BIS国际清算银行-Modelling-yields-at-the-lower-bound-through-regime-shifts_52页_495kb

Summary of "Modelling yields at the lower bound through regime shifts"

Core Content

This paper introduces a regime-switching model to analyze the behavior of yields at the zero lower bound (ZLB). The model distinguishes between two regimes: a normal regime and a lower bound (LB) regime, where the short-term interest rate is constrained by the ZLB. The approach is designed to capture the nonlinear dynamics of the yield curve during and after the ZLB period, and it allows for different macroeconomic and yield dynamics depending on the regime.

Main Viewpoints

• Regime-switching framework: The model assumes that the law of motion for the state variables (yield factors) changes depending on whether the economy is in the normal or LB regime.
• LB regime characteristics:
  • The short-term rate is constant at the ZLB.
  • The short rate is modeled as an i.i.d. process around a constant mean.
  • The state vector does not evolve in the LB regime, which reflects the stagnation of economic activity.
• Normal regime characteristics:
  • The short rate is an affine function of the state vector.
  • The state vector evolves via an unrestricted VAR process.
• State-dependent regime switching: The probability of switching to the LB regime increases as short-term rates fall closer to zero, reflecting the gradual normalization of monetary policy.
• Forecasting implications:
  • The model captures the slow normalization of interest rates after the ZLB period.
  • It rules out the possibility of deeply negative yields.
  • The model provides a more benign forecast of future yields than alternative measures as of mid-2018.

Key Information

Data and Application

• The model is applied to U.S. monthly data from January 1987 to April 2018.
• The state vector includes the curvature, slope, and short rate of the yield curve.
• The short rate is modeled as:
  $$
  r_t = \delta_0 + \delta_x' X_t
  $$
  where $\delta_0 = 0$ and $\delta_x$ is a vector with a loading on the short rate.

Model Structure

• The model incorporates stochastic discount factors (SDFs) and market prices of risk.
• The SDF is defined as:
  $$
  \log \mathcal{M}{t, t + 1} = - r_t - \Gamma{t, t + 1} - \frac{1}{2} \Psi_t' \Psi_t - \Psi_t' \varepsilon_{t + 1}
  $$
  where:
  • $\Psi_t^j$ are regime-dependent market prices of factor risk.
  • $\Gamma_{t, t + 1}$ are market prices of regime shift risk.
• The bond pricing is derived using an approximate method from Bansal and Zhou (2002):
  $$
  P_{t, n} = \exp(-A_n^j - B_n^j X_t)
  $$
  where $A_n^j$ and $B_n^j$ are recursively defined based on the regime and bond maturity.

Forecasting Performance

• The model performs competitively in out-of-sample forecasting despite its heavier parameterization.
• It accounts for the gradualism in monetary policy normalization, which is a key feature of post-ZLB environments.
• The model suggests that the probability of switching back to the LB regime remains non-negligible even after normalization, affecting expected future yields.

Comparison with Shadow Rate Model

• The shadow rate model assumes that the state vector dynamics are the same in both the normal and LB regimes, which is not empirically plausible.
• In contrast, the regime-switching model allows for different dynamics in the two regimes and provides a more reasonable long-run interest rate.
• The shadow rate model can produce implausibly high or low long-run means depending on the sample used, while the regime-switching model avoids this issue.

Conclusion

The regime-switching model is well-suited for analyzing yield dynamics at and away from the ZLB. It captures the nonlinearity and asymmetry in economic behavior during ZLB episodes, and it provides more accurate and plausible forecasts of future yields. The model is also consistent with empirical evidence from U.S. data and theoretical insights from macroeconomic models.

Key Features

• Two regimes: Normal and Lower Bound.
• State-dependent regime switching.
• Different dynamics for the state vector in each regime.
• Improved forecasting compared to shadow rate models.
• Empirical validation using U.S. data.
• Nonlinear decomposition of yields into expectations and risk premia.

Implications

• The model allows for positive risk premia even in the LB period, which is plausible given the asymmetry in macroeconomic behavior.
• It provides a better understanding of the gradual normalization of monetary policy.
• The model is flexible and can be extended to include more regimes or variables.