Advanced Search
MyIDEAS: Login to save this paper or follow this series

Differentiability of the value function without interiority assumptions

Contents:

Author Info

  • Juan Pablo Rincon-Zapatero
  • Manuel S. Santos

Abstract

This paper studies first-order differentiability properties of the value function in concave dynamic programs. Motivated by economic considerations, we dispense with commonly imposed interiority assumptions. We suppose that the correspondence of feasible choices varies with the vector of state variables, and we allow the optimal solution to belong to the boundary of this correspondence. Under minimal assumptions we show that the value function is continuously differentiable. We then discuss this result in the context of several economic models.

Download Info

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.
File URL: http://e-archivo.uc3m.es/bitstream/10016/668/1/we071405.pdf
Download Restriction: no

Bibliographic Info

Paper provided by Universidad Carlos III, Departamento de Economía in its series Economics Working Papers with number we071405.

as in new window
Length:
Date of creation: Mar 2007
Date of revision:
Handle: RePEc:cte:werepe:we071405

Contact details of provider:
Postal: C./ Madrid, 126, 28903 Getafe (Madrid)
Phone: +34-91 6249594
Fax: +34-91 6249329
Email:
Web page: http://www.eco.uc3m.es
More information through EDIRC

Related research

Keywords: Constrained optimization; Value and policy functions; Differentiability; Envelope theorem; Shadow price;

Other versions of this item:

Find related papers by JEL classification:

This paper has been announced in the following NEP Reports:

References

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.:
as in new window
  1. Christopher Phelan & Ennio Stacchetti, 2001. "Sequential Equilibria in a Ramsey Tax Model," Econometrica, Econometric Society, Econometric Society, vol. 69(6), pages 1491-1518, November.
  2. Kydland, Finn E. & Prescott, Edward C., 1980. "Dynamic optimal taxation, rational expectations and optimal control," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 2(1), pages 79-91, May.
  3. Thomas, Jonathan & Worrall, Tim, 1988. "Self-enforcing Wage Contracts," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 55(4), pages 541-54, October.
  4. Lawrence J. Christiano & Jonas D. M. Fisher, 1994. "Algorithms for solving dynamic models with occasionally binding constraints," Staff Report, Federal Reserve Bank of Minneapolis 171, Federal Reserve Bank of Minneapolis.
  5. Kocherlakota, Narayana R, 1996. "Implications of Efficient Risk Sharing without Commitment," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 63(4), pages 595-609, October.
  6. Paul Milgrom & Ilya Segal, 2002. "Envelope Theorems for Arbitrary Choice Sets," Econometrica, Econometric Society, Econometric Society, vol. 70(2), pages 583-601, March.
  7. Thomas, Jonathan & Worrall, Tim, 1994. "Foreign Direct Investment and the Risk of Expropriation," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 61(1), pages 81-108, January.
  8. Mirman, Leonard J. & Zilcha, Itzhak, 1975. "On optimal growth under uncertainty," Journal of Economic Theory, Elsevier, Elsevier, vol. 11(3), pages 329-339, December.
  9. Hopenhayn, H. & Nicolini, P.J., 1996. "Optimal Unemployment Insurance," RCER Working Papers, University of Rochester - Center for Economic Research (RCER) 421, University of Rochester - Center for Economic Research (RCER).
  10. Martin L. Weitzman, 1973. "Duality Theory for Infinite Horizon Convex Models," Management Science, INFORMS, INFORMS, vol. 19(7), pages 783-789, March.
  11. Benveniste, L M & Scheinkman, J A, 1979. "On the Differentiability of the Value Function in Dynamic Models of Economics," Econometrica, Econometric Society, Econometric Society, vol. 47(3), pages 727-32, May.
  12. Cass, David, 2006. "Competitive equilibrium with incomplete financial markets," Journal of Mathematical Economics, Elsevier, vol. 42(4-5), pages 384-405, August.
  13. Timothy J Kehoe & David K Levine, 1993. "Debt Constrained Asset Markets," Levine's Working Paper Archive 1276, David K. Levine.
  14. Luigi Montrucchio & Fabio Privileggi, 2001. "On Fragility of Bubbles in Equilibrium Asset Pricing Models of Lucas-Type," ICER Working Papers - Applied Mathematics Series, ICER - International Centre for Economic Research 05-2001, ICER - International Centre for Economic Research.
  15. Thomas J. Sargent, 1979. ""Tobin's Q" and the rate of investment in general equilibrium," Staff Report, Federal Reserve Bank of Minneapolis 40, Federal Reserve Bank of Minneapolis.
  16. Lucas, Robert E, Jr, 1980. "Equilibrium in a Pure Currency Economy," Economic Inquiry, Western Economic Association International, Western Economic Association International, vol. 18(2), pages 203-20, April.
  17. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, Econometric Society, vol. 46(6), pages 1429-45, November.
  18. Manuel S. Santos & Michael Woodford, 1997. "Rational Asset Pricing Bubbles," Econometrica, Econometric Society, Econometric Society, vol. 65(1), pages 19-58, January.
  19. Fernando Alvarez & Urban J. Jermann, 2000. "Efficiency, Equilibrium, and Asset Pricing with Risk of Default," Econometrica, Econometric Society, Econometric Society, vol. 68(4), pages 775-798, July.
  20. Amir, Rabah & Mirman, Leonard J & Perkins, William R, 1991. "One-Sector Nonclassical Optimal Growth: Optimality Conditions and Comparative Dynamics," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 32(3), pages 625-44, August.
  21. Benveniste, L. M. & Scheinkman, J. A., 1982. "Duality theory for dynamic optimization models of economics: The continuous time case," Journal of Economic Theory, Elsevier, Elsevier, vol. 27(1), pages 1-19, June.
  22. Thorsten Koeppl, 2004. "Differentiability of the Efficient Frontier when Commitment to Risk Sharing is Limited," Working Papers, Queen's University, Department of Economics 1049, Queen's University, Department of Economics.
Full references (including those not matched with items on IDEAS)

Citations

Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
as in new window

Cited by:
  1. Zhigang Feng & Jianjun Miao & Adrian Peralta-Alva & Manuel S. Santos, 2009. "Numerical simulation of nonoptimal dynamic equilibrium models," Working Papers, Federal Reserve Bank of St. Louis 2009-018, Federal Reserve Bank of St. Louis.
  2. Jaime McGovern & Olivier Morand & Kevin Reffett, 2013. "Computing minimal state space recursive equilibrium in OLG models with stochastic production," Economic Theory, Springer, Springer, vol. 54(3), pages 623-674, November.
  3. Robin C. Sickles & Jenny Williams, 1999. "Turning from Crime: A Dynamic Perspective," School of Economics Working Papers, University of Adelaide, School of Economics 1999-08, University of Adelaide, School of Economics.
  4. Strulovici, Bruno & Szydlowski, Martin, 2012. "On the Smoothness of Value Functions," MPRA Paper 36326, University Library of Munich, Germany, revised 31 Jan 2012.
  5. Pontus Rendahl, 2013. "Inequality Constraints and Euler Equation based Solution Methods," Cambridge Working Papers in Economics, Faculty of Economics, University of Cambridge 1320, Faculty of Economics, University of Cambridge.

Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:cte:werepe:we071405. 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: () The email address of this maintainer does not seem to be valid anymore. Please ask to update the entry or send us the correct address.

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.