Existence, optimality and dynamics of equilibria with endogenous time preference
AbstractAbstract This paper studies the dynamic implications of the endogenous rate of time preference depending on the stock of capital, in a one-sector growth model. The planner's problem is presented and the optimal paths are characterized. We prove that there exists a critical value of initial stock, in the vicinity of which, small differences lead to permanent differences in the optimal path. Indeed, we show that a development trap can arise even under a strictly convex technology. In contrast with the early contributions that consider recursive preferences, the critical stock is not an unstable steady state so that if an economy starts at this stock, an indeterminacy will emerge. We also show that even under a convex-concave technology, the optimal path can exhibit global convergence to a unique stationary point. The multipliers system associated with an optimal path is proven to be the supporting price system of a competitive equilibrium under externality and detailed results concerning the properties of optimal (equilibrium) paths are provided. We show that the model exhibits globally monotone capital sequences yielding a richer set of potential dynamics than the classic model with exogenous discounting.
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Bibliographic InfoArticle provided by Elsevier in its journal Journal of Mathematical Economics.
Volume (Year): 47 (2011)
Issue (Month): 2 (March)
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Web page: http://www.elsevier.com/locate/jmateco
Endogenous time preference Optimal growth Competitive equilibrium Multiple steady-states;
Other versions of this item:
- Cuong Le Van & Cagri Saglam & Selman Erol, 2011. "Existence, Optimality and Dynamics of Equilibria with Endogenous Time Preference," Working Papers 04, Development and Policies Research Center (DEPOCEN), Vietnam.
- C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
- D90 - Microeconomics - - Intertemporal Choice - - - General
- O41 - Economic Development, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models
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.:
- Amir, Rabah & Mirman, Leonard J & Perkins, William R, 1991. "One-Sector Nonclassical Optimal Growth: Optimality Conditions and Comparative Dynamics," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 32(3), pages 625-44, August.
- Glenn W. Harrison & Morten I. Lau & Melonie B. Williams, 2001.
"Estimating Individual Discount Rates in Denmark: A Field Experiment,"
NCEE Working Paper Series
200102, National Center for Environmental Economics, U.S. Environmental Protection Agency, revised Nov 2001.
- Glenn W. Harrison & Morten I. Lau & Melonie B. Williams, 2002. "Estimating Individual Discount Rates in Denmark: A Field Experiment," American Economic Review, American Economic Association, vol. 92(5), pages 1606-1617, December.
- Glenn Harrison & Morten Lau & Elisabet Rutstrom & Melonie Williams, 2002. "Estimating individual discount rates in denmark: A field experiment," Artefactual Field Experiments 00062, The Field Experiments Website.
- Araujo, A, 1991. "The Once but Not Twice Differentiability of the Policy Function," Econometrica, Econometric Society, vol. 59(5), pages 1383-93, September.
- Lucas, Robert Jr. & Stokey, Nancy L., 1984.
"Optimal growth with many consumers,"
Journal of Economic Theory,
Elsevier, vol. 32(1), pages 139-171, February.
- Shane Frederick & George Loewenstein & Ted O'Donoghue, 2002. "Time Discounting and Time Preference: A Critical Review," Journal of Economic Literature, American Economic Association, vol. 40(2), pages 351-401, June.
- DURAN, Jorge & LE VAN, Cuong, 2000.
"A simple proof of existence of equilibrium in a one sector growth model with bounded or unbounded returns from below,"
CORE Discussion Papers
2000050, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Dur n, Jorge & Le Van, Cuong, 2003. "Simple Proof Of Existence Of Equilibrium In A One-Sector Growth Model With Bounded Or Unbounded Returns From Below," Macroeconomic Dynamics, Cambridge University Press, vol. 7(03), pages 317-332, June.
- Duran, Jorge & Le Van, Cuong, 2000. "A simple proof of existence of equilibrium in a one sector growth modelp with bounded or unbounded returns from below," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 2000025, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
- Iwai, Katsuhito, 1972. "Optimal economic growth and stationary ordinal utility --A fisherian approach," Journal of Economic Theory, Elsevier, vol. 5(1), pages 121-151, August.
- Askenazy, Philippe & Le Van, Cuong, 1999.
"A Model of Optimal Growth Strategy,"
Journal of Economic Theory,
Elsevier, vol. 85(1), pages 24-51, March.
- Roger E.A. Farmer, 1994.
"Indeterminacy and Sector-Specific Externalities,"
UCLA Economics Working Papers
722, UCLA Department of Economics.
- Epstein, Larry G., 1987. "A simple dynamic general equilibrium model," Journal of Economic Theory, Elsevier, vol. 41(1), pages 68-95, February.
- Dechert, W. Davis & Nishimura, Kazuo, 1983. "A complete characterization of optimal growth paths in an aggregated model with a non-concave production function," Journal of Economic Theory, Elsevier, vol. 31(2), pages 332-354, December.
- Obstfeld, Maurice, 1990.
"Intertemporal dependence, impatience, and dynamics,"
Journal of Monetary Economics,
Elsevier, vol. 26(1), pages 45-75, August.
- Maurice Obstfeld, 1989. "Intertemporal Dependence, Impatience, and Dynamics," NBER Working Papers 3028, National Bureau of Economic Research, Inc.
- Robert J. Barro & Xavier Sala-i-Martin, 1991.
"Convergence across States and Regions,"
Brookings Papers on Economic Activity,
Economic Studies Program, The Brookings Institution, vol. 22(1), pages 107-182.
- Dana, Rose-Anne & Le Van, Cuong, 2003. "Dynamic Programming in Economics," Economics Papers from University Paris Dauphine 123456789/13605, Paris Dauphine University.
- Becker, Gary S & Mulligan, Casey B, 1997. "The Endogenous Determination of Time Preference," The Quarterly Journal of Economics, MIT Press, vol. 112(3), pages 729-58, August.
- Rolf Mantel, 1998. "Optimal Economic growth with recursive preferences: decreasing rate of time preference," Estudios de Economia, University of Chile, Department of Economics, vol. 25(2 Year 19), pages 161-178, December.
- Samwick, Andrew A., 1998.
"Discount rate heterogeneity and social security reform,"
Journal of Development Economics,
Elsevier, vol. 57(1), pages 117-146, October.
- Andrew A. Samwick, 1997. "Discount Rate Heterogeneity and Social Security Reform," NBER Working Papers 6219, National Bureau of Economic Research, Inc.
- Lawrance, Emily C, 1991. "Poverty and the Rate of Time Preference: Evidence from Panel Data," Journal of Political Economy, University of Chicago Press, vol. 99(1), pages 54-77, February.
- Azariadis, Costas & Stachurski, John, 2005.
Handbook of Economic Growth,
in: Philippe Aghion & Steven Durlauf (ed.), Handbook of Economic Growth, edition 1, volume 1, chapter 5
- Michael Stern, 2006. "Endogenous time preference and optimal growth," Economic Theory, Springer, vol. 29(1), pages 49-70, September.
- Barro, Robert J & Sala-i-Martin, Xavier, 1992.
Journal of Political Economy,
University of Chicago Press, vol. 100(2), pages 223-51, April.
- Barro, R.J. & Sala-I-Martin, X., 1991. "Convergence," Papers 645, Yale - Economic Growth Center.
- Barro, Robert J. & Sala-i-Martin, Xavier, 1992. "Convergence," Scholarly Articles 3451299, Harvard University Department of Economics.
- Barro, R.J. & Sala-I-Martin, X., 1991. "Convergence Across States and Regions," Papers 629, Yale - Economic Growth Center.
- Skiba, A K, 1978. "Optimal Growth with a Convex-Concave Production Function," Econometrica, Econometric Society, vol. 46(3), pages 527-39, May.
- Das, Mausumi, 2003. "Optimal growth with decreasing marginal impatience," Journal of Economic Dynamics and Control, Elsevier, vol. 27(10), pages 1881-1898, August.
- Dana, Rose-Anne & Le Van, Cuong, 2003. "Dynamic Programming in Economics," Economics Papers from University Paris Dauphine 123456789/416, Paris Dauphine University.
- Majumdar, Mukul & Mitra, Tapan, 1982. "Intertemporal allocation with a non-convex technology: The aggregative framework," Journal of Economic Theory, Elsevier, vol. 27(1), pages 101-136, June.
- Kazuo Nishimura & Alain Venditti, 2006. "Indeterminacy in discrete-time infinite-horizon models," Working Papers halshs-00410763, HAL.
- Quah, Danny T, 1996. " Convergence Empirics across Economies with (Some) Capital Mobility," Journal of Economic Growth, Springer, vol. 1(1), pages 95-124, March.
- Kirill Borissov, 2013. "The existence of equilibrium paths in an AK-model with endogenous time preferences and borrowing constraints," EUSP Deparment of Economics Working Paper Series Ec-01/13, European University at St. Petersburg, Department of Economics.
- Borissov, Kirill, 2013.
"Growth and distribution in a model with endogenous time preferences and borrowing constraints,"
Mathematical Social Sciences,
Elsevier, vol. 66(2), pages 117-128.
- Kirill Borissov, 2011. "Growth and Distribution in a Model with Endogenous Time Peferences and Borrowing Constraints," DEGIT Conference Papers c016_073, DEGIT, Dynamics, Economic Growth, and International Trade.
- Crettez, Bertrand & Morhaim, Lisa, 2012. "Existence of competitive equilibrium in a non-optimal one-sector economy without conditions on the distorted marginal product of capital," Mathematical Social Sciences, Elsevier, vol. 63(3), pages 197-206.
- Taketo Kawagishi & Kazuo Mino, 2012. "Time Preference and Long-Run Growth: the Role of Patience Capital," Economics Bulletin, AccessEcon, vol. 32(4), pages 3243-3249.
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