Modeling the Long Run: Valuation in Dynamic Stochastic Economies

I explore the value implications of economic models by highlighting what features persist in the long-term. I accomplish this by developing a decomposition of valuation dynamics (DVD). I use it to distinguish components of an underlying economic model that influence values over long horizons from components that impact only the short run. I apply my approach to study example economies from the asset pricing literature, and I speculate about the long-term valuation implications of a broader class of economic models. I develop a perturbation method to quantify the role of parameter sensitivity and to impute long-term risk prices. 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 currently used to identify shocks with long-run economic consequences.