Quantitative Economics: Nov, 2020, Volume 11, Issue 4

A tractable framework for analyzing a class of nonstationary Markov models

Lilia Maliar, Serguei Maliar, John B. Taylor, Inna Tsener

We consider a class of infinite‐horizon dynamic Markov economic models in which the parameters of utility function, production function, and transition equations change over time. In such models, the optimal value and decision functions are time‐inhomogeneous: they depend not only on state but also on time. We propose a quantitative framework, called extended function path (EFP), for calibrating, solving, simulating, and estimating such nonstationary Markov models. The EFP framework relies on the turnpike theorem which implies that the finite‐horizon solutions asymptotically converge to the infinite‐horizon solutions if the time horizon is sufficiently large. The EFP applications include unbalanced stochastic growth models, the entry into and exit from a monetary union, information news, anticipated policy regime switches, deterministic seasonals, among others. Examples of MATLAB code are provided.

Turnpike theorem time‐inhomogeneous models nonstationary models semi‐Markov models unbalanced growth time‐varying parameters trends anticipated shock parameter shift parameter drift regime switches stochastic volatility technological progress seasonal adjustments Fair and Taylor method extended path C61 C63 C68 E31 E52

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