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Modeling the Long Run: Valuation in Dynamic Stochastic Economies

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  • Lars Peter Hansen

Abstract

I explore the equilibrium value implications of economic models that incorporate reactions to a stochastic environment. I propose a dynamic value decomposition (DVD) designed to distinguish components of an underlying economic model that influence values over long horizons from components that impact only the short run. To quantify the role of parameter sensitivity and to impute long-term risk prices, I develop an associated perturbation technique. Finally, I use DVD methods to study formally some example economies and to speculate about others. A DVD is enabled by constructing operators indexed by the elapsed time between the date of pricing and the date of the future payoff (i.e. the future realization of a consumption claim). Thus formulated, methods from applied mathematics permit me to characterize valuation behavior as the time between price determination and payoff realization becomes large. An outcome of this analysis is the construction of a multiplicative martingale component of a process that is used to represent valuation in a dynamic economy with stochastic growth. I contrast the differences in the applicability between this multiplicative martingale method and an additive martingale method familiar from time series analysis that is used to identify shocks with long-run economic consequences.

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Bibliographic Info

Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 14243.

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Date of creation: Aug 2008
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Publication status: published as Dynamic Valuation Decomposition Within Stochastic Economies; Fisher–Schultz Lecture, Econometrica 80(3):911-967, May, 2012
Handle: RePEc:nbr:nberwo:14243

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Cited by:
  1. Ralph S. J. Koijen & Hanno Lustig & Stijn Van Nieuwerburgh & Adrien Verdelhan, 2010. "Long Run Risk, the Wealth-Consumption Ratio, and the Temporal Pricing of Risk," American Economic Review, American Economic Association, American Economic Association, vol. 100(2), pages 552-56, May.
  2. Lars Peter Hansen & José A. Scheinkman, 2009. "Long-Term Risk: An Operator Approach," Econometrica, Econometric Society, Econometric Society, vol. 77(1), pages 177-234, 01.
  3. David Backus & Mikhail Chernov & Stanley Zin, 2011. "Sources of Entropy in Representative Agent Models," Working Papers, New York University, Leonard N. Stern School of Business, Department of Economics 11-21, New York University, Leonard N. Stern School of Business, Department of Economics.
  4. Santos, Tano & Veronesi, Pietro, 2010. "Habit formation, the cross section of stock returns and the cash-flow risk puzzle," Journal of Financial Economics, Elsevier, Elsevier, vol. 98(2), pages 385-413, November.

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