Dai, Darong (2011): Time as an Endogenous Random Variable Smoothly Embedded into Preference Manifold.

PDF
MPRA_paper_40182.pdf Download (399kB)  Preview 
Abstract
A general equilibrium model has been constructed in a stochastic endogenous growth economy driven by an ItoLevy diffusion process. The minimum time to “economic maturity” for an underdeveloped economy has been computed both in the preference manifold of the modified Ramsey fashion and in that of the modified Radner fashion with its support, i.e., fiscal policies and savings strategy, endogenously determined. Furthermore, the effects of different information structures to the endogenous time have been thoroughly investigated, and local sensitivity analyses of optimal consumption per capita with respect to the initial level of capital stock per capita have been smoothly incorporated into the current macroeconomic model.
Item Type:  MPRA Paper 

Original Title:  Time as an Endogenous Random Variable Smoothly Embedded into Preference Manifold 
English Title:  Time as an Endogenous Random Variable Smoothly Embedded into Preference Manifold 
Language:  English 
Keywords:  Stochastic endogenous growth; Minimum time to “economic maturity”; Optimal taxation policies; Endogenous savings rate; Preference manifold; Information structure; Local sensitivity analyses; Optimal stopping time; Levy diffusion 
Subjects:  E  Macroeconomics and Monetary Economics > E6  Macroeconomic Policy, Macroeconomic Aspects of Public Finance, and General Outlook > E62  Fiscal Policy O  Economic Development, Innovation, Technological Change, and Growth > O1  Economic Development > O11  Macroeconomic Analyses of Economic Development H  Public Economics > H2  Taxation, Subsidies, and Revenue > H21  Efficiency ; Optimal Taxation D  Microeconomics > D9  Intertemporal Choice > D91  Intertemporal Household Choice ; Life Cycle Models and Saving C  Mathematical and Quantitative Methods > C6  Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C61  Optimization Techniques ; Programming Models ; Dynamic Analysis D  Microeconomics > D8  Information, Knowledge, and Uncertainty > D82  Asymmetric and Private Information ; Mechanism Design 
Item ID:  40182 
Depositing User:  darong dai 
Date Deposited:  20. Jul 2012 10:58 
Last Modified:  28. Sep 2015 10:44 
References:  Aghion, P., 2004. Growth and Development: A Schumpeterian Approach. Annals of Economics and Finance 5, 125. Alili, L. and A. E. Kyprianou, 2005. Some Remarks on First Passage of Lévy Processes, the American Put and Pasting Principles. Annals of Applied Probability 15, 20622080. Araujo, A. and J.A. Scheinkman, 1977. Smoothness, Comparative Dynamics, and the Turnpike Property. Econometrica 45, 601620. Atsumi, H., 1965. Neoclassical Growth and the Efficient Program of Capital Accumulation. Review of Economic Studies 32, 127136. Avram, F., A. E. Kyprianou, M. R. Pistorius, 2004. Exit Problems for Spectrally Negative Lévy Processes and Applications to (Canadized) Russian Options. Annals of Applied Probability 14, 215238. Barro, R.J., 1990. Government Spending in a Simple Model of Endogenous Growth. Journal of Political Economy 98, 103125. Bewley, T., 1982. An Integration of Equilibrium Theory and Turnpike Theory. Journal of Mathematical Economics 10, 233267. Canova, F., 1995. Sensitivity Analysis and Model Evaluation in Simulated Dynamic General Equilibrium Economies. International Economic Review 36, 477501. Cass, D., 1966. Optimum Growth in an Aggregative Model of Capital Accumulation: A Turnpike Theorem. Econometrica 34, 833850. Chamley, C., 1986. Optimal Taxation of Capital Income in General Equilibrium with Infinite Lives. Econometrica 54, 607622. Champernowne, D. G., 1962. Some Implications of Golden Age Conditions when Saving Equal Profits. Review of Economic Studies 29, 235237. Choi, K. J., H. K. Koo and D. Y. Kwak, 2004. Optimal Stopping of Active Portfolio Management. Annals of Economics and Finance 5, 93126. Coles, J.L., 1985. Equilibrium Turnpike Theory with Constant Returns to Scale and Possibly Heterogeneous Discount Factors. International Economic Review 26, 671679. Dai, D., 2012. Stochastic Versions of Turnpike Theorems in the Sense of Uniform Topology. Annals of Economics and Finance 13, 389431. Di Nunno, G., B. Oksendal and F. Proske, 2009. Malliavin calculus for Lévy processes with applications to finance. Berlin: SpringerVerlag. Drandakis, E.M., 1966. On Efficient Accumulation Paths in the Closed Production Model. Econometrica 34, 331346. Fernández, R. and R. Rogerson, 1998. Public Education and Income Distribution: A Dynamic Quantitative Evaluation of EducationFinance Reform. American Economic Review 88, 813833. Gale, D., 1967. On Optimal Development in a MultiSector Economy. Review of Economic Studies 34, 118. Gantz, D.T., 1980. A Strong Turnpike Theorem for a Nonstationary von NeumannGale Production Model. Econometrica 48, 17771790. Gong, L. and H. Zou, 2002. Effects of Growth and Volatility in Public Expenditures on Economic Growth: Theory and Evidence. Annals of Economics and Finance 3, 379406. Guo, X. and L. Shepp, 2001. Some Optimal Stopping Problems with Nontrivial Boundaries for Pricing Exotic Options. Journal of Applied Probability 38, 647658. Hicks, J. R., 1961. I. The Story of a Mare's Nest. Review of Economic Studies 28, 7788. Hobson, D.G., 1998. Volatility Misspecification, Option Pricing and Superreplication via Coupling. Annals of Applied Probability 8, 193205. Howe, C. W., 1960. An Alternative Proof of the Existence of General Equilibrium in a von Neumann Model. Econometrica 28, 635639. Inada, K. I., 1964. Some Structural Characteristics of Turnpike Theorems. Review of Economic Studies 31, 4358. Joshi, S., 1997. Turnpike Theorem in Nonconvex and Nonstationary Environment. International Economic Review 38, 225248. Judd, K.L., 1997. The Optimal Tax Rate for Capital Income is Negative. NBER working paper No. 6004. Judd, K.L., 2002. CapitalIncome Taxation with Imperfect Competition. American Economic Review 92, 417421. Kemeny, J. G., O. Morgenstern and G. L. Thompson, 1956. A Generalization of the von Neumann Model of an Expanding Economy. Econometrica 24, 115135. Kurz, M., 1965. Optimal Paths of Capital Accumulation Under the Minimum Time Objective. Econometrica 33, 4266. Kydland, F and E. C. Prescott, 1977. Rules Rather than Discretion: The Inconsistency of Optimal Plans. Journal of Political Economy 85, 473492. Kydland, F and E. C. Prescott, 1982. Time to Build and Aggregate Fluctuations. Econometrica 50, 13451370. Levine, R. and D. Renelt, 1992. A Sensitivity Analysis of CrossCountry Growth Regressions. American Economic Review 82, 942963. Long, Jr. J. B. and C. I. Plosser, 1983. Real Business Cycles. Journal of Political Economy 91, 3969. McKenzie, L., 1963a. The DorfmanSamuelsonSolow Turnpike Theorem. International Economic Review 4, 2943. McKenzie, L., 1963b. Turnpike Theorems for a Generalized Leontief Model. Econometrica 31, 165180. McKenzie, L., 1976. Turnpike Theory. Econometrica 44, 841865. McKenzie, L., 1982. A Primal Route to the Turnpike and Liapounov Stability. Journal of Economic Theory 27, 194209. McKenzie, L., 1998. Turnpikes. American Economic Review 88, 114. Merton, R.C., 1975. An Asymptotic Theory of Growth Under Uncertainty. Review of Economic Studies 42, 375393. MeyerBrandis, T., B. Oksendal and X. Y. Zhou. A stochastic maximum principle via Malliavin calculus. arXiv:0911.3720v1 [math.OC] 19 Nov 2009. Miao, J., 2009. Ambiguity, Risk and Portfolio Choice under Incomplete Information. Annals of Economics and Finance 10, 257279. Morishima, M., 1961. Proof of a Turnpike Theorem: The “No Joint Production” Case. Review of Economic Studies 28, 8997. Morishima, M., 1965. On the Two Theorems of Growth Economics: A Mathematical Exercise. Econometrica 33, 829840. Myneni, R., 1992. The Pricing of the American Option. Annals of Applied Probability 2, 123. Nikaido, H., 1964. Persistence of Continual Growth Near the von Neumann Ray: A Strong Version of the Radner Turnpike Theorem. Econometrica 32, 151162. Neumann, J. V., 19451946. A Model of General Economic Equilibrium. Review of Economic Studies 13, 19. Pearce, I. F., 1962. The End of the Golden Age in Solovia: A Further Fable for Growthmen Hoping to Be "One Up" on Oiko. American Economic Review 52, 10881097. Phelps, E.S., 1961. The Golden Rule of Accumulation: A Fable for Growthmen. American Economic Review 51, 638643. Phelps, E.S., 1962. The End of the Golden Age in Solovia: Comment. American Economic Review 52, 10971099. Phelps, E.S., 1965. Second Essay on the Golden Rule of Accumulation. American Economic Review 55, 793814. Protter, P. and D. Talay, 1997. The Euler Scheme for Lévy Driven Stochastic Differential Equations. Annals of Probability 25, 393423. Oksendal, B. and A.Sulem, 2005. Applied Stochastic Control of Jump Diffusions. Berlin: SpringerVerlag. Radner, R., 1961. Paths of Economic Growth that are Optimal with Regard only to Final States: A Turnpike Theorem. Review of Economic Studies 28, 98104. Ramsey, F. P., 1928. A Mathematical Theory of Saving. Economic Journal 38, 543559. Rebelo, S., 1991. Longrun Policy Analysis and Longrun Growth. Journal of Political Economy 99, 500521. Samuelson, P.A., 1965. A Catenary Turnpike Theorem Involving Consumption and the Golden Rule. American Economic Review 55, 486496. Shepp, L. and A. N. Shiryaev, 1993. The Russian Option: Reduced Regret. Annals of Applied Probability 3, 631640. Solow, R. M., 2003. Reflections on Growth and Development. Annals of Economics and Finance 4, 219229. Srinivasan, T. N., 1962. Investment Criteria and Choice of Techniques of Production. Yale Economic Essays 2, 1962. Tsukui, J., 1966. Turnpike Theorem in a Generalized Dynamic InputOutput System. Econometrica 34, 396407. Tsukui, J., 1967. The Consumption and the Output Turnpike Theorems in a von Neumann Type of Model—A Finite Term Problem. Review of Economic Studies 34, 8593. Turnovsky, S.J., 2000. Fiscal Policy, Elastic Labor Supply, and Endogenous Growth. Journal of Monetary Economics 45, 185210. Winter, S.G., Jr., 1967. The Norms of a Closed Technology and the StraightDowntheTurnpike Theorem. Review of Economic Studies 34, 6784. Yan, J. A., Q. Zhang and S. Zhang, 2000. Growth Optimal Portfolio in a Market Driven by a JumpDiffusionLike Process or a Lévy Process. Annals of Economics and Finance 1, 101116. Yano, M., 1984a. The Turnpike of Dynamic General Equilibrium Paths and Its Insensitivity to Initial Conditions. Journal of Mathematical Economics 13, 235254. Yano, M., 1984b. Competitive Equilibria on Turnpikes in a McKenzie Economy, I: A Neighborhood Turnpike Theorem. International Economic Review 25, 695717. Yano, M., 1985. Competitive Equilibria on Turnpikes in a McKenzie Economy, II: An Asymptotic Turnpike Theorem. International Economic Review 26, 661669. Yano, M., 1998. On the Dual Stability of a Von Neumann Facet and the Inefficacy of Temporary Fiscal Policy. Econometrica 66, 427451. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/40182 