Necessary and Sufficient Conditions for Existence and Uniqueness of Recursive Utilities |
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| Authors: | JAROSLAV BOROVI?KA JOHN STACHURSKI |
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| Institution: | 1. Jaroslav Borovi?ka is with New York University, Federal Reserve Bank of Minneapolis, and NBER. John Stachurski is with the Research School of Economics, Australian National University. The authors thank Anmol Bhandari, Tim Christensen, Ippei Fujiwara, Jinill Kim, Stefan Nagel, Daisuke Oyama, Guanlong Ren, and the anonymous referees for useful comments and suggestions. Special thanks are due to Miros?awa Zima for her valuable input on local spectral radius conditions. Borovi?ka gratefully acknowledges financial support from New York University and Federal Reserve Bank of Minneapolis. Stachurski gratefully acknowledges financial support from ARC grant FT160100423. The views expressed herein are those of the authors and not necessarily those of the Federal Reserve Bank of Minneapolis or the Federal Reserve System. We have read The Journal of Finance's disclosure policy and have no conflicts of interest to 2. disclose. |
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| Abstract: | We obtain exact necessary and sufficient conditions for existence and uniqueness of solutions of a class of homothetic recursive utility models postulated by Epstein and Zin. The conditions center on a single test value with a natural economic interpretation. The test sheds light on the relationship between valuation of cash flows, impatience, risk adjustment, and intertemporal substitution of consumption. We propose two methods to compute the test value when an analytical solution is not available. We further provide several applications. |
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