Strategic interaction and dynamics under endogenous time preference
This paper presents a strategic growth model with endogenous time preference. Due to the potential lack of concavity and the differentiability of the value functions associated with each agent’s problem, we employ the theory of monotone comparative statics and supermodular games based on order and monotonicity properties on lattices. In particular, we provide the sufficient conditions of supermodularity for dynamic games with open-loop strategies based on two fundamental elements: the ability to order elements in the strategy space of the agents and the strategic complementarity which implies upward sloping best responses. The supermodular game structure of the model lets us provide the existence and the monotonicity results on the greatest and the least equilibria. We sharpen these results by showing the differentiability of the value function and the uniqueness of the best response correspondences almost everywhere and show that the stationary state Nash equilibria tend to be symmetric. Finally, we numerically analyze to what extent the strategic complementarity inherent in agents’ strategies can alter the convergence results that could have emerged under a single agent optimal growth model. In particular, we show that the initially rich can pull the poor out of the poverty trap even when sustaining a higher level of steady state capital stock for itself.
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- Schumacher, Ingmar, 2011.
"Endogenous discounting and the domain of the felicity function,"
Elsevier, vol. 28(1-2), pages 574-581, January.
- Schumacher, Ingmar, 2011. "Endogenous discounting and the domain of the felicity function," Economic Modelling, Elsevier, vol. 28(1), pages 574-581.
- Sundaram, Rangarajan K., 1989. "Perfect equilibrium in non-randomized strategies in a class of symmetric dynamic games," Journal of Economic Theory, Elsevier, vol. 47(1), pages 153-177, February.
- 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 Across States and Regions," Papers 629, 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," Papers 645, Yale - Economic Growth Center.
- 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.
- Costas Aariadis & John Stachurski, 2004.
Department of Economics - Working Papers Series
913, The University of Melbourne.
- Dana, Rose-Anne & Le Van, Cuong, 2003. "Dynamic Programming in Economics," Economics Papers from University Paris Dauphine 123456789/416, Paris Dauphine University.
- 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.
- AMIR, Rabah, 2003.
"Supermodularity and complementarity in economics: an elementary survey,"
CORE Discussion Papers
2003104, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Rabah Amir, 2005. "Supermodularity and Complementarity in Economics: An Elementary Survey," Southern Economic Journal, Southern Economic Association, vol. 71(3), pages 636-660, January.
- Quah, Danny T, 1996. " Convergence Empirics across Economies with (Some) Capital Mobility," Journal of Economic Growth, Springer, vol. 1(1), pages 95-124, March.
- repec:hal:journl:halshs-00639731 is not listed on IDEAS
- Michael Stern, 2006. "Endogenous time preference and optimal growth," Economic Theory, Springer, vol. 29(1), pages 49-70, September.
- Benveniste, L M & Scheinkman, J A, 1979. "On the Differentiability of the Value Function in Dynamic Models of Economics," Econometrica, Econometric Society, vol. 47(3), pages 727-32, May.
- Dana, Rose-Anne & Le Van, Cuong, 2003. "Dynamic Programming in Economics," Economics Papers from University Paris Dauphine 123456789/13605, Paris Dauphine University.
- Araujo, A, 1991. "The Once but Not Twice Differentiability of the Policy Function," Econometrica, Econometric Society, vol. 59(5), pages 1383-93, September.
- 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.
- Vives, Xavier, 2005. "Games with strategic complementarities: New applications to industrial organization," International Journal of Industrial Organization, Elsevier, vol. 23(7-8), pages 625-637, September.
- 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.
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