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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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  1. Lars Peter Hansen & John C. Heaton & Nan Li, 2008. "Consumption Strikes Back? Measuring Long-Run Risk," Journal of Political Economy, University of Chicago Press, vol. 116(2), pages 260-302, 04.
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  6. Thomas Tallarini, . "Risk-Sensitive Real Business Cycles," GSIA Working Papers 1997-35, Carnegie Mellon University, Tepper School of Business.
  7. Lars Peter Hansen & Jose Alexandre Scheinkman, 1993. "Back to the Future: Generating Moment Implications for Continuous-Time Markov Processes," NBER Technical Working Papers 0141, National Bureau of Economic Research, Inc.
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  16. Lars Peter Hansen, 2007. "Beliefs, Doubts and Learning: Valuing Economic Risk," NBER Working Papers 12948, National Bureau of Economic Research, Inc.
  17. Kocherlakota, Narayana R, 1990. " Disentangling the Coefficient of Relative Risk Aversion from the Elasticity of Intertemporal Substitution: An Irrelevance Result," Journal of Finance, American Finance Association, vol. 45(1), pages 175-90, March.
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  23. Beveridge, Stephen & Nelson, Charles R., 1981. "A new approach to decomposition of economic time series into permanent and transitory components with particular attention to measurement of the `business cycle'," Journal of Monetary Economics, Elsevier, vol. 7(2), pages 151-174.
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Cited by:
  1. David Backus & Mikhail Chernov & Stanley E. Zin, 2011. "Sources of Entropy in Representative Agent Models," NBER Working Papers 17219, National Bureau of Economic Research, Inc.
  2. Lars Peter Hansen & José A. Scheinkman, 2009. "Long-Term Risk: An Operator Approach," Econometrica, Econometric Society, vol. 77(1), pages 177-234, 01.
  3. 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, vol. 100(2), pages 552-56, May.
  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, vol. 98(2), pages 385-413, November.

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