The long-run standard deviation (LRSD) of consumption growth is a key moment in determining risk premiums under Epstein-Zin preferences. Standard estimators of the LRSD are biased downward and have poor confidence interval coverage, making them overreject the long-run risk model. This paper studies a new estimator with smaller bias and accurate confidence intervals. Standard long-run risk calibrations are still rejected in the data. The LRSD of consumption growth in the postwar sample is estimated to be 2.5% per year with an upper bound to the 95% confidence interval of 4.9%. These values can be taken as benchmarks for future calibrations. Received October 29, 2014; accepted February 18, 2016 by Editor Leonid Kogan.

This paper describes the response of the economy to large shocks in a nonlinear production network. A sector's tail centrality measures how a large negative shock transmits to GDP, that is, the systemic risk of the sector. Tail centrality is theoretically and empirically very different from local centrality measures such as sales share—in a benchmark case, it is measured as a sector's average downstream closeness to final production. It also measures how large differences in sector productivity can generate cross‐country income differences. The paper also uses the results to analyze the determinants of total tail risk in the economy. Increases in interconnectedness can simultaneously reduce the sensitivity of the economy to small shocks while increasing the sensitivity to large shocks. Tail risk is related to conditional granularity , where some sectors become highly influential following negative shocks.

We quantify investors' preferences over the dynamics of shocks by deriving frequency-specific risk prices that capture the price of risk of consumption fluctuations at each frequency. The frequency-specific risk prices are derived analytically for leading models. The decomposition helps measure the importance of economic fluctuations at different frequencies. We precisely quantify the meaning of "long-run" in the context of Epstein-Zin preferences -centuries -and measure the exact relevance of business-cycle fluctuations. Finally, we estimate frequency-specific risk prices and show that cycles longer than the business cycle -long-run risks -are significantly priced in the equity market.

We study an investor who is unsure of the dynamics of the economy. Not only are parameters unknown, but the investor does not even know what order model to estimate. She estimates her consumption process nonparametrically—allowing potentially infinite-order dynamics—and prices assets using a pessimistic model that minimizes lifetime utility subject to a constraint on statistical plausibility. The equilibrium is exactly solvable and the pricing model always includes long-run risks. With risk aversion of 4.7, the model matches major facts about asset prices, consumption, and dividends. The paper provides a novel link between ambiguity aversion and nonparametric estimation. (JEL D11, D12, D81, G11, G12)

In affine asset pricing models, the innovation to the pricing kernel is a function of innovations to current and expected future values of an economic state variable, for example consumption growth, aggregate market returns, or short-term interest rates. The impulse response of this priced variable to fundamental shocks has a frequency (Fourier) decomposition, which captures the fluctuations induced in the priced variable at different frequencies. We show that the price of risk for a given shock can be represented as a weighted integral over that spectral decomposition. The weight assigned to each frequency then represents the frequency-specific price of risk, and is entirely determined by the preferences of investors. For example, standard Epstein-Zin preferences imply that the weight of the pricing kernel lies almost entirely at extremely low frequencies, most of it on cycles longer than 230 years; internal habit-formation models imply that the weight is shifted to high frequencies. We estimate the frequency-specific risk prices for the equity market, focusing on economically interesting frequencies. Most of the pricing weight falls on low frequencies -corresponding to cycles longer than 8 years -broadly consistent with Epstein-Zin preferences.

Abstract We study the effects of policies proposed to address “short-termism” in financial markets. We examine a noisy rational expectations model in which investors’ exposures and information about fundamentals endogenously vary across horizons. In this environment, taxing or outlawing short-term investment doesn’t negatively affect the information in prices about long-term fundamentals. However, such a policy reduces short- and long-term investors’ profits and utility. Changing policies about the release of short-term information can help long-term investors—an objective of some policy makers—at the expense of short-term investors. Doing so also makes prices less informative and increases costs of speculation. Received June 24, 2018; editorial decision February 19, 2019 by Editor Stijn Van Nieuwerburgh. Authors have furnished an Internet Appendix, which is available on the Oxford University Press Web site next to the link to the final published paper online.

Abstract We provide evidence on the relationship between aggregate uncertainty and the macroeconomy. Identifying uncertainty shocks using methods from the news shocks literature, the analysis finds that innovations in realized stock market volatility are robustly followed by contractions, while shocks to forward-looking uncertainty have no significant effect on the economy. Moreover, investors have historically paid large premia to hedge shocks to realized but not implied volatility. A model in which fundamental shocks are skewed left can match those facts. Aggregate volatility matters, but it is the realization of volatility, rather than uncertainty about the future, that has been associated with declines.

We study the pricing of shocks to uncertainty and volatility using a wide-ranging set of options contracts covering a variety of different markets. If uncertainty shocks are viewed as bad by investors, they should carry negative risk premiums. Empirically, however, uncertainty risk premiums are positive in most markets. Instead, it is the realization of large shocks to fundamentals that has historically carried a negative premium. In other words, we find that the return premium for gamma is negative, while that for vega is positive. These results imply that it is jumps, for which exposure is measured by gamma, not forward-looking uncertainty shocks, measured by vega, that drive investors’ marginal utility. In further support of the jump interpretation, the return patterns are more extreme for deeper out-of-the-money options.

Between 1996 and 2014, it was costless on average to hedge news about future variance at horizons ranging from 1 quarter to 14 years. Only unexpected, transitory realized variance was significantly priced. These results present a challenge to many structural models of the variance risk premium, such as the intertemporal CAPM and recent models with Epstein–Zin preferences and long-run risks. The results are also difficult to reconcile with macro models in which volatility affects investment decisions. At the same time, the data allows us to distinguish between different disaster models; a model in which the stock market has a time-varying exposure to disasters and investors have power utility fits the major features of the variance term structure.