## 6. Relative Contribution of Macro Expectations to Term Spread

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### Introduction and research question
- Investigates how unexpected upward revisions in long-run private sector debt and growth expectations contribute to movements in long-term implied forward interest rates (term spread).
- Uses qualitative cross-country survey data (Consensus Forecast and EIU) to measure long-run (five-year ahead) expectations.
- Sample frequency and period: monthly data from 1996:1 to 2013:1.
- Motivation: disentangle whether long-term rates respond more to private-sector public debt expectations (self-fulfilling concerns about debt sustainability) or to shifts in long-run growth and risk preferences following the 2008–09 global financial crisis (GFC).

### Model, identification, and data definitions
- Parsimonious reduced-form specification linking the forward five-year implied rate and the forward one-year implied rate to five-year-ahead expectations and risk aversion (equation (1) in the source).
- Key variables (five-year ahead, {t+5|t}):
  - GDP growth: y{t+5|t} — average five-year ahead forecast of real GDP (median from Consensus Forecast; semi-annual series extrapolated monthly via one-year ahead consensus and Kalman smoothing).
  - Inflation: π{t+5|t} — five-year ahead inflation expectations (controls for monetary policy effects).
  - Debt: d{t+5|t} — private sector five-year ahead expectations of the debt-to-GDP ratio (EIU data).
  - Risk aversion: measure based on the equity premium from a Gordon (1962) growth model proxy.
- Term spread constructed as the implied forward five-year rate minus implied forward one-year rate (forward rates preferred to extract information and avoid level-of-rate modeling).
- Time-varying coefficient state-dependent model with stochastic volatility in disturbances; coefficients evolve smoothly over time (equations (2)–(4) and stochastic volatility setup).
- Estimation via Bayesian methods (Metropolis-within-Gibbs); VAR coefficients with flat priors; volatility estimated as in Cogley and Sargent (2005).

### Empirical findings — coefficients and time variation
- A positive coefficient between debt expectations and the term spread is consistent with the self-fulfilling hypothesis: orthogonal upward revision in private-sector debt expectations raises long-term implied rates.
- Time-varying estimates show material changes over time:
  - From around 2003 to 2007, the sensitivity of the term spread to long-run private sector debt expectations weakened across countries.
  - Post-GFC, coefficient estimates increased for most countries; increase was more pronounced for France, Germany, Italy, and the U.K.
- Quantified effect (cross-country post-crisis implication):
  - "A one percent of GDP upward revision in long-run debt expectations leads to an increase in the implied forward long-term rate from 1.5 to 6.0 basis points over the implied forward short-term rate."
- Country-specific notes:
  - Japan shows negative or atypical coefficients consistent with the zero lower-bound policy rate covering most of the sample period.
  - Prior to the GFC, pre-2008 five-year debt expectations fell across countries, coinciding with a global savings glut and low macro volatility.

### Variance decomposition and stochastic volatility (sources of term-spread movements)
- Time-varying stochastic volatilities indicate:
  - Spikes in inflation and growth expectation shocks tended to coincide across G7 countries.
  - Pre-GFC, shocks in future debt expectations were often more volatile than innovations in long-term growth expectations; largest for high-debt Italy and Japan.
  - Crises (notably 2001 and 2008–09) led to large revisions in macroeconomic expectations, including fiscal ones.
  - For all sampled countries, the GFC saw a large spike in the size of risk preference shocks.
- Time-varying forecast-error variance decompositions (Figure 6) show:
  - Forward rates are moved by a confluence of shocks at any one time.
  - Inflation expectations gained importance before the GFC (mid-2008 oil price episode).
  - For the U.S., Italy, Japan, and the U.K., a significant proportion of the rise in interest rate volatility during 2008–09 was due to growth expectation shocks.
  - Post-crisis, shocks in risk aversion rose in importance across all countries; this is consistent with portfolio-balance safe-haven flows for the U.S. and capital reversal raising risk premia for Italy.
  - For non-euro zone countries, long-run private-sector debt expectations generally contain modest information for forward rates over the sample.
  - U.S. example: private sector debt expectations explained around 15 percent of variation in forward rates in 2007; explanatory power declined after the 2008–09 crisis.
  - France and Italy: debt expectations had significant information for long-term rates in the years preceding the GFC; this importance declined post-crisis in favor of growth expectations and risk aversion.

### Interpretation and caveats
- Main interpretation: post-GFC shifts in growth expectations and in risk aversion were more significant than fiscal expectations in explaining fluctuations in long-term implied forward rates.
- This does not imply debt is unimportant — long-run private sector debt expectations have small but significant effects at the long end of the yield curve.
- Caveats highlighted in the source:
  - Qualitative survey measures of debt expectations may not reflect "pure" private-sector public debt expectations five years ahead and may omit information used by agents.
  - Structural models may not capture all information available to agents; shocks to expectations could reflect omitted fundamentals or pure sunspot behavior.
  - Survey-based expectations differ from market-implied expectations; financial market participants ultimately drive bond flows.

### Policy implications and recommendations
- Fiscal consolidation effectiveness in reducing borrowing costs may be limited if private agents fail to observe or believe actual economic fundamentals (sticky-information/self-fulfilling environments).
- Credibility of fiscal consolidation plans is important: long-run private-sector debt expectations manifest in a small but significant manner at the long-end of the yield curve.
- Policies that influence long-run growth expectations (e.g., those that affect structural growth prospects and investor confidence) are relatively more important than projected fiscal outturns for affecting long-term government borrowing costs.
- Additional study and comparison of survey-based and market-based expectations are needed to better understand properties of fiscal expectations and their transmission to interest rates.

### Appendix A. Linking the Term Spread and Fiscal Position — key relations
- Monetary policy rule (Taylor-type) linking the short-term nominal interest rate to real output and inflation (equation (A.1) in the source), with variables defined as:
  - ݅௧ଵ: short-term nominal interest rate in period ݐ.
  - ݎ௧∗: real interest rate that would prevail in the absence of nominal rigidities.
  - ߨ௧: inflation; ߨ௧∗: inflation target.
  - ݕ௧: real output; ݕ௧∗: potential output.
- Expectational conditions for long-horizon short-term rates (equations (A.2)–(A.3) in the source).
- Term spread expression and term premium decomposition following Kitchen and Chinn (2011) (equations (A.4)–(A.5) in the source):
  - Term premium ߪ௧ decomposed as ߛ௧ (risk premium resulting from financial uncertainty associated with a deteriorating fiscal position) plus ߤ௧ (other unidentified risk factors).
  - Asset-pricing consistency: long-horizon interest rates = expected short-term rates + risk premium.
- Combined relation (equation (A.6) in the source) implies the long–short spread is a function of inflation (ߨ), real output (ݕ), a fiscal-risk-related premium (ߛ௧), and other unidentified risk factors (ߤ௧).
- Interpretation: changes in supply and demand for public debt show up on the long end of the yield curve via the term premium ߪ௧; short-term rates are determined by the monetary policy rule.

*Source: 6. Relative Contribution of Macro Expectations to Term Spread, _wp1594 (excerpt), pages 18–20; Appendix A, _wp1594.*

### 1. Five Year Growth and Debt Expectations .............................................................................4

### 1. Five Year Growth and Debt Expectations .............................................................................4

### Listed sections and figures
- 1. Five Year Growth and Debt Expectations .............................................................................4
- 2. Scatter Plot of Five Year Debt and Growth Expectations .....................................................7
- 3. Scatter Plot of Five Year Debt Expectations and the Forward Term Spread ........................7
- 4. Coefficient Between Forward Rates and Debt Expectations ...............................................10
- 5. Size of Macroeconomic Expectation Shocks ................................................................. 13-15

*Source: _wp1594 - 1. Five Year Growth and Debt Expectations (PDF chapter/section).*

### 6. Relative Contribution of Macro Expectations to Term Spread ..................................... 18-20

### 6. Relative Contribution of Macro Expectations to Term Spread

### Introduction and research question
- Investigates how unexpected upward revisions in long-run private sector debt and growth expectations contribute to movements in long-term implied forward interest rates (term spread).
- Uses qualitative cross-country survey data (Consensus Forecast and EIU) to measure long-run (five-year ahead) expectations.
- Sample frequency and period: monthly data from 1996:1 to 2013:1.
- Motivation: disentangle whether long-term rates respond more to private-sector public debt expectations (self-fulfilling concerns about debt sustainability) or to shifts in long-run growth and risk preferences following the 2008–09 global financial crisis (GFC).

### Model, identification, and data definitions
- Parsimonious reduced-form specification linking the forward five-year implied rate and the forward one-year implied rate to five-year-ahead expectations and risk aversion (equation (1) in the source).
- Key variables (five-year ahead, {t+5|t}):
  - GDP growth: y{t+5|t} — average five-year ahead forecast of real GDP (median from Consensus Forecast; semi-annual series extrapolated monthly via one-year ahead consensus and Kalman smoothing).
  - Inflation: π{t+5|t} — five-year ahead inflation expectations (controls for monetary policy effects).
  - Debt: d{t+5|t} — private sector five-year ahead expectations of the debt-to-GDP ratio (EIU data).
  - Risk aversion: measure based on the equity premium from a Gordon (1962) growth model proxy.
- Term spread constructed as the implied forward five-year rate minus implied forward one-year rate (forward rates preferred to extract information and avoid level-of-rate modeling).
- Time-varying coefficient state-dependent model with stochastic volatility in disturbances; coefficients evolve smoothly over time (equations (2)–(4) and stochastic volatility setup).
- Estimation via Bayesian methods (Metropolis-within-Gibbs); VAR coefficients with flat priors; volatility estimated as in Cogley and Sargent (2005).

### Empirical findings — coefficients and time variation
- A positive coefficient between debt expectations and the term spread is consistent with the self-fulfilling hypothesis: orthogonal upward revision in private-sector debt expectations raises long-term implied rates.
- Time-varying estimates show material changes over time:
  - From around 2003 to 2007, the sensitivity of the term spread to long-run private sector debt expectations weakened across countries.
  - Post-GFC, coefficient estimates increased for most countries; increase was more pronounced for France, Germany, Italy, and the U.K.
- Quantified effect (cross-country post-crisis implication):
  - "A one percent of GDP upward revision in long-run debt expectations leads to an increase in the implied forward long-term rate from 1.5 to 6.0 basis points over the implied forward short-term rate."
- Country-specific notes:
  - Japan shows negative or atypical coefficients consistent with the zero lower-bound policy rate covering most of the sample period.
  - Prior to the GFC, pre-2008 five-year debt expectations fell across countries (Figure 1), coinciding with a global savings glut and low macro volatility.

### Variance decomposition and stochastic volatility (sources of term-spread movements)
- Time-varying stochastic volatilities indicate:
  - Spikes in inflation and growth expectation shocks tended to coincide across G7 countries.
  - Pre-GFC, shocks in future debt expectations were often more volatile than innovations in long-term growth expectations; largest for high-debt Italy and Japan.
  - Crises (notably 2001 and 2008–09) led to large revisions in macroeconomic expectations, including fiscal ones.
  - For all sampled countries, the GFC saw a large spike in the size of risk preference shocks.
- Time-varying forecast-error variance decompositions (Figure 6) show:
  - Forward rates are moved by a confluence of shocks at any one time.
  - Inflation expectations gained importance before the GFC (mid-2008 oil price episode).
  - For the U.S., Italy, Japan, and the U.K., a significant proportion of the rise in interest rate volatility during 2008–09 was due to growth expectation shocks.
  - Post-crisis, shocks in risk aversion rose in importance across all countries; this is consistent with portfolio-balance safe-haven flows for the U.S. and capital reversal raising risk premia for Italy.
  - For non-euro zone countries, long-run private-sector debt expectations generally contain modest information for forward rates over the sample.
  - U.S. example: private sector debt expectations explained around 15 percent of variation in forward rates in 2007; explanatory power declined after the 2008–09 crisis.
  - France and Italy: debt expectations had significant information for long-term rates in the years preceding the GFC; this importance declined post-crisis in favor of growth expectations and risk aversion.

### Interpretation and caveats
- Main interpretation: post-GFC shifts in growth expectations and in risk aversion were more significant than fiscal expectations in explaining fluctuations in long-term implied forward rates.
- This does not imply debt is unimportant — long-run private sector debt expectations have small but significant effects at the long end of the yield curve.
- Policy relevance: policies that directly influence long-run growth expectations are relatively more important than projected fiscal outturns in helping determine government borrowing costs in most G7 countries.
- Caveats highlighted in the source:
  - Qualitative survey measures of debt expectations may not reflect "pure" private-sector public debt expectations five years ahead and may omit information used by agents.
  - Structural models may not capture all information available to agents; shocks to expectations could reflect omitted fundamentals or pure sunspot behavior.
  - Survey-based expectations differ from market-implied expectations; financial market participants ultimately drive bond flows.

### Policy implications and recommendations (as stated)
- Fiscal consolidation effectiveness in reducing borrowing costs may be limited if private agents fail to observe or believe actual economic fundamentals (sticky-information/self-fulfilling environments).
- Credibility of fiscal consolidation plans is important: long-run private-sector debt expectations manifest in a small but significant manner at the long-end of the yield curve.
- Policies that influence long-run growth expectations (e.g., those that affect structural growth prospects and investor confidence) are relatively more important than projected fiscal outturns for affecting long-term government borrowing costs.
- Additional study and comparison of survey-based and market-based expectations are needed to better understand properties of fiscal expectations and their transmission to interest rates.

*Source: 6. Relative Contribution of Macro Expectations to Term Spread, _wp1594 (excerpt), pages 18–20.*

### Appendix A. Linking the Term Spread and Fiscal Position

### Appendix A. Linking the Term Spread and Fiscal Position

### Model setup and monetary policy rule
- Starts from a Taylor-type rule linking the short-term nominal interest rate to real output and inflation:
  - ݅௧ଵ ܧൌ ݎ௧∗ ߨ௧ାଵ ݎ൅ ௧ ∗ ߙ൅ ሺߨ௧ ߨെ௧∗ ሻ ݕሺߚ൅ ௧ ݕെ௧∗ ሻ  (A.1)
- Definitions from the model:
  - ݅௧ଵ is the short-term nominal interest rate in period ݐ.
  - ݎ௧∗ is the real interest rate that would prevail in the absence of nominal rigidities.
  - ߨ௧ is inflation and ߨ௧∗ denotes the inflation target.
  - ݕ௧ is a measure of real output and ݕ௧∗ is a measure of potential output.
- Expectational condition when extrapolating expectations sufficiently far into the future:
  - ܧ௧ ߨ௧ା௞ ߨൌ ∗  (A.2)
- Since ݎ௧∗ is outside monetary control, the expected long-horizon short-term rate equates to:
  - ܧ௧ ݅௧ା௞ ଵ ܧൌ ௧ ߨ௧ା௞ ∗  (A.3)

### Term spread expression and term premium decomposition
- The spread between the long-term and short-term interest rate follows Kitchen and Chinn (2011):
  - ݅௧ହ ݅େ௧ଵ ೎ ሺ௜ ೟,భ ାா ೟ ௜ ೟శఱ భ ሻ ହ ߪ൅ ௧,ହ ݅େ௧ଵ  (A.4)
- Term premium definition used in the paper:
  - ߪ௧ ߛൌ ௧ ߤ൅ ௧  (A.5)
  - ߛ௧ is a risk premium resulting from financial uncertainty associated with a deteriorating fiscal position.
  - ߤ௧ captures other unidentified risk factors.
- Asset-pricing consistency: long-horizon interest rates = expected short-term rates + risk premium.

### Combined relation and implications for spreads
- Combining (A.1)–(A.4) yields:
  - ݅௧ହ ݅େ௧ଵ ߨൌ ೀ ௧ ݕె ௧ ߛ൅ ௧ ߤ൅ ௧  (A.6)
- Interpretations and implications:
  - Short-term rates are determined by the monetary policy rule (A.1).
  - Changes in supply and demand for public debt show up on the long end of the yield curve via the term premium ߪ௧.
  - The long–short spread is a function of:
    - inflation (ߨ),
    - real output (ݕ),
    - a fiscal-risk-related premium (ߛ௧),
    - other unidentified risk factors (ߤ௧).

*Source: _wp1594 - Appendix A. Linking the Term Spread and Fiscal Position*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2015/_wp1594.pdf_