Recursive utility in a Markov environment with stochastic growth

• Published in: Proceedings of the National Academy of Sciences - PNAS Vol. 109; no. 30; pp. 11967 - 11972
• Main Authors: Hansen, Lars Peter, Scheinkman, José A.
• Format: Journal Article
• Language: English
• Published: United States National Academy of Sciences 24.07.2012; National Acad Sciences
• Subjects: Consumption; Economic Development - statistics & numerical data; Economic growth models; Economic growth rate; Eigenfunctions; Eigenvalues; Humans; Macroeconomics; Markov analysis; Markov Chains; Markov processes; Models, Econometric; Recursion; Risk Assessment; Risk aversion; Social Sciences; Stochastic models; Stochastic Processes; Utility functions; Utility models
• ISSN: 0027-8424; 1091-6490
• DOI: 10.1073/pnas.1200237109

Recursive utility models that feature investor concerns about the intertemporal composition of risk are used extensively in applied research in macroeconomics and asset pricing. These models represent preferences as the solution to a nonlinear forward-looking difference equation with a terminal condition. In this paper we study infinite-horizon specifications of this difference equation in the context of a Markov environment. We establish a connection between the solution to this equation and to an arguably simpler Perron–Frobenius eigenvalue equation of the type that occurs in the study of large deviations for Markov processes. By exploiting this connection, we establish existence and uniqueness results. Moreover, we explore a substantive link between large deviation bounds for tail events for stochastic consumption growth and preferences induced by recursive utility.