1999年-BIS国际清算银行_A_note_on_alternative_measures_of_real_bond_rates__50页_498kb

Summary of BIS Working Paper No. 80 - November 1999

Core Content

This BIS Working Paper explores alternative measures of ex ante long-term real interest rates, aiming to better approximate Fisher's long-run relationship between inflation expectations and nominal interest rates. It highlights the challenges in directly observing expectations and discusses the implications of using different methods to estimate real bond rates.

Main Viewpoints

• Fisher's Long-Run Relationship: Fisher's notion of a long-run relationship between inflation and interest rates is central to the paper. Traditional methods of estimating real rates by subtracting current inflation from nominal rates are not always reliable, especially in periods of unstable inflation or supply shocks.
• Cointegration and Long Memories: The paper emphasizes the importance of cointegration in capturing the long-run equilibrium relationship between real rates and inflation. It also notes that inflation expectations often exhibit long memories, meaning they are influenced by past inflation trends.
• International Linkages: The paper acknowledges that financial market integration implies that national bond rates may be influenced by global factors. Therefore, a backward-looking approach that incorporates foreign rates is considered more appropriate than purely domestic methods.
• Methodology: A backward-looking approach is adopted, using cointegration analysis and error-correction models. The method allows for the estimation of real rates while accounting for both domestic and international influences.

Key Information

1. Deriving Real Interest Rates

• The paper derives real interest rates using a model that incorporates:

  • Domestic nominal bond rates
  • Domestic and foreign inflation rates
  • Moving averages of inflation to capture long memories
  • Cointegration analysis to ensure the long-run equilibrium condition is met

• The derived real rate is given by:
  $$
  r_t = i_t - \left(\beta \pi_t + \phi \pi_{\text{movavg}, t}\right) / (\phi + \beta)
  $$
  where:

  • $i_t$ = nominal bond rate
  • $\pi_t$ = 12-month inflation rate
  • $\pi_{\text{movavg}, t}$ = moving average of inflation

• If a foreign rate is cointegrated with the domestic rate, the model adjusts for international linkages:
  $$
  r_{i,t} = \left(\eta + \varphi r_t^{us} + \varphi \left(\pi_t^{us} - \pi_{i,t}^*\right)\right) / (\phi + \beta + \varphi)
  $$
  where:

  • $r_t^{us}$ = US real rate
  • $\pi_t^{us}$ = US inflation rate
  • $\pi_{i,t}^*$ = long-term average of domestic inflation

2. Estimation Procedure

• The estimation process involves five steps:

  1. Estimating the model with two foreign rates and lagged changes in domestic and foreign rates
  2. Eliminating variables with t-values below 1
  3. Imposing the homogeneity condition on the remaining level variables
  4. Re-estimating the model and testing for homogeneity
  5. Repeating the process if the homogeneity condition is strongly violated

• The results show that:

  • For 16 out of 17 countries, the homogeneity condition is satisfied
  • The cointegration coefficient is generally below unity, indicating that nominal and inflation rates are not perfectly cointegrated
  • The average memory lag is about 46 months (almost four years), with Japan having the longest and Switzerland the shortest

3. Empirical Findings

• Main Results:

  • Cointegration was not rejected for any country
  • The homogeneity condition was satisfied for most countries
  • Memory lags range from 7.5 to 15 years, with over half of the countries having lags of 10 years
  • Only Switzerland and a few others did not show significant influence from foreign rates
  • The steady-state real interest rates range from 0.45% to 3.90%, with Germany having the highest and Japan the lowest

• Volatility and Sensitivity:

  • Real rates derived from longer memory models have significantly lower volatility
  • The average volatility of real rates is reduced by more than 50% compared to traditional methods
  • The real rate based on long memories is closer to consensus forecasts for about half the countries

• Cross-Country Correlations:

  • Nominal rates tend to have higher cross-country correlations than real rates
  • Real rates show low correlations with each other within countries, suggesting a "inflation wedge"
  • The correlation between real rates and nominal rates is higher for rate 2 (long memory) than for rate 1 (contemporaneous inflation)

Conclusion

• The paper concludes that while the derived real rates better approximate Fisher's long-run equilibrium conditions, their forecasting ability remains untested.
• The measures account for both long memories in inflation expectations and international linkages, providing a more comprehensive approach than traditional methods.
• The paper suggests that the derived measures could be a useful tool for future research, but further work is needed to assess their predictive power and to understand the factors influencing real rate movements.

Annex: Global Models of Nominal and Real Interest Rates

• The paper briefly reviews global models of interest rates, including:

  • The use of cointegration and error correction models
  • The idea that global real rates are influenced by both global and country-specific factors
  • The role of government debt/GDP ratios, equity returns, and other macroeconomic variables in determining global rates

• A global real rate is defined as a combination of:

  • A global component
  • A country-specific component

• The paper notes that while global models are promising, they are not yet fully developed, and significant variations in steady-state real rates across countries remain unexplained.