Stochastic Versions of Turnpike Theorems in the Sense of Uniform Topology

Dai, Darong (2011): Stochastic Versions of Turnpike Theorems in the Sense of Uniform Topology. Forthcoming in: Annals of Economics and Finance

Abstract

In this paper, a stochastic endogenous aggregative growth model is constructed and two main results are established, based on endogenous horizon of the economy and endogenous terminal capital stock, which is also efficient capital accumulation in some sense. First, strong turnpike theorems under uncertainty and in the sense of uniform topology are obtained; second, inefficacy of temporary fiscal policy, which is chosen to be capital income taxation, has been demonstrated in comparatively weak conditions different from Yano (1998)’s.

• Item Type: MPRA Paper
• Language: English
• Keywords: Stochastic endogenous growth; Uniform-topology turnpike theorems; Endogenous terminal stock; Endogenous welfare function; Capital income taxation
• Subjects: E - Macroeconomics and Monetary Economics > E6 - Macroeconomic Policy, Macroeconomic Aspects of Public Finance, and General Outlook > E62 - Fiscal Policy; E - Macroeconomics and Monetary Economics > E2 - Consumption, Saving, Production, Investment, Labor Markets, and Informal Economy > E22 - Investment ; Capital ; Intangible Capital ; Capacity; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C61 - Optimization Techniques ; Programming Models ; Dynamic Analysis; E - Macroeconomics and Monetary Economics > E2 - Consumption, Saving, Production, Investment, Labor Markets, and Informal Economy > E21 - Consumption ; Saving ; Wealth; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C62 - Existence and Stability Conditions of Equilibrium

References

Aghion, P., 2004. Growth and Development: A Schumpeterian Approach. Annals of Economics and Finance 5, 1-25.

Araujo, A. and J.A. Scheinkman, 1977. Smoothness, Comparative Dynamics, and the Turnpike Property. Econometrica 45, 601-620.

Barro, R.J., 1990. Government Spending in a Simple Model of Endogenous Growth. Journal of Political Economy 98, 103-125.

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

Bomze, I.M., 1991. Cross entropy minimization in uninvadable states of complex populations. Journal of Mathematical Biology 30, 73-87.

Coles, J.L., 1985. Equilibrium Turnpike Theory with Constant Returns to Scale and Possibly Heterogeneous Discount Factors. International Economic Review 26, 671-679.

Drandakis, E.M., 1966. On Efficient Accumulation Paths in the Closed Production Model. Econometrica 34, 331-346.

Gale, D., 1967. On Optimal Development in a Multi-Sector Economy. Review of Economic Studies 34, 1-18.

Gantz, D.T., 1980. A Strong Turnpike Theorem for a Nonstationary von Neumann-Gale Production Model. Econometrica 48, 1777-1790.

Gong, L. and H. Zou, 2000. Foreign Aid Reduces Domestic Capital Accumulation and Increases Foreign Borrowing: A Theoretical Analysis. Annals of Economics and Finance 1, 147-163.

Gong, L. and H. Zou, 2002. Fiscal Federalism, Public Capital Formation, and Endogenous Growth. Annals of Economics and Finance 4, 471-490.

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.

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

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.

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

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

McKenzie, L., 1963. Turnpike Theorems for a Generalized Leontief Model. Econometrica 31, 165-180.

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

McKenzie, L., 1982. A Primal Route to the Turnpike and Liapounov Stability. Journal of Economic Theory 27, 194-209.

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

Morishima, M., 1961. Proof of a Turnpike Theorem: The “No Joint Production” Case. Review of Economic Studies 28, 89-97.

Morishima, M., 1965. On the Two Theorems of Growth Economics: A Mathematical Exercise. Econometrica 33, 829-840.

Oksendal, B., 2003. Stochastic Differential Equations. Universitext. Berlin: Springer-Verlag, sixth edition.

Oksendal, B. and A.Sulem, 2007. Applied Stochastic Control of Jump Diffusions. Berlin: Springer- Verlag, second edition.

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.

Rebelo, S., 1991. Long-run Policy Analysis and Long-run Growth. Journal of Political Economy 99, 500-521.

Tsukui, J., 1966. Turnpike Theorem in a Generalized Dynamic Input-Output System. Econometrica 34, 396-407.

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, 85-93.

Turnovsky, S.J., 2000. Fiscal Policy, Elastic Labor Supply, and Endogenous Growth. Journal of Monetary Economics 45, 185-210.

Winter, S.G., Jr., 1967. The Norms of a Closed Technology and the Straight-Down-the-Turnpike Theorem. Review of Economic Studies 34, 67-84.

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

Yano, M., 1984b. Competitive Equilibria on Turnpikes in a McKenzie Economy, I: A Neighborhood Turnpike Theorem. International Economic Review 25, 695-717.

Yano, M., 1985. Competitive Equilibria on Turnpikes in a McKenzie Economy, II: An Asymptotic Turnpike Theorem. International Economic Review 26, 661-669.

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