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The intrinsic comparative dynamics of infinite horizon optimal control problems with a time-varying discount rate and time-distance discounting

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  • Caputo, Michael R.

Abstract

The intrinsic comparative dynamics of a ubiquitous class of optimal control problems with a time-varying discount rate and time-distance discounting are derived and shown to be characterized by a positive semidefinite matrix. It is also shown that the said comparative dynamics are invariant to the functional form of the discount rate function and the type of agent. Consequently, if one limits econometric testing to the basic comparative dynamics of the given class of control problems, one cannot determine (i) the functional form of the discount rate function used by an agent, and thus if an agent is a time-consistent or time-inconsistent decision maker, or (ii) if an agent commits to a plan of action or takes into account the changing nature of his preferences when choosing a plan.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Dynamics and Control.

Volume (Year): 37 (2013)
Issue (Month): 4 ()
Pages: 810-820

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Handle: RePEc:eee:dyncon:v:37:y:2013:i:4:p:810-820

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Web page: http://www.elsevier.com/locate/jedc

Related research

Keywords: Comparative dynamics; Optimal control; Precommitment solution; Sophisticated solution; Time-distance discounting; Time inconsistency; Time-varying discount rate;

References

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  1. Saul Pleeter & John T. Warner, 2001. "The Personal Discount Rate: Evidence from Military Downsizing Programs," American Economic Review, American Economic Association, vol. 91(1), pages 33-53, March.
  2. Robert J. Barro, 1999. "Ramsey Meets Laibson In The Neoclassical Growth Model," The Quarterly Journal of Economics, MIT Press, vol. 114(4), pages 1125-1152, November.
  3. Christopher Harris & David Laibson, 1999. "Dynamic Choices of Hyperbolic Consumers," Harvard Institute of Economic Research Working Papers 1886, Harvard - Institute of Economic Research.
  4. Karp, Larry, 2004. "Non-Constant Discounting in Continuous Time," Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series qt7pr05084, Department of Agricultural & Resource Economics, UC Berkeley.
  5. Gong Liutang & Zhu Shenghao, 2006. "Does observational equivalence always hold in hyperbolic discounting models?," Economics Bulletin, AccessEcon, vol. 5(8), pages 1-8.
  6. Thaler, Richard, 1981. "Some empirical evidence on dynamic inconsistency," Economics Letters, Elsevier, vol. 8(3), pages 201-207.
  7. Eric Rasmusen, 2008. "Some Common Confusions about Hyperbolic Discounting," Working Papers 2008-11, Indiana University, Kelley School of Business, Department of Business Economics and Public Policy.
  8. Loewenstein, George & Prelec, Drazen, 1992. "Anomalies in Intertemporal Choice: Evidence and an Interpretation," The Quarterly Journal of Economics, MIT Press, vol. 107(2), pages 573-97, May.
  9. Uri Benzion & Amnon Rapoport & Joseph Yagil, 1989. "Discount Rates Inferred from Decisions: An Experimental Study," Management Science, INFORMS, vol. 35(3), pages 270-284, March.
  10. Glenn W. Harrison & Morten I. Lau & Melonie B. Williams, 2001. "Estimating Individual Discount Rates in Denmark: A Field Experiment," NCEE Working Paper Series 200102, National Center for Environmental Economics, U.S. Environmental Protection Agency, revised Nov 2001.
  11. Laibson, David, 1997. "Golden Eggs and Hyperbolic Discounting," The Quarterly Journal of Economics, MIT Press, vol. 112(2), pages 443-77, May.
  12. repec:ebl:ecbull:v:5:y:2006:i:8:p:1-8 is not listed on IDEAS
  13. Rubinstein, Ariel, 2001. "A theorist's view of experiments," European Economic Review, Elsevier, vol. 45(4-6), pages 615-628, May.
  14. Marín-Solano, Jesús & Navas, Jorge, 2009. "Non-constant discounting in finite horizon: The free terminal time case," Journal of Economic Dynamics and Control, Elsevier, vol. 33(3), pages 666-675, March.
  15. Caputo, Michael R., 2003. "The comparative dynamics of closed-loop controls for discounted infinite horizon optimal control problems," Journal of Economic Dynamics and Control, Elsevier, vol. 27(8), pages 1335-1365, June.
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