Abstract
When the growth of aggregate consumption exhibits no serial correlation, the socially efficient discount rate is independent of the time horizon, because the wealth effect and the precautionary effect are proportional to the time horizon. In this paper, we consider alternative growth processes: an AR(1), a Brownian motion with unknown trend or volatility, a two-state regime-switching model, and a model with an uncertain return of capital. All these models exhibit some persistence of shocks on the growth rate of the economy and fat tails, which implies that one should discount more distant costs and benefits at a smaller rate.
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Notes
See Gollier (2007) for a formal proof.
Using the trick of the Arrow-Pratt formula being exact in this specification, we have indeed that
$$ \frac{Ec_{t}}{c_{0}}=E\exp (x_{t})=\exp \big(Ex_{t}+0.5Var(x_{t})\big)=\exp g_{t}t. $$See also the recent analysis and discussion by Buchholz and Schumacher (2008).
References
Backus, D., Foresi, S., & Telmer, C. (1998). Discrete-time models of bond pricing. NBER Working Paper 6736.
Barro, R. J. (2006). Rare disasters and asset markets in the twentieth century. Quarterly Journal of Economics, 121, 823–866.
Breeden, D. T. (1986). Consumption, production, inflation, and interest rates: A synthesis. Journal of Financial Economics, 16, 3–40.
Buchholz, W., & Schumacher, J. (2008). Discounting the long distant future: Simple explanation for the Weitzman-Gollier-puzzle. Mimeo.
Campbell, J. Y. (1986). Bond and stock returns in a simple exchange model. Quarterly Journal of Economics, 101, 785–804.
Cecchetti, S. G., Lam, P.-S., & Mark, N. C. (2000). Asset pricing with distorted beliefs: Are equity returns too good to be true. American Economic Review, 90, 787–805.
Cochrane, J. H. (1988). How big is the random walk in GNP? Journal of Political Economy, 96, 893–920.
Cochrane, J. (2001). Asset pricing. Princeton: Princeton University Press.
Cogley, T. (1990). International evidence on the size of the random walk in output. Journal of Political Economy, 98, 501–518.
Gollier, C. (2002a). Discounting an uncertain future. Journal of Public Economics, 85, 149–166.
Gollier, C. (2002b). Time horizon and the discount rate. Journal of Economic Theory, 107, 463-473.
Gollier, C. (2004). Maximizing the expected net future value as an alternative strategy to gamma discounting. Finance Research Letters, 1, 85–89.
Gollier, C. (2007). The consumption-based determinants of the term structure of discount rates. Mathematics and Financial Economics, 1(2), 81–102.
Gollier, C., Koundouri, P., & Pantelides, T. (2008). Declining discount rates: Economic justifications and implications for long-run policy. Economic Policy (in press).
Groom, B., Koundouri, P., Panipoulou, K., & Pantelides, T. (2007). Discounting the Distant Future: How much does model selection affect the certainty equivalent rate? Journal of Applied Econometrics, 22, 641–656.
Hansen, L., & Singleton, K. (1983). Stochastic consumption, risk aversion and the temporal behavior of assets returns. Journal of Political Economy, 91, 249–265.
IPCC (2008). Climate change 2007 - mitigation of climate change. Working Group III contribution to the Fourth Assessment Report of the IPCC Intergovernmental Panel on Climate Change, Cambridge University Press.
Kimball, M. S. (1990). Precautionary savings in the small and in the large. Econometrica, 58, 53–73.
Kocherlakota, N. R. (1996). The equity premium: It’s still a puzzle. Journal of Economic Literature, 34, 42–71.
Lomborg, B. (2004). Global crises, global solutions. Cambridge: Cambridge University Press.
Mankiw, G. (1981). The permanent income hypothesis and the real interest rate. Economic Letters, 7, 307–311.
Newell, R., & Pizer, W. (2003). Discounting the benefits of climate change mitigation: How much uncertain rates increase valuations? Journal of Environmental Economics and Management, 46(1), 52–71.
Stern, N. (2006). The economics of climate change: The Stern Review. Cambridge: Cambridge University Press.
Vasicek, O. (1977). An equilibrium characterization of the term structure. Journal of Financial Economics, 5, 177–188.
Weitzman, M. L. (1998). Why the far-distant future should be discounted at its lowest possible rate? Journal of Environmental Economics and Management, 36, 201–208.
Weitzman, M. L. (2001). Gamma discounting. American Economic Review, 91, 260–271.
Weitzman, M. L. (2007). Subjective expectationsand asset-return puzzle. American Economic Review, 97, 1102–1130.
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The financial support of the Chair “Sustainable Finance and Responsible Investment” is gracefully acknowledged.
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Gollier, C. Discounting with fat-tailed economic growth. J Risk Uncertain 37, 171–186 (2008). https://doi.org/10.1007/s11166-008-9050-0
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DOI: https://doi.org/10.1007/s11166-008-9050-0