional averages over 16 currencies, quarter-end values. Sample period 2001q2 to 2017q4.
  - *, **, *** denote significance at 10%, 5%, and 1%.

### Table 7 — Five-year bilateral forecasting (univariate regressions)
- Univariate specification: ∆s_j,t^20 = α1 + β1 D_j,$,t + ε_t+20.
- Panel A (individual USD asset share D_j,$,t): D_j,$,t [%] coefficients and R^2 (columns correspond to currencies; selected examples):
  - AUD: coefficient -1.58*** (0.24), N=48, R^2=0.24
  - BRL: -4.55*** (0.85), N=43, R^2=0.57
  - CAD: 0.67* (0.34), N=48, R^2=0.04
  - JPY: 1.25*** (0.41), N=48, R^2=0.11
  - MXN: -0.77*** (0.19), N=43, R^2=0.27
  - MYR: 2.33*** (0.67), N=21, R^2=0.33
  - SGD: 2.23*** (0.23), N=36, R^2=0.63
  - ZAR: -1.86** (0.84), N=14, R^2=0.33
- Panel B (cross-sectional average USD asset share D̅$,t): coefficients on D̅$,t [%] and R^2 (selected examples):
  - ALL (cross-sectional average): -2.87*** (0.36), N=48, R^2=0.52
  - MXN: -0.59** (0.26), N=48, R^2=0.10
  - MYR: -5.46*** (0.71), N=30, R^2=0.56
  - AUD: -2.87*** (0.36), R^2=0.52 (see column mapping)
  - Coefficient point estimates on D̅$,t vary from 0.59% per annum (for MXN) to 5.46% per annum (for MYR) as reported; R^2 varies from 10% (MXN) to 69% (MYR) in the sample.
- Forecasting conclusion:
  - USD asset share from each economy predicts USD exchange rate at the 5% significance level or above for 10 out of 16 currencies (Panel A).
  - Cross-sectional average D̅$,t predicts bilateral exchange rates at the 5% significance level or above for all 16 currencies (Panel B).
  - These results suggest the common global component in USD asset share forecasts USD exchange rates against individual currencies.

### Out-of-sample forecasting (five-year horizon, h=20)
- Method: rolling-window OOS forecasts using regression ∆s_j,t^h = α1 + β1 D_j,$,t; compare MSEs against random walk; use Diebold-Mariano (1995) and West (1996) statistics and Clark-West (2006) adjustment for nested model bias.
- Baseline: P = round(T/2), K = T − P; alternative P = round(T*2/3) yields robust results.
- Table 8 — Diebold-Mariano (Panel A) and Clark-West (Panel B) outcomes (selected highlights):
  - Panel A: MSE_r − MSE_u for ALL = 13.49; OOS-T statistic = 2.40*** (cross-sectional average over 16 currencies, Column 1).
  - Panel A OOS-T statistics significant at 1% for columns: ALL (2.40***), AUD (2.89***), CAD (1.65**), CHF (2.31***), EUR (2.34***), INR (4.37***), JPY (1.21), MYR (2.18**), NOK (2.42***), SEK (2.39***), SGD (0.78), TRY (4.33***), ZAR (2.68***).
  - Panel B: MSE_r − (MSE_u − Adj.) for ALL = 19.70; C-W statistic = 2.47***.
  - Panel B C-W statistics significant at 1% for many currencies; summary: forecasting model outperforms random walk for 11 out of 16 currencies at 10% significance level or above (Diebold-Mariano), and outperforms in 15 out of 16 currencies at 10% significance level or above after Clark-West adjustment.
- Overall out-of-sample conclusion:
  - The forecasting model using USD asset share significantly outperforms the random walk benchmark for the USD exchange rate against a basket of 16 currencies (1% significance for cross-sectional average) and for the majority of individual currencies.

### Interpretation and mechanism
- The empirical evidence supports an overshooting mechanism in the spirit of Dornbusch (1976): strong USD asset demand by non-U.S. banks contemporaneously appreciates the USD and induces expected future depreciation.
- The authors emphasize an intermediary asset pricing story: the marginal investor role of non-U.S. banks, their risk-taking capacity, and measures such as leverage are candidate explanatory variables linking USD asset scarcity to time-varying FX risk premia and exchange rate predictability.
- The forecasting power of the USD asset share is robust both in-sample and out-of-sample.

### Robustness: measurement and identification caveats
- Measurement caveat:
  - Data measure aggregated value of USD assets over aggregated values of total assets of non-U.S. banks at nationality level; cannot separate quantity from exchange rate and price effects.
  - Adjustments made using BIS Locational Banking Statistics (LBS) and bottom-up consolidated approach (FitchConnect and Factset); do not adjust local currency positions for exchange rate movements in contemporaneous relationship analysis to avoid bias.
  - After adjusting local positions for exchange rate movements (Appendix Table 1), contemporaneous relationship persists for cross-sectional average but magnitudes decline by around 30% relative to unadjusted series; contemporaneous relationship becomes insignificant prior to the Global Financial Crisis; for individual currencies holds at 10% significance level or above for 8 out of 16 currencies.
- Validity of instrumental variables (IVs) and identification concerns:
  - Observed changes in USD asset share reflect both demand and supply of USD assets; large economies both demand and provide USD assets, complicating identification.
  - The validity of IVs depends on exogeneity to USD asset supply conditions; concerns include correlation of non-U.S. banks’ balance sheet capacity with propensity to lend in USD and FX swaps supply affecting the Treasury premium.
  - Proposed refinements:
    - Restrict 2SLS sample to smaller countries acting more as price takers.
    - Use sovereign CDS only as IV.
    - Focus safety measures on Canadian Dollar, Swiss Franc, and Swedish Krona as substitute currencies to reduce correlation with USD asset supply.

*Italic source: Source PDF filename: wpiea2020101-print-pdf - 2.02 and 2.75 per annum from one-year to five-year horizon at 5% significance level or above.*

### Appendix Table 2 reports the results of the 2SLS. In the upper panel, we present the results for

### wpiea2020101-print-pdf - Appendix Table 2 reports the results of the 2SLS. In the upper panel, we present the results for

### 2SLS results (first and second stages, refined IV strategy)
- First stage (upper panel):
  - Coefficient point estimates on ∆푆표푣푒푟푒푖푔푛 퐶퐷푆
̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅
푡
푠푢푏
 are positive and significant at the 1% level across all specifications.
  - Based on critical values reported in Stock and Yogo (2002), the null that the proposed IV is a weak instrument can be rejected for 4 out of 5 specifications at the 5% significance level or above.
- Second stage (lower panel):
  - Coefficient point estimates on ∆퐷
̅
̂
$,푡
 are positive and significant at the 1% level across all specifications.
  - Magnitudes of the refined 2SLS coefficient point estimates on ∆퐷
̅
̂
$,푡
 are around three times as large as those obtained by OLS in Appendix Table 3.
  - The 퐹 statistic of the Durbin-Wu-Hausman test of endogeneity allows rejection that the USD asset share is exogenous from all specifications at the 10% level or higher.
  - Interpretation: OLS underestimates the slope of the supply curve; the refined IV strategy corrects this bias and increases confidence in a causal relationship between USD safe asset demand and USD exchange rate movements.

### Forecastability of exchange rates (robustness and horse race)
- Forecasting exercise:
  - Compared forecasting performance of augmented models that include the USD asset share as an additional predictor against 9 exchange rate forecasting models discussed in the literature.
  - Models considered (guided by Rossi (2013)) include: (1) UIP; (2) monetary model with flexible prices (“Frankel-Bilson”); (3) monetary model with sticky prices (“Dornbusch-Frankel”); (4) productivity differentials (“Balassa-Samuelson”); (5) Taylor rule; (6) net foreign asset (“Gourinchas-Rey”); (7) dollar liquidity (Adrian, Etula, and Shin (2010)); (8) Treasury premium (Jiang, Krishnamurthy, and Lustig (2018)); (9) U.S. foreign bond flow (Lilley, Neiman, Maggiori, and Schreger (2019)).
- Out-of-sample performance (Appendix Table 3):
  - Diebold-Mariano difference in MSEs reported as 푀푆퐸
푒푥푖푠푡푖푛푔
−
푀푆퐸
푎푢푔푚푒푛푡푒푑
 is positive across all models.
  - The OOS-T statistic is significant at the 10% level or above across all 9 comparisons.
  - Conclusion: Including the USD asset share as an additional predictor improves out-of-sample forecasting performance for each of the 9 models.

### Summary of empirical robustness and main mechanism
- Contemporaneous relationship:
  - The contemporaneous relationship between changes in the USD asset share of non-U.S. banks and changes in the USD exchange rate holds when local currency positions are considered, though the relationship is somewhat weaker and complete isolation of quantity from value is limited by data.
- IV validity:
  - The refined IV strategy addresses several validity concerns and strengthens causal inference between contemporaneous changes in USD safe asset demand and USD exchange rate.
- Forecasting improvement:
  - The cross-sectional average of USD asset share from non-U.S. banks across 16 economies improves forecasting performance of 9 existing exchange rate models.
- Economic interpretation:
  - Exchange rates deviate significantly from the random walk benchmark as a function of the USD asset demand share of non-U.S. banks, indicating exchange rate overshooting driven by time-varying intermediary risk premia.

### Implications for the literature (four strands)
- United States as provider of world safe assets:
  - Evidence supports theories where RoW financial intermediaries accumulate USD safe assets counter-cyclically, paying a safety premium and driving contemporaneous USD appreciation following negative shocks.
- Exchange rate disconnect and quantity measures:
  - Links demand-for-safety measures (e.g., Treasury premium) and FX market quantities (e.g., order flows); shows a quantity-based measure captures foreign safe asset demand, especially for marginal investors.
  - Novel IV approach identifies a causal link between safe asset demand from non-U.S. banks and the USD exchange rate.
- Global financial cycle and USD cycle:
  - Establishes causal relationships among USD asset demand from non-U.S. banks, U.S. dollar exchange rate, U.S. Treasury premium, and LIBOR CIP deviation.
  - Provides evidence that balance sheet constraints of non-U.S. intermediaries matter in the U.S. interbank market but not in the U.S. Treasury market, differentiating “safe asset demand” and “financial intermediation” channels.
- Intermediary asset pricing:
  - Shows non-U.S. banks’ leverage significantly accounts for changes in their demand for USD denominated assets.
  - Average USD asset shares of non-U.S. banks help explain variation in currency excess returns, contributing to cross-sectional asset pricing theory.

### Key quantitative findings and forecasting magnitudes
- Shock and immediate appreciation:
  - A positive shock to the USD asset share by non-U.S. banks of one-standard deviation (around 0.33 percent from Table 1) is associated with appreciation of the USD by 8.1 percent per annum on average in that same year (Column (4) of Table 3).
- Subsequent reversal:
  - The same one-standard deviation shock forecasts a depreciation of the USD by an average of 0.67 percent per annum over the next five years (Column (5) of Table 6).
- Forecasting R2:
  - In-sample 푅
2
s are 36 percent at the two-year horizon and 67 percent at the five-year horizon.
- Interpretation:
  - Results consistent with Dornbusch (1976) overshooting: USD asset demand shocks compress risk premia and drive contemporaneous appreciation, which then reverts over five years.
  - Time-varying FX risk premia linked systematically to demand for USD denominated safe assets from non-U.S. banks produce strong forecastability and reject the random walk hypothesis.
- Cross-sectional asset pricing:
  - In Fama-MacBeth regressions, currencies and carry-trade portfolios earn significant excess returns with higher loadings on the global USD asset demand factor; the price of risk on the USD asset demand factor is negative.

*Source: wpiea2020101-print-pdf - Appendix Table 2 reports the results of the 2SLS. In the upper panel, we present the results for*

### REFERENCES

### wpiea2020101-print-pdf - REFERENCES (Appendix tables summary)

### Appendix Table 1 — Valuation Adjusted USD Assets Share and Exchange Rates: setup and sample
- Dependent variable: ∆s_{j,t} = annualized quarterly change in the log nominal exchange rate of the USD vis-à-vis currency j (an increase means USD appreciates).
- Key regressors:
  - ∆D_{$,j,t} (Adj.) = quarterly changes in the USD asset share of non-U.S. banks from economy j (local positions adjusted for exchange rate movements).
  - ∆Φ_{j,t} = quarterly changes in the U.S. Treasury premium vis-à-vis economy j.
  - ∆(y_{j,t}^{Govt} − y_{$,t}^{Govt}) = quarterly changes in the interest differential of economy j over the United States.
  - X_{j,t} includes controls: D_{$,j,t−1}, Φ_{j,t−1}, (y_{j,t−1}^{Govt} − y_{$,t−1}^{Govt}).
- All series are cross-sectional averages over 16 currencies (quarter end) for Columns (1)–(7); Columns (8)–(23) are bilateral regressions by currency.
- Estimation: OLS with Newey-West heteroskedasticity-and-autocorrelation-consistent asymptotic standard errors (reported in parentheses).
- Significance notation: *, **, and *** denote 10%, 5%, and 1%.
- Sample period: 2001q2 to 2017q4.
- Includes indicator 1[quarter=2008Q4] and a constant (constant not reported).

### Appendix Table 1 — Key coefficient estimates (selected)
- Regressor ∆D_{$,t} (Adj.) [%] — coefficients and standard errors (selected columns):
  - (1) Cross-sectional Average, Full Sample: 15.35*** (5.26)
  - (2) 9.72** (4.32)
  - (3) 15.28*** (5.22)
  - (4) 9.28** (4.24)
  - (5) 10.68** (4.37)
  - (6) Pre-GFC: 9.23 (6.75)
  - (7) Post-GFC: 16.38** (7.25)
  - Selected bilateral (examples):
    - AUD: 16.27*** (4.51)
    - BRL: 45.53** (20.54)
    - CAD: 2.64 (1.87)
    - CHF: 4.24*** (1.57)
    - EUR: 11.37*** (3.23)
    - GBP: -3.63* (2.04)
    - JPY: 16.11*** (4.89)
    - KRW: 7.23 (5.60)
    - MXN: 6.17** (10.18)
    - TRY: 8.58*** (5.01)
    - ZAR: 14.01* (2.74)
- Regressor ∆Φ_{t} [%] — coefficients and standard errors (selected columns):
  - (1) 20.17*** (7.58)
  - (2) 21.37*** (6.82)
  - (3) 24.97*** (6.14)
  - (4) -11.62 (26.14)
  - (5) 34.99*** (10.48)
  - Bilateral examples:
    - AUD: 28.88** (12.73)
    - BRL: 37.22*** (9.93)
    - CAD: 45.68*** (12.84)
    - EUR: 26.41*** (7.63)
    - GBP: 3.89* (2.08)
    - JPY: 25.25*** (4.83)
    - KRW: 19.55*** (7.36)
    - TRY: 27.95 (24.08)
    - ZAR: 13.84 (18.64)
- Regressor ∆(y_{t}-y_{$,t}) [%] — coefficients and standard errors (selected):
  - (1) -3.08 (4.29)
  - (2) -4.92 (4.99)
  - (3) -4.37 (4.51)
  - (4) 17.18 (10.46)
  - (5) -10.14 (10.17)
  - Bilateral examples:
    - AUD: -19.46*** (7.06)
    - BRL: -18.10** (6.99)
    - CAD: -15.16*** (5.11)
    - EUR: -10.86 (6.93)
    - GBP: 0.13 (3.54)
    - JPY: -17.38*** (4.58)
    - KRW: -16.72** (6.42)
    - MXN: -17.00** (6.62)
    - TRY: 5.95*** (1.98)
    - ZAR: 7.08 (13.83)
- Observations (N) and R^2 (selected):
  - Cross-sectional Average (columns 1–5): N = 67; R^2 ranges: 0.19, 0.28, 0.20, 0.29, 0.33.
  - Pre-GFC (col 6): N = 23; R^2 = 0.41.
  - Post-GFC (col 7): N = 32; R^2 = 0.48.
  - Bilateral examples R^2:
    - AUD (col 8): 0.48 (N = 67)
    - BRL (col 9): 0.45 (N = 43)
    - JPY (col 15): 0.24 (N = 64)
    - TRY (col 22): 0.49 (N = 51)
    - ZAR (col 23): 0.26 (N = 33)

### Appendix Table 2 — Refined Two-Stage Least Squares: setup and sample
- Scope: 2SLS contemporaneous relationship between USD exchange rate and USD asset share of non-U.S. banks for six emerging markets: Brazil, India, Malaysia, Mexico, South Africa, Turkey.
- First-stage specification:
  - Dependent variable ∆D̅_{$,t} = average quarterly changes in USD asset share of non-U.S. banks (across the six EMs).
  - Instrument: ∆Sovereign CDS̅_{t}^{sub} = average quarterly changes in sovereign CDS spread of substitute government bonds (substitute countries: Canada, Switzerland, Sweden).
  - Controls X̅_{t} include D̅_{$,t−1}, Φ̅_{t−1}, and (ȳ_{t−1}^{Govt} − y_{$,t−1}^{Govt}).
- Second-stage specification:
  - Dependent variable ∆s̅_{t} = cross-sectional average USD exchange rate change (annualized %).
  - Uses fitted ∆D̅̂_{$,t} from first stage.
- Estimation details:
  - Newey-West heteroskedasticity-and-autocorrelation-consistent asymptotic standard errors (in parentheses).
  - Stock-Yogo weak instrument critical value: 13.91 for 1 endogenous regressor, 3 instruments, desired maximal bias 0.05.
  - Endogeneity test: Durbin-Wu-Hausman F statistics reported.
  - Significance notation: *, **, *** denote 10%, 5%, 1%.
  - Sample period: 2001q2 to 2017q4.
  - All series are cross-sectional averages over 6 currencies (quarter end).

### Appendix Table 2 — First-stage and second-stage key estimates
- First stage: ∆Sovereign CDS_{sub,t} [bps] coefficients:
  - (1) 0.01*** (0.00)
  - (2) 0.01*** (0.00)
  - (3) 0.01*** (0.00)
  - (4) 0.01*** (0.00)
  - (5) 0.01** (0.00)
- Stock-Yogo F Statistics (first-stage weak instrument test):
  - (1) 19.34**
  - (2) 31.10**
  - (3) 27.00**
  - (4) 26.17**
  - (5) 5.66
- Second stage — Fitted ∆D_{$,t} [%] coefficients:
  - (1) 90.58*** (9.82)
  - (2) 91.47*** (12.03)
  - (3) 87.84*** (7.86)
  - (4) 89.31*** (11.77)
  - (5) 99.80*** (36.22)
- Second stage — other regressors (selected):
  - ∆Φ_{t} [%]: (1) 3.36 (7.10); (2) 6.89 (8.27); (3) 2.03 (14.25)
  - ∆(y_{t}-y_{$,t}) [%]: (1) -11.16 (10.07); (2) -12.60 (11.15); (3) -17.82 (20.15)
- Endogeneity: Durbin-Wu-Hausman F statistics (for second stage):
  - (1) 44.34***
  - (2) 68.49***
  - (3) 51.79***
  - (4) 63.99***
  - (5) 43.67***
- Observations (N): typically 67 (66 in column 5); some specifications include controls (col 5).

### Appendix Table 3 — Robustness of Out-of-sample Forecastability: setup
- Goal: Investigate robustness of out-of-sample forecasting performance of the USD asset share in predicting U.S. dollar exchange rates against a basket of 16 currencies at the 5-year horizon.
- Method: Compare 9 existing exchange rate models to augmented versions that include the USD asset share as an additional predictor.
- Statistics reported:
  - Diebold-Mariano difference in MSEs: MSE_existing − MSE_augmented.
  - OOS-T statistics (HAC standard errors following Clark and West 2006).
- Critical values for OOS-T (k^2 = 1 and π = 0.2) from McCracken (2007) Table 1:
  - 90%: 0.780
  - 95%: 1.111
  - 99%: 1.784
- Series: cross-sectional averages over 16 currencies (quarter end).
- Significance notation: *, **, *** denote 10%, 5%, 1%.
- Sample period: 2001q2 to 2017q4.

### Appendix Table 3 — Results (MSE difference and OOS-T statistics)
- (1) UIP model: MSE_existing − MSE_augmented = 6.19; OOS-T = 2.32***.
- (2) Monetary model with flexible prices (Frankel-Bilson model): 0.69; 0.84*.
- (3) Monetary model with sticky prices (Dornbusch-Frankel model): 0.82; 1.14**.
- (4) Productivity differentials model (Balassa-Samuelson model): 1.17; 2.01***.
- (5) Taylor rule model: 4.63; 3.85***.
- (6) Net foreign asset model (Gourinchas-Rey model): 8.15; 2.61***.
- (7) U.S. dollar liquidity model (Adrian-Etula-Shin model): 7.53; 2.41***.
- (8) U.S. Treasury premium model (Jiang-Krishnamurthy-Lustig model): 10.84; 3.56***.
- (9) U.S. foreign bond flow model (Lilley-Neiman-Maggiori-Schreger model): 10.27; 3.19***.

*Source: wpiea2020101-print-pdf - REFERENCES (appendix tables and notes).*

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_Source: https://www.imf.org/-/media/files/publications/wp/2020/english/wpiea2020101-print-pdf.pdf_