A Robust Turnpike Deduced by Economic Maturity

Dai, Darong (2012): A Robust Turnpike Deduced by Economic Maturity.

Abstract

In the paper, a one-sector neoclassical model with stochastic growth has been constructed. The key concept of economic maturity is well-defined in the abstract model economy, and also a thorough characterization of the minimum time needed to economic maturity is supplied for the first time. Moreover, it is confirmed that the capital-labor ratio corresponding to the state of economic maturity indeed provides us with a robust turnpike of the optimal path of capital accumulation.

• Item Type: MPRA Paper
• Language: English
• Keywords: Stochastic growth; Economic maturity; Asymptotic turnpike theorem; Neighborhood turnpike theorem; Robustness.
• Subjects: C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C60 - General; E - Macroeconomics and Monetary Economics > E1 - General Aggregative Models > E13 - Neoclassical; E - Macroeconomics and Monetary Economics > E2 - Consumption, Saving, Production, Investment, Labor Markets, and Informal Economy > E22 - Investment ; Capital ; Intangible Capital ; Capacity

References

[1] Benaïm, M., J. Hofbauer and W. H. Sandholm, 2008. Robust Permanence and Impermanence for the Stochastic Replicator Dynamic. Journal of Biological Dynamics 2, 180-195.

[2] Bewley, T., 1982. An Integration of Equilibrium Theory and Turnpike Theory. Journal of Mathematical Economics 10, 233-267.

[3] Bomze, I. M., 1991. Cross Entropy Minimization in Uninvadable States of Complex Populations. Journal of Mathematical Biology 30, 73-87.

[4] Cass, D., 1965. Optimum Growth in an Aggregative Model of Capital Accumulation. Review of Economic Studies 32, 233-240.

[5] Cass, D., 1966. Optimum Growth in an Aggregative Model of Capital Accumulation: A Turnpike Theorem. Econometrica 34, 833-850.

[6] Chakraborty, S., 2004. Endogenous Lifetime and Economic Growth. Journal of Economic Theory 116, 119-137.

[7] Chang, F.-R. and A. G. Malliaris, 1987. Asymptotic Growth under Uncertainty: Existence and Uniqueness. Review of Economic Studies 54, 169-174.

[8] Dai, D., 2012. Stochastic Versions of Turnpike Theorems in the Sense of Uniform Topology. Annals of Economics and Finance 13, 389-431.

[9] de la Croix, D. and G. Ponthiere, 2010. On the Golden Rule of Capital Accumulation Under Endogenous Longevity. Mathematical Social Sciences 59, 227-238.

[10] Higham, D. J., X. R. Mao and A. M. Stuart, 2003. Strong Convergence of Euler-Type Methods for Nonlinear Stochastic Differential Equations. SIAM Journal on Numerical Analysis 40, 1041-1063.

[11] Jeanblanc, M., P. Lakner and A. Kadam, 2004. Optimal Bankruptcy Time and Consumption /Investment Policies on an Infinite Horizon with a Continuous Debt Repayment until Bankruptcy. Mathematics of Operations Research 29, 649-671.

[12] Joshi, S., 1997. Turnpike Theorem in Nonconvex and Nonstationary Environment. International Economic Review 38, 225-248.

[13] Karatzas, I. and S. E. Shreve, 1991. Brownian Motion and Stochastic Calculus. Volume 113 of Graduate Texts in Mathematics. New York: Springer-Verlag, second edition.

[14] Karatzas, I. and H. Wang, 2001. Utility Maximization with Discretionary Stopping. SIAM Journal on Control and Optimization 39, 306-329.

[15] Kurz, M., 1965. Optimal Paths of Capital Accumulation Under the Minimum Time Objective. Econometrica 33, 42-66.

[16] Imhof, L. A., 2005. The Long-Run Behavior of the Stochastic Replicator Dynamics. Annals of Applied Probability 15, 1019-1045.

[17] McKenzie, L., 1976. Turnpike Theory. Econometrica 44, 841-865.

[18] McKenzie, L., 1983. Turnpike Theory, Discounted Utility, and the von Neumann Facet. Journal of Economic Theory 30, 30-52.

[19] Merton, R. C., 1975. An Asymptotic Theory of Growth Under Uncertainty. Review of Economic Studies 42, 375-393.

[20] Mirman, L. J., 1972. On the Existence of Steady State Measures for One Sector Growth Models with Uncertain Technology. International Economic Review 13, 271-286.

[21] Øksendal, B. and A. Sulem, 2005. Applied Stochastic Control of Jump Diffusions. Berlin: Springer-Verlag.

[22] Radner, R., 1961. Paths of Economic Growth that are Optimal with Regard only to Final States: A Turnpike Theorem. Review of Economic Studies 28, 98-104.

[23] Ramsey, F. P., 1928. A Mathematical Theory of Saving. Economic Journal 38, 543-559.

[24] Riedel, F., 2009. Optimal Stopping with Multiple Priors. Econometrica 77, 857-908.

[25] Samuelson, P. A., 1965. A Catenary Turnpike Theorem Involving Consumption and the Golden Rule. American Economic Review 55, 486-496.

[26] Scheinkman, J., 1976. On Optimal Steady States of n-Sector Growth Models when Utility is Discounted. Journal of Economic Theory 12, 11-20.

[27] Schreiber, S. J., M. Benaïm and K. A. S. Atchadé, 2011. Persistence in Fluctuating Environments. Journal of Mathematical Biology 62, 655-683.

[28] Solow, R. M., 1956. A Contribution to the Theory of Economic Growth. Quarterly Journal of Economics 70, 65-94.

[29] Song, Z., K. Storesletten and F. Zilibotti, 2011. Growing Like China. American Economic Review 101, 202-241.

[30] Yano, M., 1984. The Turnpike of Dynamic General Equilibrium Paths and Its Insensitivity to Initial Conditions. Journal of Mathematical Economics 13, 235-254.

[31] Yano, M., 1998. On the Dual Stability of a Von Neumann Facet and the Inefficacy of Temporary Fiscal Policy. Econometrica 66, 427-451.