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Monetary Policy Regimes and the Term Structure of Interest Rates

10 min read

Problem

Existing finance models of the term structure with regime shifts (Bansal & Zhou 2002, Dai-Singleton-Yang 2007, Ang-Bekaert-Wei 2008, etc.) are reduced-form: they let parameters switch but cannot separate the regime switches in structural shocks to the economy from the regime switches in monetary policy. The macro VAR literature on policy regimes (Cogley & Sargent 2005, Sims & Zha 2006, Primiceri 2005, Fernandez-Villaverde et al. 2010) does not use yield-curve information at all and reaches contradictory conclusions about whether U.S. monetary policy has been changing. Bikbov & Chernov build the bridge: a structural, regime-switching no-arbitrage term-structure model in which the policy switch lives inside the Taylor rule itself, identified jointly off macro data and the yield curve.

Key idea

Embed three independent Markov regime variables — s_t^v (volatility of private- sector shocks), s_t^m (systematic monetary policy coefficients in a forward- looking Taylor rule), s_t^d (volatility of monetary policy shocks) — directly in a small forward-looking New-IS / NK Phillips-curve / Taylor-rule system on three observable variables (output gap g_t, inflation pi_t, short rate r_t). Solve for the regime-conditional rational-expectations equilibrium with a generalisation of the Cho-Moreno (2011) forward method. Close the model with an essentially affine stochastic discount factor (Duffee 2002 / Dai-Singleton-Yang 2007 form) so that bond prices satisfy no-arbitrage. The resulting reduced form is a regime-switching VAR with eight compound regimes (2 × 2 × 2) and nonlinear cross-equation restrictions imposed by the structural model. Estimating this on U.S. macro + Fama-Bliss yields lets the authors isolate policy regime switches from volatility regime switches — something no reduced-form TSM can do.

Method

State dynamics (Eqs. 2.1-2.3 in the paper).

  • IS curve: g_t = m_g + (1-mu_g) g_{t-1} + mu_g E_t g_{t+1} - phi (r_t - E_t pi_{t+1}) + sigma_g(s_t^v) eps_t^g
  • NK Phillips: pi_t = m_pi + (1-mu_pi) pi_{t-1} + mu_pi E_t pi_{t+1} + delta g_t + sigma_pi(s_t^v) eps_t^pi
  • Forward-looking Taylor rule with inertia and regime-dependent coefficients: r_t = m_r(s_t^m) + (1 - rho(s_t^m)) [alpha(s_t^m) E_t pi_{t+1} + beta(s_t^m) g_t] + rho(s_t^m) r_{t-1} + sigma_r(s_t^d) eps_t^r

Private-sector parameters (m_g, m_pi, mu_g, mu_pi, phi, delta) are constant; only volatilities and Taylor-rule coefficients switch. The three regime chains are mutually independent — eight compound regimes total.

Rational-expectations solution. Stack as B_0(s_t^m) x_t = m_0 + B_{-1}(s_t^m) x_{t-1} + B_1(s_t^m) E_t x_{t+1} + Gamma(S_t) eps_t, then look for a regime- switching VAR x_t = mu(S_t) + Phi(S_t) x_{t-1} + Sigma(S_t) eps_t whose coefficients satisfy the coupled system (A.3)-(A.5) of quadratic matrix equations. The authors generalize the Cho-Moreno (2011) forward method to the regime- switching case: iteratively substitute the LHS into the expectation on the RHS, giving recursive formulas for m_n, F_n, A_n, Sigma_n. They formulate existence and uniqueness conditions in the Online Appendix, including a determinacy condition that generalizes Cho-Moreno to compound regimes — this is the direct ancestor of the determinacy check used in the cre-asset-pricing-model project (check_determinancy_fmsre).

No-arbitrage pricing. Stochastic discount factor log M_{t,t+1} = -r_t - 0.5 Lambda' Lambda - Lambda' eps_{t+1} with essentially affine market price of risk Lambda_{t,t+1} = Sigma'(S_{t+1}) [Pi_0 + Pi_x x_t]. “Preferences” Pi_0, Pi_x are constant across regimes (consistent with constant private-sector parameters); regime risk itself is not priced (justified by the structural assumption that constant private-sector parameters fix the preference block). Bond prices B_t^n = E[M_{t,t+n} | x_t, S_t] have no closed form; the appendix introduces an approximate pricing method that the authors show is more accurate than the standard log-linearization.

Estimation. Maximum likelihood on quarterly U.S. data 1970-2008: inflation (annual log diff of GDP deflator), linearly detrended log real per-capita GDP, and the unsmoothed Fama-Bliss yields at maturities {3M, 2Y, 5Y, 10Y}. Macro observed without error, 3-month yield observed without error (so the state vector x_t is observed), longer yields with iid Gaussian measurement error of common standard deviation sigma_y. Means m_g, m_pi pinned to long-run sample means following Ang-Bekaert-Wei 2008 / Dai-Singleton-Yang 2007. Global optimization: 1,000,000 Sobol starting points → top 10,000 by likelihood → local optimization from each → keep best. Inference via Conley-Hansen-Liu (1997) parametric bootstrap (1,000 simulated paths) since standard asymptotics are unreliable on the highly persistent macro+yield panel.

Two estimation regimes. TSM = full term-structure model (uses the full yield panel). SRM = “short-rate model” = identical specification estimated on macro + 3-month yield only. The TSM-vs-SRM comparison is the paper’s identification experiment.

Results

Eight regimes. The authors find clear evidence of all three regime chains. (See Tables 1-3 in the paper.)

  • Volatility of private-sector shocks s_t^v: high vol (sigma_g, sigma_pi) = (1.06, 0.56) vs low vol (0.66, 0.23). The high-vol regime concentrates in the 1970s, the monetary experiment, 1998 (Russia/LTCM), 2000-2001 (Nasdaq / 9/11), and 2004-2008 (oil shock + credit crisis). All recessions except 1991 fall in the high-vol regime.
  • Systematic monetary policy s_t^m: “active” regime with alpha(1) = 3.53, beta(1) = 2.18, rho(1) = 0.97 vs “passive” regime with alpha(2) = 0.36, beta(2) = 1.27, rho(2) = 0.81. Active regime: 1970s portions, Volcker disinflation, 1991-1995, 2002-end-of-sample. Passive: 1973-1975, monetary experiment 1979-1982, 1988-1991, internet bubble 1995-2001, 2005-2007. Crucially: in the active regime alpha > 1 (Taylor principle holds), in the passive regime alpha < 1. Passive regime survives in the rational- expectations equilibrium because agents anticipate the eventual switch back to active, eliminating sunspot dynamics — an answer to the Clarida-Gali- Gertler (2000) sunspot puzzle.
  • Volatility of monetary policy shock s_t^d: “discretion” sigma_r(1) = 2.84 vs “commitment” sigma_r(2) = 1.41. Discretion appears sporadically; smoothed regime probabilities are sharp 0/1, so this regime is well- identified.
  • Persistence of regimes: monetary s_t^m is most persistent (P(active | active) = 98%); volatility s_t^v slightly less; discretion s_t^d least persistent (P(stay) ~ 79%).

Bond identification of policy regimes. The headline identification result. Comparing TSM vs SRM:

  • Volatility regime estimates s_t^v, s_t^d are very similar across TSM and SRM — they are pinned down by the macro variables alone.
  • Monetary policy regime estimates s_t^m differ dramatically between TSM and SRM. Without long yields, the loadings alpha, beta are estimated with enormous confidence intervals (e.g. SRM: alpha(1) in (1.50, 38.0) vs TSM: (1.44, 6.90)).
  • A simulation study reports that using the yield curve reduces the bias of the estimated monetary policy regime by a factor of 20. Intuitively, long yields contain expectations about future short rates and so reflect agents’ beliefs about which policy regime is currently active.

Reduced-form implications. The structural eight-regime model generates volatility and correlation dynamics in (g_t, pi_t, r_t) that are quantitatively comparable to richer reduced-form regime-switching TSMs (e.g. Ang-Bekaert-Wei 2008’s six regimes, Dai-Singleton-Yang 2007’s two regimes, Campbell-Sunderam- Viceira 2010’s stochastic-volatility specification) — but with the structural identification added. Inflation persistence (a Cogley-Sargent style measure that nets out volatility variation) declines over the sample, consistent with Cogley & Sargent.

Counterfactuals. Holding shocks to their realised sample paths but forcing a single one of the eight regimes to prevail throughout, the authors decompose the great moderation:

  • A near-permanent transition from high to low volatility of exogenous shocks is the largest single contributor to the great moderation in macro variables.
  • Active vs passive monetary policy generates asymmetric responses to output vs inflation shocks, with no single regime dominating across both objectives — there is a genuine policy trade-off, and the changing monetary policy contributed materially to the great moderation in addition to the lucky low-volatility shocks.

Limitations

  • Empirical specification, not microfounded. The IS / Phillips / Taylor block is an empirical NK-style specification, not derived from preferences and technology. The authors are explicit that “preferences” Pi_0, Pi_x cannot be interpreted structurally.
  • Constant private-sector parameters. By construction, private-sector forward-looking coefficients (mu_g, mu_pi, phi, delta) and the risk-price block do not switch. This is what makes the structural identification work but it rules out richer extensions (e.g., Dai-Singleton-Yang 2007 prices the risk of regime change itself, which is impossible here).
  • Bond prices have no closed form. They use an approximation; accuracy is shown in the Online Appendix but the approximation is not the standard log-linearization. (The Leather-Sagi project later revisits this with a Riccati / quadratic-pricing-factor approach.)
  • Many local optima. A 1M Sobol + top-10K local-search procedure is needed. Asymptotic standard errors are unreliable; inference requires a 1000-path parametric bootstrap. This compute cost is structural to the problem, not to the approximation.
  • Three independent chains. The compound regime is 2 x 2 x 2 = 8 but the three chains are assumed mutually independent — a tractability assumption, not an empirical one.
  • Macro observed without error. Treats inflation and detrended output as perfectly observed; this is convenient for the likelihood but tightens the fit in a way that may bias the macro residuals.

Open questions

  • Can the regime-switching forward solution be extended to state-dependent transition probabilities without losing the affine pricing structure?
  • Does pricing the risk of regime change (a la Dai-Singleton-Yang) materially change the identification of the policy regimes, or does the structural identification dominate?
  • How well does the eight-regime model handle the post-2008 zero-lower-bound episode? The sample ends in 2008 — the active/passive dichotomy in alpha needs reinterpretation when the short rate is bounded.
  • Is the local identification result of structural parameters from observed output / inflation / short rate alone (Section “The role of bonds in estimating monetary policy”) robust to the specific Taylor-rule specification? Cochrane (2011) argues structural restrictions need not imply identification.

My take

This is the closest published precursor to the cre-asset-pricing-model project. Bikbov & Chernov nail the structural-vs-reduced-form distinction that is the entire reason the CRE pipeline carries construct_structural_matrices_macro and transform_struct_to_rf as separate stages. Their three independent binary chains map almost directly onto the CRE setup’s two independent binary chains (monetary policy x wage rigidity → 4 compound states; BC has 3 chains → 8 states). Their generalization of Cho-Moreno’s forward method to the regime- switching case is what get_forward_solution_msre and check_determinancy_fmsre implement under the hood. The TSM-vs-SRM comparison is the closest published analog to “why does the CRE pipeline need cap-rate observations on top of the macro panel?” — BC report a 20x bias reduction on policy regimes from adding yields, which is in the same order of magnitude as the ~1572-nat Hamilton-vs-RBPF gap measured in the CRE project (Hamilton ignores cap rates → loses ~1572 nats vs RBPF). The fact that BC need a 1M-Sobol + 10K-local-restart optimisation pipeline on eight regimes and a smaller free-parameter count than the CRE setup is also a useful sanity check on the CRE arc’s optimisation budget. Two things to bring back: (i) BC’s structured comparison between active- and passive-regime impulse responses suggests that a CRE-side counterfactual “active vs passive monetary policy with cap rates fixed at sample shocks” would be a clean, publishable result; (ii) BC’s “preferences” Pi_0, Pi_x essentially- affine specification is the same Duffee/Dai-Singleton-Yang form the CRE pipeline uses, which is reassuring on the no-arbitrage block. Importance 5 because it is the unique structural-NK + no-arbitrage TSM + regime-switching-Taylor- rule paper in the literature, and the project’s main contribution is a descendant of this design.

The published online appendix bc4_12_app_els.mmd is the canonical source for the rational-expectations forward method, the local-identification proof, and the approximate bond-valuation algorithm — all directly relevant to anyone re-implementing the BC pipeline or extending it.

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