The paper by Lars Peter Hansen and Ravi Jagannathan explores the implications of security market data for models of dynamic economies. The authors propose a non-parametric approach to restrict the admissible region for the means and standard deviations of intertemporal marginal rates of substitution (IMRSs) of consumers. This approach applies to a broad class of dynamic economy models, characterizes the duality between the mean-standard deviation frontier for IMRSs and asset returns, and exploits the positivity of IMRSs. The resulting region provides a summary of how asset market data deviate from the predictions of intertemporal asset pricing theory. The paper begins by introducing a general model of asset pricing, where multiple consumers trade in securities markets with heterogeneous preferences and information sets. The authors derive restrictions on the IMRSs based on the law of one price and the absence of arbitrage opportunities. They then construct minimum variance random variables that satisfy these restrictions, leading to volatility bounds for IMRSs. These bounds are expressed as regions of admissible mean-standard deviation pairs for IMRSs. The authors also discuss the connection between the mean-standard deviation frontier for IMRSs and the mean-standard deviation frontier for asset returns, showing that the former can be interpreted as the dual of the latter. They further explore the implications of imposing additional restrictions on IMRSs, such as requiring them to be strictly positive, and derive more restrictive volatility bounds. Finally, the paper illustrates the results using alternative data sets and parametric models, providing insights into the plausibility of various asset pricing models. The authors conclude by highlighting the usefulness of their non-parametric approach in complementing parametric methods and in understanding the limitations of different models in explaining asset market data.The paper by Lars Peter Hansen and Ravi Jagannathan explores the implications of security market data for models of dynamic economies. The authors propose a non-parametric approach to restrict the admissible region for the means and standard deviations of intertemporal marginal rates of substitution (IMRSs) of consumers. This approach applies to a broad class of dynamic economy models, characterizes the duality between the mean-standard deviation frontier for IMRSs and asset returns, and exploits the positivity of IMRSs. The resulting region provides a summary of how asset market data deviate from the predictions of intertemporal asset pricing theory. The paper begins by introducing a general model of asset pricing, where multiple consumers trade in securities markets with heterogeneous preferences and information sets. The authors derive restrictions on the IMRSs based on the law of one price and the absence of arbitrage opportunities. They then construct minimum variance random variables that satisfy these restrictions, leading to volatility bounds for IMRSs. These bounds are expressed as regions of admissible mean-standard deviation pairs for IMRSs. The authors also discuss the connection between the mean-standard deviation frontier for IMRSs and the mean-standard deviation frontier for asset returns, showing that the former can be interpreted as the dual of the latter. They further explore the implications of imposing additional restrictions on IMRSs, such as requiring them to be strictly positive, and derive more restrictive volatility bounds. Finally, the paper illustrates the results using alternative data sets and parametric models, providing insights into the plausibility of various asset pricing models. The authors conclude by highlighting the usefulness of their non-parametric approach in complementing parametric methods and in understanding the limitations of different models in explaining asset market data.