## _wp13223

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---

### Introduction and research question
- Investigates why yield curves shift across countries and what determines time variation in the “price of risk” for long-term bonds.
- Emphasizes importance of time-varying term premia for central bank policy and measurement of risk on long-term bonds.
- Notes limited attention in the literature to international spillovers in yield curves despite financial integration and global holdings of domestic government debt.

### Data scope and modeling approach
- Sample: yields to maturity on zero coupon yield curves for seven open economies (United Kingdom, Canada, Germany, Japan, Australia, New Zealand and Switzerland), starting in 1990 and ending in the first quarter of 2009; quarterly frequency computed as simple averages of monthly observations; maturities from three months to ten years resulting in 40 series of zero coupon yields per country.
- US yields used to construct global factors but US not modeled as a small open economy.
- Modeling: discrete-time affine term structure model embedded in a factor-augmented VAR (FAVAR) framework.
  - State vector Y_it = [X_it ; F_t] with country-specific X_it (local level, slope, curvature) and global F_t (global level, global slope, global curvature).
  - Price of risk λ_it affine in Y_it: λ_it = λ_0 + λ_1' Y_it.
  - Short rate linear in Y_it: 1_it y = δ_0 + δ_1' Y_it.
  - Dynamics: X_it = μ_i + Φ_i X_{t-1} + Λ_i F_{t-1} + v_it; F_t = μ_F + F_{t-1} Ω + η_t.
- Identification: shocks to local and global factor equations assumed uncorrelated (0 = E_t η_t υ'_t); structural identification via B^0 and C^0 with Σ_υ = B^0 B^0' and Σ_η = C^0 C^0'.

### Estimation strategy
- Four-step estimation:
  1. Extract global factors F_t and country latent factors X_it via principal components.
  2. Estimate FAVAR parameters (Γ, Ψ, μ~) conditional on factors via OLS.
  3. Estimate δ_0 and δ_1 via OLS of short-rate on Y_it.
  4. Estimate λ_0 and λ_1 by minimizing sum of squared differences between actual and fitted yields (equation (4)).
- Latent factors:
  - Country-specific X_it: first three principal components of each country's zero-coupon yields (labeled "local level", "local slope", "local curvature").
  - Global F_t: first three principal components extracted from matrix M_t that includes term structures of all N countries and the U.S.; the first three global principal components account for more than 96 percent of total variance of all yields.
- Small-sample bias correction: inverse bootstrap/indirect inference bias correction following Bauer, Rudebusch and Wu (2012, 2013) and stationarity adjustment (Kilian (1998)); standard bootstrap gives similar qualitative results.

### Key empirical findings — global factors and economic interpretation
- Global factors are the ultimate drivers of both yield curve and term premia dynamics across countries.
- Economic interpretation of global factors:
  - Global level ≈ global expected inflation:
    - Constructed as first principal component of one-year-ahead CPI inflation forecasts across countries.
    - Correlation with inflation factor: 0.94.
  - Global slope ≈ global real activity:
    - Constructed as first principal component of real GDP growth, industrial production and unemployment across countries.
    - Correlation with real activity index: 0.77.
  - Global curvature (third global factor) ≈ long-term risk factor related to future financial and economic instability:
    - Third global factor spikes precede U.S. recession probabilities and increases in standard deviation of one-year-ahead US GDP growth forecasts.
    - Correlation with inflation uncertainty: 77% up to early 2000s recession; 64% in overall sample.
    - Leads St. Louis Fed financial stress index inversions (2003 and onset of recent crisis) and U.S. economic policy uncertainty index in recent crisis.
    - During 2007–2009, peaks in third global factor precede global expansionary monetary policies; example equally weighted average yield curve: Q2 2007 flat at 4.5 percent; by Q4 2008 short-end around 2 percent.

### Model fit, block exogeneity, and factor importance
- Block exogeneity tests (likelihood ratio) strongly reject null that global factors do not affect domestic factor dynamics (0 = Λ_i rejected for all countries).
- Fit of affine term structure model — root mean square fitting error (RMSE) in percentage points (Table 2):
  - JPN 0.0212
  - UK 0.0606
  - GER 0.0214
  - SWI 0.0406
  - CAN 0.0371
  - AUS 0.0317
  - NZL 0.0155
- Root mean square fitting errors of yields typically range between 1.5 and 6 basis points; New Zealand, Germany and Japan exhibit the best fit.
- Variance decompositions of local factors:
  - At 1 quarter horizon:
    - Global factors explain on average: 54 percent of the local level, 24 percent of the local curvature, and 3 percent of the local slope.
  - At 40 quarters horizon:
    - Global factors explain almost entirely the level of interest rates: proportion ranges between 95.5 percent in Japan and 99.3 percent in Germany.
    - Global factors explain more than 50 percent of variance of domestic slope and curvature in most countries.
- Contribution of global shocks to variance of domestic yields:
  - At 40-quarter horizon, global shocks explain more than 80 percent of variance of yields across all maturities.
  - Effect increases with maturity, reaching a maximum between 15 and 25 quarters (country-dependent).
  - By h = 1 quarter domestic shocks explain most variance; by h = 4 quarters global shocks dominate.

### Term premia dynamics and drivers
- Term premia definition: difference between model-implied 5-year forward rate 5 years from now and average expected one-year rates 5 to 10 years from now (Wright (2011) approach).
- Cross-country patterns:
  - Term premia declined from early 1990s until early 2000s, then increased afterwards; at onset of the Great Recession term premia increased by about 4 percentage points in most countries.
  - Western economies show more volatile term premia than Pacific countries (Japan, Australia, New Zealand).
  - Term premia sometimes negative after mid-1990s in some countries.
- Comparison to other studies:
  - Term premia here more volatile and countercyclical than in Wright (2011) and Bauer, Rudebusch and Wu (2013).
  - Bias correction increases volatility relative to simple OLS; inclusion of global factors further increases volatility of expectations of future short-term rates, especially at longer horizons.
- Counterfactuals and variance decompositions:
  - Counterfactuals with only global shocks reproduce the long-term decline and steep increase during the Great Recession and closely track actual term premia; local-only counterfactuals often diverge from actual series.
  - Contribution of global factors to term premia variation ranges between 65 percent (Germany) and 92 percent (UK).
  - Global curvature factor explains around 60 percent of total variance at 40 quarters horizon on average.
  - Global level factor is most important in explaining forward rates dynamics.
- Impulse responses of term premia to global shocks:
  - Positive global real activity (slope) shock → reduction in term premium in most countries (except small positive effect in Australia and New Zealand).
  - Positive global curvature shock → increase in term premia across countries; effect large and persistent (usually > 30 quarters). Mechanism: risk-neutral rate decreases more than long (forward) rate due to credible monetary policy easing, raising the term premium.
  - Positive global level (expected inflation) shock → increase in term premium in all countries except Germany (in Germany term premium decreases because risk-neutral rate increases by more than long/forward rates due to high monetary policy credibility).
- Country examples:
  - Japan: term premium dynamics similar to counterfactual with global level shock only (global expected inflation explains most variance).
  - UK: term premium dynamics mostly explained by global long-run risk factor; global inflation factor responsible for downward trend early in sample.
- Overall pattern:
  - Global expected inflation mainly responsible for downward trend of term premia in early sample.
  - Global real activity and especially global long-run risk (curvature) drive short-run fluctuations and the large increase at the onset of the Great Recession.

### Quantitative summary and sensitivity
- When estimated on the full sample, average contribution of global factors to term premia dynamics is 85 percent.
- Re-estimated over 1990Q1–2007Q2 (omitting last eight observations), average contribution is 77 percent.
  - In the 1990Q1–2007Q2 subsample:
    - Expected inflation increases in relative importance, explaining on average 47 percent of the variance of the term premia.
    - The third global factor accounts for 13 percent of the total variance.
- Country-level contribution range: global factors explain between 65 percent and 92 percent of term premia variation across countries (examples: Germany 65 percent, UK 92 percent).
- Robustness to bias correction:
  - Bias correction materially affects identification of term premium: OLS-identified term premium shows clearer downward trend, is less volatile/countercyclical, and exhibits a smaller increase in the Great Recession.
  - Despite differences, conclusions about the importance of global factors hold under OLS: global shocks still account, on average, for more than 70 percent of total variance in term premia.
  - Under OLS, contribution of global expected inflation shock increases (e.g., nearly doubles from 16 percent to 29 percent in reported comparisons) while the third global factor’s contribution is reduced.
- Alternative global factor definition:
  - Using first three principal components of the US yield curve as global factors still yields above 80 percent explanation of term premia variation; global curvature remains the most important factor though its relative explanatory power shifts toward the global cycle factor.

### Policy implications and suggested extensions
- International financial linkages embedded in global financial markets matter for term structures in open economies even with no-arbitrage affine specifications.
- Prominent role of global expected inflation in explaining long-run declines in term premia suggests global disinflationary trends and expectations formation are key drivers of bond risk premia in small-open economies.
- Identification of a global long-run risk factor that rises in crisis times indicates analyses of term premia should account for macro-financial risk channels and international spillovers.
- Authors’ stated future work:
  - Examine term structure implications of the zero–or near zero–interest rate lower bound in years beyond sample.
  - Analyze international spillovers of unconventional monetary policies implemented during and after the crisis period.

*Italic: Source — _wp13223*

### 1. Block Exogeneity Test ...............................................................................................

### 1. Block Exogeneity Test

### Introduction and research question
- Investigates why yield curves shift across countries and what determines time variation in the “price of risk” for long-term bonds.
- Emphasizes the importance of time-varying term premia for central bank policy and measurement of risk on long-term bonds.
- Highlights limited attention in the literature to international spillovers in yield curves despite financial integration and global holdings of domestic government debt.

### Data scope and modeling approach
- Sample covers the yield curves of seven open economies: Canada, United Kingdom, Japan, Germany, Australia, New Zealand and Switzerland.
- Introduces global factors into an affine term structure model by modeling yield curve dynamics as a factor augmented VAR (FAVAR) in the spirit of Stock and Watson (2005).
- Traditional latent yield factors (level, slope, curvature) augmented with global counterparts: “global level”, “global slope” and “global curvature”.

### Key empirical findings
- Global factors are the ultimate drivers of both yield curve and term premia dynamics across countries.
- Global factors have clear economic interpretation:
  - Global level corresponds to global expected inflation.
  - Global slope mimics global growth.
  - Global curvature is identified as a distinct and important factor, akin to a long-run risk factor related to future financial and economic instability.
- A shock to global curvature substantially increases the term premium.
- During the recent credit crisis, central banks engaged in unconventionally persistent expansionary policies; expected short-rates fell relative to long-rates and this contributed to an increase in the risk component of long-term bonds.

### Novel contributions relative to existing literature
- Extends Diebold, Li and Yue (2008) by demonstrating the importance of a third global factor—global curvature—alongside global level and global slope.
- Unlike approaches that impose international finance restrictions (for example, assuming complete markets and uncovered interest rate parity), the model allows both global and local/idiosyncratic factors to matter.
- Adopts elements from Moench (2008) by collapsing macroeconomic information into a small number of latent factors within an affine term structure framework.
- Employs the inverse bootstrap bias correction in the estimation of the FAVAR, following Bauer, Rudebush and Wu (2012, 2013), to mitigate small sample bias due to high persistence in affine term structure models.

### Economic interpretation and policy implications
- Global curvature acts as a forward indicator of financial and macroeconomic risk and triggers immediate expectations of expansionary monetary policy when it spikes.
- Monetary policy responses to global shocks influence term premia: persistent expansionary policy in times of global liquidity scarcity can lower expected short rates relative to long rates, raising the term premium.
- Central banks monitoring term premium dynamics are essential for assessing liquidity-stimulating or -restraining effects of policy, particularly in the presence of international transmission of macro-finance shocks.

### Methodological notes and roadmap
- The paper integrates multi-country affine term structure modeling with a FAVAR structure to capture global and local dynamics.
- Section II (not included here) presents data and descriptive evidence for global factors.
- Section III (not included here) describes building blocks of the term structure model.
- Section IV (not included here) explains the estimation methodology.

*Italic: Source — _wp13223 - 1. Block Exogeneity Test ...............................................................................................*

### Section  V  discusses  our  main  results.  Section  VI  briefly  highlights  some  robustness  checks

### _wp13223 - Section  V  discusses  our  main  results.  Section  VI  briefly  highlights  some  robustness  checks

### II. Data and motivation
- Dataset: yields to maturity on zero coupon yield curves for seven countries (United Kingdom, Canada, Germany, Japan, Australia, New Zealand and Switzerland) starting in 1990 and ending in the first quarter of 2009; quarterly frequency computed as simple averages of monthly observations; maturities from three months to ten years resulting in 40 series of zero coupon yields per country.
- US yields not modeled as a small open economy, but the US yield curve is used to construct global factors.
- Empirical observation:
  - Cross-country term structures are strongly correlated; the level of the yield curves displays a strong downward trend from the early 1990s.
  - Yield curves generally positive-sloped, slope degree varies by country.
  - The first three principal components ("level", "slope", "curvature") span yield curves; the first factor shows strong co-movement across countries with correlation coefficients ranging from 0.83 to 0.98.
  - The other two factors are more volatile, with stronger correlations starting from 2000 onwards.
- Research questions motivated: identify the global forces and quantify their importance for the shape/evolution of yield curves and term premia.

### III. A global term structure model
- Model class:
  - Discrete-time affine term structure model (extension of Ang and Piazzesi (2003), Cochrane and Piazzesi (2008), Wright (2011)).
  - Pricing kernel assumed conditionally lognormal with time-varying price of risk it λ and i.i.d. shock 1+it ε ~ N(0,I). (If 0=it λ, model yields pure "expectational hypothesis".)
- State vector specification:
  - State vector Y_it = [X_it ; F_t] comprising country-specific state vector X_it and global state vector F_t.
  - Price of risk λ_it assumed affine in Y_it: λ_it = λ_0 + λ_1' Y_it (equation (1)).
  - Short rate 1_it y = δ_0 + δ_1' Y_it (linear relation).
- Dynamics:
  - Factor-augmented VAR (FAVAR):
    - X_it = μ_i + Φ_i X_{t-1} + Λ_i F_{t-1} + v_it
    - F_t = μ_F + F_{t-1} Ω + η_t
  - Nested cases: closed economy (0=Λ_i) and full global-driven domestic (0=Φ_i).
  - FAVAR can be rewritten as VAR(1) in stacked form (equation (3)).
- No-arbitrage bond pricing:
  - Bond prices p_{n,it} = exp(n A_n + B_n' Y_it); recursion for A_n, B_n given with dependence on Ψ, Γ, μ~, λ, δ.
  - Model generates yields and forward rates; term premia computed as difference between model-implied 5-year forward rate 5 years from now and average expected one-year rate 5 to 10 years from now.
- Identification of global vs local shocks:
  - Shocks to local and global factor equations assumed uncorrelated (0 = E_t η_t υ'_t).
  - Structural matrices B^0 and C^0 such that Σ_υ = B^0 B^0' and Σ_η = C^0 C^0' yield structural identification.
  - Impulse responses obtained by inverting the FAVAR and via moving average representations; local factor responses to local shocks: X_it = [I - L(Φ - ΛΦ)^{-1}] C_0 ε_it; to global shocks: X_it = [I - L(Φ - ΛΦ)^{-1}] B_0 u_it (operational expressions as in text).

### IV. Estimation strategy
- Four-step estimation:
  1. Estimate global factors F_t and country latent factors X_it (via principal components).
  2. Estimate FAVAR parameters (Γ, Ψ, μ~) conditional on factors via OLS.
  3. Estimate δ_0 and δ_1 via OLS of short-rate on Y_it.
  4. Estimate price-of-risk parameters λ_0 and λ_1 by minimizing sum of squared differences between actual and fitted yields (equation (4)).
- Latent factors:
  - Country-specific X_it: first three principal components of each country's zero-coupon yields (three months to ten years) labeled "local level", "local slope", "local curvature".
  - Global F_t: principal components extracted from matrix M_t including term structures of all N countries in sample, including the U.S.: M_t = {..., y_{1t}^1,..., y_{Nt}^n}.
  - First three global principal components account for more than 96 percent of total variance of all yields; three global factors used.
- Additional methodological points:
  - Treatment of "unspanned" factors: country-specific factors X_it treated as "spanned"; global factors F_t treated as unspanned (they do not enter directly in cross-section determination of current yields but affect domestic factors contemporaneously via spillovers and help forecast future yields).
  - Addressing small-sample bias in estimated state dynamics: use indirect inference bias correction methodology from Bauer, Rudebusch and Wu (2012) and stationarity adjustment suggested in Kilian (1998). A standard bootstrap bias correction yields similar results (no effect on main results).

### V. Results
#### A. Estimates of the global factors
- Extraction approach: principal components (Stock and Watson (2002)); first three principal components account for more than 96 percent of total variance.
- Economic interpretations:
  - Global level ≈ "global expected inflation factor":
    - Constructed as first principal component of one-year-ahead CPI inflation forecasts across countries.
    - Correlation between global level factor and this inflation factor: 0.94.
  - Global slope ≈ "global real activity indicator":
    - Constructed as first principal component of real GDP growth, industrial production and unemployment across countries.
    - Correlation between global slope factor and this real activity index: 0.77.
    - Captures downward movements in global slope between 1990-1995, 2000-2005, and during the Great Recession (drops less during the last period).
  - Global curvature (third global factor) interpreted as a long-term risk factor:
    - Third global factor precedes macro-finance stress indicators.
    - Empirical associations:
      - Third global factor spikes precede U.S. recession probabilities (Chauvet and Piger) and increases in standard deviation of one-year-ahead US GDP growth forecasts.
      - Correlation with inflation uncertainty: 77% up to early 2000s recession; 64% in overall sample.
      - Leads St. Louis Fed financial stress index inversions (2003 and onset of recent crisis).
      - Leads U.S. economic policy uncertainty index (Baker et al. (2013)) in recent crisis.
      - During 2007-2009, third factor peaks precede global expansionary monetary policies; global yield curve becomes convex with a hump-shape (example: equally weighted average yield curve: Q2 2007 flat at 4.5 percent; by Q4 2008 short-end around 2 percent).
    - Conclusion: third global factor signals medium/long-term macro and financial risk and is dubbed a long-term risk factor; monetary policy expectations reflected with a reduction of intermediate maturities.

#### B. Model performance
- Block exogeneity tests (likelihood ratio tests) strongly reject null that global factors do not affect domestic factor dynamics (i.e., 0 = Λ_i rejected for all countries).
- Fit:
  - Root mean square fitting errors of yields (square root of minimum value in equation (4)) typically range between 1.5 and 6 basis points.
  - New Zealand, Germany and Japan exhibit the best fit.

#### C. Importance of global factors for domestic factors and yields
- Identification/order: global factors ordered for Choleski as global slope (real activity) first, global curvature (long-run risk) second, global level (expected inflation) last; but principal components are orthogonal so ordering within VAR is not critical.
- Impulse responses (example: UK; similar for others):
  - Positive global slope shock → positive effect on domestic level and slope (delayed and persistent).
  - Positive global curvature shock → increase in domestic curvature; reduction in domestic level and slope (small on impact, persistent > 30 quarters).
  - Positive global level shock → positive loading on country's level factor; small effects on local slope and curvature.
- Variance decompositions of local factors (Table 3) at horizons:
  - At 1 quarter horizon (short):
    - Global factors explain on average: 54 percent of the local level, 24 percent of the local curvature, and 3 percent of the local slope.
  - At 40 quarters horizon (10 years):
    - Global factors explain almost entirely the level of interest rates: proportion ranges between 95.5 percent in Japan and 99.3 percent in Germany.
    - Global factors explain more than 50 percent of variance of domestic slope and curvature in most countries.
- Contribution of global shocks to variance of domestic yields (Figure 7):
  - At 40-quarter horizon, global shocks explain more than 80 percent of variance of yields across all maturities.
  - Effect increases with maturity, reaching a maximum between 15 and 25 quarters (country-dependent).
  - By h=1 quarter domestic shocks explain most variance; by h=4 quarters global shocks dominate.
- Decomposition of global contribution by global factor (Table 4):
  - Global long-run risk and global real activity explain on average more than 35 percent of the 3 month rate variance; global expected inflation accounts for 12 percent of short-rate forecasting variance.
  - At longer maturities, expected inflation factor importance increases while the other two slightly reduce.
- Overall message: global factors (including a third long-run risk factor) are crucial determinants of domestic yield curves and term premia.

#### D. Term premia dynamics
- Term premia computed as difference between model-implied 5-to-5 year forward rate and average expected one-year rates 5-to-10 years hence (Wright (2011) approach).
- Cross-country patterns (Figure 8):
  - Term premia declined from early 1990s until early 2000s, then increased afterwards; at onset of the Great Recession term premia increased by about 4 percentage points in most countries.
  - Western economies show more volatile term premia than Pacific countries (Japan, Australia, New Zealand).
  - Term premia sometimes negative after mid-1990s in some countries.
- Comparison to other studies:
  - More volatile and countercyclical than Wright (2011) and Bauer, Rudebusch and Wu (2013).
  - Bias correction increases volatility relative to simple OLS; presence of global factors further increases volatility of expectations of future short-term rates, especially at longer horizons.
- Interpretation:
  - Decline in early sample consistent with inflation-targeting anchoring inflation expectations.
  - Increase during Great Recession suggests additional drivers beyond domestic inflation expectations; motivates decomposition into global vs local contributions.

#### E. Global factors and term premium dynamics
- Counterfactual exercise (only global shocks vs only local shocks):
  - Term premia dynamics mainly determined by global factors: global-only series reflect both long-term decline and steep increase during Great Recession and closely track actual term premia.
  - Local-only series sometimes depart significantly from actual term premia.
- Variance decomposition of term premia (Table 5):
  - Contribution of global factors to term premia variation ranges between 65 percent (Germany) and 92 percent (UK).
  - Global curvature factor explains around 60 percent of total variance at 40 quarters horizon on average.
  - Mechanism: shocks to global curvature explain most variance of the risk-neutral rate → large forecasting power for future short-term yields.
  - Global level factor is most important in explaining forward rates dynamics (Table 6).
- Impulse responses of term premia to global shocks (Figure 10):
  - Positive global real activity shock → reduction in term premium in most countries (except small positive effect in Australia and New Zealand).
  - Positive global curvature shock → increase in term premia across countries; effect large and persistent (usually > 30 quarters). Reason: risk-neutral rate decreases more than long (forward) rate due to credible monetary policy easing, raising the term premium.
  - Positive global level (expected inflation) shock → increase in term premium in all countries except Germany (in Germany term premium decreases because risk-neutral rate increases by more than long/forward rates due to high monetary policy credibility).
- Country illustrations:
  - Japan: term premium dynamics similar to counterfactual with global level shock only (global expected inflation factor explains most variance).
  - UK: term premium dynamics mostly explained by global long-run risk factor; global inflation factor responsible for downward trend early in sample.
- Overall pattern:
  - Global expected inflation factor mainly responsible for downward trend of term premia in early sample.
  - Global real activity and especially global long-run risk (curvature) drive short-run fluctuations and the large increase at the onset of the Great Recession.

### VI. Robustness checks
- Three main robustness exercises; summarized first comparison:
  - Compare main results (with indirect inference bias correction) to results without bias correction (simple OLS).
  - Findings on bias correction:
    - Bias correction has important effects on identification of term premium: OLS-identified term premium shows clearer downward trend, is less volatile/countercyclical, and exhibits a smaller increase in the Great Recession.
    - Conclusions about the importance of global factors hold regardless of bias correction (Table 7).
    - Bias correction slightly increases total contribution of global shocks; but under OLS global shocks still account, on average, for more than 70 percent of total variance in term premia.
    - Bias correction affects relative contributions of the three global shocks:
      - Under OLS, contribution of global expected inflation shock nearly doubles from 16 percent to 29 percent.
      - Under OLS, contribution of the third global factor is reduced.
- Additional robustness notes:
  - Use of indirect inference bias correction with stationarity adjustment (Kilian (1998)) is the primary correction; standard bootstrap bias correction produces similar qualitative results.

*Italic: Source: _wp13223 - Section  V  discusses  our  main  results.  Section  VI  briefly  highlights  some robustness checks*

### conclusions by Bauer, Rudebusch and Wu (2012 and 2013) and Abbritti, Alana, Lovcha and

### _wp13223 - conclusions by Bauer, Rudebusch and Wu (2012 and 2013) and Abbritti, Alana, Lovcha and

### Main findings: role of global factors in term premia
- Global factors explain an important share of fluctuations in the term premia of a panel of small-open economies, and are more important for long-run trends than for short-run fluctuations.
- When the model is estimated on the full sample, the average contribution of global factors to term premia dynamics is 85 percent; when re-estimated over 1990Q1–2007Q2 (omitting the last eight observations), the average contribution is slightly reduced to 77 percent.
- In the 1990Q1–2007Q2 subsample:
  - Expected inflation increases in relative importance, explaining on average 47 percent of the variance of the term premia.
  - The third global factor accounts for 13 percent of the total variance.
- A new global factor — a global long-run risk factor related to future macroeconomic and financial risks — is identified as the third principal component of international yield curves and plays a central role in explaining term premium dynamics during the recent crisis period.
- Treating US factors as the global factors yields results where:
  - Global factors still explain above 80 percent of term premia variation.
  - Global curvature is the most important factor under this specification, although it loses explanatory power relative to the baseline in favor of the global cycle factor.

### Robustness and sensitivity exercises
- Subsample sensitivity (1990Q1–2007Q2): global contribution to term premia falls from 85 percent to 77 percent; expected inflation rises to explain 47 percent; third global factor falls to 13 percent (Table 8).
- Bias-correction robustness: results are compared using OLS and inverse bootstrap bias correction (as in Bauer, Rudebusch and Wu, 2012); Table 7 reports term premia variance decompositions with and without bias correction (horizon = 40).
- Alternative global factor definition: substituting global factors with the first three principal components of the US yield curve produces Table 9 results showing country-level term premia variance decompositions when US-based global factors are used.

### Model fit and diagnostics (selected statistics)
- Fit of affine term structure model — root mean square fitting error (RMSE) in percentage points (Table 2):
  - JPN 0.0212
  - UK 0.0606
  - GER 0.0214
  - SWI 0.0406
  - CAN 0.0371
  - AUS 0.0317
  - NZL 0.0155
- Block exogeneity tests (Table 1) report likelihood ratio test p-values for testing no-significance of global factors on domestic factors (table header and note present in the source).

### Mechanisms and interpretation
- Global expected inflation is identified as the main driver of the downward trend in term premia from 1990 to 2007.
- The third global factor (global long-run risk) is associated with macroeconomic and financial risk indicators:
  - It aligns with US recession probabilities, the standard deviation of one-year-ahead US GDP growth forecasts, the St. Louis Fed financial stress index, the Baker et al. (2013) policy uncertainty index, and measures of US inflation forecast uncertainty and skewness (Figure 4 panels).
- Historical decompositions show that counterfactuals with only global shocks versus only domestic shocks illustrate the dominant role of global shocks in shaping term premia dynamics across countries (Figure 9).

### Impulse responses and historical decompositions
- Impulse responses of local yield factors to global factor shocks (example shown for the UK, Figure 6) illustrate that global shocks induce responses in domestic level, slope and curvature over horizons up to 40 periods, with 95 percent confidence intervals reported.
- Impulse responses of term premia to shocks to the three global factors are plotted for all sample countries for horizons up to 40 quarters (Figure 10); dynamic responses differ by country and by which global factor shocks occur.
- Country-specific historical decompositions (examples for Japan and the UK in Figures 11 and 12) show the contribution of each global shock (Global Growth/Slope, Global LR Risk, Global Exp. Inflation) to actual term premia and to counterfactual series omitting particular global shocks.

### Policy-relevant implications and suggested extensions
- International financial linkages embedded in global financial markets matter for term structures in open economies even when retaining no-arbitrage affine specifications.
- The prominent role of global expected inflation in explaining long-run declines in term premia suggests that global disinflationary trends and expectations formation are key drivers of bond risk premia in small-open economies.
- The identification of a global long-run risk factor that rises in crisis times indicates that analyses of term premia should account for macro-financial risk channels and international spillovers.
- Future work (stated by the authors) intends to:
  - Examine term structure implications of the zero–or near zero–interest rate lower bound in years beyond the paper’s sample.
  - Analyze international spillovers of unconventional monetary policies implemented during and after the crisis period.

*Source: _wp13223 - conclusions by Bauer, Rudebusch and Wu (2012 and 2013) and Abbritti, Alana, Lovcha and (IMF PDF content provided).*

### REFERENCES

### REFERENCES

### Term Premia and Term Structure Studies
- Abbritti, M., Gil-Alana, L., Lovcha, Y., and Moreno, A., 2012, “Term Premim Persistence,” School of Economics and Business Administration, University of Navarra, Working Paper No. 26, 2012.
- Gil-Alana, L., and Moreno, A., 2012, “Uncovering the US Term Premium: An Alternative Route,” Journal of Banking and Finance, 36, pp. 1181–1193.
- Gürkaynak, R., Sack, B., and Wright, J., 2007, “The U.S. Treasury Yield Curve: 1961 to the Present,” Journal of Monetary Economics, 54, pp. 2291–2304.
- Hellerstein, R., 2011, “Global Bond Risk Premiums,” Federal Reserve Bank of New York Staff Reports, Staff Report No. 499, June 2011.
- Dahlquist, M, and Hasseltoft, H, 2012, “International Bond Risk Premia,” Forthcoming, Journal of International Economics.
- Wright J., 2011, “Term Premia and Inflation Uncertainty: Empirical Evidence from an International Panel Dataset,” American Economic Review, 101(4): 1514–34.
- Dell'Erba, S, and Sola, S., 2013, “Fiscal Policy, Interest Rateds and Risk Premia in Open Economy,” IHEID Working Papers 5–2013, Economics Section, The Graduate Institute of International Studies.

### Dynamic Term Structure Models, Factor Models, and Estimation
- Ang, A., and Piazzesi, M, 2003, “ A No-Arbitrage Vector Autoregression of Term Structure Dynamics with Macroeconomic and Latent Variables,” Journal of Monetary Economics, Elsevier, Vol. 50(4), pp. 745–787, May.
- Bauer, G., Rios, A., 2012, “An International Dynamic Term Structure Model with Economic Restrictions and Unspanned Risks,” Working Papers 12–5, Bank of Canada.
- Bauer, M., Rudebusch, G., and Wu, J., 2012, “Correcting Estimation Bias in Dynamic Term Structure Models,” Journal of Business & Economic Statistics, 2012, Vol 30 (3), pp. 454–467.
- __________, Rudebusch, G., and Wu, J., 2013, “Comment on “Term Premia and Inflation Uncertainty: Empirical Evidence from an International Panel Dataset,” Forthcoming, American Economic Review.
- Joslin, S., Priebsch, M., and Singleton, K., 2012, “ Risk-Premiums in Dynamic Term Structure Models with Unspanned Macro Risks,” MIMEO, Stanford University.
- Joslin, S., Singleton, K., and Haoxiang Zhu, 2011, “A New Perspective on Gaussian Dynamic Term Structure Models,” Review of Financial Studies 24(3), pp. 926-970.
- Cochrane, J., and Piazzesi, M., 2008, “Decomposing the Yield Curve,” Working Paper, MIMEO University of Chicago.
- Moench, E., 2008, “Forecasting the Yield Curve in a Data-Rich Environment: A No Arbitrage Factor Augmented VAR Approach,” Journal of Econometrics 146 (2008), pp. 26–43.
- Diebold, F., Li, C., and Yue, V., 2008, “Global Yield Curve Dynamics and Interactions: A Dynamic Nelson-Siegel Approach,” Journal of Econometrics, 146(2), pp. 351–363.
- Duffee, G., 2011, “Information In (And Not In) The Term Structure,” Review of Financial Studies 24, pp. 2895–2934.
- Ludvigson, S., and Ng, S., 2009, “Macro Factors in Bond Risk Premia,” Review of Financial Studies, Oxford University Press for Society for Financial Studies, Vol. 22(12), pp. 5027–5067, December.
- Forni, M., Giannone, D., Lippi, M., and Reichlin, L., 2009, “Opening The Black Box: Structural Factor Models With Large Cross Sections,” Econometric Theory, Cambridge University Press, Vol. 25(05), pp. 1319–1347, October.
- Geweke, J., 1977, “The Dynamic Factor Analysis of Economic Time Series Models,” Latent Variables in Socioeconomic Models, Amsterdam, North Holland, pp. 365–383.
- Rudebusch, G., and Swanson, E., 2008, “Examining the Bond Premium Puzzle with a DSGE Model,” Journal of Monetary Economics, Elsevier, Vol. 55 (Supplement), pp. S111-S126, October.

### Macro-Finance, Monetary Policy, and Open-Economy Interdependence
- Bernanke, B., 2006, “Remarks before the Economic Club of New York,” New York March 20, 2006.
- Bernanke, B., Boivin, J., and Eliasz, P., 2005, “Measuring the Effects of Monetary Policy: A Factor-augmented Vector Autoregressive (FAVAR) Approach,” The Quarterly Journal of Economics, MIT Press, Vol. 120(1), pp. 387–422, January.
- Spencer, P., and Liu, Z., 2010, “An Open-Economy Macro-Finance Model of International Interdependence: The OECD, US and the UK,” Journal of Banking and Finance, Elsevier, Vol. 34(3), pp. 667–680, March.
- Campbell, J., Sunderam, A., and Viceira, L., 2013, “Inflation Bets or Deflation Hedges? The Changing Risks of Nominal Bonds,” Working Paper, MIMEO Harvard University.
- Fleckenstein, M., Longstaff, F., and Lustig, H., 2013, “Deflation Risk,” NBER Working Paper N. 19238, July 2013.
- Jotikashtira, C., Le, A., and Lundblad, C., 2012, “Why Do Term Structures in Different Countries Comove,” MIMEO, University of North Carolina.
- Bauer, G., Rios, A., 2012, “An International Dynamic Term Structure Model with Economic Restrictions and Unspanned Risks,” Working Papers 12–5, Bank of Canada.

### Forecasting, Uncertainty, and Methodological Tools
- Baker, S., Bloom, N., and Davis, S., 2013, “Measuring Economic Policy Uncertainty,” MIMEO Stanford University.
- Kilian, L., 1998, “ Small-Sample Confidence Intervals for Impulse Response Functions,” Review of Economics and Statistics, 1998, 80 (2), pp. 218–230.
- Stock, J., and Watson, M., 2005, “Understanding Changes in International Business Cycle Dynamics,” Journal of European Economic Association, Vol. 3(5), pp. 968–1006.
- __________, and Watson, M., 2002, “Forecasting Using Principal Components from a Large Number of Predictors,” Journal of the American Statistical Association, 97 (2002), pp. 1167–1179.
- Modugno, M., and Kleopatra, N., 2009, “The Forecasting Power of International Yield Curve Linkages,” ECB WP No. 1044, April 2009.
- Geert, B, Cho, S., and Moreno, A., 2010, “New Keynesian Macroeconomics and the Term Structure,” Journal of Money, Credit and Banking, Blackwell Publishing, Vol. 42(1), pp. 33–62, 02.
- Hellerstein, R., 2011, “Global Bond Risk Premiums,” Federal Reserve Bank of New York Staff Reports, Staff Report No. 499, June 2011.

*Source: _wp13223 - REFERENCES*

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