Working Paper: NBER ID: w14243
Authors: 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.
Keywords: dynamic value decomposition; long run valuation; stochastic growth
JEL Codes: C0; E44; G1
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| nonlinear economic models with stochastic growth (O41) | long-term valuation implications (G32) |
| risk aversion (D81) | long-term valuations (G19) |
| technology shocks (D89) | long-term valuations (G19) |
| sensitivity of long-run valuations to changes in preferences (D11) | long-term valuation implications (G32) |
| sensitivity of long-run valuations to changes in technology (O33) | long-term valuation implications (G32) |
| transient changes (E32) | long-term valuations (G19) |
| marginal changes in risk exposure of growth processes (D25) | risk premia (G22) |
| risk prices (G13) | investment horizons (G11) |