Bounding the CRRA Utility Functions
The constant-relative-risk-aversion (CRRA) utility function is now predominantly used in quantitative macroeconomic studies. This function, however, is not bounded and thus creates problems when applying the standard tools of dynamic programming. This paper devises a method for "bounding" the CRRA utility functions. The proposed method is based on a set of conditions that can establish boundedness among a broad class of utility functions. These results are then used to construct a bounded utility function that is identical to a CRRA utility function except when consumption is very small or very large. It is shown that the constructed utility function also satisfies the Inada condition and is consistent with balanced growth.
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- LE VAN, Cuong & MORHAIM, Lisa, 2001.
"Optimal growth models with bounded or unbounded returns: a unifying approach,"
CORE Discussion Papers
2001034, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Le Van, Cuong & Morhaim, Lisa, 2002. "Optimal Growth Models with Bounded or Unbounded Returns: A Unifying Approach," Journal of Economic Theory, Elsevier, vol. 105(1), pages 158-187, July.
- Le Van, C. & Morhaim, L., 2000. "Optimal Growth Models with Bounded or Unbounded Returns : a Unifying Approach," Papiers d'Economie MathÃ©matique et Applications 2000.64, UniversitÃ© PanthÃ©on-Sorbonne (Paris 1).
- Juan Pablo RincÛn-Zapatero & Carlos RodrÌguez-Palmero, 2003. "Existence and Uniqueness of Solutions to the Bellman Equation in the Unbounded Case," Econometrica, Econometric Society, vol. 71(5), pages 1519-1555, 09.
- Huggett, Mark, 1997. "The one-sector growth model with idiosyncratic shocks: Steady states and dynamics," Journal of Monetary Economics, Elsevier, vol. 39(3), pages 385-403, August.
- Masao Ogaki & Carmen M. Reinhart, 1998.
"Measuring Intertemporal Substitution: The Role of Durable Goods,"
Journal of Political Economy,
University of Chicago Press, vol. 106(5), pages 1078-1098, October.
- Ogaki, M & Reinhart, C-M, 1995. "Measuring Intertemporal Substitution : The Role of Durable Goods," RCER Working Papers 404, University of Rochester - Center for Economic Research (RCER).
- Reinhart, Carmen & Ogaki, Masao, 1995. "Measuring intertemporal substitution: The role of durable goods," MPRA Paper 13690, University Library of Munich, Germany.
- Jianjun Miao, 2003.
"Competitive Equilibria of Economies with a Continuum of Consumers and Aggregate Shocks,"
- Miao, Jianjun, 2006. "Competitive equilibria of economies with a continuum of consumers and aggregate shocks," Journal of Economic Theory, Elsevier, vol. 128(1), pages 274-298, May.
- Jianjun Miao, 2004. "Competitive Equilibria of Economies with a Continuum of Consumers and Aggregate Shocks," CEMA Working Papers 460, China Economics and Management Academy, Central University of Finance and Economics.
- Barelli, Paulo & de Abreu Pessoa, Samuel, 2003. "Inada conditions imply that production function must be asymptotically Cobb-Douglas," Economics Letters, Elsevier, vol. 81(3), pages 361-363, December.
- Huggett, Mark & Ospina, Sandra, 2001. "Aggregate precautionary savings: when is the third derivative irrelevant?," Journal of Monetary Economics, Elsevier, vol. 48(2), pages 373-396, October.
- Palivos, Theodore & Wang, Ping & Zhang, Jianbo, 1997. "On the Existence of Balanced Growth Equilibrium," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 38(1), pages 205-224, February.
- S. Rao Aiyagari, 1993.
"Uninsured idiosyncratic risk and aggregate saving,"
502, Federal Reserve Bank of Minneapolis.
- Steger, Thomas M., 2000. "Economic growth with subsistence consumption," Journal of Development Economics, Elsevier, vol. 62(2), pages 343-361, August.
- Boud, John III, 1990. "Recursive utility and the Ramsey problem," Journal of Economic Theory, Elsevier, vol. 50(2), pages 326-345, April.
- Geweke, John, 2001. "A note on some limitations of CRRA utility," Economics Letters, Elsevier, vol. 71(3), pages 341-345, June.
- Barelli, Paulo & Pessoa, Samuel de Abreu, 2003. "Inada conditions imply that production function must be asymptotically Cobb-Douglas," Economics Working Papers (Ensaios Economicos da EPGE) 477, FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
- Annette Vissing-Jorgensen, 2002. "Limited Asset Market Participation and the Elasticity of Intertemporal Substitution," NBER Working Papers 8896, National Bureau of Economic Research, Inc.
- Annette Vissing-Jorgensen, 2002. "Limited Asset Market Participation and the Elasticity of Intertemporal Substitution," Journal of Political Economy, University of Chicago Press, vol. 110(4), pages 825-853, August.
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