In applied work in macroeconomics and finance, nonoptimal infinite horizon economies are often studied in the the state space is unbounded. Important examples of such economies are single vector growth models with production externalities, valued fiat money, monopolistic competition, and/or distortionary government taxation. Although sufficient conditions for existence and uniqueness of Markovian equilibrium are well known for the compact state space case, no similar sufficient conditions exist for unbounded growth. This paper provides such a set of sufficient conditions, and also present a computational algorithm that will prove asymptotically consistent when computing Markovian equilibrium.
Morand, Olivier F. and Reffett, Kevin L., "Existence and Uniqueness of Equilibrium in Nonoptimal Unbounded Infinite Horizon Economies" (2001). Economics Working Papers. 200102.