Time-varying rational expectations models. (English) Zbl 1425.91330
Summary: This paper develops a comprehensive theory for rational expectations models with time-varying (random) coefficients. Based on the multiplicative ergodic theorem it develops a “linear algebra” in terms of Lyapunov exponents, defined as the asymptotic growth rates of trajectories. Together with their associated Lyapunov spaces they provide a perfect substitute for the eigenvalue/eigenspace analysis used in constant coefficient models. In particular, they allow the construction of explicit solution formulas similar to the standard case. These methods and their numerical implementation is illustrated using a canonical New Keynesian model with a time-varying policy rule and lagged endogenous variables.
MSC:
| 91B64 | Macroeconomic theory (monetary models, models of taxation) |
| 91B84 | Economic time series analysis |
| 37A20 | Algebraic ergodic theory, cocycles, orbit equivalence, ergodic equivalence relations |
Keywords:
time-varying rational expectations models; Lyapunov exponents; multiplicative ergodic theoremReferences:
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