TY  - JOUR
AU  - Hansen,Lars Peter
TI  - Modeling the Long Run: Valuation in Dynamic Stochastic Economies
JF  - National Bureau of Economic Research Working Paper Series
VL  - No. 14243
PY  - 2008
Y2  - August 2008
UR  - http://www.nber.org/papers/w14243
L1  - http://www.nber.org/papers/w14243.pdf
N1  - Author contact info:
Lars P. Hansen
Department of Economics
The University of Chicago
1126 East 59th Street
Chicago, IL 60637
Tel: 773/702-8170
Fax: 773/702-8490
E-Mail: lhansen@uchicago.edu
AB  - 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.
ER  -