Incomplete information and macro-finance

Abstract

This paper provides a tractable stochastic differential utility (SDU) – Gaussian framework with constant-absolute-risk atemporal averse (CARA) to theoretically and quantitatively explore how the interactions of intertemporal substitution, atemporal risk aversion, and induced uncertainty due to the preference for robustness (RB) and rational inattention (RI) affect agent’s optimal consumption-portfolio choice and precautionary savings. Specifically, the derived analytically optimal solution shows two important points: (i) induced uncertainty increases precautionary savings and reduces amount invested in risky assets; and (ii) intertemporal substitution attitude, which is now disentangled with atemporal risk aversion, also affects agent’s precautionary savings and portfolio allocation decisions, with the direction depending on the relative value of risk-free interest rate and subjective discount factor. Furthermore, we analytically investigate how induced uncertainty and SDU affects the risk-free rate, the risk premium, and the relative volatility of consumption growth to income growth in general equilibrium. First, it is found that the presence of SDU can reduce the co-movement of the risk premium and and the risk-free rate. Therefore, the high equity premium can be consistent with the low risk-free rate in general equilibrium. Second, we show that induced uncertainty due to RI and RB reduces the risk-free rate, increases the risk premium and decreases the relative volatility of consumption to income in equilibrium. Finally, after calibrating and estimation using PSID, we show that our model can generate the realistic risk-free rate, the equity premium, and the relative volatility of consumption to income which match their empirical counterpart quite well, with plausible parameter values.