Long-Run Risk Through Consumption Smoothing

Abstract

We show that a standard production economy model where consumers have Epstein-Zin preferences can jointly explain the low volatility of consumption growth and a high market price of risk with a low coe¢ cient of relative risk aversion (5). Endogenous consumption smoothing increases the price of risk in this economy as it induces highly persistent time-variation in expected aggregate consumption growth (long-run risk), even though technology follows a random walk. As is usual in production economy models, the volatility of equity returns is quite low. We propose an extension where we calibrate the wage process to the data and show that this brings the equity volatility, and thus the equity premium, much closer to historical values. The model identi…es an observable proxy for otherwise hard to measure expected consumption growth. Using this proxy, we test and …nd support for key predictions of our model in the time-series of consumption growth and the cross-section of stock returns.

Asset Prices in a News Driven Real Business Cycle Model

“…Dividends sensitivity to the output increase is only ; therefore dividend can actually become negative after the shock. This result is in line with Kaltenbrunner and Lochstoer (2007). In Model I dividends rise after the news shock at the same time as consumption.…”

“…We assume all innovations are perfectly observable. This general speci…cation nests several models as special cases: the standard growth model, the long-run productivity risk model (Croce (2008)), a model with anticipated shocks (Schmitt-Grohe and Uribe (2008)) as well as models with transitory shocks around a time trend in productivity growth (Kaltenbrunner and Lochstoer (2007)). We postpone the modeling of stochastic volatility until Section 6.…”

“…This paradox is documented in Kaltenbrunner and Lochstoer (2007). The Sharpe ratio of the dividend process in the calibration without news (Model II) is equal to the ratio of the consumption claim.…”

“…Kaltenbrunner and Lochstoer (2007) answer in the a¢ rmative by pointing out that in the simple real business cycle model i.i.d. shocks to productivity growth generate predictable movements in consumption growth provided the elasticity of intertemporal substitution is high enough.…”

“…Anticipated shocks are not the only way to create long-run risk in consumption. Indeed, Kaltenbrunner and Lochstoer (2007) show that persistent time variation in expected consumption growth is a salient feature of real business cycle models even with unanticipated i.i.d. productivity shocks provided the propensity to smooth consumption is not too high (elasticity of intertemporal substitution not too low).…”