Comparative precautionary saving under higher-order risk and recursive utility
Measuring and comparing the precautionary saving motive rest almost exclusively on the expected utility framework, and only focus on income risk or coefficients of the Arrow–Pratt type. We generalize the standard approach by characterizing comparative precautionary saving under recursive utility for increases in income risk and increases in risk on the saving return, including higher-order risk effects. We express the comparisons in terms of precautionary premia. In addition, we define a new class of preference coefficients, and derive the associated conditions to predict a stronger precautionary motive. The coefficients provide a detailed picture of the preferences sustaining precautionary saving and could be useful in applications.
KeywordsPrecautionary saving Prudence Recursive utility Higher-order risk Precautionary premium Preference coefficient
JEL ClassificationD91 D81
We are grateful for valuable comments made by Sebastian Ebert and two anonymous reviewers, as well as Arthur Charpentier, Louis Eeckhoudt, Rachel Huang, Olivier l’Haridon, Liqun Liu, Debrah Meloso, Richard Peter, Art Snow, and participants in the 2016 International Conference on Economic and Financial Risks in Niort, the CEAR/MRIC Behavioral Insurance Workshop in Munich, and the 2017 EGRIE seminar. This research was partially supported by the European Union’s Seventh Framework Programme FP7/2007-2011, Grant Agreement no. 290693 (FOODSECURE), and by the William J. Fulbright Foundation.
- Bostian, A.A. and Heinzel, C. 2018. Consumption smoothing and precautionary saving under recursive preferences. Working paper.Google Scholar
- Gollier, C. 2001. The Economics of Risk and Time. Cambridge, MA: MIT Press.Google Scholar
- Gollier, C. 2013. Pricing the Planet’s Future: The Economics of Discounting in an Uncertain World. Princeton, NJ: Princeton University Press.Google Scholar
- Li, J. 2009. Comparative higher-degree Ross risk aversion. Insurance: Mathematics and Economics 45: 333–336.Google Scholar
- Lugilde, A., R. Bande, and D. Riveiro. 2017. Precautionary saving: A review of the theory and the evidence. MPRA Paper No. 77511.Google Scholar
- Menezes, C.E., C. Geiss, and J. Tressler. 1980. Increasing downside risk. American Economic Review 70: 921–932.Google Scholar
- Mirrlees, S.J., S. Adam, T. Besley, R. Blundell, S. Bond, R. Chote, M. Gammie, P. Johnson, G. Myles, and J. Poterba. 2010. Dimensions of tax design: The Mirrlees review. Oxford: Oxford University Press.Google Scholar