The Stochastic Turnpike Property without Uniformity in Convex Aggregate Growth Models
An important stochastic turnpike property in optimal growth models asserts that optimal programs of capital accumulation from different initial stocks converge almost surely in a suitable metric. Its proof requires constructing a value-loss process satisfying both uniform boundedness in expectation and sensitivity (in the sense of recording a strictly positive value-loss when the capital stocks being compared diverge). Uniformity assumptions strengthen sensitivity by ensuring that value-loss is independent of time and state of environment in which the divergence occurs. They are imposed either directly on the value-loss process, or indirectly through bounds on the degree of concavity of the felicity or production functions, and are acknowledged as strong restrictions on the model. This paper argues, within the context of a convex aggregate growth model, that uncertainty can obviate the need for uniformity. The multiplicity of states afforded by a stochastic framework permits constructing a value-loss process over an "extended" time-line that is a martingale and, hence, relatively easy to uniformly bound in expectation. Further, if capital stocks diverge by some critical amount in any time and state, then the martingale registers an upcrossing across a band of uniform width on its extended time-line for that state thereby giving uniform value-loss. Probabilistic arguments based on the Martingale Upcrossing theorem and the Borel-Cantelli lemma then clinch the turnpike property.
To our knowledge, this item is not available for
download. To find whether it is available, there are three
1. Check below under "Related research" whether another version of this item is available online.
2. Check on the provider's web page whether it is in fact available.
3. Perform a search for a similarly titled item that would be available.
|Date of creation:||Jun 1999|
|Date of revision:|
|Contact details of provider:|| Postal: |
Phone: (011) 27667005
Fax: (011) 27667159
Web page: http://www.cdedse.org/
More information through EDIRC
|Order Information:|| Web: http://www.cdedse.org/ Email: |
References listed on IDEAS
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.:
- Nishimura, Kazuo & Sorger, Gerhard & Yano, Makoto, 1994. "Ergodic Chaos in Optimal Growth Models with Low Discount Rates," Economic Theory, Springer, vol. 4(5), pages 705-17, August.
- Brock, William A. & Mirman, Leonard J., 1972. "Optimal economic growth and uncertainty: The discounted case," Journal of Economic Theory, Elsevier, vol. 4(3), pages 479-513, June.
- Brock, William A & Mirman, Leonard J, 1973. "Optimal Economic Growth and Uncertainty: The No Discounting Case," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 14(3), pages 560-73, October.
- Marimon, Ramon, 1989. "Stochastic turnpike property and stationary equilibrium," Journal of Economic Theory, Elsevier, vol. 47(2), pages 282-306, April.
- McKenzie, Lionel W, 1976.
Econometric Society, vol. 44(5), pages 841-65, September.
- Joshi, Sumit, 1997. "Turnpike Theorems in Nonconvex Nonstationary Environments," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 38(1), pages 225-48, February.
- Majumdar, Mukul & Mitra, Tapan, 1994. "Periodic and Chaotic Programs of Optimal Intertemporal Allocation in an Aggregative Model with Wealth Effects," Economic Theory, Springer, vol. 4(5), pages 649-76, August.
- Boldrin, Michele & Montrucchio, Luigi, 1986. "On the indeterminacy of capital accumulation paths," Journal of Economic Theory, Elsevier, vol. 40(1), pages 26-39, October.
- Amir, Rabah, 1997. "A new look at optimal growth under uncertainty," Journal of Economic Dynamics and Control, Elsevier, vol. 22(1), pages 67-86, November.
- Bewley, Truman, 1982. "An integration of equilibrium theory and turnpike theory," Journal of Mathematical Economics, Elsevier, vol. 10(2-3), pages 233-267, September.
- Tapan Mitra & Yaw Nyarko, 1991. "On the existence of optimal processes in non-stationary environments," Journal of Economics, Springer, vol. 53(3), pages 245-270, October.
- Mirman, Leonard J. & Zilcha, Itzhak, 1977. "Characterizing optimal policies in a one-sector model of economic growth under uncertainty," Journal of Economic Theory, Elsevier, vol. 14(2), pages 389-401, April.
- Joshi, Sumit & Vonortas, Nicholas S., 2001. "Convergence to symmetry in dynamic strategic models of R&D: The undiscounted case," Journal of Economic Dynamics and Control, Elsevier, vol. 25(12), pages 1881-1897, December.
- Wilbur John Coleman II, 1989.
"Equilibrium in a production economy with an income tax,"
International Finance Discussion Papers
366, Board of Governors of the Federal Reserve System (U.S.).
- Coleman, Wilbur John, II, 1991. "Equilibrium in a Production Economy with an Income Tax," Econometrica, Econometric Society, vol. 59(4), pages 1091-1104, July.
- Chang, Fwu-Ranq, 1982. "A note on the stochastic value loss assumption," Journal of Economic Theory, Elsevier, vol. 26(1), pages 164-170, February.
- Romer, Paul M, 1986.
"Increasing Returns and Long-run Growth,"
Journal of Political Economy,
University of Chicago Press, vol. 94(5), pages 1002-37, October.
- Montrucchio, Luigi, 1995. "A New Turnpike Theorem for Discounted Programs," Economic Theory, Springer, vol. 5(3), pages 371-82, May.
- Cesar Guerrero-Luchtenberg, 1998. "- A Turnpike Theoreme For A Family Of Functions," Working Papers. Serie AD 1998-07, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
- Budd, Christopher & Harris, Christopher & Vickers, John, 1993. "A Model of the Evolution of Duopoly: Does the Asymmetry between Firms Tend to Increase or Decrease?," Review of Economic Studies, Wiley Blackwell, vol. 60(3), pages 543-73, July.
- Lucas, Robert Jr., 1988. "On the mechanics of economic development," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 3-42, July.
- Becker, Robert A., 1985. "Capital income taxation and perfect foresight," Journal of Public Economics, Elsevier, vol. 26(2), pages 147-167, March.
- Sorger, Gerhard, 1992. "On the minimum rate of impatience for complicated optimal growth paths," Journal of Economic Theory, Elsevier, vol. 56(1), pages 160-179, February.
- Mirman, Leonard J. & Zilcha, Itzhak, 1975. "On optimal growth under uncertainty," Journal of Economic Theory, Elsevier, vol. 11(3), pages 329-339, December.
- Majumdar, Mukul & Zilcha, Itzhak, 1987. "Optimal growth in a stochastic environment: Some sensitivity and turnpike results," Journal of Economic Theory, Elsevier, vol. 43(1), pages 116-133, October.
- Brock, W. A. & Majumdar, M., 1978. "Global asymptotic stability results for multisector models of optimal growth under uncertainty when future utilities are discounted," Journal of Economic Theory, Elsevier, vol. 18(2), pages 225-243, August.
When requesting a correction, please mention this item's handle: RePEc:cde:cdewps:67. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Sanjeev Sharma)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.