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.

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.

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.

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.