Statement
For any determinacy-admissible Markov-switching rational expectations model, the MOD (minimum of modulus) solution — the MSV solution with the smallest mean-square stability spectral radius — provides a complete, three-way classification: (1) determinacy iff the MOD solution is MSS AND its forward operator has spectral radius < 1; (2) indeterminacy iff the MOD solution is MSS but the forward spectral radius >= 1; (3) no stable solution iff the MOD solution itself is not MSS. The full solution set need not be computed.
Evidence summary
Cho (2020) proves this as Proposition 3, building on two intermediate results: (a) Proposition 1 (the forward operator spectral radius controls sunspot existence) and (b) Proposition 2 (the MOD identification condition ensures uniqueness of the stable MSV). The paper also demonstrates equivalence to standard eigenvalue methods for the LRE special case (Table 2). The forward method (iterative recursion from B) computes the MOD solution in 10^{-3} to 10^{-2} seconds and coincides with the MOD in all experiments.
Conditions and scope
- MSRE models with any number of regimes and any dimension, as long as the model is determinacy-admissible.
- Stability concept is mean-square stability; comparison with bounded stability (Barthelemy-Marx) remains open.
- The MOD solution is always well-defined; determinacy can only arise in the determinacy-admissible region.
Counter-evidence
None identified. The classification is proved as exhaustive and the conditions as necessary and sufficient.
Linked ideas
(none yet)
Open questions
- Formal proof of forward method = MOD equivalence for MSRE.
- Prevalence of determinacy-inadmissible models in empirical applications.
- Extension to non-linear or higher-order perturbation approximations.