Two-step estimator maps term structure models to bond supply shocks
A Bank of Canada working paper introduces a two-step estimator that bypasses fixed-point problems by mapping Gaussian dynamic term structure models into portfolio-balance primitives. The framework identifies structural debt-supply shocks using factor-mimicking bond portfolios.
Bypassing the arbitrageur feedback loop
Traditional portfolio-balance models create circular fixed-point feedback loops because required risk compensation depends on how strongly yields respond to debt supply shifts.
The paper proves observational equivalence between Gaussian term structure models and discrete-time portfolio-balance equilibria under stationary state dynamics.
Applying this two-step estimator to U.S. Treasury yields from 1986 to 2025 isolates three structural shocks: hedging risk premium, risk-bearing capacity, and monetary policy.
Calibrating arbitrageur relative risk aversion to 16 matches the 100-basis-point yield decline observed across pre-pandemic asset purchase programs.
Hedging dominates the long end
Variance decompositions demonstrate stark yield curve segmentation.
Hedging-risk-premium shocks account for 96.3 percent of the one-quarter-ahead forecast variance in ten-year yields and 88.2 percent of ten-year term premia at a ten-year horizon.
Conversely, short-rate variability is driven initially by monetary policy at 49.5 percent before risk-bearing-capacity shocks dominate medium-term variance at 63.5 percent.
The implied forward-looking policy rule estimates an inflation response of 1.67.
Elegant math with data limits
The mathematical bypass neatly eliminates numerical instability without requiring granular holding records.
However, the inability to identify maturity-specific demand elasticities directly from yields leaves supply allocations stylized.
For debt management, the framework works best when combined with sector-level balance sheet data.