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.
(This abstract was borrowed from another version of this item.)
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
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.:
- Boldrin, Michele & Montrucchio, Luigi, 1986. "On the indeterminacy of capital accumulation paths," Journal of Economic Theory, Elsevier, vol. 40(1), pages 26-39, October.
- Coleman, Wilbur John, II, 1991.
"Equilibrium in a Production Economy with an Income Tax,"
Econometric Society, vol. 59(4), pages 1091-1104, July.
- 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.).
- 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.
- Mirman, Leonard J. & Zilcha, Itzhak, 1975. "On optimal growth under uncertainty," Journal of Economic Theory, Elsevier, vol. 11(3), pages 329-339, December.
- L. W. McKenzie, 2010.
Levine's Working Paper Archive
1389, David K. Levine.
- 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.
- Marimon, Ramon, 1989. "Stochastic turnpike property and stationary equilibrium," Journal of Economic Theory, Elsevier, vol. 47(2), pages 282-306, April.
- Bewley, Truman, 1982. "An integration of equilibrium theory and turnpike theory," Journal of Mathematical Economics, Elsevier, vol. 10(2-3), pages 233-267, September.
- 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).
- 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.
- Lucas, Robert Jr., 1988. "On the mechanics of economic development," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 3-42, July.
- 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.
- 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.
- Paul M Romer, 1999.
"Increasing Returns and Long-Run Growth,"
Levine's Working Paper Archive
2232, David K. Levine.
- 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.
- Montrucchio, Luigi, 1995. "A New Turnpike Theorem for Discounted Programs," Economic Theory, Springer, vol. 5(3), pages 371-82, May.
- Becker, Robert A., 1985. "Capital income taxation and perfect foresight," Journal of Public Economics, Elsevier, vol. 26(2), pages 147-167, March.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- Chang, Fwu-Ranq, 1982. "A note on the stochastic value loss assumption," Journal of Economic Theory, Elsevier, vol. 26(1), pages 164-170, 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.
When requesting a correction, please mention this item's handle: RePEc:eee:dyncon:v:27:y:2003:i:7:p:1289-1315. 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: (Zhang, Lei)
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.