Ebook Intertemporal substitution and equity premium: A perspective with habit in Epstein-Zin preferences
Risk aversion has long been the focus of the consumption based asset pricing literature on the equity premium puzzle. Since Mehra and Prescott (1985), many studies have recognized that large risk aversion is necessary in order to reconcile the high levels of average stock returns and return volatilities with smooth consumption growth.
In contrast, the role of intertemporal substitution has been largely under researched as most studies cannot effectively differentiate its effect from that of risk aversion. Often this is because many models are based on power utility. Consequently, with the constraint that the elasticity parameter is the inverse of the risk aversion parameter, they cannot vary independently. Moreover, even in models using Epstein and Zin (1989) utility that differentiates the two parameters, a random walk consumption growth process renders Epstein-Zin utility equivalent to power utility [Kocherlakota (1990)].
This paper presents a model that reveals intertemporal substitution as a distinctive and important channel, separate from risk aversion, in generating equity premium, return volatility, and their cyclical variations. The model is able to distinguish the two channels as a result of two critical ingredients. First, the model is based on Epstein-Zin utility that differentiates the two parameters. Second, the model incorporates external habit following Campbell and Cochrane (1999). With habit formation, the agent really cares about surplus consumption, or consumption in excess of habit. Even though consumption growth is a random walk in the model, surplus consumption varies counter-cyclically. Consequently, the model in this paper does not reduce to power utility.
In the model, consumption growth shocks drive the habit process to generate persistent variations in surplus consumption across time. The agent, however, prefers a smooth stream of surplus consumption, and consequently demands compensation for consumption risk. This gives rise to the intertemporal substitution channel, and it is different from the risk aversion channel, in which consumption growth shocks generate variations in surplus consumption across future states, which the agent dislikes and also demands compensation for. Both channels make positive contributions to equity premium.
Moreover, the contributions from both channels are time varying. The model analyses imply an effective elasticity of intertemporal substitution that is much lower than the parameter value and varies pro-cyclically. On the other hand, the effective risk aversion is counter cyclical and much higher than the parameter value. Both of them drive counter-cyclical variations in equity premium. It is thus important to distinguish the effective contributions of the two channels from their respective parameter values.
In accordance with the empirical fact of small volatility in the real risk-free rate, this study, similar to Campbell and Cochrane (1999), devises the model to achieve a constant risk-free rate. This requirement further accentuates the significance of the intertemporal substitution effect. The results indicate that the model’s asset pricing implications are very sensitive to the elasticity parameter, often more so than to the risk aversion parameter. In particular, the market price of risk, and subsequently the Sharpe ratio of the return to the dividend claim, increase with a decreasing elasticity parameter, but remain largely unchanged with respect to variations in the risk aversion parameter. Therefore, to match the large Sharpe ratio of the aggregate stock market, a small elasticity parameter is essential. On the other hand, the beta, or the loading of the return innovations on consumption risk, turns out to decline with an increasing risk aversion parameter, and so do both the average return and the volatility.
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