Statement
The long-run Taylor principle (LRTP) of Davig and Leeper (2007) — requiring all generalized eigenvalues of (diag(Gamma_1,...,Gamma_h), P kron I_n) to exceed unity — is a necessary condition for MSRE determinacy but is sufficient only within the restricted class of solutions that do not depend on the previous regime s_{t-1}. In general MSRE models, solutions depend on the lagged regime through the expectations mechanism, the DL representation is invalid, and the LRTP can hold while the model is indeterminate under mean-square stability.
Evidence summary
Hayashi (2017) identifies the precise restriction: the DL stacking requires E(y_{j,t+1} | s_t=i, Omega_t^{-s}) to be independent of i, which holds iff y_{t+1} does not depend on s_t. Under this restriction, the MSRE reduces to a standard linear RE model in the augmented state vector and the eigenvalue condition is sufficient. FWZ (2009) and (2010) provide counterexamples; Cho (2020) formalizes the gap as first-moment vs. second-moment stability.
Conditions and scope
- The LRTP is always necessary for determinacy (it ensures at least first-moment convergence).
- The sufficiency restriction (solutions independent of lagged regime) may hold in some economic models but not in general.
- Under mean-square stability, the gap between the LRTP region and the true determinacy region can be substantial in calibrated models.
Counter-evidence
None against the claim itself. The claim accurately characterizes the LRTP’s scope; the debate is about whether the regime-independence restriction is economically reasonable.
Linked ideas
(none yet)
Open questions
- In which economic models does regime-independence naturally hold?
- How large is the LRTP-vs-MSS gap in empirically estimated models?