Statement
In a New Keynesian DSGE model with Markov-switching monetary policy, where prices are indexed to steady-state inflation and the output gap is defined relative to steady state, inflation target switching does not affect the determinacy of equilibrium. The determinacy regions of the no-switching and target-switching models are identical; the determinacy regions of the response-switching and full-switching models are identical.
Evidence summary
Foerster (2016, Theorem 1) proves this using the Partition Principle of Foerster et al. (2014): the perturbation parameter chi separates the switching inflation target from the determinacy-relevant quadratic equation. Because prices are indexed to Pi_ss, all steady-state real variables are independent of Pi*_ss, and hence the first-order coefficient matrix F_x is independent of the target levels. This means only the inflation response parameters and their transition probabilities matter for determinacy.
Conditions and scope
- Full-price indexation to steady-state inflation is essential; without it, trend inflation effects could break the result.
- The output gap is defined as deviations from steady state, not from potential output.
- The result is established for first-order perturbation; second-order terms that break certainty equivalence do not affect determinacy.
Counter-evidence
Woodford (2003), Ascari and Ropele (2009), Coibion and Gorodnichenko (2011) show that in models without full indexation, positive trend inflation can affect determinacy even without switching. The present result depends critically on the indexation assumption.
Linked ideas
(none yet)
Open questions
- Does the result extend to partial indexation or models with non-zero trend inflation effects?
- In models with endogenous inflation targets (policy optimization), does target switching matter?