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Expected Net Present Value, Expected Net Future Value, and the Ramsey Rule

  • Economics


discount_jeem2.dvi 09-049 Research Group: Finance in Toulouse June 13, 2009 Expected Net Present Value, Expected Net Future Value, and the Ramsey Rule CHRISTIAN GOLLIER Expected net present value, expected net future value, and the Ramsey rule Christian Gollier∗ Toulouse School of Economics (LERNA and IDEI) June 13, 2009 Abstract Weitzman (1998) showed that when future interest rates are un- certain, using the expected net present value implies a term structure of discount rates that is decreasing to the smallest possible interest rate. On the contrary, using the expected net future value criteria im- plies an increasing term structure of discount rates up to the largest possible interest rate. We reconcile the two approaches by introducing risk aversion and utility maximization. We show that if the aggregate consumption path is optimized and made flexible to news about future interest rates, the two criteria are equivalent. Moreover, they are also equivalent to the Ramsey rule extended to uncertainty. Keywords: Discount rate, Ramsey rule, climate change, cost-benefit analysis. ∗This paper benefited from the financial support of the Chair "Sustainable finance and responsible investment" at TSE. The research leading to these results has also received funding from the European Research Council under the European Community’s Seventh Framework Programme (FP7/2007-2013) Grant Agreement no. 230589. 1 1 Introduction The emergence of the public awareness about the long term sustainability of our growth has been accompanied over the last decade by an important effort from many prominent economists to clarify the way future generations are treated in the standard cost-benefit methodology. Indeed, this methodology is often criticized for sacrificing distant generations. This raises the ques- tions of the level and of the term structure of the discount rate. There is no consensus in our profession about the rate that should be used to discount long

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