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Monetary Policy Regime Switches and Macroeconomic Dynamics

4 min read

Problem

The literature on MSRE monetary policy models separately considers switching in the inflation target and switching in the inflation response coefficient, but no unified analysis exists. Prior determinacy results (Farmer et al. 2009, Cho 2014) applied only to forward-looking models without predetermined variables. The paper asks: (1) How do different types of monetary policy switching (target vs. response) affect determinacy? (2) How do they differentially impact macroeconomic distributions?

Key idea

Two key results. First, inflation target switching is irrelevant for determinacy (Theorem 1): because prices are indexed to steady-state inflation, the determinacy region depends only on the inflation response parameters and their transition matrix, not on the level of inflation targets. Second, an overly aggressive active regime can cause indeterminacy: when the active regime responds too strongly to inflation, it enables explosive paths in the passive regime that are still mean-square stable, creating a second MSS solution. The paper also establishes that target switching primarily affects the level of inflation while response switching primarily affects volatility.

Method

  1. NK DSGE model with two independent Markov chains: one for inflation target (s_t^pi in {L,H}), one for inflation response (s_t^psi in {A,P}), giving 4 compound regimes.
  2. Perturbation solution method (Foerster et al. 2014) for MSV solutions with predetermined variables; second-order approximation breaks certainty equivalence.
  3. Theorem 1 (target irrelevance): Proved via the Partition Principle: the quadratic equation governing determinacy depends on F_x(Y_ss, X_ss, x_ss, 0, 0) which, due to price indexation to Pi_ss, is independent of Pi^*_L and Pi^*_H.
  4. Numerical determinacy regions for inflation response switching: vary (psi_A, psi_P) with transition probabilities, interest rate smoothing, and output gap response as controls.
  5. Ergodic and counterfactual simulations: 50,000 simulations x 10,000 periods at second-order accuracy to isolate realization effects from expectation formation effects.

Results

  • Theorem 1: Inflation target level does not affect determinacy, even with switching targets. This means determinacy analysis need only consider inflation response switching.
  • Taylor principle failure with switching: Satisfying the Taylor principle period-by-period is neither necessary nor sufficient for determinacy. Too-aggressive active response can create MSS explosive passive-regime solutions.
  • Both-regimes-stable (BRS) vs. MSS: When both BRS and MSS produce a unique solution, the active and passive regimes are both stable. When MSS gives indeterminacy but BRS gives determinacy, one MSS solution has an explosive regime.
  • Transition probability effects: More persistent passive regimes expand indeterminacy; the passive regime can be weaker if it has shorter expected duration.
  • Interest rate smoothing: Higher smoothing expands determinacy for low psi_A but restricts it for high psi_A.
  • Output gap response: Positive output gap response shrinks the indeterminacy region.
  • Distribution effects: Target switching affects inflation level (mean), response switching affects inflation volatility (std dev). This holds for both ergodic and counterfactual (expectations-only) simulations.

Limitations

  • Determinacy analysis is MSV-based: a unique MSV solution does not guarantee determinacy in the full solution class (as Farmer et al. 2009 showed).
  • The model assumes full-price indexation to steady-state inflation, which is crucial for Theorem 1.
  • Constant transition probabilities; endogenous switching (threshold models) not considered.
  • Calibration-dependent determinacy regions; the specific numbers depend on the parameterization.

Open questions

  • Determinacy in the full solution class (not just MSV) with predetermined variables and regime switching.
  • Endogenous switching probabilities dependent on economic outcomes.
  • Whether inflation target or response switches best explain U.S. monetary history (an empirical question).
  • Optimal policy design in a switching environment.

My take

A well-executed applied paper that bridges the theoretical determinacy literature (FWZ 2009, Cho 2014) to a realistic NK-DSGE model with multiple switching dimensions. Theorem 1 (target irrelevance) is a clean result that simplifies the analysis considerably. For the CRE asset pricing project, this paper directly supports the model’s 4-regime structure (2 independent binary chains) and confirms that the determinacy check need only focus on the inflation response chain, not the discretion chain.

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