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Modeling the Long Run: Valuation in Dynamic Stochastic Economies

Author

Listed:
  • 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.

Suggested Citation

  • Lars Peter Hansen, 2008. "Modeling the Long Run: Valuation in Dynamic Stochastic Economies," NBER Working Papers 14243, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberwo:14243
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    References listed on IDEAS

    as
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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, vol. 100(2), pages 552-556, May.
    2. Lars Peter Hansen & José A. Scheinkman, 2009. "Long-Term Risk: An Operator Approach," Econometrica, Econometric Society, vol. 77(1), pages 177-234, January.
    3. David Backus & Mikhail Chernov & Stanley Zin, 2014. "Sources of Entropy in Representative Agent Models," Journal of Finance, American Finance Association, vol. 69(1), pages 51-99, February.
    4. Lars Hansen & José Scheinkman, 2012. "Pricing growth-rate risk," Finance and Stochastics, Springer, vol. 16(1), pages 1-15, January.
    5. Jaroslav Borovicka, 2009. "Heterogeneous beliefs under recursive preferences," 2009 Meeting Papers 892, Society for Economic Dynamics.
    6. 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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    JEL classification:

    • C0 - Mathematical and Quantitative Methods - - General
    • E44 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Financial Markets and the Macroeconomy
    • G1 - Financial Economics - - General Financial Markets

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