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.
|Date of creation:||07 Feb 2009|
|Contact details of provider:|| Postal: Ludwigstraße 33, D-80539 Munich, Germany|
Web page: https://mpra.ub.uni-muenchen.de
More information through EDIRC
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- S. Rao Aiyagari, 1994.
"Uninsured Idiosyncratic Risk and Aggregate Saving,"
The Quarterly Journal of Economics,
Oxford University Press, vol. 109(3), pages 659-684.
- 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).
- 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, 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).
- Geweke, John, 2001. "A note on some limitations of CRRA utility," Economics Letters, Elsevier, vol. 71(3), pages 341-345, June.
- 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 205-24, February.
- Boud, John III, 1990. "Recursive utility and the Ramsey problem," Journal of Economic Theory, Elsevier, vol. 50(2), pages 326-345, April.
- 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, 2003. "Competitive Equilibria of Economies with a Continuum of Consumers and Aggregate Shocks," Macroeconomics 0310001, EconWPA.
- 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.
- 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).
- 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, 5/05. "Measuring intertemporal substitution: The role of durable goods," MPRA Paper 13690, University Library of Munich, Germany.
- 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.
- Steger, Thomas M., 2000. "Economic growth with subsistence consumption," Journal of Development Economics, Elsevier, vol. 62(2), pages 343-361, August.
- Annette Vissing-Jorgensen, 2002. "Limited Asset Market Participation and the Elasticity of Intertemporal Substitution," NBER Working Papers 8896, National Bureau of Economic Research, Inc.
- 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.
- 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.
When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:13260. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Joachim Winter)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.