Expected Returns and the Business Cycle: Heterogeneous Goods and Time-Varying Risk Aversion

Abstract

We propose a representative agent habit formation model where preferences are defined over both luxury goods and basic goods. The model matches the equity risk premium, risk free rate, and volatilities. From the intratemporal first order condition we can substitute out basic good consumption and the habit level, yielding a stochastic discount factor driven by two observable risk factors: luxury good consumption growth, and the relative price of the two goods. We estimate these processes and find them to be heteroskedastic, implying time-variation in the conditional volatility of our stochastic discount factor. These dynamics occur both at the business cycle frequency and at a lower, generational frequency. Consistent with the model's predictions, we empirically document the existence of these two frequencies in the equity premium, where the lower frequency is quantitatively more important. We also investigate the model's implications for bond returns, and relate their predictability to the low frequency variation in the conditional volatility of the relative price growth.