Time Horizon and the Discount Rate

We discuss the selection of the socially efficient discount rate for public investment projects that entail costs and benefits in the far distant future. We show that the discount rate should be a decreasing function of time horizon under some specific restrictions on the distribution of uncertain growth and on preferences. We consider a logarithmic random walk for consumption. The benchmark result is that, in the absence of any risk of recession, the yield curve is decreasing if relative risk aversion is decreasing. Relaxing the assumption on the absence of recession requires more restrictions on preferences, as increasing relative prudence.

[1]  Christian Gollier,et al.  Discounting an uncertain future , 2002 .

[2]  Oldrich A. Vasicek.  An equilibrium characterization of the term structure , 1977 .

[3]  S. Ross,et al.  A theory of the term structure of interest rates'', Econometrica 53, 385-407 , 1985 .

[4]  Masao Ogaki,et al.  Decreasing Relative Risk Aversion and Tests of Risk Sharing , 2001 .

[5]  R. Lucas.  ASSET PRICES IN AN EXCHANGE ECONOMY , 1978 .

[6]  J. MacKinnon.  Generalized Method of Moments , 2020 .

[7]  H. Leland..  Saving and Uncertainty: The Precautionary Demand for Saving , 1968 .

[8]  Jacques H. Dreze,et al.  Cosumption decisions under uncertainty , 1972 .

[9]  D. E. Bell.  One-switch utility functions and a measure of risk , 1988 .

[10]  T. Jappelli,et al.  Income Risk, Borrowing Constraints, and Portfolio Choice , 2016 .

[11]  M. Weitzman.  Why the Far-Distant Future Should Be Discounted at Its Lowest Possible Rate , 1998 .

[12]  Miles S. Kimball.  Precautionary Saving in the Small and in the Large , 1989 .

[13]  S. Ross,et al.  AN INTERTEMPORAL GENERAL EQUILIBRIUM MODEL OF ASSET PRICES , 1985 .

[14]  T. Alderweireld,et al.  A Theory for the Term Structure of Interest Rates , 2004, cond-mat/0405293.

[15]  Christian Gollier,et al.  Risk Vulnerability and the temper-ing E ect of Background Risk , 1996 .

[16]  Jacques H. Dreze,et al.  Consumption decisions under uncertainty , 1972 .

[17]  Richard J. Zeckhauser,et al.  Proper risk aversion , 1987 .

[18]  Miles S. Kimball,et al.  Standard Risk Aversion , 1991 .

[19]  Oldrich A. Vasicek,et al.  Abstract: An Equilibrium Characterization of the Term Structure , 1977, Journal of Financial and Quantitative Analysis.