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The Time Path of the Saving Rate: Hyperbolic Discounting and Short-Term Planning

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  • Y. Hossein Farzin

    ()
    (University of California at Davis)

  • Ronald Wendner

    ()
    (Karl-Franzens University of Graz)

Abstract

The standard neoclassical growth model with Cobb-Douglas production predicts a monotonically declining saving rate, when reasonably calibrated. Ample empirical evidence, however, shows that the transition paths of most countries saving rates exhibit a statistically significant hump-shaped pattern. Prior literature shows that CES production may imply a hump-shaped pattern of the saving rate (Gomz, 2008). However, the implied magnitude of the hump falls short of what is seen in empirical data. We introduce two non-standard features of preferences into a neoclassical growth model with CES production: hyperbolic discounting and short planning horizons. We show that, in contrast to the commonly accepted argument, in general (except for the special case of logarithmic utility) a model with hyperbolic discounting is not observationally equivalent to one with exponential discounting. We also show that our framework implies a hump-shaped saving rate dynamics that is consistent with empirical evidence. Hyperbolic discounting turns out to be a major factor explaining the magnitude of the hump of the saving rate path. Numerical simulations employing a generalized class of hyperbolic discount functions, which we term regular discount functions, support the results.

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Paper provided by University of Graz, Department of Economics in its series Graz Economics Papers with number 2014-04.

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Date of creation: Apr 2014
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Handle: RePEc:grz:wpaper:2014-04

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Keywords: Saving rate dynamics; non-monotonic transition path; hyperbolic discounting; short-term planning; neoclassical growth model;

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References

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  1. Laibson, David I., 1997. "Golden Eggs and Hyperbolic Discounting," Scholarly Articles 4481499, Harvard University Department of Economics.
  2. Timo Trimborn & Karl-Josef Koch & Thomas Steger, 2006. "Multi-Dimensional Transitional Dynamics: A Simple Numberical Procedure," CESifo Working Paper Series 1745, CESifo Group Munich.
  3. Caliendo, Frank & Aadland, David, 2007. "Short-term planning and the life-cycle consumption puzzle," Journal of Economic Dynamics and Control, Elsevier, vol. 31(4), pages 1392-1415, April.
  4. Kent Smetters, 2003. "The (Interesting) Dynamic Properties of the Neoclassical Growth Model with CES Production," NBER Technical Working Papers 0290, National Bureau of Economic Research, Inc.
  5. Thaler, Richard, 1981. "Some empirical evidence on dynamic inconsistency," Economics Letters, Elsevier, vol. 8(3), pages 201-207.
  6. Caliendo, Frank N. & Findley, T. Scott, 2014. "Discount functions and self-control problems," Economics Letters, Elsevier, vol. 122(3), pages 416-419.
  7. Hall, Robert E, 1988. "Intertemporal Substitution in Consumption," Journal of Political Economy, University of Chicago Press, vol. 96(2), pages 339-57, April.
  8. V. V. Chari & Patrick J. Kehoe & Ellen R. McGrattan, 1996. "The Poverty of Nations: A Quantitative Exploration," NBER Working Papers 5414, National Bureau of Economic Research, Inc.
  9. Maddison, Angus, 1992. " A Long-Run Perspective on Saving," Scandinavian Journal of Economics, Wiley Blackwell, vol. 94(2), pages 181-96.
  10. T. Findley & Frank Caliendo, 2009. "Short horizons, time inconsistency, and optimal social security," International Tax and Public Finance, Springer, vol. 16(4), pages 487-513, August.
  11. Shafer, Jeffrey R & Elmeskov, Jorgen & Tease, Warren, 1992. " Saving Trends and Measurement Issues," Scandinavian Journal of Economics, Wiley Blackwell, vol. 94(2), pages 155-75.
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