The COVID-19 pandemic that we are experiencing is both tragic and shocking. There is no question that, except in some Asian countries trained by prior infectious outbreaks, most policy makers around the world have been ill-prepared to respond to the crisis. The effects of the coronavirus on our mental and physical health has been indeed calamitous, and the economic and financial impacts for many have been truly unfortunate. Furthermore, the extreme nature of the event is challenging researchers to compile and interpret new evidence that is arriving at a rapid pace. The editors Hui Chen, Thierry Foucault, Jeffrey Pontiff, and Nikolai Roussanov and contributing authors are to be commended for assembling and collating a thought-provoking collection of papers. More time and study will be needed to fully sift through the evidence and to glean the lessons to be learned from this pandemic for policy makers and investors. But the evidence and insights in this volume are a very good start.

In this article, the authors 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 chi square statistics associated with null hypotheses that models are correct, the authors' measures of model performance do not reward variability of discount factor proxies. One of their measures is designed to exploit fully the implications of arbitrage-free pricing of derivative claims. The authors demonstrate empirically the usefulness of their methods in assessing some alternative stochastic factor models that have been proposed in asset pricing literature.

We show how to use security market data to restrict the admissible region for means and standard deviations of intertemporal marginal rates of substitution (IMRSs) of consumers. Our approach (i) is nonparametric and applies to a rich class of models of dynamic economies, (ii) characterizes the duality between the mean--standard deviation frontier for IMRSs and the familiear mean- standard deviation frontier for asset returns, and (iii) exploits the restriction that IMRSs are positive random variables. The region provides a convenient summary of the sense in which asset market data are anaomalous from the vantage point of intertemporal asset pricing theory.

This paper studies the time-series behavior of asset returns and aggregate consumption. Using a representative consumer model and imposing restrictions on preferences and the joint distribution of consumption and returns, we deduce a restricted log-linear time-series representation. Preference parameters for the representative agent are estimated and the implied restrictions are tested using postwar data.

This paper examines the hypothesis that the expected rate of return to speculation in the forward foreign exchange market is zero; that is, the logarithm of the forward exchange rate is the market's conditional expectation of the logarithm of the future spot rate. A new computationally tractable econometric methodology for examining restrictions on a k-step-ahead forecasting equation is employed. Using data sampled more finely than the forecast interval, we are able to reject the simple market efficiency hypothesis for exchange rates from the 1970s and the 1920s. For the modern experience, the tests are also inconsistent with several alternative hypotheses which typically characterize the relationship between spot and forward exchange rates.

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.]

This essay examines the problem of inference within a rational expectations model from two perspectives: that of an econometrician and that of the economic agents within the model. The assumption of rational expectations has been and remains an important component to quantitative research. It endows economic decision makers with knowledge of the probability law implied by the economic model. As such, it is an equilibrium concept. Imposing rational expectations removed from consideration the need for separately specifying beliefs or subjective components of uncertainty. Thus, it simplified model specification and implied an array of testable implications that are different from those considered previously. It reframed policy analysis by questioning the effectiveness of policy levers that induce outcomes that differ systematically from individual beliefs.