I explore the equilibrium value implications of economic models that incorporate responses to a stochastic environment with growth. I propose dynamic valuation decompositions (DVD's) designed to distinguish components of an underlying economic model that influence values over long investment horizons from components that impact only the short run. A DVD represents the values of stochastically growing claims to consumption payoffs or cash flows using a stochastic discount process that both discounts the future and adjusts for risk. It is enabled by constructing operators indexed by the elapsed time between the trading date and the date of the future realization of the payoff. Thus formulated, methods from applied mathematics permit me to characterize valuation behavior and the term structure of risk prices in a revealing manner. I apply this approach to investigate how investor beliefs and the associated uncertainty are reflected in current-period values and risk-price elasticities.

[This paper studies estimators that make sample analogues of population orthogonality conditions close to zero. Strong consistency and asymptotic normality of such estimators is established under the assumption that the observable variables are stationary and ergodic. Since many linear and nonlinear econometric estimators reside within the class of estimators studied in this paper, a convenient summary of the large sample properties of these estimators, including some whose large sample properties have not heretofore been discussed, is provided.]

The purpose of this paper is to investigate testable implications of equilibrium asset pricing models. We derive a general representation for asset prices that displays the role of conditioning information. This representation is then used to examine restrictions implied by asset pricing models on the unconditional moments of asset payoffs and prices. In particular, we analyze the effect of information omission on the mean-variance frontier of one-period returns on portfolios of securities. Also, we deduce an information extension of equilibrium pricing functions that is useful in deriving restrictions on the unconditional moments of payoffs and prices.

[This paper describes a method for estimating and testing nonlinear rational expectations models directly from stochastic Euler equations. The estimation procedure makes sample counterparts to the population orthogonality conditions implied by the economic model close to zero. An attractive feature of this method is that the parameters of the dynamic objective functions of economic agents can be estimated without explicitly solving for the stochastic equilibrium.]

In this article we develop alternative ways to compare asset pricing models when it is understood that their implied stochastic discount factors do not price all portfolios correctly. Unlike comparisons based on χ 2 statistics associated with null hypotheses that models are correct, our measures of model performance do not reward variability of discount factor proxies. One of our measures is designed to exploit fully the implications of arbitrage-free pricing of derivative claims. We demonstrate empirically the usefulness of our methods in assessing some alternative stochastic factor models that have been proposed in asset pricing literature.

In this article we develop alternative ways to compare asset pricing models when it is understood that their implied stochastic discount factors do not price all portfolios correctly. Unlike comparisons based on statistics associated with null hypotheses that models are correct, our measures of model performance do not reward variability of discount factor proxies. One of our measures is designed to exploit fully the implications of arbitrage‐free pricing of derivative claims. We demonstrate empirically the usefulness of our methods in assessing some alternative stochastic factor models that have been proposed in asset pricing literature.

The authors show how to use security market data to restrict the admissible region for means and standard deviations of intertemporal marginal rates of substitution of consumers. Their approach (1) is nonparametric and applies to a rich class of models of dynamic economics; (2) characterizes the duality between the mean-standard deviation frontier for intertemporal marginal rates of substitution and the familiar mean-standard deviation frontier for asset returns; and (3) exploits the restriction that intertemporal marginal rates of substitution are positive random variables. The region provides a convenient summary of the sense in which asset market data are anomalous from the vantage point of intertemporal asset pricing theory.