Stationary Distributions in Monotone Markov Models: Theory and Applications

Takashi Kamihigashi and John Stachurski
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Takashi Kamihigashi: Center for Computational Social Science (CCSS) and Research Institute for Economics & Business Administration (RIEB), Kobe University, JAPAN
John Stachurski: National Graduate Institute for Policy Studies, JAPAN

No DP2026-09, Discussion Paper Series from Research Institute for Economics & Business Administration, Kobe University

Abstract: Many economic models feature monotone Markov dynamics on state spaces that may be noncompact. Establishing existence, uniqueness, and stability of stationary distributions in such settings has required a patchwork of sufficient conditions, each tailored to specific applications. We provide a single necessary and sufficient condition:a monotone Markov process has a globally stable stationary distribution if and only if it is asymptotically contractive and has a tight rajectory. This characterization covers both compact and noncompact state spaces, discrete and continuous time, and extends to nonlinear Markov operators that depend on aggregate state. We demonstrate the result through applications to wage dynamics, Bayesian learning with belief shocks, and income processes that generate Pareto tails.

Pages: 46 pages
Date: 2026-03
New Economics Papers: this item is included in nep-mic
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